By Fraunhofer diffration theory and numerical analysis method, the relation of beam separation distance, fill factor, phase change and far-field intensity distribution of laser coherent combination is calculated. The influences of transformation characteristic of phase and polarization on intensity distribution of coherent combination are studied by heterodyne method and liquid phase modulator. The characteristics of phase change for beam in fiber transmission is obtained. As a result of the random change of phase, the intensity of laser combination is reduced and the excursion of background comes forth. The contrast of fringes can be changed with the transformation of polarization. In vibrant and temperature changed environment, the frequency for phase change in beam is higher than that in natural environment.

In angular multiplexing excimer laser system, studies on energy amplification of a train of laser pulses are crucial to determine beam number for reducing optical complexity, while strict requirements on alignment are needed for experiments. Based on principles of displacement and angular drift adjusted by near field and far field respectively, an optical automatic alignment system is designed, and corresponding computer software for closed-loop feedback controll is compiled. High adjustment accuracy with allignment errors of 21 μm in near field and 1.3″ in far field is obtained by using He-Ne laser. This system is applied to two pulse amplification experiment and works effctively.

Laser synthesis aims at synthesising a number of discrete laser beams into a coaxial beam to achieve higher output power which is several times of that of a single laser to achieve the higher output power. A novel hollow beam convertor is designed, which can be used in N (N≥3) way coaxial laser beam synthesis, and the numerical calculation and experimental study are done. Using this technology in the three-beam synthesis, laser synthesis efficiency is 89%, the time jitter is no more than 2 ns, laser pulse-width reaches about 10 ns (FWHM), and laser beam divergence angle is no more than 2 mrad.

In order to improve the accuracy of an off-axis reflected space optical system, researches have been made to its distortion feature. In the research, some distortion features different from the radial distortion model are found. So the previous solutions are no longer suitable for this problem. A method using two-dimension Lagrange interpolation is introduced to correct the distortion of the off-axis system. As the system is still in design, these methods are verified and analyzed by simulating in computer. The results show that by using this method, the distortion of the off-axis system can be well corrected.

In this paper, the wavefront properties of large aperture optics such as neodymium glass, reflecting mirrors and crystals have been systematically studied. Static and dynamic wavefront aberration of multi-beams laser system have been statistically analyzed. The results show that one kind of optics have similar wavefront properties, and different laser beams also have similar characteristics on static wavefront aberration. The chief static aberration of main amplifier is astigmatism with the PV value about 2λ～3λ (λ=1053 nm), and in 90° rotation reversal multi-pass amplifier laser system, the chief dynamic aberration of main amplifier is defocus with the PV value about 4λ～5λ. After excluding defocus, the dynamic wavefront aberration PV value is about 1λ～2λ, and maximum aberration of the whole laser system is likely to exceed 6λ.

The properties of Modified Laguerre-Gaussian beams (MLGBs) propagating through a fractional Fourier transform (FRFT) optical system are investigated. The analytical transformation formula for MLGBs propagation through an FRFT optical system is derived based on definition of the FRFT in the cylindrical coordinate system. By using the derived formula, the normalized intensity distribution of MLGBs in the FRFT plane is graphically illustrated with numerical examples, and the influence of different parameters on the normalized intensity distribution is discussed.

Based on the unified theory of coherence and polarization of random electromagnetic beams and the propagation law of cross-spectral density matrix,the closed-form expression for the 2×2 cross-spectral density matrix of random cosh-Gaussian(ChG) electromagnetic beams propagating through a lens is derived,and used to formulate the degrees of cross-polarization,i.e.,the longitudinal degree of cross-polarization (LDCP) and the transverse degrees of the cross-polarization (TDCP) between two arbitrary points upon propagation. It is shown that the degrees ofcross-polarization depend on the focal length of the lens and beam parameters,such as the coefficient ratio,decentered parameter and self-correlation length. The degrees of cross-polarization of radom Gaussion Schell-model (GSM) electromagnetic beams propagating through a lens can be treated as a special case that the decentered parameter of random ChG electromagnetic beams approaches to zero. The main results are illustrated numerically and interpreted physically.

Based on vectorial Debye integral,the light field and intensity distribution expressions are presented when partially polarized Gaussian beams pass through a high numerical-aperture objective. Numerical calculations are taken to analyze the tightly focusing properties of partially polarized Gaussian beams with various degrees of polarization. The research results show that the total intensity distribution and each direction components of partially polarized Gaussian beams on the focal plane will change with the change of polarization. It is also found that the values of the maximal angle of the high numerical-aperture objective will influence the total intensity on the focal plane. Therefore,the intensity distribution of partially polarized Gaussian beam on the focal plane can be controlled by adjusting the polarization and the maximal angle of the high numerical-aperture objective.

Based on holographic optical holographic imaging theory,a wavelength beam combining approach of fiber coupling lasers using off-axial holographic optical elements is proposed in this paper. This method for beam combining is easy constructed and high efficiency. This paper designs the off-axis holographic optical element (HOE),and gives the phase distribution of the element. We use the stimulation software Zemax and angular spectrum theory to calculate the combined beam divergence angle and the beam quality. The stimulation shows that for fiber lasers with wavelength at 635,808,975 nm,maximum M2 increases from 23.5 to 47.9 and the theoretical efficiency is 95%.

In order to get the characteristics of optical field in the pigtail fiber of fiber coupled laser diode and increase the pump efficiency of fiber laser,propagation ray calculation and experiments of transmission efficiency in bending pigtail fiber are presented. In bending fiber experiments,it is found that more than 15% of output power differences are given by fiber coupled laser diode with the same nominal output power and pigtail fiber. It means optic modes need to be chosen so as to maintain the pumping efficiency and stability in pumping application. Based on the analysis of propagation ray theory,a new approach to judge the beam quality of fiber coupled laser diode by bending fiber is presented. It also can be used in detecting the fiber coupled efficiency of laser diode.

Phase-only spatial light modulators are employed to generate controllable wavefront distortion,which is incorporated into a coherent beam combining system to investigate the influence of wavefront distortion in single laser channel on phase control system. Experimental results show that the phase control system is almost not affected in the case of wavefront distortion with small root mean square (RMS) value (i.e.,RMS<π/10). As an increase in the wavefront distortion,the optical phase cannot be totally controlled,residual phase error goes with excursion in the interference patterns exists in the system. When the RMS value of the wavefront distortion is as large as π,the phase control system is in invalidation state and the beamlets cannot be phase locked. Our experimental results present reference for designing and manufacturing high energy laser system based on coherent beam combining.

A method based on the G-S algorithm is presented,using beam angular spectrum transmit formula to iterate the phase that the compensation for the near-field intensity distribution requires. The iterative algorithm used in the control of beam near-field intensity is presented. Based on this algorithm,an adaptive optics system to achieve control of beam near-field intensity is designed,and numerical simulation and experiments verify the feasibility of this method. The experimental results show that the similarity value ε,which is the distribution of beam near-field amplitude comparing to the ideal distribution of the amplitude,has been improved from 0.718 to 0.966 when the adaptive system working. This indicates that the system is effective in controlling the beam near-field intensity.

Beams combination is an important way for development of high power solid state lasers,and the phase control electronics contributes greatly to the success of the coherent combining. The method of phase detection for beamlets in a 4 rectangle spot beams array is analyzed,and its mathematical model of coherent combination under phase-locked condition is established. A high-speed wavefront sensor is used to sample the wavefront of one beamlet in laser array,and phase difference between the beamlet and reference beam is detected by the way of heterodyne method from the beat frequency signal,which results from the interference of the reference beam with each beamlet. The phase difference is used to actively control the phase modulator of the beamlet,and then all of the output phases are exactly aligned. Some simulated waveform signals changing versus time are presented during the locking loop is closed,and it is also simulated that the intensity distribution of combined far-field spots changes with phase difference and random aberration among these beamlets,which is compared with that when the locking loop is opened. It is concluded from the simulated results that all output phases of each beamlets can be exactly aligned when the locking loop is closed. The control precision and condition of closing-loop are also analyzed.

A beam shaping method for laser diodes stack by superposition of tilted fundamental mode Gaussian beams to form a nearly uniform illumination is proposed. The analytical formula for average intensity of the multi-tilted Gaussian beams (MTGB) propagating is derived and used to study the uniform properties of the beam profile by the Fourier analysis method. It is found that the MTGB maintain the flat-topped shape as it propagates. And the uniform properties of the MTGB are closely related to the parameters of fundamental beams and superposition. Both analytical formula derivation and the numerical examples are illustrated. The method is then used to reconfigure the beams of a high power laser diodes stack to form a multi-tilted Gaussian beam shape for a 12°×10° field angle illumination,which is simulated in ASAP software. The shaping method with the proper uniformity and high efficiency is well suitable for laser illuminator in laser active imaging and detecting system.

In the coherent beam combination of lasers array,the duty ratio has influence on efficiency of coherent beam combination,which is researched with mathematic analysis. Coherent beam combination experiment with 1×2 laser arrays is carried out in self-Fourier cavity. The result of mathematic analysis shows that through increasing the duty ratio,the energy duty of the central spot increases,and the number of secondary spot decreases.It is proved by the results of experiment that the energy duty of the central spot decreases from 42% to 11.13%,when the distance of two adjacent beam increases from 2.06 mm to 6.02 mm.

Based on Richards and Wolf vectorial diffraction integral,three-dimensional light field complex amplitude function is presented when circularly polarization vortex Bessel-Gaussian beam passes through a high numerical-aperture system with primary coma aberration. The highly-focusing fields with different comatic aberration coefficients are presented. The results show that the presence of primary coma aberration makes the pattern and position of light distribution change. The pattern of light distribution does not depend on sign of comatic aberration coefficient. As for intensity distribution along the optical axis,primary coma aberration does not change its symmetry,but affects its form.

Propagation properties of four combined beams,i.e.,coherently combined single mode laser,incoherently combined single mode laser,coherently combined multi-mode laser and incoherently combined multi-mode laser,in turbulent atmosphere are analyzed by using extended Huygens-Fresnel principle. The propagation efficiency and effective range are numerically evaluated. The calculating results show that there is no significant difference in propagating efficiency and effective range of coherent or incoherent beam combining,and the single mode laser array has advantages in propagation efficiency over multi-mode beams. The advantage of coherent beam combining decreases with an increase in the intensity of turbulence,and there is no difference between coherent and incoherent combining in strong turbulence. The adaptive phase-locked single mode laser array that can correct tilted aberration is the best choice for developing a 100 kW tactical laser system.

Based on the generalized Rayleigh-Sommerfeld diffraction integrals,the analytical expression for the 3×3 cross-spectral density matrix of nonparaxial off-axis Gaussian-Schell model (GSM) electromagnetic beams propagating in free space is derived and used to formulate the spectral density (intensity),degree of polarization and spectral degree of coherence of electromagnetic beams at the z plane. Nonparaxial on-axis GSM electromagnetic beams and nonparaxial off-axis Gaussian electromagnetic beams can be treated as special cases of our results. The effect of off-axis parameter,self- and cross-correlation lengths on the intensity,the degree of polarization and the spectral degree of coherence of electromagnetic beams are stressed. The results are illustrated by numerical examples.

