梯形透过率光栅远场光强分布及光栅方程的解析推导  

Analytical derivation of far-field intensity distribution and grating equation for trapezoidal transmission grating

作　　者：范全平[1] 杨祖华[1] 魏来[1] 彭倩[1] 王心怡[1] 张强强[1] 陈勇[1] 巫殷忠[1] 晏卓阳 钱凤[1] 曹磊峰[1] 

机构地区：[1]中国工程物理研究院激光聚变研究中心,等离子体物理重点实验室,四川绵阳621900

出　　处：《强激光与粒子束》2017年第2期11-17,共7页High Power Laser and Particle Beams

基　　金：国家自然科学基金项目(11375160);国家重大仪器设备开发专项(2012YQ130125)

摘　　要：二值化梯形透过率光栅是一种具有离轴衍射级次的二维光栅,其各衍射点光强信息和位置信息的确定对该新型光栅的实际应用具有重要意义。然而,目前尚无相关解析理论对其进行合理的描述。为了解决上述问题,通过二维傅里叶变换方法获得了该光栅各个衍射级次光强分布的解析表达式,并根据二维光栅的结构特征给出了在透射式和反射式情况下该光栅满足的光栅方程。这为该新型光栅的光线追迹计算打下了理论基础。最后,将解析表达式计算结果与采用X-Lab软件标量衍射模块计算的数值模拟结果进行比较,验证解析理论的正确性。Previously,we proposed a binary trapezoidal transmission grating with the properties of quasi single-order diffraction.Numerical simulations based on the scalar diffraction theory and a visible experiment have been carried out to verify the diffraction properties in far-field.However,this work didn＇t give the analytic expression of the far-field intensity distribution and grating equation of the novel two-dimensional grating.Therefore,it is impossible to estimate the intensity distribution and position on the screen of every diffraction order quickly when the grating is applied to the actual spectral measurement,and at present these could only be obtained by the numerical simulation based on the theory of scalar diffraction slowly.To solve the above problem and use this novel grating in ray-tracing calculations,the analytic theory must be improved to describe the intensity distribution and grating equation of every diffraction order.In this paper,we give the analytical expression of the intensity distribution and the grating equation satisfies both transmission type and reflection type cases by using the method of analytical derivation.Finally,comparisons are made between the results of calculation by our analytical expression and simulation by the scalar diffraction module of the X-Lab to prove the validity of the analytical theory.

关 键 词：梯形透过率光栅 光栅方程 单级衍射 光线追迹 

分 类 号：O436.1[机械工程—光学工程]