Using Richards-Wolf vectorial diffraction integral, three-dimensional light field complex amplitude function was derived when vectorial polarized Bessel-Gaussian beam passed through a high numerical-aperture system with primary coma aberration. In the case of radially and azimuthally polarized Bessel-Gaussian beam, focused optical field was simulated under different comatic aberration coefficients. The results show that the presence of primary coma produces a positional shift of the high intensity lobes and make the intensity distribution transformed in the high focused optical field, and the intensity distribution on focal plane and light maximum along the optical axis depend on primary coma and polarization. In the case of intensity distribution along the optical axis, polarization and primary coma aberration doesn’t change its symmetry.

Kernel Fisher discriminant analysis (KFDA) method is a more prominent method in pattern recognition to extract non-linear characteristics. Kernel Fisher discriminal analysis was introduced in the palmprint recognition to extract non-linear characteristics. Wavelet transform was used to reduce palmprint image dimension based on retaining the original image information and features. Kernel Fisher discriminant analysis was used to extract features and the null-space KFDA method(ZKFDA) was introduced to solve the problem of small samples. A classifier to palmprint match was used based on minimum distance. Experimental results show that KFDA performs better than two-dimensional FLD(2DFLD) when the principal component numbers are different. ZKFDA performs better than KFDA in the average recognition rate, and computation is significantly decreased. The recognition performance of radial basis function is the best in the selection of kernel functions.

A simple improved direct method is presented to find equivalence transformation for a class of Camassa-Holm equation. Applying this equivalence transformation, the theorem of symmetry group for the Camassa-Holm equation is obtained, which describes the relationship between the new solutions and the old ones. Some new exact and explicit solutions of the Camassa-Holm equation are obtained by the present references.

The rate equations are theoretical tools for research of the transient process of semiconductor lasers. Under the arbitrary intensity modulation, the rate equations were solved by using the small-signal approximation in order to analyze some properties of modulation response. The real and analytic solutions of the rate equations were obtained in these circumstances. And a specific example was given in which the modulation signal is a rectangular pulse current. Some properties of the modulation response were analyzed by the real and analytic solutions. The rigorous conditions of accuracy of the small-signal approximation were obtained. The approximate expressions of these conditions in some circumstances were obtained by the parameters of some semiconductor lasers.

The electron acceleration based on the inverse multi-photon nonlinear Compton scattering in the extra-intense stationary laser field is studied by using an inelastic collision model of electron with a multi-photon group. The results show that the Landau course electron before the inverse multi-photon nonlinear Compton scattering in the extra-intense stationary laser field are not hot electron, but electron in an excited state. When the frequency of the coupling optical field equals the frequency of the electron in an excited state, the inverse multi-photon nonlinear Compton scattering take place and put out the high γ-ray. But, the probability of the high γ-ray is less than that of the low γ-ray. When the electron is captured by the extra-intense stationary laser field, a great acceleration energy can be obtained by the electron.

Classic logic relationship can be represented by logic functions. Quantum logic function can be defined similarly. However, quantum logic gates are unitary transformations, which are reversible. So it can not realize irreversible transformation directly. By introducing auxiliary qubits and adding the output signal of quantum bits, the irreversible logic operations can be achieved. The sample irreversible logic gates of OR, NOR, and NAND were studied. Their corresponding reversible realization was proposed. At the cost of losing part of quantum information, the optimized circuits were finally obtained.

The quantum key generation efficiency and the transmission distances of two kinds of point-to-multi-point quantum key distribution (QKD) system are discussed. How to select the devices’ parameters is considered detailedly when designing a multi-user QKD system. Decoy state techniques can enhance the security of point-to-multi-point QKD systems, for example, the transmission distance is extended two times and the quantum key generation efficiency is improved a factor of ten. Based on point-to-multi-point QKD systems, a protocol which can realize secret key sharing between two arbitrary receivers is proposed.

The concurrence of the two atoms with dipole-dipole interaction in the Tavis-Cummings model in an initial х state is derived. The influence of the dipole-dipole interaction on the entanglement time evolution and the entanglement sudden death (ESD) is analysed. The relation between the concurrence and the atomic interaction energy is investigated. The results show that the dipole-dipole interaction affects the concurrence and ESD remarkably, leads periods and amplitudes of the concurrence oscillation to change and time interval and number of the ESD to decrease. The relation between the concurrence and interaction energy relies on initial states of the atoms.

The time evolution property of the atomic information entropy squeezing in Bose-Einstein condensate atom interacting with the Schrodinger cat-states are studied by means of quantum theory. The results indicate that when phase angle φ is at π/2 between the two coherent states in the Schrodinger cat state, atomic information entropy shows squeezing effects alternately with the variation of the intensity of optical field and coupling coefficients.

The exact solution of time evolution of quantum state in the mesoscopic LC circuit driven by a time dependent source were obtained by applying the Wei-Norman method. The quasi-probability distribution functions of phase space was used to investigate the quantum state of the mesoscopic LC circuit in coherent state. The results show that the function of the system is two dimension motional Gauss wave-packet. The centre charge and flux of the wave-packet vary with cosine and sine wave.