With the elliptical gradient-index medium used as the optical system to implement two-dimensional axial symmetric fractional Fourier transforms (FRFT),the analytical formula of the beam width and the intensity distribution for two-dimensional axial symmetric fractional Fourier transform of elliptical Gaussian beams have been derived,based on the equivalence between the rotation of the Wigner distribution function and the fractional Fourier transform. By employing the derived formula,the influence of the fractional order on the properties of elliptical Gaussian beams in the fractional Fourier transform plane has been studied in detail. The results indicate that the on-axis intensity and the beam width of elliptical Gaussian beams change asynchronously along the x,y axises and the two parameters are dependent on the fractional order px and py respectively. The circular Gaussian beams will be obtained in specific output plane. Meanwhile,it will appear that the beam width satisfies wx>wy in specific output plane in spite of wx<wy in the input plane. The results will have applications in beam coupling,shaping and material thermal processing by laser beam. The approach presented in this paper can be extended to analyze and calculate the two-dimensional axial symmetric fractional Fourier transform of other beams and related results are straightforward.

A polar coordinates N-axis finite-difference beam propagation method (FD-BPM) based on a novel step-length setting mode has been deducted,and an idea named variational polar coordinates FD-BPM is advanced in this paper,which will bring higher precision,more convenient computation and analysis. Comprehensive analysis to the rigorous two-dimensional (2D) circle waveguide is achieved. When the light wave is transmitted in the waveguide with different curvatures,a maximum ratio of conductible mode energy to initial energy existing is discovered,and short wave is easier to be formed conductible mode compared with in the same waveguide. Furthermore,investigation about S shape and C shape waveguide has been performed in depth. The propagation capability of C shape waveguide is more excellent than S shape waveguide,as the latter has a higher tangent loss,whereas this distinction reduces while the curvature increasing. Some available propagation rules of S and C shape waveguide with different curvatures are described. The transparence boundary condition (TBC) is thought as practicable while using the polar coordinates N-axis FD-BPM presented in this paper to research the rigorous 2D circle waveguide. So-called boundary echo disturbance caused by TBC,is proved inexistent.

The scaling laws of high energy laser propagation through atmosphere are numerically analyzed by the four-dimension simulation program of high energy laser in atmosphere. The scaling relations of the 63.2% encircled energy beam radius spreading and the average energy intensity in the different encircled energy radius are obtained in the focal plane. The scaling relations are applicable to different atmospheric turbulence effects. Based on the relations,the atmospheric propagation effects of high energy laser can be predicted and estimated effectively.

Single-photon acquisition is the key technology of free-space quantum key distribution. Single-photon acquisition probability is very important. Based Hermite-Gaussian beams in TEM20,TEM02,TEM30,TEM03 and TEM11,the theoretical model of single-photon acquisition probability is established. And the probability in different modes is shown by numerical simulation. The physical model of time filtering is established,the limited mode and optimal mode are analyzed. The results can provide theoretical basis for the design of single-photon source,and optimize the system of free-space quantum key distribution.

Laser holds a higher output power when working in high-order-mode than working in fundamental mode, coherent combining of high-order mode lasers is a promising way for higher output power. For the inside 0-π phase difference of the wave front, the beam quantity of the high-order mode is not as good as that of the fundamental mode, therefore the brightness of the coherent combining is limited. Coherent combining of high-order mode lasers with wave front compensation is proposed. Inside 0-π phase differences of high-order mode laser are compensated using beam cleanup technology firstly, and then coherent combining is implementing with the wave front compensated lasers. Results of simulation and experiment of inside wave front compensation using optimal algorithm based beam cleanup technology are given. Numerical simulation of coherent combining of high-order Hermite-Guass mode lasers with and without inside wave front compensation is done. Result shows that the power in bucket of one time diffraction limitation of the combining beams with inside wave front compensation is at least 10 times or even more than 1000 times of that value of the combining beams without inside wave front compensation.

The discrete equivalent spherical scatterers aggregate model is developed to investigate the photon′s transport characteristics in highly scattering media. Based on Monte-Carlo method, we propose a new ellipse algorithm to determine the scattering point distributions. According to Mie theory and the radiative transfer equation, combined with the obtained scattering point distributions, path-length dependent scattering order distribution and scattering intensity in different scattering orders with different particle sizes are numerically calculated. The results show that the photon's transport in highly media is essentially a multiple scattering process. The numerical algorithm can be used effectively to analyze dynamic scattering properties of scattered light from single-scattering to multiple-scattering regime.

The beam divergence angle of lidar returned signals which is directly influenced by propagation properties of Gaussian beam affects the properties of Fabry-Perot etalon (FPE). In this paper, the three-dimensional interference rings of Gaussian beam are investigated and manifested to some trend. Gaussian beam with small divergence may be propitious to obtain higher energy of FPE zero-order or first-order interference ring. For a lidar system, the effects of beam quality factor M2 and expander coefficient on returned signals are discussed. The numerical results indicate that FPE transmission is changed clearly with the height in the near field and leveled off in the far field, and at a given height, it decreases with the enhance of the value of M2 and increases with the expander. It is supposed that laser with lower beam quality factor M2 and the transmitter with higher expander coefficient are chosen and developed to improve FPE transmission and in the near field decrease the measurement error in lidar using an FPE as spectroscope, which is expected to supply numerical foundation for the lidar system.

Based on the multi-beam interference principle and Gaussian beam transmission equation in the free space, the intensity expression of a Gaussian beam incidenting obliquely on an angle-tuned narrowband filter has been derived. According to the result, the influence and relationship of the incident angle on the reflection of a Gaussian beam have been investigated theoretically. The calculation and experiment results show that the size of the transmitting beam spot will be brodened obviously when the incident angle is increasing. However, the size of reflecting beam spot will be a little brodened for a relatively large incident angle, which extent is much less than that of the transmitting beam. The reflecting port of the angle-tuned narrowband filter does not need facular-shaping fitting as the transmitting port within its tuanble range.

Based on the extended Huygens-Fresnel principle and the method of second moments of the Wigner distribution function, the analytical formulas for the root-mean-square (RMS) spatial width, the RMS angular width, and the M2-factor of the partially coherent cosh-Gaussian (ChG) beam in turbulent atmosphere have been derived, which can be applied to cases of different spatial power spectra of the refractive index fluctuations of the turbulent atmosphere. It can be shown that the RMS angular width, M2 factor and relative M2 factor of a partially coherent ChG beam in turbulence increase with the propagation distance and depend on the waist width, wavelength, coherent parameter, decentered parameter, and spatial power spectrum of the refractive index fluctuations. The RMS angular width as a function of the decentered parameter has a minimum at any given propagation distance. For long propagation distance, the M2-factor as a function of the decentered parameter also has a minimum, and the beams with a larger decentered parameter are less affected by the turbulence.

Parasitic reflection is one of the most important fact impacts the laser′s near-field quality. Based on Bespalov-Talanov theory, the small-scale self-focusing caused by parasitic reflection and the parameter′s contribution to the growth of ripple in wedged optical device of high power system are discussed. By analyzing the interference field caused by the main beam and the reflected beam, the expression of small-scale modulated gain spectrum in no-linear media is found. The laws that the maxium gain of small-scale modulation grows with the window′s wedged angle of Nd-glass slab amplifier when the media gain or propagation distance changed are concluded. The influence of the length and wedge angle of amplifier window on the gain of perturbation is analyzed, additionally variation relation between the gain of perturbation and the width of the pulse with fixed window is derived.

The physical model of ultra-short laser pulse propagation during quasi-phase matched crystal is built and modified nonlinear Schrdinger equation is solved with step Fourier method. The temporal and spatial characteristics of femto-second laser pulse propagation in periodically poled lithium niobate (PPLN) crystal are achieved numerically. It is found that when the fundamental power is beyond the critical power, temporal splitting and spatial focusing of pulse are induced by self-focusing effect. Temporal splitting results in pulse width decrease with the increment of propagation distance, and minimal width is obtained at the focal point. On the other hand, spatial focusing brings decrement of focused diameter with the increment of propagation distance, and minimal diameter is obtained at the focal point and then diffused outward. Finally, the peak intensity of the pulse reaches maximal value at the focal point, and then reduces gradually. The length of quasi-phase matched crystal is restricted by self-focusing effect during ultra-short laser frequency doubling process.

In order to convert a laser Gaussian beam to a collimated flat-top beam, a new reshaper with only one aspheric lens is designed based on double aspheric lenses reshaper. In the theoretical model, a more accurate calculation method of curves function of aspheric lens is given. The reshaping effection, brought by the change from the parameter of system and laser beam, is given through numerical analysis and optical design software simulation. It is illustrated that the flatten degree of the laser beam can be improved apparently using this new kind of reshaper. The novel method avoids some shortcomings of traditional refractive optical reshaper such as large volume, complexity of regulating, etc, and enhances the reliability and practicability of device.

Based on the idea that the cat-eye effect reflected light of defocused optical lens can be regarded as a spherical wave, and by using Collins formula and the method of expanding the aperture function into a finite sum of complex Gaussian functions, the distribution formula of the cat-eye effect reflected light interfered with the reference incident light is deduced. Through numerical computation, laws governing the variation of the distribution and stripe series of the interference field with the focal shift are obtained. Then an experiment is done to validate the laws. The results show that off-focus of the optical lens is a necessary condition for the cat-eye effect reflected light to be interfered with the incident light and stripes are brought, the interference cirque gradually moves inside and the stripe number becomes larger with the increasing of the focal shift, and the relation between the interference stripe number and the focal shift can be correctly described by the geometric optical path function on nearby condition.

An online-offline program which is applied to find out the optimum matching angular of the frequency tripling of high power laser are intraduced in this paper. Comparing with determining the optimum matching angular by laser energy meter or naked eyes, the laser near field CCD diagnostic device is more reliable. The result shows that the adjusting precision of the optimum matching angular of the frequency tripling can reach 20″, which can meet the requirement of engineering application.

The wavefront, such as power, astigmatism, coma and spherical aberration distortion etc., was currently generated by Zernike polynomial with the P-V value less than 5λ (1053 nm). Then with the generated wavefront added the continuous phase plate (CPP), which was designed for backlight with the methods of improved Gerchberg-Saxton (G-S) algorithm, the focus process was simulated by fast Fourier transform (FFT) algorithm. The influences of wavefront distortion type and wavefront distortion value on the 3ω (351 nm) shaping focal spots were studied in details through three factors, energy efficiency, the uniformity of the 10～100 μm scale of focus and the size of the focal spot. The results showed it had a relatively wider tolerance for wavefront distortions due to the energy efficiency and the size of the focal spot, the variances will be no more than 5% as the P-V of the generated wavefront distortion was analogous with the CPP. The uniformity of the focal spot was very sensitive to wavefront distortion, with 1λ (1053 nm) wavefront distortion, the root-mean-square (RMS) of focal spots will be increased about 38.5%, from 0.325 to 0.45. Therefore, it indicates that it is necessary to control the wavefront distortions of the whole laser systems.

Due to the extensive application of radially polarized beams, the generation and propagation of this kind of beam are investigated theoretically and experimentally in this paper. In theory, the generation of TEM01 and TEM10 beams and radially polarized light beam are simulated by the integral of scalar diffraction. In experiment, by the use of phase step, two orthogonally polarized TEM00 beams are converted to TEM01 and TEM10 beams with orthogonal polarization respectively outside the cavity. Then the radially polarized light beam is obtained by coherent superposition of TEM01 and TEM10 beams. The influence of experimental error on the generation of radially polarized light beam, and the change of the light spot of radially polarized light beam in propagation are investigated. A longitudinal electric field and teeny focal spot can be generated by focusing the radially polarized light beam, therefore, it may have extensive application in many fields, such as particle acceleration, high-resolution microscopy and material processing etc.

