The thermal instability is a big problem in arrayed-waveguide gratings (AWG). A general method to study the central wavelength temperature sensitivity is developed with theoretically considering thermo-optic effect, stress-optic effect, thermal expansion and stress-strain relation. By combination of elastic multilayer theory and stress concentration effect, analytical stress solutions in the core layer are obtained. Based on the results of asymmetrical anisotropy planar waveguides, the effective index and its temperature coefficient in buried channel waveguides are calculated by using the effective index method. And then, the solutions are used to estimate temperature sensitivity of AWG central wavelength. The temperature sensitivity controlled by the thermal stresses induced by attaching an aluminum plate is also discussed. The results show that the temperature sensitivity could be optimized after attaching an aluminum plate on the bottom of arrayed waveguides. For the TE mode, the temperature coefficient of central wavelength is reduced to 5.9 pm/℃, and for the TM mode, that is reduced to 8.0 pm/℃.

A novel long-period fiber grating (LPFG) is fabricated in common communication optical fiber by using a edge-written exposure method with high-frequency CO2 laser pulses. Studies show that this kind of long-period fiber grating has refractive index disturbance mainly in cladding of optical fiber, and its excess loss is less than 0.5 dB. Experimental results of the refractive index characteristic show that it has a resonant peak shift of 15.52 nm when the surrounding refractive index varies in the range of 1.41～1.45, which is three times higher than that of a conventional long-period fiber grating due to especial refractive index disturbance. The novel long-period fiber grating can find important applications in the field of optical sensing.

Some issues in recording and reconstruction of near distance digital holography are discussed where the recording distance is shorter than the Fresnel diffraction distance. The compensation of the higher-order phase in recording and reconstruction of in a hologram is analyzed. It is indicated that when the size of CCD and recording distance are determined, and some conditions of the object size and position of the spherical reference light are satisfied, the effect of higher-order phase can be compensated to small enough, even if the recording distance is shorter than the Fresnel diffraction distance. The higher-order phase compensation condition and numerical reconstruction equation are derived. Under the compensation condition, the fast Fourier transform algorithm can be used in numerical reconstruction. Experimental results are accordant with analysis conclusions. A correction method of difference between actual reference wave-front with the spherical reference wave-front in reconstructing is introduced.

A method of hyperspectral image data compression using partitioned Karhunen-Loeve transform (PKLT) and integer wavelet transform (IWT) is proposed. IWT technique and set partitioning in hierarchical trees (SPIHT) compression coding are used to compress the PKLT data. In comparison with other methods, PKLT/IWT/SPIHT not only reserves the compression performance of KLT and the performance of IWT's high compression rate, but also is easy to implement real-time transmission. Experimental results show that the peak signal-to-noise ratio(PSNR) of PKLT/IWT/SPIHT improves 6 dB, 9 dB and 8 dB comparing with KLT/WT/WSFCVQ, KLT/WT/IBBZTC and KLT/WT/FSVQ in the condition of same compression rate respectively, computation hours decrease half, and the whole compression performance is enhanced much more.

There is high correlation among each channel in RGB color space. If the color inverse halftoning method with discrete channel is applied there are large worms and color differences which is sensitized by human visual will be left. Based on the model of vector error diffusion the halftoning noise characteristics for color image are developed, and a color inverse halftoning method based on Karhunen-Loeve transform and multi-scale pyramid transform is presented. Using the Karhunen-Loeve transform the correlation among color components are reduced, then the halftoning noise in high frequency detail is separated and de-noised by multi-scale median interpolating pyramid transform and Wiener filter. Finally the color inverse halftone is constructed from the inverse pyramid and Karhunen-Loeve transform. Experimental results demonstrate the proposed method can remove halftoning noise effectively and overcome chromatic aberration. Peak signal-to-noise ratio is increased for about 2～3 dB higher than the color inverse halftoning method with disrete channel, and the excellent visual effect is obtained.

An illumination-independent wavelet scale multiplication edge detection method is proposed to detect edges from the non-uniform weak illumination image. Based on the illumination-reflected image formation model and CCD camera imaging formula, the image wavelet transform formula is deduced. The wavelet module coefficients of the background pixel, noise, edges are observed and analyzed in the local region, and the illumination-independent wavelet edge detection algorithm is worked out. To enhance edge pixels and reduce noise, an improved wavelet scale multiplication edge detection algorithm is applied to orient edges accurately. Through utilizing edge pixels' characteristics after wavelet transform, the single-pixel edges are taken out of the image. In the end, the edge detection experiments for synthetic and real non-uniform weak illumination images were conducted, and its performance is analyzed and compared with other two edge detection methods qualitatively and quantitatively. The experimental result proves it correct and effective when used in the non-uniform gray and low contrast images to detect edges.

