We theoretically study the optimum design of anisotropic acousto-optic modulator (AOM) based on lithium niobate crystal. Four different kinds of operating modes in the XOZ and YOZ acousto-optic (AO) planes are systematically analyzed by the tangent condition theory and the optimized operating mode is determined. Furthermore, the dependence of the AO merit on the operating frequency and the off-axis angle of the AOM are also obtained by numerical simulations.

We present theoretical studies on the wideband design of bulk lithium niobate (LN) acousto-optic deflector (AOD) through the walk-off design of the ultrasonic vector, which satisfies the momentum match condition. The ultrasonic properties of LN crystal are studied by solving the Christopher equation and the reciprocal velocity curves in the operating planes XOZ and YOZ are systematically obtained. The calculation results show that the bandwidth of the AOD is highly dependent on the incident angle of light beam and the velocity of the ultrasonic waves, which show strict linear properties in the operating bandwidth. Furthermore, the dependence of the central frequency of the AOD on the angle of incident light and the ultrasonic velocity are also analyzed.

利用缓变包络近似，给出了一组傍轴波动方程的解析解,该解可以表示一组新型超短脉冲光束，即超短双曲余弦高斯脉冲光束。对超短双曲余弦高斯脉冲光束在自由空间的传输性质进行了详细的研究，给出了传输时的轴向光强、横向光强分布、极性反转、脉冲时间延迟、功率谱等。结果表明，超短双曲余弦高斯脉冲光束的轴上光强随着传输距离的增加而平滑地减小。双曲余弦函数的参数对脉冲光束的空间强度分布及脉冲宽度都有影响。给出了超短双曲余弦高斯脉冲光束功率谱的解析表达式，研究表明随着双曲余弦函数参数的变大，功率谱会分裂成几个峰，远离光束中心的边缘会出现红移现象。

从描述强非局域介质中光束传输的非线性薛定谔方程出发，研究了(2+1)维双曲余弦高斯光束在强非局域介质中的传输性质及其相互作用，给出了双曲余弦高斯光束在强非局域非线性介质中传输的解析表达式和二阶矩束宽的解析表达式，同时对两束双曲余弦高斯光束之间的相互作用进行了解析和数值分析。结果表明单光束入射强非局域介质时，存在一个临界功率，当入射功率等于临界功率时，光束在传输过程中的二阶矩束宽可以保持不变；当入射功率不等于临界功率时，光束的二阶矩束宽呈周期性变化。两束双曲余弦高斯光束共同传输时会相互吸引，并且横向强度分布变的较为复杂，给出了两束光传输时相互作用后的强度分布和轴上光强演化等结果。

The carrier-envelope phase of the ultrashort pulsed Laguerre-Gaussian beam is studied. The order of Laguerre function affects seriously the variations of the carrier-envelope phase with the propagation distance increasing. The beam waist also affects the carrier-envelope phase in a few Rayleigh distances. The variation of the carrier-envelope phase is larger on the axis than on the beam periphery in propagation.

以Gauss、Hyperbolic Secant、Lorentz三种脉冲为例，利用理论推导和数值模拟的方法研究了载波相位对超短脉冲时间重心的影响，并给出了三种脉冲的时间重心与载波相位的解析表达式和数值模拟的图形．研究结果表明：当脉冲包络的宽度短于一个光学振荡周期时，载波相位对超短脉冲的时间重心开始有较显著的影响．

研究了超短脉冲贝塞尔光束在色散介质中的传输特性，指出空间诱导色散效应可以用来补偿介质色散作用，从而可以在色散介质中实现无衍射无色散的类时空孤子波的传输。用理论推导和数值模拟的方法得到的具有反常色散性质的空间诱导色散可以有效地补偿介质色散。数值模拟的结果表明，由于超短脉冲贝塞尔光束的无衍射无色散传输距离受到高阶色散效应和贝塞尔光束空间受限两方面的限制，无衍射无色散传输只能在有限距离内近似实现。通过增加脉冲长度可以减小高阶色散效应的影响。在传输距离小于衍射距离时，空间诱导色散效应可以很好地描述脉冲演化和色散补偿过程。

The nonparaxial property of the chirped pulsed beam is analyzed both quantitatively and qualitatively. Through the qualitative investigation of the paraxial approximation condition, we show there are chirpinduced changes in the nonparaxial propagation of the chirped pulsed beam. A quantitative nonparaxial correction was developed by use of the perturbational technic and the Fourier transform for a few-cycle chirped pulsed beam with relative small chirp parameter. It was shown that the nonparaxial corrections were enhanced near the leading or trailing edge of pulse depending on weather the chirp parameter is positive or negative. An example for pulsed Gaussian beam driven by a chirped Gaussian pulse is shown in the numerical result to confirm our analysis.