Based on Richards-Wolf vectorial diffraction integral, the focusing properties of elliptically polarized vortex beams through a high-numerical aperture objective is studied in this paper. The intensity, phase and orbital angular momentum distribution properties of tightly focused vortex beams are presented. The influence of corresponding parameters on the tight focusing properties is also investigated. It is shown that elliptical light spots of great application can be obtained near the focus. Moreover the elliptical spot may rotate and the size and shape of the spot may change with the change of certain parameters. It is also found that the spin angular momentum of the elliptically polarized vortex beam will convert to orbital angular momentum by the tight focusing. These properties are quite important for the applications of this kind of elliptically polarized vortex beams.

Using geometrical optics, a laser beam homogenizer for high power CO2 has been designed. Laser beam is homogenized by means of waveguide, separate beam with spectroscope, so the device can be used to sintering ceramics on double sides. The waveguide is composed of a square-section tube with four flat rectangular mirrors, and its length is 200 mm, cross section 10 mm×10 mm. Two mirrors that has an angle with each other forms the spectroscope. The uniformity of the power distribution is stable without being affected by original laser beam. Using Fourier optics to analyze system, the method to improving the uniformity has been discussed. Because all the elements have reflecting surface, energy loss is not serious, optical path adjusting is convenient.

Based on the Fresnel diffraction integral, complex Gaussian function expansion and complex analytical signals method, the approximate analytical expression for ultrashort pulsed Bessel-Gaussian beams diffracted by an circular aperture in free space is derived. The normalized power spectrum, transversal intensity distribution, and optical pulse shape of ultrashort pulsed Bessel-Gaussian beam are studied in detail.

According to the analysis of stray light in high power solid-state laser system, the ghost image was 3D demonstrated in the structure model of the facility by software Wildfire-PRO/E3.0. The simulation model to describe the ghost-image distribution was also established. The position of the one-or-more order ghost image in the facility can be fully displayed in all directions so that the ghost-image harmfulness can be easily found. The hazard analysis of typical ghost-image was made and method to avoid the damage of ghost image was put forward. The research results will be in favor of stray light management.

Based on the theoretical and experimental results of adaptive optics system application in SG-Ⅲ prototype facility, the main scientific and technical problems were researched and solved, the efficiency was verified by experiment. In order to fulfill need of future high power solid-state laser driver wavefront correction, the scheme of combined adaptive optics system with continuous phase plate (CPP) was researched in theory. “One big deformable mirror (DM) with one CPP ”and “One small DM with two CPPs” schemes were analyzed by numerical modeling. The result showed that the latter scheme can achieve the goal of controlling the entire beam wavefront, and fulfill the need of focal spot size and uniformity for physics experiment. The results can also provide theoretical reference to design wavefront correction system in high power solid-state laser facility.

Many biological tissues consist of fibril structures. The scattered light of tissues provides abundant information about the properties of tissues. The polarization property of scattered light can reveal structure and type of tissue. Understanding the propagation property of polarirzed light in scattering medium is helpful to improve imaging gating method and diagnosis technology. In this paper, the transmitted light from a section of dentin was measured. A linearly polarized He-Ne laser beam was incident on the sample, and the transmitted light is recorded. The image showed anisotropic spatial distribution, indicating the light propagating along the fibers. The polarization property of the scattered light was related to the polarization direction of the incident light. A Monte Carlo simulation considering cylindrical scatterers was utilized to model the scattering property of microstructure in dentin. The experimental results are compared with the simulation. The ordered fibers have influence on the spatial distribution and the polarization state of scattered light.

The crosstalk between two adjacent signal channels of concave grating demultiplexer is composed of the transverse mutual coupling efficiency between two output waveguides and the response efficiency of output waveguide for the central wavelength of adjacent signal channels. Under the condition of weak coupling approximation, based on the mutual coupling coefficient between two nonparallel rectangular waveguides which derived from the method of field distribution analysis, the mutual coupling characteristic between two identical structure output waveguides in concave grating demultiplexer is discussed, and the relationship between the crosstalk and the basic structure parameters of the output waveguides is clarified. As the spectral response efficiency which is derived from the diffraction factor of grating facet, emission factor of input waveguide and receive factor of output waveguide is employed, the relationship between the spectral response characteristic of the signal channel and the basic structure parameters of the Rowland circle structure concave grating demultiplexer is clarified. These results will provide theoretical support for designing the basic structure parameters of concave grating demultiplexer.

The propagation properties of the 1+2-dimensional super Gaussian shaped optical beam in strongly nonlocal nonlinear media are discussed by means of variational approach. A set of parameter evolution equations, a critical power and an approximate evolution law of the beam width are obtained. In the general case, the beam width of the 1+2-dimensional super Gaussian shaped optical beam in strongly nonlocal media takes periodical oscillating variation with sine and cosine shape. But the beam width remains constant and the spatial optical soliton is formed when the input power equals the critical power. The critical power increases with the order of optical beam, but is independent on the order of phase factor. The speed of phase shift of the spatial optical soliton is related with the order of optical beam, the order of phase factor and the initial power. As the order of optical beam gets higher, the order of optical beam and the initial power plays more important role, and the effect of the order of phase factor can be ignored.

A fast steering mirror based on novel piezoelectric actuator was designed. The size of the mirror was 20 mm×15 mm. The optical scanning angle reached ±0.7°. The first step resonance frequency was 1872 Hz. Fast steering mirror was based on two amplified piezoelectric actuator .The structure was analyzed by finite element analysis software, and the frequency response was measured. The linearity of open loop scanning was improved by using the method of combining software which compensated the hysteretic behavior of piezoelectric actuator and notch filter circuit which restrained the structure resonance of the scanner. Accordingly, the triangle wave with high rate scanning was achieved. The sine wave with high precision scanning was realized by using the digital proportional-integral differential (PID) controller based on repetitive control principle. Test results shown that the scanner can steer the beam at high speed with high precision. The scanner also had other advantages such as small size and simple structure.

It is necessary to develop a miniaturization of the holographic disc storage systems for its practical and commercial application. A novel coaxial system of holographic disc driver was designed. One laser beam was used as information beam and reference beam simultaneously. The center part of the laser beam acts as the information beam. And the other part of the laser beam around the ring, which becomes a convergent beam after it is reflected by two annulus shaped mirrors, acts as the reference beam. The information beam and the reference beam interfere in the back focal plane of the first Fourier transform lens. The larger angle between the information beam and the reference beam can be obtained through optimizing the geometric parameters of the mirrors. Then the complex level of holographic storage is improved and the better selectivity is provided. This system has a compact profile and is useful to make a miniaturization holographic disc driver in the future.

Based on the extended Huygens-Fresnel principle, the propagation formulas for focusing of partially coherent electromagnetic vortex beams by an aperture lens have been derived. Based on these formulas, the intensity distribution and the degree of coherence near the geometrical focus are investigated. It is found that the topological charges, normalized coherence lengths and the truncated parameter play an important role in controlling the size of the partially coherence vortex dark core and the distribution of coherence in the focal region. The size of the vortex dark core increases with increasing the topological charge and the normalized coherent length. Moreover, the intensity of the vortex bright ring moves to the aperture with decreasing the normalized coherent length and the perceptive parameter. The effective coherent length in the focal region decreases with increasing the normalized coherence lengths and topological charges. It is also found that the effective coherent length increases with increasing the propagating distance. Therefore, the desired vortex dark core near the geometrical focus can be achieved by choosing appropriate values of parameters.

The principle and progress of polarized beam coherent combination is described. The influence factors, such as beam parameters, the change of amplitude-ratio and phase-difference, beam overlap-ratio and parallelism on the combining efficiency, are researched. The experimental parameters and methods of operating combining are also discussed. The results show that the influence of phase-difference variation on combining efficiency is much greater rather than the change of amplitude-ratio, and the effect of the overlap-ratio error is so small that it can be ignored when it is smaller than 2.5%. Moreover, the parallelism error makes the combining efficiency have a significant decrease. It is found that combining beams with large beam diameter have a benefit for the effective reduction of combining loss caused by the parallelism error, the combining efficiency is greater than 95% when the beam diameter is 8 mm and interference of equal thickness is used to test the coincidence. In addition, beam combination with identical intensity is the best method for getting the maximum intensity and simplifying operation.

According to principle of lidar and experiences, the automatic alignment system of lidar beam controlled by computer procedure has been designed. By controlling the position of gimbal-mounted mirror, the direction of light beam scanning was east-west and south-north. Echo signals were analyzed, and final position was obtained to make transmitting and receiving systems parallel. The process needs 10-20 min for once, and accuracy is about 0.1 mrad. In atmospheric temperture monitoring, measuring results compared with CIRA86 data. The error of altitude at 30-45 km is 1-3 K, 2-5 K for 45-65 km.

The beam combination characteristics of partially coherent beams, which are aligned along one dimension, are studied by use of Wigner distribution function. The formulae of intensity profiles, beam propagation factor (M2) and kurtosis parameter (K) are derived. The analysis shows that the intensity profiles,beam width, beam propagation factor (M2) and kurtosis parameter (K) are dependent on the spatial coherent length, propagation distance, separation and numbers of the beamlets.

Recently, the widely used Stokes parameters are generalized from one-point quantities into two-point counterparts, and used to determine the degree of polarization and degree of coherence of stochastic electromagnetic beams. On the basis of the generalized diffraction integral formula for an ABCD optical system in spatial domain, we derive a propagation law for the generalized Stokes parameters of a stochastic electromagnetic beam passing through an ABCD optical system, and use the Stokes parameters to investigate properties of the state of polarization of stochastic electromagnetic beams. As an example, we study the changes in the state of polarization of a stochastic electromagnetic Gaussian Schell-model beam propagating through a dual-focus system.

Lorentz-Gauss beams have been introduced to describe some certain laser sources with high divergence. When the q parameter at the source plane tends to infinity, Lorentz-Gauss beams reduce to be Lorentz beams. Based on the Collins integral formula, an analytical propagation formula of a Lorentz-Gauss beam passing through a paraxial abcd optical system is derived. Within the paraxial framework, the propagation properties of Lorentz-Gauss beam are illustrated with numerical examples. Based on the vectorial Rayleigh-Sommerfeld integral formulae, the analytical propagation equation of a nonparaxial Lorentz-Gauss beam in free space is presented, and the corresponding numerical examples are also given. Moreover, the far field expression and the scalar paraxial result are dealt with as special cases of the general formulae.

Based on the extended Huygens-Fresnel principle, the analytical expression for the spectral degree of coherence of partially coherent annular beams propagating in atmospheric turbulence is derived by using the quadratic approximation of Rytov’s phase structure function, and the spatial correlation properties are studied. It is shown that the oscillatory behavior and phase singularities of the spectral degree of coherence may appear when partially coherent annular beams propagate in free space, and the oscillatory behavior becomes stronger with increasing the beam obscure ratio ε. However, the oscillatory behavior becomes weaker and even disappears as the strength of turbulence increases. The curves of the spectral degree of coherence of partially coherent annular beams with different values of ε are close to each other and turn into Gaussian-like profile with increasing turbulence. The larger ε is, the less the spatial correlation is affected by the turbulence. In addition, it is found that in free space for small α the mean-squared width of the spectral degree of coherence wc can be either larger or smaller than that of the spectral density wi depending on ε， and critical value ε0 increases with increasing α. As α increases, there is wc>wi for different values of ε. However, there always exists wci when the turbulence is strong enough.