As two of the most important resolution enhancement technology (RET), off-axis illumination (OAI) and attenuated phase-shift mask (AttPSM) can not only improve image quality, but also improve the depth of focus (DOF) to get a better process window which make a great contribution to the realization of 65～32 nm technological mode. A consistent frequency-space analysis of the off-axis illumination and attenuated phase-shift mask is presented here to explain its influence to the transmission cross coefficient (TCC) and image frequency distribution. Study on the optical mechanism of these resolution erbancement technology can benefit the design of projection lens optical system, optimization of resolution enhancement technology and the parameter setting of lithographic tool .It shows resolution erbancement technology can adjust image frequency distribution to enhance the lithographic resolution and image quality. As for 65 nm node pattern, off-axis illumination and phase-shift mask can improve image contrast to 0.948, process window to depth of focus 0.51 μm while exposure latitude is 5%.

Based on the development of digital neutron imaging system, the restoration algorithm was presented to remedy the geometric unsharpness of digital neutron radiation images. Firstly, the collimation component of digital neutron imaging system was analyzed, and the point spread function (PSF) which results in the geometric unsharpness of the neutron radiation image was estimated. Hereby, a regularized Lucy-Richardson(LR) algorithm was proposed, the algorithm investigated the bivariate model of wavelet coefficients using Bayesian maximum a posteriori(MAP) estimation theory to derive an efficient denoising method, and incorporated the wavelet denoising into the iterative step of original LR algorithm to solve the drawback of noise amplification. A real neutron radiation image of the specimen under test has been restored using this reformed algorithm. Experiments show that the restoration results are improved significantly compared with the results obtained by using the traditional LR algorithm and Fourier-Wavelet regularized algorithm. This method can also be applied to other image restoration problems.

The lidar polarization system realizes imaging for targets by the polarization differences of light scattered by the different targets. Because there exist the depolarization effects in a majority of systems, the depolarization problem of system itself must be considered in the process of imaging. According to the adaxial theory and requirement of optical aberration, the geometrical structure of Cassegrain telescope is designed. Then the depolarization behavior of the interface between air and reflecting mirrors of Cassegrain telescope is analyzed by using Jones formalism, coherent matrices of optical waves and law of Fresnel reflection. And the polarization degree of light is emulated, which is reflected from every point of reflecting mirror coated with and without thin film, relative to the diameter of Cassegrain telescope through the help of Matlab software. Based on the simulation, it is deduced that the polarization degree of light reflected from the telescope overcoated with aluminium film in the imaging system can be ignored in the imaging process.

A new analysis method is proposed for calculating the flux density distribution on focal plane of solar concentrators. On the basis of considering the optical errors and the influence factors which are the sunshape,the random surface error of concentrators, the tracking error, the position error of receivers, the diffuse reflection and the shadow of receivers, with the optical properties of concentrators, the finite element method is used to calculate the flux distribution on the focal plane. The validity and the feasibility of the method are demonstrated by comparing results with those in references. The flux density of hemispheric receiver and cylindrical receiver are also calculated. The results show that the method is independent of the surface contour of concentrators or receivers. It is a simple and universal method that establishes the base for optimizing the system efficiency and measuring the flux-density distribution.

Based on the model of two-dimensional scanning observation, the two-deimensional image shift compensation (ISC) model is proposed with an ellipsoid model for the Earth. Meanwhile, a fast iterative algorithm is also set up for the position determination of the observed objects from space. The real performances of this model are validated with some practical orbital elements and simulated attitudes. The results show that, for the long-term (namely more than one scanning period in the west-east direction) errors from orbit and attitude, ISC is realized by adjusting the scanning traces in the instrumental reference frame. The instant compensations in both azimuth and elevation are in the order of 0.01°～0.1° under the condition of the existing orbit measurement and control capabilities, and vary with the orbital positions. A real example of adjusting attitude misalignments in yaw direction of FY-2C validates the performance of the above model further.

