GRIN光学中光线追迹的一种新方法

由哈密顿光学中的拉格朗日方程推出光线方程，用Runge—Kutta方法求解光线方程，给出光线追迹的新方法。     

Ray aberrations of two-dimensional oblique lattices on the self-image plane

We extend the geometrical theory of aberration for a self-imaging system to the case of two-dimensional oblique lattices. In our approach, the fundamental translation vectors of the lattice are not restricted in both length and orientation. Evaluating the disturbance of light through the oblique lattice under coherent illumination, we find the conditions of constraint which limit the self-imaging of the oblique lattice. Various types of oblique lattices are shown to obey the self-imaging conditions. We derive the equations to trace the optical paths of self-imaging rays and then analyze the ray aberrations which arise from the difference between the optical paths of a self-imaging ray and of the corresponding actual ray. The ray aberrations are shown to disappear when the periods of the lattice are large compared with the wavelength of light. We find that the ray aberrations carried by self-imaged oblique lattices are totally undercorrected and the aberrated image patches are displaced along the direction tangent vector of a chief ray.     

D形截面环流器中的磁面及LHCD的研究

本文利用环形系统的Ｇｒａｄ－Ｓｈａｆｒａｎｏｖ方程得到了Ｄ形截面的托卡马克磁面位形，并利用射线追踪技术研究了Ｄ形磁面位形下低杂波的运动形态。定性地研究了Ｄ形磁面位形下利用低杂波驱动电流的可行性，优化地给出了驱动电流的最佳方式。     

A Public-Key Traitor Tracing Scheme with Revocation Using Dynamic Shares

We proposed a new public-key traitor tracing scheme with revocation capability using dynamic shares and entity revocation techniques. Our schemes traitor tracing and revocation programs cohere tightly. The size of the enabling block of our scheme is independent of the number of receivers. Each receiver holds one decryption key only. The distinct feature of our scheme is that when traitors are found, we can revoke their private keys (up to some threshold z) without updating the private keys of other receivers. In particular, no revocation messages are broadcast and all receivers do nothing. Previously proposed revocation schemes need update existing keys and entail large amount of broadcast messages. Our traitor tracing algorithm works in a black-box way. It is conceptually simple and fully k-resilient, that is, it can find all traitors if the number of them is k or less. The encryption algorithm of our scheme is semantically secure assuming that the decisional Diffie-Hellman problem is hard.AMS Classification: 11T71, 68P30     

一种基于Zernike多项式的波前探测和重构方法

运用Ｎｏｌｌ建议的Ｚｅｒｎｉｋｅ多项式形式表征大气扰动的波面，求出由两个离焦面上的光强分决定的Ｚｅｒｎｉｋｅ多项式的前ｎ项在特定的探测器上的响应矩阵Ｒ。由Ｒ和输入的随机波面在两个离焦面上的光强分布，可方便地求出其Ｚｅｒｎｉｋｅ多项式的系数，从而实现了波前的探测和重构。采用光线追迹的变方法，用计算机模拟验证了这种方法的原理和可行性。     

机械刻划光栅的光线追迹方法

为了评价光栅的光谱质量,完成所设计光栅的光线追迹,针对机械刻划光栅的光线追迹提出了一种改进方法.在费马原理的基础上利用光程函数法得到入射光通过光栅后的光谱分布情况,再使用传输矩阵的计算方法构造出光谱的点列图.该方法适用于刻划在平面、球面和非球面基坯上的等间距和变间距光栅,光栅的光谱面可以为平面或者二次曲面. 通过刻划在非球面基坯上的凹面光栅验证了光线追迹方法的可靠性.     

Analytical derivation of a formula for the reduction of computation time by the voxel crossing technique used in room acoustical simulation

Computation times of room acoustical simulation algorithms still suffer from the time consuming search for ray-wall-intersections. Spatial subdivision may speed up ray tracing considerably. For room acoustics, where the number of surface polygons (walls) is not so high, the voxel technique appears suitable. The voxel crossing algorithm is very fast. However, its performance was not yet investigated up to now. Voxels are small cubes by which the space is subdivided periodically. The advantage: Only in the rare case a voxel intersects a wall the intersection point needs to be computed. In this paper, by estimating the probabilities of such intersections, an analytical formula is derived, by which the optimum degree of spatial subdivision and the factor of acceleration of the algorithm can be forecasted. It turns out that the computation time increases only with instead of with K₀ (the number of polygons of the room). Thus, on a modern PC, computation time for a full room acoustical simulation even for highly complicated rooms may be reduced by a factor in the order of 100, i.e. to a few seconds.     

Analysis of ray tube area in geometrical shock dynamics

We provide a rigorous analysis of structure of a ray tube in geometrical shock dynamics. Our aim is to shed more lights on the cross-sectional area function of a ray tube. We have shown that for a given ray tube and a given initial value of cross-sectional area, then its cross-sectional area can be determined uniquely everywhere. We give a definition of cross-sectional area of a ray tube in precise mathematical terms and from that we derive a set of relations, each describing the cross-sectional area for an arbitrary ray tube in geometrical shock dynamics. We have shown that from our results one can deduce Whitham’s area function relation as a partial differential equation from our general formulations. Some applications are discussed.     

Asymptotic analysis of the Hermite polynomials from their differential–difference equation

We analyze the Hermite polynomials H _n (x) and their zeros asymptotically, as n → ∞ We obtain asymptotic approximations from the differential–difference equation which they satisfy, using the ray method. We give numerical examples showing the accuracy of our formulas.     

An electromagnetic parameters extraction method for metamaterials based on phase unwrapping technique

Abstract

A new method of extracting effective permittivity and permeability of metamaterials has been developed in this paper. Scattering parameters are used to represent effective wave impedance and refractive index of the metamaterials. Considering analytical continuation of effective refractive index of the metamaterials in the upper half of a complex angular frequency plane, a phase unwrapping technique has been implemented to solve branch ambiguity of the refractive index caused by complex inverse cosine function. An empirical formula to estimate the starting frequency in the phase unwrapping technique has been developed to improve the efficiency of the parameter retrieval procedure. Numerical results including five slabs of rods and split-ring resonators (SRRs) and a structure composed of two SRRs and four capacitively loaded strips are given to demonstrate good accuracy, high efficiency, and noise insensitivity of the proposed retrieval method.