The composite optical vortices (OVs) formed by two parallel, off-axis Hermite-Gaussian (H-G) vortex beams at the waist plane and their evolution behavior are studied. It is shown that the number, position and net topological charge of composite OVs depend not only on the control parameter, including the relative phase, amplitude ratio, waist width ratio and off-axis distance, but also on the mode structure of H-G vortex beams. By appropriately varying the control parameter and mode of H-G vortex beams and in the free-space evolution, the motion, creation and annihilation of composite vortices may appear, and the topological charge does not always remain unchanged. In particular, for the composite OVs formed by TEM00 and TEM01 vortex beams, the topological charge is not conserved by changing relative phase. The results are useful for the composite OV control and applications.

The ray transmission characteristics of off-axis prism-pair are analyzed using geometrical optics method at different offset. The numerical model of off-axis prism-pair is built by ray tracing. The numerical relationship between the offset d and hypotenuse L of the off-axis prism-pair is obtained. The transmission direction, the number of ray transmission and the distribution of ray in the off-axis prism-pair are discussed at three different cases.The results show that the rays transmitting in the off-axis prism-pair have equal distance space distribution pattern when d=L/2n (n=1,2,3…)so it is much more benefit to obtain unform gain for each pass of rays and to realize multi-pass and amplification of slab-shaped gain medium.

It is inconvenience for the practical application of beam quality assessment because of the uncertainty when test beam quality factor about non-circular symmetry beam is done. The value of M2 will change if the reference frame or other experimental conditions are different because the test for M2 is based on reference frame. To have a unity of different laboratory coordinate systems of the M2, two cross-terms were introduced into present the relationship of beam spot spindle and laboratory coordinates under test. For describing the beam quality convenient, the M2 factor matrix is defined. The principle and method for test is studied, and a system to test the M2 factor matrix has been built. The law of beam width and quality factor M2 vary with the rotation of the coordinates has been studied by using two laser diodes who have the non-circular symmetry beam on the test system. Their M2 factor matrix have been tested and calculated at last.

An adaptive phase-locked fiber laser array with piston and tip-tilt error correction capability is investigated. The propagation performance of the adaptive phase-locked fiber laser array in different turbulent atmosphere is numerically studied by using multiple phase screen method. BPF is introduced as beam quality factor to study the effect of turbulence atmosphere on the propagation performance quantitatively. The influence is neglectable and the field intensity distribution remains unchanged compared to free space when the intensity of turbulence is weak (C2n=1×10－15 m－2/3, propagation distance z=10 km, coherence length=4.3 cm). The BPF value becomes 86% and 70% of the idea case when C2n=5×10－15 m－2/3 and 1×10－14 m－2/3 (corresponding coherence length are 1.6 cm and 1 cm, respectively), while the BPF value for the fiber laser array propagating in the same atmosphere without correcting piston and tip-tilt error are 55% and 38% of the idea case. The calculation results reveal that the energy centrality can be advanced evidently by the adaptive phase-locked fiber laser array.

Coherent combining of laser arrays is an important technique in realizing high power high brightness laser system. The coherent combining of two orthogonal polarized lasers is achieved by using polarization phase locking technique. Experimental results show that this scheme can achieve above 90% combining efficiency even when the power of the two lasers is highly imbalanced. The combining method can be scaled to a large number of lasers.

The principle of the adaptive optics system for all-path aberration correction is presented. And the correction ability of the adaptive optics system for all-path aberration correction is confined by the aberration of the retro reflector array. Three kinds of the retro reflector arrays are numerically simulated for the appointed wavelength adaptive optics system for all-path aberration correction. It is studied that the aberration of the retro reflector array can be neglected while all-angle error of cell of the retro reflector array lies in 2＂. The simulation result is approved by the all-angle error based on the aberration of retro reflector in retro reflector array measured by WYKO interferometer.

In order to improve the extender ratio of parallelism beam splitting, a new design scheme of bireflective parallel distensible beam splitting prism is proposed. By using prism expanded beam principle and Fresnel formula, some factors, such as structure angle and refractive index, which influence the extender ratio and transmissivity are analyzed. The effects of increasing shear difference on the basis of high transmissivity and the optimal design of structure are properly realized in the new scheme. The scheme has the deflecting function which could decrease the linear length of rays path building and save space of flat roof in experiment. The testing results show that the transmissivity and the shear difference of this new polarization prism are perfect and the experimental values are in consistent with the theoretical analysis. It is an ideal parallel beam splitting polarization device and has important practical merits.

Decomposed by Zernike polynomials of the wavefront, the relationship between beam quality factor β and static and dynamic aberration are analyzed. The formula between β and Zernike polynomials are obtained. After numerical calculation, the first 65 order fitted coefficients about the formula are offered. The approximate formula corresponding to Kolmogorov atmosphere turbulence is given. These approximate formulas are compared and verified well with the results of numerical calculation.

Utilizing the image of spatial filter’s pinhole of high power laser systems and diffraction of sample grating, with an insertable negative lens for the pinhole’s on-axial illumination, a new system for far-field detection of laser beam is presented. This far-field detection system, which is fully demonstrated on the experimental system, can fully use space through off-axial grating sampling. The experimental results indicate, that the average far-field alignment error is less than 1.42% of spatial filter pinhole diameter, which meets the alignment system requirements (5% of spatial filter pinhole diameter).

In order to achieve high brightness fiber-coupled output of diode laser array, a simple but efficient system was designed. Firstly, the output beam from a laser diode arrays (LDA) was collimated by fast and slow axis collimation module. Secondly, the collimated beam in the slow axis was divided into 4 parts (any other amount of the divided parts if needed) by the beam-shaping set of two parallel plane mirrors, and then reordered in the fast axis. Finally, the shaped beams were focused into a fiber (600 μm, NA=0.37) by a focusing lens. The beam-shaping efficiency was 98.87％, and the total system efficiency was 77.2％. This beam-shaping system is simple but effective and useful.

In one-dimensional quadratic crystals with modulation of both the linear and nonlinear susceptibilities, the transmission properties of the beam, whose wave form is the square of hyperbolic secant, are investigated by split-step integral approach. Numerical calculations indicate that fundamental soliton is rapidly excited when only fundamental wave (FW) is launched, and it presents inherent oscillation. The second harmonic wave (SHW) excites soliton, but the corresponding dispersive wave is obvious. However, while both FW and SHW are launched, and their amplitudes and beam widths are appropriate, both excited solitons are stable. The periodicity of fundamental soliton oscillation is move evident, and the dispersive wave of SHW is extremely weak. Moreover, there is a critical value of the launched SHW amplitude for the excited soliton to reach the optimum state.

Within the framework of static scattering, scattering-induced spectral changes in the forward-scattered component of polychromatic Gaussian beams transmitting through an insulating plate with rough surface are discussed. It is shown that the spectrum may be red-shifted and blue-shifted in comparison with the source spectrum, and the spectral switch may also take place. The H-parameter (the maximum deviation of the surface profile from the mean surface line) influences spectral behavior greatly. The spectrum remains unchanged if H=0. The phenomenon of scattering-induced spectral switches of polychromatic Gaussian beams in the far zone belongs to the effect in singular optics.

In order to study the transformation properties of a Hermite-Laguerre-Gaussian (HLG) beam though a fractional Fourier transform (FRFT) system in detail， the analytical expressions for the intensity distribution of HLG beam on the FRFT plane are derived from Collins formula. By using the derived expressions,numerical calculation examples have been presented to illustrate its propagation properties. It is shown that apart from the mode indices m,n, the intensity distribution on the FRFT plane depends on the fractional order p and parameter α, the variation with fractional order p and α is periodic,with the periods of 2 and 2π respectively. Furthermore, the beam shape of HLG beam maintains invariable in FRFT plane.

The process of the bottle beam generated from an axicon-lens system is described by a novel method based on the ray-tracing. The intensity distribution of the bottle beam in propagation is analyzed. Using ray-tracing,the influence of the focal length of the lens on the sizes of bottle beam is analyzed. The result shows that the sizes of bottle beams increase with the increasing of the focal length of the lens. Experimentally the bottle beams are generated by using an axicon-lens system. The beam patterns are captured in different propagation position,and the evolution and transversal intensity distribution of bottle beam is analyzed. The experimental results fit well with the theoretical simulation. Therefore,we can choose right size bottle beam to manipulate different particles.

For beam passing through cavity mirror twice in multi-pass amplifier laser facility,deformable mirror is often applied at location of cavity mirror for the goal of improving correction range. However,multi-pass amplifier with U-turn for improving optical quality has its own feature different from other facilities. Beam has 90° rotation and size change between 1-2 pass and 3-4 pass propagation. A new mathematical method is described to prove the solution existence of cavity deformable mirror and the application of cavity deformable mirror is verified in Xingguang-Petawatt (XG-PW),facility with U-turn reverser. The results are important for the adaptive optics system design of succeeding large-scale laser facility.

By using the theory of partially coherent light and the basis set of biorthogonal elegant Hermite-Gaussian (EHG) modes,the analytical expressions for the mode coherence coefficients (MCCs) and M2-factor of laser light have been derived. The relation between the coherent-mode representation of laser beams in terms of EHG modes and that in terms of corresponding standard Hermite-Gaussian (SHG) modes has been built up. Furthermore,two typical application examples have been discussed. It can be shown that the MCCs in EHG coherent-mode representation can be obtained by use of the MCCs in SHG coherent-mode representation;for the case of the modes with the same orders having the same weight factors,the beam quality of the laser beams that are made up of a superposition of mutually uncorrelated EHG modes is better than that of mutually uncorrelated SHG modes.

The influence of dispersive magnetic permeability on spatiotemporal instability (STI) in metamaterials is identified based on the Drude model. In the case of co-existence of cubic nonlinearity,pseudo-fifth-order nonlinearity and self-steepening,a generic expression for instability growth rate is derived. It is found that in the negative-index region,the pseudo-fifth-order nonlinearity increases the range of spectrum and the gain value of STI for the case of self-focusing material while it do opposite for the case of self-defocusing material,which are different from the results in ordinary materials,in the negative-index region,the pseudo-fifth-order nonlinearity will suppress the emergence of STI for the case of self-focusing material,which exhibits the same features for the case of ordinary material. In any way the self-steepening in metamaterials always tends to suppresses appearance of STI regardless of its sign.

Based on the Fresnel diffraction integral,the intensity distribution of Laguerre-Gaussian beam transmitted through a single-slit has been investigated. It is found that the diffraction fringes of vortex beams will dislocation and shift in the diffraction field,and the direction and the amplitude of the shifts is closely related with the topological charge. These results have been demonstrated experimentally in this paper. In addition,the spiral spectral of vortex beams transmitted through the single-slit has also been discussed. It is shown that the spiral spectrum will be broadened due to the limit of the single-slit,and the broadening depends on the topological charge,the beam size,and the width of the single-slit.

An experiment study on the bottle beam which are produced by the interfering of the two Bessel beams generated from the axicons is proposed. Based on the “bottle beam with Talbot effect generated by interfering Bessel beam”,the three-dimensional optical intensity distribution of the superimposed optical field along the propagation distance and the intensity evolution of the bottle beams in a complete period are simulated numerically. In the experiment,the bottle beam is generated by two interfering Bessel beams with different radial wave vector. Our result fits well with theoretical calculation and numerical simulation.

A method utilizing rotation effect of the quartz crystal to generate vectorial polarized beam is proposed. The quartz crystal is divided into twelve sectors with the same angle, and the thickness of the individual sector is designed with specific value. According the property of the crystal, the polarization direction of the incoming planar polarized beam is changed with different rotation angle in different sectors. So the beam with spatially different polarization is formed. Furthermore the irradiance distribution near the focus with a high-numerical aperture lens is also calculated with two-dimensional Simpson calculus(ZDSC) method. It is found that the focusing property of the vector beam is very similar to that of the cylindrically polarized beam. The method can be used to generate cylindrically polarized beam to meet the practical application needs.