The multiple exposure method has been proposed to fabricate combined diffractive optical element,but the multiple etch processing is complex and large alignment error will be introduced. According to error-diffusion method in computer-generated hologram (CGH) and partial coherent imaging theory, a new method to design coding mask of profile-combined element with error-diffusion method is presented. The designed coding mask for color-separation grating and beam-sampling grating (CSG-BSG) combined optical element with error-diffusion method is illustrated , and the intensity distribution of the spatial image in partial coherent imaging system is simulated, compared with ideal combined element relief. It shows that mean-square error is 7.5% and volume error is 10.2% after correction.

Passive ring resonator (PRR) is the critical sensing component of a resonator optic gyroscope (ROG) and the scale factor of a resonator optic gyroscope is mainly determined by the coupling coefficient through the full width at half maximum of the passive ring resonators transfer function. A method to determine the optimal value of coupling coefficient is elaborated based on the theory of coupled-mode theory and frequency-modulation (FM) spectroscopy. Finally, emulation results is given to verify the method and prove that the value of about 5% is only correct in the situation of fiber optic gyros (FOG).

The properties of several solid active material for solar pumped lasers were studied. We used Matlab software to process solar spectrum with cubic spline interpolation. A local discrete model of solar spectrum was set up. With this model, we calculated the percentage of the solar energy which can be absorbed by different laser material such as Ruby, Nd∶YAG, Yb∶YAG, Nd∶YVO4, Cr∶Nd∶GSGG, Nd3+-doped glass ceramic and Yb3+-doped silica fiber are 24.51%, 15.98%, 2.35%, 6.46%, 43.91%, 15.98%, 7.63% respectively. Then in a assumed condition, we calculated the threshold of pumped power density of each active medium. Taking the thermal property of each medium into consideration, we chose Nd∶YAG, Nd3+-doped glass ceramic and Cr∶Nd∶GSGG as the most suitable medium with high couple efficiency, low threshold and good thermal property for solar-pumped solid state laser.

The semiconductor optical amplifier has the feature of inhomogeneous broadening, which makes it an ideal gain medium for constructing multiwavelength fiber lasers. A novel multiwavelength fiber laser employing a semiconductor optical amplifier within a fiber ring cavity is proposed on the basis of the theoretical analysis of the Lyot-Saganc filter with two segments of polarization-maintaining fiber (PMF). This fiber laser can generate 18-wavelength laser output with signal-to-noise ratio (SNR) 30 dB and wavelength through the wavelength selection by the Lyot-Saganc filter, ranging from 1556 nm to 1577 nm. The grid spacing of the output laser can be selected between ITU grid spacings, 0.4 nm and 0.8 nm, at room temperature by tuning the polarization controller in the Lyot-Saganc ring. This fiber laser has good tunability and stability with a high signal-to-noise ratio.

A novel fiber-type widely tunable continuous-wave Mid-IR laser source was present and demonstrated. The Mid-IR laser system was based on the difference-frequency generation (DFG) and the quasi-phase-matched (QPM) techniques. The nonlinear crystal used is a periodically poled MgO-doped LiNbO3 (PPMgLN) crystal with multiple-periods structure. An ytterbium-doped fiber laser and a tunable laser cascaded with an erbium-doped fiber amplifier (EDFA) were used as the pump and the signal sources for the DFG process, respectively. With such a fiber-type QPM-DFG system, the continuous-wave Mid-IR radiation was obtained. It was found that the FWHM of the phase mismatching due to the temperature was about 4.5 ℃. By suitable choosing the crystal period combined with controlling the temperature and the wavelength of signal, Mid-IR radiation with continuously tuning range between 3.1 to 3.6 μm has been achieved with the system.

The supermode in multicore fiber was analyzed by using coupled-mode theory, and analytical expression for the mode distribution in multicore fiber was derived. The beam quality of the supermode were numerically calculated. Among all the supermodes, only the in-phase mode has preferable far-field intensity distribution, and mode selection scheme using Talbot cavity was proposed and studied numerically on the isometric and ring distribution multicore fiber lasers. The results show that the in-phase mode can be selected effectively in Talbot cavity using appropriate parameters.

The continuum-wave laser operation of a new self-frequency-doubled Yb∶Gd0.2Y0.75(BO3)4 (Yb:GdYAB) crystal under high-power diode-end-pumping was reported. To achieve compact all-solid-state laser's operation, a plane-parallel cavity was employed with two mirrors separated by 1 cm, and obtained the fundamental-wave laser with central wavelength at 1044 nm. The maximal output power of 1.38 W was obtained with an absorbed power of 4.22 W, which corresponded to slope efficiency of 54%. A plano-concave cavity was used to obtain efficient self-frequency-doubled (SFD) generation. Self-frequency-doubled green laser with a center wavelength of 522 nm was also obtained, and the threshold absorbed pump power was only 900 mW. The maximal output power was 144 mW when pumped power was 3.9 W. A diode-to-green optical conversion efficiency of 3.7% was achieved. The results indicate that the Yb∶GdYAB crystal is of great potential in applications of both 1 μm fundamental wave and self-frequency-doubled visible light lasers.