Based on the Mie scattering theory and the low density approximation, Anderson localization of reverse opal photonic crystal constituted by metal oxide are studied. The results show that many area of photonic forbidden bands appear in the crystal while the incidence wavelength is from 14 μm to 18 μm. And the factors which influence the Anderson localization parameter (ηˉ1sca) are analyzed. These results provide theoretical reference to obtain the photonic localization phenomenon of reverse opal photonic crystal in experiment.

The propagation characteristics of one-dimensional photonic crystal with inhomogeneous Kerr medium were studied, and a new algorithm for dealing with nonlinear part of the layer was created. It’s very convenient to simulate the transfer behavior of one-dimensional Kerr medium. Optical bistable switching of 1D photonic crystal with Kerr defect was investigated by this method, and the results were well in line with those of sub-layer recursive reverse transfer matrix method. Moreover, the new method exhibits simple, rapid and easy-to-understand.

The dynamical properties of two-dimensional 3×3 lattice arrays of single-mode Nd:YAG lasers are investigated by numerical simulation. The lasers of the array are locally coupled and interacted through their optical fields and accommodated by setting some certain parameters of lasers. The results show that the intensities between some corresponding lasers can reach the state of chaotic synchronization under the rigor suitable parameters, when the distance between arbitrary two adjacent coupled lasers is in the proper area, and they also have the characteristics of chaotic synchronization between the lasers in the situation of minor diagonal or the parallel diagonal with minor diagonal. Through the computations and the analysis of the power spectra and Lyapunov exponents, it can be convinced that the states of the laser system are chaotic.

A novel approach for generating n×m-scroll chaotic attractors is proposed. The grid multi-scroll chaotic system is constructed by triangular wave series and step function sequence, and the value of the turning point and the balance point in above function are found. Basic dynamic properties of the system are investigated via theoretical analysis and computer simulation. Modularization design of circuit based on field programmable gate array (FPGA) was used to realize the chaotic system, then the relevant experimental results are given. Circuit experiment is identical to computer simulation, so chaotic characteristic is verified.

Steady-state bright (dark) spatial solitons are predicted for biased two-photon photovoltaic photorefractive media, which are due to two-photon photorefractive effect. When the photovoltaic effect is neglectable, these solitons are just like the two-photon screening solitons. If the applied field absent, these solitons degenerate to the two-photon photovoltaic solitons under the close-circuit condition. Screening solitons and photovoltaic solitons theories can be obtained by simplifying this theory under the appropriate conditions.

Using the symmetrical split-step Fourior method, the evolution and linear chirp of the fundemental soliton under different gain parameters are numerically investigated in the erbium-doped fiber amplifier. The results show that when the gain parameter μ》1, the linear chirp can be generated after the fundemental soliton propagates along the fiber amplifier, and it’s found that the chirp characteristics are influenced by the fiber length. Meanwhile the part with linear chirp for the pulse is narrower if the chirp is more obvious. Moreover, further study found that the initial positive chirp parameter and the high soliton orders have an obvious and active effect on the linear chirp, which strengthens the pulse linear chirp. So the linear chirp can be generated by use of the nonlinear effects, when the fundemental soliton propagates along the erbium-doped fiber amplifier, which has an impact on pulse compression.

The launched pulses for dense wavelength-division-multiplexing (DWDM) system with intensity modulated and direct-detection（IM/DD）scheme are assumed to be chirped Gaussian pulses. The pattern and initial phase of bit sequence in each channel are random. A statistical method is used to analyze these random quantities and a semi-analytic calculation model applied to evaluate the variance of degenerate four-wave-mixing (FWM) noise is obtained. The model also accounts for walk-off effect between channels. The results of calculation show that, to the value of deviation of degenerate FWM noise of chirped Gaussian pulse, not only the group velocity and channel separation are important, but also the initial delay of bit sequence of each channel and initial chirp of pulse are important in the case of small values of launched pulse width. It is also shown that, when the width of launched pulse is small, the change of pulse width with distance due to dispersion effect must be considered to avoid relative large error.

The algorithm of one-dimensional address code cross-correlation value was given from the shift of discrepancy of location “1” of arbitrary two codes among codes with occuring of the collision of “1”. By using this method, some of the typical one-dimensional code cross-correlation value distribution was analyzed, the average cross-correlation value formula was given by using the probability analysis method, then on the basis of one-dimensional address code analysis, the algorithm of the symmetric two-dimensional code ф(N×L,w,1) cross-correlation value distribution was given.

An exact formula of reflection coefficient and transmission coefficient suitable for arbitrary inhomogeneous medium waveguide is derived by defining general wave number and using the analytical transfer matrix method which is considered sub-wave phase shift. Results show that the reflection coefficient and transmission coefficient are very simple and clear. And the formula is suitable for not only arbitrary inhomogeneous medium waveguide, but also arbitrary homogeneous medium waveguide in the refractive index. It is expected that this technology has prospects in the thin-film machining processing.