Crossed phase defocus gratings are designed and a new technique for real-time measurement of beam quality factor M2 is achieved. We can get the beam spots at 9 various positions to be measured simultaneously by using the defocus gratings closely connecting with a short-focal-length lens. The lens provides the majority of the focusing power and the grating provides 9 separate optical axes and effectively modifies the focal length of each axis. The value of M2 is determined by calculating the beam diameters using the second moment method and curve-fitting. A He-Ne laser beam is measured by using the gratings designed and a M2 value of 5.775 is achieved. Compared with a conventional measurement, the error is 5.1%.

We designed a binary optic element (BOE) applying in the excimer laser wavefront shaping, which can obtain an optical field of Butterworth distribution. We employed the Gerchberg-Saxton (GS) algorithm for realizing the optimization and MATLAB was utilized to simulate the change of optical field. By comparing the simulation results of iterative number with 10, 100 and 1000 respectively, we studied the impacts of iterative number on shaping effects in Gerchberg-Saxton algorithm. Through the shaping result by cimulating about 106 time′s iterations, the phase distribution of binary optic element was obtained. The results present that the distribution of emergent optic field is Butterworth whose energy is 75.62% of total energy and the root mean square (RMS) of uniformity is 0.1394%.

Pulse-shaping of nanosecond broadband KrF laser is studied in this paper. Short pulse is obtained through the stimulated Brillouin scattering (SBS) pulse compression, and then the pulse-shaping is realized by using the pulses-stacking. According to the amplification of stacking-pulses in KrF laser amplifier, KrF laser amplifier has great influence on the shape of stacking-pulse. Through adjusting the shape of stacking-pulse, the anticipated shaped pulse can be gained after amplification. The energy of shaped-pulse reaches 50mJ after once amplification, and reaches 300mJ after twice amplifications. The theoretical analysis agrees well with the experimental results. The results show that the combined scheme of pulse-stacking and the amplification of amplifier have strong ability of pulse-shaping.

This paper investigated the self-imaging properties of waveguides and its potential applications in laser power coherent combing. Based on phase propagation constant and mode propagation analysis method, the self-imaging formation process of waveguides was analyzed and simulated. The self-image lengths of several regular waveguides and corresponding requests were confirmed in detail. Its characteristics were also gathered up by the numbers. Two kinds of waveguides of square and equilateral triangle were used to simulate combining for multi-beams. The calculation results show applying self-imaging of waveguides to coherent combining will be propitious to exalt output power and keep high quality beam transmitting. It is a good approach to realize high power and high quality laser radiation.

Through focusing Q-switched laser pulses into FC-72 medium, the intensity profile of backward stimulated Brillouin scattering (SBS) spot is investigated experimentally by charge-coupled device (CCD) camera and digital image processing technology, and the rules of intensity profile and spot size versus pump energy are obtained. The results show that the intensity profile of backward SBS spot turns from quasi-Gaussian to Gaussian profile when the pump energy increases. And the size of SBS spot decreases gradually in a whole with pump energy. When pump energy is near the SBS threshold, the size of SBS spot is maximum, and larger than that of pump spot. When pump energy is three times larger than the SBS threshold, the size of SBS spot is minimum and smaller than that of pump spot.

The influence on outcoupled phase mode by introducing intracavity tilt-perturbation in confocal unstable resonators is researched by adopting Fox-Li prony method. The distribution of wavefront has been analyzed by using Zernike aberration and mode reconstruction theory. The front 35-order Zernike aberration coefficient, point spread function (PSF) and the integrated relative far-field intensity are obtained, so the beam quality can be known fully. The properties of mode distortion are also studied experimentally by adopting Hartmann-Shack (H-S) wavefront sensor. Finally, a set of control system for intracavity perturbation is constructed and the correction for intracavity low-order aberration is performed experimentally. The result of intracavity correction shows that the system can achieve good correction for static intracavity perturbation when the control loop is closed after tilt is introduced. The front 10-order Zernike aberration, the peak value (PV) and root-mean-square (RMS) error of the wavefront have been reduced remarkably.

The nonuniformity of the irradiation on the target is eliminated by adjusting the intensity distribution on the cross section of the incident laser beams while keeping the position and direction of the beams that are used for indirect-driven laser fusion unchanged. A simulating program that can calculate the intensity distribution on spherical target with several beams irradiating on it is written. The intensity distribution on the target and its nonuniformity are worked out according to the condition of the incident beams. Then the distribution on the focal plane of the beams is educed by using the principle of weighted average. Finally the laser′s electric field distribution before the lens that is necessary for the uniform irradiation is obtained based on the laser transmission theory.

The nonlinear scattering loss in the single-mode fiber is analyzed. It is proved theoretically and experimentally that the maximal transmitting power in an optical fiber is limited by the stimulated Brillouin scattering (SBS). Based on mode field coupling theory, a model to calculate the butt-joint coupling efficiency between a multi-mode fiber and a single-mode fiber is presented. The dependence of the coupling efficiency between the multi- and single-mode fibers on the core radius of the multi-mode fiber is investigated. A experiment is conducted with 532 nm laser, multi-mode fiber (NA=0.11, a=12.5 μm) and single-mode fiber (NA=0.11, a=1.75 μm) to measure the butt joint coupling efficiency of multi-mode fiber to single-mode fiber. Good agreement is obtained between the experimental results and the theoretical predictions. A combined multi- and single-mode fiber relay system is proposed to transport laser beams with high power and good beam quality.

Based on the unified theory of coherence and polarization of random electromagnetic beams and the propagation law of partially coherent light, the change in the degree of polarization of beams which is generated from a partially coherent source after passing through a series of circular apertures was investigated. Gaussian Schell-model beam was taken as an example to study the change in the degree of polarization for on-axial points. It is found that, with the increase of the number of circular apertures, the degree of polarization for on-axial points will change. It is shown that for a sufficiently long propagation distance, the degree of polarization for on-axial points will tend to a certain value. And three circular apertures are chosen as a typical multiple circular apertures system for investigating change in the degree of polarization. It is shown that, the change in the degree of polarization depends on the size of circular apertures, the distance between circular apertures, the correlation length in the source plane and the degree of polarization in the source plane.

The finite-sized light beam reflected from a weakly absorbing dielectric slab would experience a longitudinal displacement. The longitudinal displacement of a linear-polarized light beam reflected from the single metal layer is theoretically investigated. It is shown that, in the region of absorbed frequency, the longitudinal displacement of TE polarized light beam is not only positive and very small but also grows slowly. The displacement is saturated to maximum when the incidence angle is very large. The longitudinal displacement of TM polarized light beam is negative and has a peak near 80°. The peak value is about one wavelength. It is also shown that the longitudinal displacement of TE polarized light beam keeps a similar action and its maximum is smaller in the region of reflected frequency. The negative displacement of TM polarized light beam is several wavelengths near 90°.

For studying the character of Hermite-sine-Gaussian (HSiG) beam in non-paraxial case, based on the theory of the second intensity moment and a series of complex calculations, the results of the far-filed divergence angle, waist width and M2 factor of non-paraxial Hermite-sine-Gaussian beams are derived, and the relationship of them versus the acentric parameters are studied by calculation and plot. The result indicates that the relationship of non-paraxial HSiG beam characters versus the acentric parameter is different from paraxial case. As the parameter w0/λ decrease, α→0, the far-filed divergence angle with even and odd orders approach 73.898° and 63.435°, respectively. With increasing the parameter, the waist width and M2 factor show large changes. Because of the effect of parameters, non-paraxial M2 factor can be less than 1 as well as approaching 0, which is different from paraxial case.

The distribution of transverse modes of the laser, especially the ratio of fundamental mode is proposed to evaluate laser beam quality, and the measuring method is studied. The beam spot images captured by a CCD detector are input into a nonlinear network which bases on the Hopfield network principle. The dynamics steady state is obtained by computing the energy function of the network and performing training arrangement. The proportion of all ranks of transverse mode in the steady state is the measurement result. During the experiment, a laser diode-pumped solid-state laser was used to emit laser beam, and the captured beam spot images were input into the nonlinear network after image processing, and the proportion of fundamental mode was 69%. The results were used to compose a new spot digital image, and the relative error compared the original image was 3.53%.

The transverse modes of a high power transverse-flow CO2 laser are on-line measured by using a laser beam analyzer. The temporal evolution of the transverse modes is observed also. The output beams are characterized with “double mode”, i.e., two higher-order modes spacing 8 mm between the mode centers, and overlapping unsymmetrical configurations. There is evidence to whow that such “double mode” arises from a misaligned axes of the resonator consisting of two tandem resonators, and a distorted cathode-copper tube. The transverse mode are more degenerated into complicated shapes as the lasing operating duration increases. An initial investigation shows that the temporal evolution of the modes depends on the gaseous component varying in the resonator during the lasing operation.

In order to scientifically evaluate the near field parameters involving the modulation and contrast ratio in space region for high power solid-state laser facility, the grey threshold of image segmentation in image processing is used to separate the noise and signal for the image of near field picked by CCD. The maximum square difference value is taken as the main criterion for noise threshold. The grey background can be obtained from the grey value of the most probability in the noise region. The oddity spot in laser near field can be judged based on whether the intensity is greater than Iavg(1+5σ) or not. The image smoothness technique of eight neighbor regions is adopted to process the oddity spots of pixel. Two evaluated methods for modulation are analyzed and compared with many experimental data. It is shown that two calculation results of modulation are identical, and present evaluated methods of high power laser near field parameters are much more normative.

Based on the generalized Huygens-Fresnel diffraction integral, the analytic propagation expressions for Lorentz beams passing through first-order axisymmetric optical system are derived. The expressions of the beam-width, Rayleigh distance and divergence angle of Lorentz beam are given, and their transform characteristics in free space are discussed. It is shown that the Rayleigh distance of Lorentz beams is larger than that of Gaussian beam. However, the expansion speed of the beam-width of Lorentz beams is lower than that of Gaussian beams and the far-field divergence angle of Lorentz beams is smaller than that of Gaussian beams. Moreover, the transfrom laws of the above parameters for Lorentz beams are the same as those for Gaussian beams passing through free space.

For improving the uniformity of the focal spot in the inertial confinement fusion (ICF) experiments, we simulated the effects of the different spectral shapes of broadband light with the focused spot through phase plate, such as random phase plate (RPP) or continuous phase plate (CPP), and the uniform bandwidth and maximal dispersive angle. The power spectral density (PSD) and root mean square (RMS) of the focused spot intensity were used to evaluate smoothing effect. The results show that the optimized spectrum can improve smoothing efficiently, and the RMS can be improved by 43.7% compared with the sinusoidal phase modulated spectrum. Generally, the smoothing efficiency would be better if the weighting of the different spatial frequencies of the focused spot was considered to design phase plate.

Based on the characteristic of the beam propagation factor of the diffractive beam from the end surface of dielectric planar waveguide, the rationality of the Gaussian approximation for the mode field distribution of planar waveguide TE0 mode is clarified. As the computing formula of the matching efficiency between two field distributions is engaged, the method of equivalent matching efficiency is advanced for ascertaining the equivalent mode field half width of the Gaussian approximation expression, and the computing formula of equivalent mode field half width which is expressed by the half thickness of core layer, the normalized standing wave parameter of core layer and the normalized evanescent wave parameter of cladding layer of the planar waveguide are acquired, and the matching efficiency between the Gaussian distribution and the eigen mode field distribution of planar waveguide TE0 mode is presented. The rationality of the method of equivalent matching efficiency for computing equivalent mode field half width is explained. Finally, as the method of solving the equations is introduced, the fitting expression of equivalent mode field half width which is expressed by the half thickness of core layer and the normalized frequency of planar waveguide is suggested, and the accuracy of fitting expression is showed by the error analysis.