An external-cavity semiconductor laser was built by using a semiconductor laser, collimating cylindrical column lens for fast axis beam and a volume Bragg grating (VBG) as a feedback element to get semiconductor lasers wavelength locked to the Bragg wavelength of the VBG. Its spectral characteristics varied with pump current, heat-sink temperature and different beam collimation optics were measured experimentally. The dependence of the spectral stabilization on gain spectrum of the laser and the parameters of the external cavity were analyzed. The results indicated that good wavelength stabilization could be obtained when a collimating cylindrical lens with diameter of 0.4 mm was used. In the case semiconductor lasers wavelength was measured to be locked at the Bragg wavelength of VBG in the driving current range from 0.5 A to 1.5 A when the heat-sink temperature kept at 30 ℃, and in the temperature range between 20 ℃ and 25 ℃ when the driving current applied at 1.5 A. Compared with spectra of the semiconductor laser at free running, it means that wavelength stabilization can be obtained when difference between the VBG peak and the laser wavelength at free running is smaller than 2.6 nm. The experiment showed also that wavelength stabilization became degraded when the difference increased to larger than 4.8 nm.

Existence of parasitic oscillation makes the amplifier consume lots of inversed population before the arrival of signal pulse, which reduces peak gain and storage efficiency and influence amplification performance greatly, especially for high-power amplifiers. By pumping Nd∶YAG slab with 8 laser diode arrays, parasitic oscillation in high-power amplifier was studied both theoretically and experimentally. The parasitic oscillations in the slab with different surfaces treatment were compared. When the pump energy was 1.28 J and the input pulse energy was 140 mJ, the single-pass amplification of β=2 and the output pulse energy of 278 mJ was obtained.

In this paper, a laser-diode pumped passively Q-switched Nd∶GdVO4 self-Raman laser is studied theoretically and experimently in detail. In the experiment, by using Nd∶GdVO4 as the gain medium and Raman medium simultaneously, using two Cr4+∶YAG crystals with different initial transmissivity as the saturable absorber, respectively, the passively Q-switched operation of the self-Raman Nd∶GdVO4 laser at 1176 nm was investigated and compared. The average power, pulse energy, pulse width and pulse repetition rate of diode pumped passively Q-switched Nd∶GdVO4 self-Raman laser at 1176 nm with respect to the incident pump power were measured. The obtained maximum output average power is 244.6 mW with respect to incident power of 5.7 W and the corresponding conversion efficiency is 4.3% with initial transmissivity of 0.91. In the theoretical part, we used the rate equations to obtain the theoretical results. In the rate equations, the Gaussian distributions of the intracavity photon densities of the fundamental and Raman lasers and the initial population inversion density were taken into account. The obtained theoretical results were in agreement with the experimental results on the whole.

In high-power lasers, nonlinear hot image is likely to damage expensive optical components. The damage risk of hot image to optical components may be reduced by identifying and eliminating the obscurations which induce the most intense hot images. The relationship between intensity of nonlinear hot image and dimensions of obscurations has been investigated theoretically and numerically. According to the theory of propagation of light spectrum and the Bespalov-Talanov theory, an expression for intensity of hot image through thick nonlinear medium is derived; the relationship between intensity of hot images and dimensions of obscurations is investigated and verified by numerical simulation. It is shown that, the bigger the obscuration is, the more intense the hot image is, when obscurations reach a certain size which is approximately determined by the fastest growing spatial frequency of the Bespalov-Talanov theory, the hot image becomes the most intense one, for a bigger obscuration, the intensity of its hot image decreases.

For requriement of plasma diagnostic system in inertial confinement fusion (ICF) drivers, simple lens which can be substituted for logarithmic axicon is designed by nonlinear-phase fitting method. Required sperhical lens parameters are determined by fitting the phase of sperhical lens and logarithmic axicon. A long-focal-depth lens applied for plasma diagnostic system is designed, and the optical performance of lens is analyzed, such as long focal depth, homogeneous axial , transverse intensity distribution and side lobe of focal spot. Numerical results show that long-focal-depth lens has the same phase distribution with logarithmic axicon, its optical performance can satisfy the requirements of plasma diagnostic system, so the nonlinear phase fitting method is valid.