The characteristic of the light propagation across the wide angle crossed waveguide is analyzed using the finite difference beam propagation method (FDBPM). Padé approximation is used to deal with the wide angle problem and the transparent boundary condition is used to deal with the optical reflection at the boundary. Through calculating the finite difference equations using the pursue after method, the relationship between the propagation loss and the intersection angle has been obtained. On this basis, the crossed silica waveguides are fabricated on silicon substrate by low pressure chemical vapor deposition method. Experiments show that the presented FDBPM has good accuracy and can be used to analyze wide angle crossed waveguides.

Based on the Sommerfeld diffraction integral, the anomalous spectral properties of an ultrashort pulsed Hermite-Gaussian beams propagating in dispersive media are studied , and its comparisons with anomalous spectral behaviors in free space are analyzed. It is found that the on-axis spectrum blueshift of ultrashort pulsed Hermite-Gaussian beams is relative to group velocity and pulse duration, but not to group velocity dispersion. The size of relative spectral shift in dispersive media is slightly smaller than that in free space, and the relative spectral shifts decrease with increasing the pulse duration. The location of spectral switching is relative to the transversal distance, transmission media,and the Hermite function indexes m and n, but not to pulse duration. The transversal distance of spectral switching in dispersive media is less than that in free space, the relative spectral shift slowly decreases as the order number of the spectral switching increases.

Based on the general Huygens-Fresnel diffraction integral formula, the focal switch effect of Hermite-cosine-Gaussian beams passing through an astigmatic lens is investigated in detail. The results of numerical calculations show that this kind of focal switch is dependent of the geometric parameter of the optical system δ, and the focal switch effect occurs regardless of whether the δ is 1.0 or not, i.e. the focal switches could occur not only at geometric focus but also at the right or the left of the geometric focus. The influence of beam parameter on the occurrence and the position of focal switches is discussed. The dependence of the relative focal shift on the astigmatic parameter is examined at different geometric parameters of the optical system δ for a particular beam parameter and Fresnel number. The result shows that the occurrence and the position of focal switches can be controlled by changing the beam parameter and astigmatic parameter.

The principle of optical rotation due to the transfer of spin angular momentum from light to particles was discussed by analyzing the interaction between the beam of light and birefringent crystal particles. Through MATLAB simulation, the dependence of the rotation frequency of the trapped particle on the laser power was analyzed, it was obtained that the rotation frequency was proportional to the laser power. The birefringent different particles were rotated by the optical tweezers, the wavelength of He-Ne laser was 632.8 nm, at the same time the rotation frequency was measured, and the maximum speed could reach 5 r/s. The dependence of the rotation frequency of the trapped particle on the laser-power was experimentally studied for several birefringent particles with different sizes in the optical tweezers. When experimental results were compared with theoretical results, experimental results and theoretical analysis were agreeing very well, and the reasons for the error were analyzed, which the bottom friction affected the most.

Based on the unified theory of coherence and polarization, the expression for the degree of polarization of partially coherent electromagnetic Hermite-Gaussian (EHG) beams in atmospheric turbulence is derived, and the conditions for keeping polarization invariance are also given. It is shown that the degree of polarization of partially coherent EHG beams in atmospheric turbulence at the observation point (x,y,z) depends on refraction index structure constant of turbulence, coherence length of the source, order numbers of Hermite polynomial, and constant associated with the degree of polarization of the source. However, after a long-propagation distance, the degree of polarization in turbulence tends to the value at the source plane. The result is independent of coherent length and order number of Hermite polynomial, and the strength of turbulence. The change in the polarization of electromagnetic Gaussian Schell-model (EGSM) beams is just a special case of the obtained results.

To improve the ratio of the power of in-phase mode to the total power of output signal (Q) for the 19-core fiber laser, two improved methods are presented. In the first improved scheme, three pieces of undoped fiber, with the same structure and numerical aperture as the ytterbium-doped 19-core fiber, are introduced into the Talbot cavity of the fiber laser. In the second improved scheme, the output beam from the single mode fiber laser is transformed to match the in-phase mode using the double convex lenses. The improved schemes are numerical simulated and analyzed based on a set of rate equations. The ratio Q and the output power of each mode are investigated for different parameters such as the distance between fiber ends (a), the power refraction factor of mirror on the signal output end (RM2), and the pump power. The quantitative analysis shows that, for the first scheme, the optimum distance a exists for the fixed RM2, and the Q can be increased from 79.06% to 88.25%; For the second scheme, the ratio Q can be increased to 95.74%, which ensures better beam quality.

Based on the theory of light propagation and diffraction characteristics of grating, the optical energy transfer of bi-grating imaging system is studied and the expression for the intensity of combined beams is given. Combined with bi-grating imaging formula, the influence of bi-grating properties and imaging place on intensity of combined beams is analyzed. The results show that intensity of combined beams is closely related with diffraction efficiency and location of two gratings. In three bi-grating imaging systems, the intensity of combined beams is measured. The experimental results are consistent with theoretical anticipation.

The relationship between the beam excursion error and the beam quality β factor of long-term exposure spot was analyzed with and without random wavefront error. The formula to calculate the beam quality β factor of long-term exposure spot with beam excursion error was given. The theoretic analysis and the numerical calculation results indicate that beam quality affected by beam excursion error was independent of the beam quality without beam excursion error, but relative to the criterion of the beam quality β factor and the obstructed ratio of optics system. The beam excursion error request in application was analyzed. The results indicate that the better the beam quality wanted, the smaller the beam excursion error needed.

A new calculation method is proposed for studying the characteristics of liquid crystal spatial light modulator (LC-SLM) when the incident readout light is oblique. The theoretical model is established, and the simulative results are given. According to the relationship of driving voltage to intensity of readout light at normal incidence, rotation angles of LC-SLM molecule with different modulation voltages are deduced and modulation depth is calculated. Phase modulation depth decreases with the incident angle increasing, while phase modulation depth increases with the obliquity of LC-SLM molecule decreasing, i.e., driving voltage of the LC-SLM increases with the intensity of write-in light increasing. With the incident angle increasing, initial phase of readout light decreases, but the maximal initial phase is 0.21π at the incident angle of 10°. The simulative results accord with the experimental data.

Beam′s oblique incidence and manufacture error of an axicon have a great influence on the quality of zero-order Bessel beams. Generally, the manufacture error is that the cross section of the axicon is not a circle but an ellipse. Based on the diffraction and geometry optics, the quality equivalence between the beam′s oblique incidence in a circular axicon and beams incidence in vertical angle in an elliptical axicon are analyzed. The diffractive optical patterns in oblique illumination on a circular axicon and the manufacture error in an elliptical axicon were simulated according to the calculation. The method to modify the influence on the nondiffraction Bessel beam of an elliptical axicon by rotating the axicon is proposed and the approximately perfect Bessel beams are obtained. The experimental result agrees with the theoretical analysis and numerical simulation.

An experiment of laser beam propagation in the atmosphere with stimulated Brillouin scattering (SBS) phase-conjugated compensation at long distance (10.5 km) is reported. On the normal atmosphere condition of a city, the conversion efficiency of the SBS phase-conjugated laser is about 4.4% through a 10.5 km distance, which is 2.4 times than the normal laser transimission efficiency on the same condition. Meanwhile, the phase-conjugated laser neturns to the emission position through the original path, and assembles again.

In order to numerically simulate the diffraction propagation of convergence/divergence optical beams, the complex amplitude pulse response function of lens imaging is researched. A novel method called object-image conjugation translation is presented, in which the spherical wave phase factor in convergence/divergence beams is equivalent to a lens, and the spherical wave phase factor is removed in the diffraction propagation with the pulse response function and the object-image translation. This idea is simple but efficient, with a visual physical meaning. The simulation of the diffraction propagation of the optical beam with square aperture-lens assembly, proves the practicality and the validity of the idea.

Wavelet Transform is a new technique for singnal processing. Based on the principle and algorithm of wavelet transform and discrete wavelet transform, a method of fittering with localized protecting by wavelet transform coefficient is presented. The method is used to process a simulating image and some real images, and all the results show that the new method is quite suitable for two dimensional the image with single spot.

To high power laser driver, the disk amplifiers are the most important sources of energy and power. The energy transmission and conversion in high power laser disk amplifier are discussed. The energy transmission is achieved by the energy bank modules, pulse flash-lamp, pump cavity and gain medium. The effects of different energy transmission process on the whole performance of disk amplifiers are researched by simulation and experiments. Results show that the small signal gain coefficient of 5.0%cm-1 and energy storage efficiency of about 3.0% are achieved by primary optimization in technical integration line (TIL). But because of the quality of some key elements, the best results are not obtained. High efficiency does not only improves the disk amplifier performance, reduce the cost, but also improves the amplifier reliability and stability.

High quality far-field determined by the phase and amplitude distribution of focal beam is necessary for inertial confinement fusion (ICF). To the high power laser system, the amplitude distribution of the output laser beam mainly derives from input beam, while phase distribution mainly come from the large aperture optical elements, especially for the Nd:glass amplifier slab. Nonlinear self-focusing of ripple can effect on far field in high energy too. Based on these factor, the transmit character of high power laser with fourth-pass amplifier was simulated, and the effect of amplitude and phase distribution on far field was analyzed by numerical was. The conclusion is that the most important effect factor on far field is phase distortion come from large aperture optics.

The relation between particle movement and atmospheric turbulence is discussed starting from the particle movement function in the atmospheric turbulence. It is found that the longer the particle movement relaxation time, the more evident the inertial effect, and the more different the particle movement and atmospheric movement are. The mathematic model is set up by using physics image analysis, the expression of aerosol concentration field in limited space is derived, and the correspondent numerical analysis is carried out. The experimental data of visibility sensor in short time indicate the influence of the aerosol concentration field fluctuation on intensity and phase of light on the path of light propagation.

Using geometrical optics theory and off-axis aberration analysis, a set of crossed double strip integrators for high power CO2 laser beam homogenizing has been designed. The uniformity of the power distribution on the working plane can be improved without being affected by the change of original laser beam. And because all the elements have reflecting surface, energy loss is not serious and water cooling can be easily used.

The way to simulate the visible signal and infrared signal from satellite in space based on TracePro is intraduced. First, the satellite position's coordinate, satellite surface's coordinate and the earth's coordinate are converted to one unite coordinate, then the temperature model from Sinda/G is inserted in Tracepro, and the surface properties, such as the reflectivity and emissivity are built. The infrared characteristic of satellite radiation is obtained, using the gray radiation in the software. The distances between the satellite, the earth and the sun are determined by the above conversion. This simulation could directly show the optical action on the satellite surface, is propitious to analyze the process and improve the precision.

Laser driven fusion requires a high degree of uniformity in laser energy deposition in order to achieve the high density compression required for sustaining a thermonuclear burn. While, filamentation severely affects laser irradiation uniformity, which often encountered in indirect-drive research. Therefore, a proper smoothing method must be adopted. With smoothing by spectral dispersion (SSD), the size of focal spot increases greatly for the introduction of phase plate, and pinhole closure will likely happen when the light injected into the hohlraum. To solve this problem, angular spectral dispersion of stacked chirped pulse is proposed here to decrease the target nonuniformity of scale 10 μm to 100 μm. By analyzing the propagating characteristics of frequency-modulated light, mathematical representations are deduced. Simulation indicates, compared with one-dimensional SSD [without random phase plate (RPP)], chirped pulse stacking is more effective in diminishing high frequency modulations on target plane, and the size of smoothed area is dependent on the bandwidth of the stacked pulse in the dispersing direction. These advantages make the technique a promise in promising method laser irradiation uniformity.

The intrinsic field of the waveguide by numeric solution is calculated. The mathematical model of bend waveguide refractive index is given. The curved optical waveguide is calculated analyzed with FDTD. By numeric calculation, the evolution of the pulse entering the bend waveguide, the pulse propagating in bend waveguide and its energy loss in the condition of different bend radius are obtained. The smaller the bend radius is, the more noticeable of the pulse moves and deforms, the more serious the energy loss. The bended waveguide is widely used to integrate optics and optical detection. etc.

Based on the flat-topped beam model proposed by Li and the partially coherent light theory, the spectral propagating expression of the partially coherent flat-topped beam is derived, and its variation of spectral properties is studied quantitatively in the free space. The variation rule of the on-axis spectrum of the flat-topped light beam for different orders in the propagating process is analyzed in detail. The effects of the source's spectrum width and the spatial coherence parameter on the spectral properties are discussed. It shows that when the partially coherent flat-topped beam propagates in the free space, the light source parameters have more effects on the value of the relative frequency shift than on the total change trend of the spectrum along the propagation distance, which is primarily determined by the order of flat-topped beam.

The expression of the M2 factor of the beam generated by Gaussian mirror resonator is derived based on the two-order matrix method, and the effects of the peak reflectivity value and the radius of the light spot on the film of the Gaussian mirror on the M2 factor are explored. The curves of the M2 factor are plotted with different peak reflectivity values and the radii of the light spot on the film. Integrating the whole beams from the Gaussian mirror resonator, the propagation property of the beam through an ABCD system with the diaphragm effect neglected is discussed, based on scalar diffraction theory and matrix optics theory. The curve of normalized optical intensity distribution versus different positions in free-space propagation is plotted.

Using period resonance gain structure, a laser diode (LD) pumped 980 nm vertical external-cavity surface-emitting laser (VECSEL) with active region of InGaAs/GaAsP/AlGaAs system is developed. The characteristic parameters such as longitudinal confinement factor, threshold gain, optical gain and output power etc. are calculated through theoretical model. With the optimized characteristic parameters, the structure of VECSEL is designed. Theoretical calculations show that the output power of a LD-pumped VECSEL can be higher than 1.0 W.

The transverse mode distribution of THz wave near the position of focus point was studied in this paper. It is important to know the transverse distribution of THz wave, which can be referenced as an evidence of sample positioning in THz spectroscopy and THz imaging experiments. By using THz point-by-point imaging technology, THz transverse mode distribution in the positions, where samples are usually placed, is analyzed qualitatively. By applying “slit method”, the beam width of THz wave was measured. The results show that the shapes of the transverse modes of THz wave in different positions around the focus have much difference. To the maximum wavelength of about 1.5 mm of THz wave in the system, the minimum diameter of THz beam at the focus point is around 1.0 mm. The results provide a basic reference for further application of THz Spectroscopy and THz Imaging.

Based on the method of matrix decomposition and expanding the rectangular function into a sum of complex Gaussian functions and the Collins diffraction integral formulae, the propagation characteristics of a Gaussian beams passing through spatial filter are studied. As a result, corresponding analytical formulae are obtained respectively. By using the numerical method, the analytical formulae are numerically simulated and the results can be got from the simulated figure. Numerical calculations have shown the dependence of the optimum pinhole size on the truncation parameters of the beams. As further extension , numerical calculations are performed for Gaussian beams and flattened Gaussian beams (N=12) propagating in spatial filter of B=0. The relation of truncation parameter and intensity distribution of Gaussian beams passing through filter is obtained.

Taking account of the transmission characteristics of the diaphragm and the saturation of the gain in the process of light amplifying, the evolution of the beam inside the Cassegrain multi-pass amplifier is numerically simulated by using the ray-tracing and split-step fast Fourier-Bessel transform (SSFFT) methods, the annular beam is coming from Q-switched Nd∶glass laser with ring cavity. Preliminary experimental verification has been carried out. Analysis indicates that the staircase-like features of the input and output mirror reflections are responsible for the poor quality of the output annular beam, and special attention has been paid on optimizing amplifier configuration. As a result, a new type of amplifier configuration is proposed, whose input mirror has an anti-super Gaussian reflection distribution and output mirror has a super-Gaussian reflection distribution. The simulated results indicate that the use of the mirror couple can improve the quality of the output annular beam considerably.

According to the third order aberration theory of binary optical element, the optical coupler system with one diffractive surface, telecentric optical path structure in the object space is shown with calculation and optimization of optical design software ZEMAX, whose operating wavelength is 0.4～0.7 μm, focal length is 27 mm, and optical length is 62.9 mm. The result is available for the image fiber bundle, whose single core diameter is 16 μm and section diameter is 6 mm. Compared with the conventional optical coupler, the hybrid refractive-diffractive system offers considerable reduction in the apparent size, weight, and improves the image quality. The simulation results of optical design software are proved well by the experiments on scenic imaging both indoors and outdoors.

Supercontinuum spectra can be generated in a novel multi-core microstructure fiber (MF) with random air lines. Over 600-nm-wide broadening spectrum (400～1000 nm) is obtained after the 20 fs laser pulse train from a Ti∶sapphire laser oscillator at 820 nm wavelength transmitting a 40-cm-long multi-core MF. The visible light can be tuned by adjusting input end of the MFs. The experimental results show that super non-linearity occurs as the MFs with random air lines are used for generation of supercontinuum.

Cylindrical lenses have been widely used for collimating laser diode beam, but the collimating performance is usually not high. A new collimating element-double half-cylindrical lens (DHCL) was proposed. The theoretical expressions of the collimated beam of a DHCL are derived by transmission theory, and the numerical results are also given. Both theoretical and numerical results indicate that a DHCL can be made from the high refractive index material but a normal cylindrical lens cannot, and the collimating performance of a DHCL is much better than that of a normal cylindrical lens. The divergence angle of the collimated beam could be as small as 0.1 mrad.

Based on Huygens-Fresnel diffraction integral theory and stationary phase method, the influence of the axicon with non-circular symmetry manufacture error on the zeroth order Bessel beam (J0 beam) is analyzed. The numerical simulation is compared with the beam patterns photographed by a charge coupled device (CCD) camera. Results show that if the cross-section of the axicon is ideally manufactured in circular symmetry, the field distribution behind the axicon is approximately an ideal Bessel beam. But if non-circular symmetry manufacture error exists, with the cross-section as an oval, the diffraction beam patterns will deviate the J0 beam. The greater is the difference between elliptical semimajor axis and semiminor axis, the larger is the deviation from the J0 beam. The experimental results fit the theoretical simulation very well.

The experimental demonstration of the little-size serrated aperture instead of circular aperture in the laser system is given. The intensity distributing and the contributing range for using the serrated aperture are analyzed based on Fresnel diffraction theory. The pictures are recorded by charge coupled device (CCD) system. The intensity ripples of Fresnel diffraction are suppressed and the filling factor is improved by using the serrated aperture.

The microring resonator coupled with the input/output channel waveguides can be applied in filter due to its compactness, functionality, and the possibility of dense integration. In order to achieve flatter tops and sharper rolloff in the passband, the multiple-ring higher order structure is employed. Both the transfer functions of “series-coupled” and “parallel-coupled” multi-ring high order filters are derived using the transfer matrix method. For the “parallel-coupled” structure, the symmetric spectral response is achieved by optimizing the ring distance, while for the “series-coupled” structure, the performance is determined by the coupling coefficients between the ring and ring. In order to obtain maximally flat response passbands, the numerical results show that the proper coupling coefficients should be symmetric and smaller in the middle of the structure.

Beam-converting annular resonator (BCAR) possesses outstanding characteristics of high extraction efficiency and near-diffractive beam quality. It is applied specially to annular HF/DF gain medium. In this paper, numerical model of rear cone misalignment and compact leg tilt is presented, and this numerical model has been used in physical optics code. The numerical result shows that the output power is insensitive to rear cone decentration and compact leg tilt, but beam quality is very sensitive to the decentration and tilt. The rear cone decentration and compact leg tilt can both result in a phase shear and twist on the optical field, and lead to phase jump and tilt along the misalignment direction. When the misalignments increase, the phase distribution of BCAR output field is twisted more severely. The directions of misalignments have little effects on the output field. Among these misalignments, rear cone decentration has more severe effect on the output field, and it must be controlled carefully in engineer.

The relationship between beam quality factor β and wavefront error was analyzed in this paper. Approximate formulas to calculate β from room-mean-square (RMS) of wavefront error were deduced. The relationship between β and several Zernike polynomials was obtained by numerical calculation through fast Forier transform (FFT) method. The approximate formula to estimate β from atmosphere disturbed wavefront error was given too. These approximate formulas were compared and verified well with the results of numerical calculation.

The Gaussian beam theory has been developed to describe the power characteristics of intracavity continuous-wave singly resonant optical parametric oscillator (ICCWSRO). The second-order nonlinear interaction in the resonant cavity of laser is treated as the output loss of laser. The nonlinear reflectivity of the laser and the power characteristics of the signal and idler waves are obtained, based on the solution for the equations describing the power characteristics of laser. The stand-wave cavity structure, the properties of the four-level, end-pumped laser gain medium, the mean-field approximation of second-order nonlinear interaction, the diffractive effect of the interacting waves are all considered in the derivations. If the diffractive effect in the laser gain medium is neglected and only the first-order approximation is retained, the nonlinear reflectivity of laser is obtained, based on the solution for the transcendental equation. In the numerical calculation, the Nd∶YVO4 is taken as the laser gain medium, and the periodically poled LiNbO3 (PPLN) is taken as the second-order nonlinear crystal.

According to the more accurate Helmholtz equation, the conventional finite-difference beam propagation method (FD-BPM) is modified and a new algorithm is proposed. Compared with the old algorithm in calculation of slab waveguide, the calculated precision is improved without extending culculating time for the new algorithm

The Wolf effect, i.e., the spectrum of partially coherent light generally changes on propagation even in free space unless the light obeys the scaling law, is a well-known phenomenon of the correlation-induced spectral changes. This paper deals with the influence of turbulence on the spectral shift of the Gaussian Schell-model (GSM) beam, which is taken as a typical example of partially coherent light. Based on the propagation law of partially coherent light and consideration of the presence of turbulence, an expression for the spectrum of GSM beams propagating through turbulence media is derived and numerical calculations are performed. It is shown that the turbulence affects the spectrum of GSM beams, whenever the scaling law holds or does not hold true. The stronger the turbulence is, the larger spectral shift appears in comparison to the case without turbulence. In particular, there is off-axis spectral splitting if the scaling law fails. The spectral shift of GSM beams in turbulence media depends on the beam spatial coherence, refraction index structure constant c2n and position parameter in general.