Scattering characteristic of an inhomogeneous cylindrical particle plays an important role in the measurement of parameters of complicated particles. Based on Debye theory, scattering by an infinite multi-layered cylinder in an on-axis Gaussian beam is discussed in detail. Scattering coefficient formulas of Debye series are obtained. With the formulas, distributions of total scattering intensities, Debye component scattering intensities by a homogeneous and a two-layered cylinder are calculated. And the results of total scattering intensities are in line with those of generalized Lorentz Mie theory. It is indicated that the different scattering angle interval of total scattering intensities comes from the contribution of different-order scattering intensities. Presence of two maximums in two order scattering intensities of Debye series is determined by radius and refractive index of a two-layered cylinder. For a two layered cylinder with a thin shell, there are two maximums between 120° and 150°, which is called dual first-order rainbow. Otherwise, when the external layer is thicker than the inner one, there is only one maximum.

Based on the diffraction theory of the monochromatic scalar wave, an optical trap using a red-detuned small-hole diffracted light field is investigated. The intensity distribution of the optical trap and its optical potential and optical dipole force are colculated by aperture diffraction theory, and derive some analytical relations between the characteristic parameters of the optical trap (including geometric parameters, intensity gradients and theirs curvatures) and the parameters of the optical system (including laser wavelength and aperture radius) are derived. The study shows that when P=500 W, λ=1.080 μm and a=20 μm, the optical trapping potential for cold CH4 molecules is about 57.9 μK. So our trap scheme is not only simple and convenient in the manipulation and control of cold molecular (or cold atoms), but also has wide potential applications in the fields of cold molecular physics, atomic optics, molecule optics even quantum optics,and so on.

In an approach to construct coherent states proposed recently, there is the requirement to solve a time-dependent ordinary differential equation (TDODE). Based on the consideration that the equation possesses SU(1,1) dynamical symmetry, we propose a uniform method for solving the TDODE exactly by means of the theory of algebraic dynamics, whatever the time-dependent frequency takes what form as a function of time. Then, after impacting the time-dependent frequency take a specific form, which is a sudden change function, we obtain the exact solution with the method. Next, we construct the corresponding coherent states with the help of this exact solution. Then the evolution of quantum fluctuation (quantum noise) is discussed. According to the property of the curve of the uncertainty of momentum operator, we point out some properties which can be utilized when preparing the squeezed states of this quntum system. At last, the evolution of the uncertainty relation with time is discussed.

As a branch of quantum information technology, ghost imaging comes to front for its unique “ghost” feature, i.e. the image would appear on the optical path that actually never pass the object. For a time, entanglement was thought to be a prerequisite, while we know now that classical thermal light can imitate this kind of imaging and there is no need for entangled beams. Based on the theory of statistical optics, we modeled the dynamic process of thermal variation, the propagation of optical fields and the optical modulation by objects, and then retrieved the Fourier transform patterns of both an amplitude-only object and a pure phase object. The latter experimental results demonstrate the accordance of numerical prediction based on statistical optics.

An instantaneous spectrum detection apparatus, consisting of monochromator, piezoelectric pressure sensor and oscilloscope was applied to study quick reaction and ignition delay time of benzene. On account of the pyrolysis of benzene easily driven under shock compression, a new method was introduced to determine ignition delay time of energetic materials and prevent advance trigger under incident shock wave. Comparison of calculated concentration of major species (C2) by the chemical kinetic program plotted against time with the experimental data recorded by oscilloscope. A fairly good agreement between calculated results and recorded data was obtained. It proved that using this apparatus can study the behavior of instantaneous emission spectrum preferably. Combination of experiment and chemical kinetic analyzed the reaction mechanism of formation of carbon in thermal decomposition process under shock wave.

Residual amplitude modulation (RAM) in electro-optical phase modulators (EOM) results in unequal amplitude of modulation sidebands. Different amplitude attenuation of the first-order sidebands is undergone by means of transmission characteristic of Fabry-Pérot cavity and the Pound-Drever-Hall technique. Thus the amplitude of modulation sidebands is equal and the residual amplitude modulation can be suppressed. The beat signal between carrier and modulation sidebands is calculated theoretically after transmitting the Fabry-Pérot cavity, and the asymmetry of sidebands is reduced by four orders of magnitude once the Fabry-Pérot cavity is locked properly. Finally in experiment, the optical heterodyne spectrum is obtained after the modulated laser beam transmitted the Fabry-Pérot cavity. The result shows that the suppression of the residual amplitude modulation in electro-optical phase modulators is about 45 dB when the Fabry-Pérot cavity is locked to the central zero point of optical heterodyne spectrum.