Based on the nonparaxial vectorial moment theory of light beam propagation, the propagation of TE (transverse electric) vector Gaussian beam has been investigated, and the integral expressions of beam waist, transversal divergence angle and beam propagation factor have been presented. The results reveal that both the transversal beam widths defined as second order moment of energy flux follow a very simple hyperbolic law upon propagation. The numerical calculations show that TE polarization results in different propagating characteristic in the two transversal directions for highly nonparaxial case, and the maximum transverse divergences exceed the divergence angle limit of nonparaxial scalar Gaussian beam 63.43° and are close to 90°, which is in accordant with the theory of wave optics. Moreover, the divergence in the x direction is slightly larger than that in the y direction. Under paraxial condition of nonparaxial scalar Gaussian beam, the propagation of TE vector Gaussian beam is reduced to that of transversal fundamental mode paraxial scalar Gaussian beam for paraxial case. However, the beam propagation factor will always be greater than unity and cannot accurately equal to unity forever.

The atmospheric coherence length is a very important parameter of atmospheric propagation and adaptive optics. The principle of atmospheric coherence length measurement via differential image motion measure (DIMM) angle-of-arrival fluctuation of optical wave and the measurement method dealing with the irradiance scintillation of laser propagation are introduced. The atmospheric coherence length along level propagation path is measured via differential image motion measure angle-of-arrival fluctuation of optical wave. In addition, the measurement systems dealing with the irradiance scintillation of laser propagation are used to check the results of the atmospheric coherence length measurement, and its time variation is similar, but they can be much different from each other under other conditions. Last, various errors caused by instrument are analyzed and discussed.

A novel supercell lattice method (SLM), induced from both the plane wave expansion method (PWM) and the semi vector method, is presented to analyze the photonic crystal fibers (PCF). The electric field is still expanded with the Hermite-Gaussian function, the dielectric constant of the PCF missing the center air hole can be considered as the sum of two perfect PCFs, which have different dielectric constant and different structure parameters (the hole pitch, the hole diameter). The periodical dielectric structures of the two perfect PCFs are expanded in cosine function with different periods. From the wave equation and the properties of Hermite-Gaussian function, the propagation characteristics of the PCF, such as the mode field distribution, birefringence, the dispersion property, can be obtained. The accuracy of the SLM can be scaled by the birefringence because the ideal triangular lattice PCF has no birefringence based on the group theory.

Some parameters for describing optical qualities of a short-term beam pattern of a collimated laser beam propagating through a turbulent atmosphere are evaluated for a series of numerically-generated patterns. These parameters include the on-axis, peak, and energy Strehl ratios and the sharpness. Their statistical characteristics are analyzed and the validity of these parameters for describing optical qualities of the beam pattern is discussed. Main results could be summarized as follows. The energy Strehl ratio could reflect the energy concentration of the whole beam; the sharpness well reflects the energy concentration in a local area, and could be used for describing the optical quality of laser beam in the turbulence. Generally the turbulence is benefit for promoting the pattern sharpness.

The study on laser transmission and scattering characteristics in complex environments is the basis research of light scattering from target and environment. The severe attenuation caused by laser propagation in sand and dust storms was mainly discussed in this paper. The attenuation characteristic of laser was studied with Mie theory for single scattering of sand and dust particles with special size distribution. Based on Mie theory, the average scattering cross section, albedo, asymmetry factor, and phase function were calculated. The laser multiple scattering and attenuation characteristics of slanting transmission in the layering sand dust atmosphere were studied by using four-flux model method and Monte-Carlo method, and the relationship between attenuation and visibility in difference heights was also given. Finally, after considening of multi-scattering, numerical calculations of specify attenuation were made for laser signal of 1.06 μm in sand and dust atmosphere by using the above two methods respectively, and the results were compared to the condition of single scattering. It is shown that biggish error can be brought in the low visibility take no account of multiple scattering, and that the more layers of the sand and dust atmosphere is divided into for slanting transmission, the more accurate the result is.

The propagation properties of laser beams are of much significance in applications of laser technology. The analytical propagation equation for beams is one of the focuses in laser optics. Starting from the Collins formula, the properties of the off-axis Gaussian beam (OAGB) propagating through a paraxial ABCD optical system with an aperture are studied in detail. Moreover, the analytical equations for the off-axis Gaussian beam propagating through a paraxial ABCD optical system with hard-edged aperture, Gaussian aperture or cosine aperture are derived. The relationship among hard-edged aperture, Gaussian aperture and cosine aperture is discussed. The validity and advantage of results are confirmed and illustrated by numerical calculations. The difficulty of finding the analytical propagation formula of laser beams propagating through a paraxial ABCD optical system with multi-aperture is analyzed. It is shown that the difficulty is due to the existence of an error function in the analytical propagation formula for single-apertured laser beams.

In the process of laser propagation in the atmosphere, the technique of optical phase conjugation can be used to compensate for the wavefront aberration produced by the atmospheric turbulence or bloom effects. Pretilting mirror method to realize the tracing and aiming at moving target and to compensate for the wavefront aberration was presented, also indoor simulating experiment is studied. The effectiveness of this method has been proved by experiment.

Although for a real high-power and high-energy laser the propagation distance of lasers in the beam control system (or called the inner optical system) is much shorter than that in the long-distance atmosphere, the thermal effect of a high-power-density laser beam passing through the inner optical system remarkably affects the far-field beam quality. By using a four-dimensional simulation code, detailed numerical calculations are performed for the high-power laser propagation in the inner optical system, where an annular profile with linear non-uniformity in the x direction is used to model the high-power laser. The astigmatic parameter, power in the bucket (PIB) and position of the peak intensity are chosen as the parameters for characterizing beam quality in the far-field. It is found that the thermal effect in the inner optical system reduces the peak intensity and beam focusability, thus degrades the far-field beam quality. In addition, the non-uniformity of the initial beam affects the focusability and gives rise to the astigmatism. It is worth noting that the thermal blooming is a nonlinear effect, which affects the intensity distribution and results in a shift of the position of peak intensity in the far-field. The physical interpretation is given and confirmed by numerical results.

A wide angle beam propagation method in an oblique coordinate system (OCS WA BPM) based on coordinate transformation is used to simulate optical waveguides. Compared with conventional wide angle BPM in rectangular coordinate system (RCS WA BPM), much better results are obtained with this method especially for waveguides with large tilted angle. This approach is also applied to Y junctions, and expected results are obtained.

Using numerically calculation, it is proved that the bound and high order soliton might be formed when Gauss pulse propagated in optical fiber grating though there are extremely strong GVD around the photo band gap. The characteristic of the fiber soliton is analysed, and then the applications on the WDM system is put forward.

In this paper, it is analyzed the propagation of a Gaussian beam in fiber media with ray tracing under the paraxial approximation. Using different refractive index distributions, the phenomena of plasma waveguide and the application of a ring shaped beam in the manipulation of particles are discussed, separately.

Using the self-convergent beam width method, the beam width propagation and beam-propagation parameters of hard-edge diffracted super-Gaussian beams are studied. It is found that the self-convergent beam width of super-Gaussian beams obeys the same law as that of the beam width based on the second-order moments without truncation, when the self-convergent-width factor satisfies a certain condition. Therefore, the beam propagation factor (M2-factor) obtained by using this method is invariable upon propagation. Meanwhile, a detailed comparison between the self-convergent beam width method and the asymptotic approach is made and the equivalence between the two methods is discussed. In addition, a concise physical meaning of the self-convergent beam width method is given.

By treating photorefractive spatial soliton as rays in geometric optics, the action of the diffusion effect on propagation of PR spatial solitons is analyzed. Based on similarity between ray picture and classical mechanics picture, ray Hamiltonian equations of motion in a diffusion potential created by the induced change in the refractive index are resolved exactly by integrating. Results indicate that the center of the optical spatial solitons moves on a parabolic trajectory and the spatial frequency transverse component shifts linearly with propagation distance.

The straight waveguide transmission characteristics of two dimensional photonic crystal are investigated based on the overall space theory of vector scattering. The relationship between transmission efficiency and waveguide length is calculated. The coupling of butterfly waveguide is discussed.

By a simplified model of gain region, the propagation and amplification of capillary discharge X ray within the cylindrical plasma with linear eletron density profile are studied with the geometrical optics approximation. The angle of refraction and the relation between out put intensity and deflection angle are given. The saturation length of X ray is given, too.

The dual layer dielectric reflection film of GeO 2/Al is deposited on inner wall of the quartz capillary by CVD. The inner surface reflectivity is increased, and transmission losses are decreased. The transmitting energy hollow fiber can transmit more than 80 W power of CW carbon dioxide laser.

Through numerical simulation, it is demonstrated that, at zero averaged path dispersion managed optical fiber links, after both second order dispersion and third order dispersion are full compensated, nonlinear effect can make optical pulse narrower. So, optical pulse's peak power has to be kept very small. However, when polarization mode dispersion is considered, the nonlinear effect can be balanced. As a result, the system can be operated in higher power, so that signal to noise ratio of system will be improved.

By expanding the rect function into a finite sum of complex Gaussian functions, the propagation of flattened Gaussian beams through an apertured optical ABCD system is studied in the rectangular coordinate system, and approximate analytical propagation formulas of flattened Gaussian beams are derived. The validity of our formulas is illustrated with numerical examples.

When a high power laser beam propagates through a multi-stage amplifier, distances separating different stages play an important role in deciding the characteristics of the output beam. The concept of the relative intensity noise (RIN) has been adapted to quantitatively analyse the experiment results.

An adaptive beam expander to control the focusing characteristics of flying optics, was proposed and its operating principle and adjusting characteristics were analyzed. The simulation results indicate that the adaptive beam expander can be used to control the focusing length and spot size.

By means of 1-D elastic-plastic hydrodynamic model and finite differential method, it is studied that formation, sustain, and decay of shock wave were induced by powerful pulsed excimer laser in target materials. By using the criterion of accumulate damage and dynamic fracture, the spall thicknesses are given in aluminum and C/Ph, respectively. These calculation results are in agreement with the experimental measurements reported, and reasonably explained experimental phenomena.

When GS method are used for retrieving wavefront, the results are not determinate. This paper reported our work of the uniqueness of phase in which GS method are used for retrieving wavefront of laser beam propagation through the turbulent atmosphere by using Numerical simulation, and put forward some new quadratic driving mends to GS method. Meanwhile, the results getting from GS method are given, and wavefront errors are also compared and analyzed. It is shown that the mends of GS method can not only resolve the uniqueness problems of GS method, but also quicken the speeds of the convergence.

The thermal effects, produced by the high energy laser in a beam control system, are numerically analyzed in this paper. The effects on the laser density and beam facula quality at far field are studied in particular. The propagation of laser is described by the paraxial wave equations, solved by the phase screen technique and the FFT method. The thermal turbulence motion and the air density variation are governed by the complete Navier Stokes equations, so that the variety factors could be in consideration. The Navier Stokes equations are solved by using the LU SGS factorization technique. The numerical results show that, with the additional initial thermal phase at the emitter exit, the energy density and the quality of the laser beam at far field would be prominently degraded for the typical situations.

Besides the effective radius R eff , the robust radius R rbt  and the sharpness radius R shp  are introduced. The validity of three kinds of radii, two characteristic radii, for describing the pattern quality are test through numerically generated patterns of a collimated laser beam propagating through a turbulent atmosphere, and main results could be summarized as follows. R rbt  and R eff  are equivalent for Gaussian beams, but the former can be used for more general patterns. Both of them are not valid for evaluating the pattern quality; and R shp  can well used for the purpose. For laser beam patterns in the turbulence under very weak fluctuation condition, in a very limited extent, the pattern quality for half of them will be degraded, and for another half the quality will be refined. With increase of the fluctuation condition, the quality of more and more patterns will be degraded, and there still be some patterns whose quality will be refined in a deeper extent.