The infrared spectral and thermal imaging experiments on infrared attenuation factors of foam were carried out. The infrared spectral characteristics of solution determine the absorption peaks, with a stronger absorption for a higher content. The foam structure is an important factor of attenuation, the transmission intensity decreases by the times of transmission through foam interfaces, and the smaller bubble diameter it is, the less dosage is used with the same shield effect. Once the bubble diameter is much larger than radiation wavelength, the transmissivity will depend less on the sizes of beam. Temperature rising can increase the infrared absorption intensity in some extent. The grade of impact factors declines in the sequence of foam structure, spectral characteristics, refractive index of inner gas, bubble diameter, and temperature.

The completely diagonalized Hamiltonian matrixes of 120 orders of 3d3/3d7 ions configuration in the trigonal symmetry were established by irreducible representation method and group theory, taking into account spin-orbit interaction, spin-spin interaction and spin-other-orbit interaction. The ground-state energy levels, the zero-field splitting parameter were calculated with the matrixes. The contributions of spin doublets for the ground-state energy levels were studied. The values of theoretical calculation were consistent with the experimental ones. The results showed that the contributions of doublets could not be neglected. On these bases, the effects of spin-spin interaction and spin-other-orbit interaction on the fine structures of spectra and zero-field splitting parameter of YAG∶Cr3+ crystal were further studied, and we found that the influence of spin-spin interaction and spin-other-orbit interaction on the fine structures of spectra and the zero-field splitting parameter could not be neglected. By comparing the values of theoretical calculation with the experiments, the existence of Jahn-Teller effect in the YAG:Cr3+ crystal spectra was confirmed.

Based on the total-reflection phase transformation theory, the Fresnel rhomb retarder is obtained with a structure angle with which the phase retardation is insensitive to the angle of incidence. According to thin film polarization effect and eigenmatrix, the Fresnel retarder's achromatic width is expanded by evaporating dielectric membrane in two total-reflection surfaces of the rhomb. Using the ML_EB900 film coating machine, the rhomb achromatic phase delay membrane is fabricated with appropriate deposition condition. The experimental result indicated, in 530～700 nm wavelength ranges, 90° phase retardation and maximum deviation within 0.7° were obtained.

The optical response of oxygen-deficient La0.6Ca0.4MnO3-δ (LCMO) thin films was studied using continuous wave and pulsed lasers with wavelength of 532 nm. The influence of oxygen deficiency on the optical response of LCMO thin films in metallic and insulating state has been analyzed. At room temperature, oxygen-deficient LCMO thin films show obvious optical response with photo-conductivity improved by 36.4% and rise time of 30 ns when illuminated by a laser pulse of 7 ns duration at the light power of 750 mW. Since the laser photon energy is larger than the band gap of the thin films, electron-hole pairs are created in the film. For the electrons can be captured by the oxygen vacancy easily, then extra holes carriers are produced, which can induce local insulator-metal phase change and obvious optoelectronic effect. The results show potential application of oxygen-deficient LCMO thin films in optoelectronic devices.

The spectral interference between two white-light continuum beams is adopted to measure the Gouy phase shift of focused femtosecond laser pulses near the lens focus. From the spectral interference signal, the relative phase is extracted by the Fourier transform method. The beam waist of the laser pulses after the focusing lens is measured by imaging method. According to the beam radius, the curves of nonlinear fitting are drawn, and fit the data of experiments very well. The Gouy phase shift at the positions of 1 mm before and after the focal spot is presented.

The phase transformation of rutile TiO2 single crystal irradiated by femtosecond laser pulses was studied by micro-Raman spectroscopy. It is found that when the femtosecond laser average power is 300 mW, with the increase of irradiation time, the intensity of Raman active mode Eg increases while that of A1g decreases, which suggests that the color center is induced. When the irradiation time is about 10 s, the component of anatase emerges and with increase of the irradiation time the intensity of Raman active modes of anatase increases while that of rutile decreases. But if the irradiation time is 1/63 s, with the increase of average power of laser, the intensity of Eg increases and that of A1g decreases apparently within the ablation crater, and no anatase appears.