Characterization of the classical domains by Carathèodory volume elements and Eisenman-Kobayashi volume elements

We give a sufficient and necessary condition that a domain is biholomorphic to the classical domain.     

Maximal Classes of Topological Spaces and Domains Determined by Function Spaces

In this paper the question of what classes A of T ₀-spaces should be paired with classes of domains in order that all function spaces [AB] for AA and B are -compact domains is considered. It is shown that core compact spaces are paired with bounded complete domains and a class of topological spaces called RW-spaces (with finitely many components) is paired with the class of -compact pointed L-domains (L-domains).     

Variations of Constrained Domain Functionals Associated with Boundary-Value Problems

We study variational formulas for maximizers for domain functionalsF(x0, u(x0)), x0, and F(x,u(x))dxover all Lipschitz domains satisfying the constraintg(x) dx=1. Here, u is the solution ofa diffusion equation in . Functional variations arecomputed using domain variations which preserve the constraint exactly. Weshow that any maximizer solves a moving boundary problem for the diffusionequation. Further, we show that, for problems with symmetry, the optimaldomains are balls.     

p-Adic Dynamics and Sullivan's No Wandering Domains Theorem

In this paper we study dynamics on the Fatou set of a rational function . Using a notion of components of the Fatou set defined by Benedetto, we state and prove an analogue of Sullivan's No Wandering Domains Theorem for p-adic rational functions which have no wild recurrent Julia critical points.     

Product-trace-rings and a question of G. S. Garfinkel

It is an open question as to whether every left coherent ring satisfying the intersection property for finitely generated left ideals of is a right-product-trace-ring or not. is a right-product-trace-ring iff every product of trace-right--modules (= universally torsionless-right--modules) is a trace-right--module. This question is shown to have a negative answer. Furthermore, looking at all valuation domains, the complete product-trace-rings, the product-trace-rings and the product-content-rings are characterized.

     

Enhancement of the SHG efficiency in a doubly resonant 2D-photonic crystal microcavity

In this paper we discuss the conditions to obtain the enhancement of second harmonic generation in a two-dimensional circular photonic crystal AlGaAs cavity. The photonic crystal circular cavity offers the possibility of having high-Q resonance modes with respect to those obtained with other types of photonic crystal lattices. The crystallographic cut of the AlGaAs provides a strong nonlinear coupling between a transverse-magnetic (TM) polarized resonant mode at the fundamental wavelength and a transverse-electric (TE) polarized resonant mode at second harmonic wavelength. The double resonance condition leads to a strong improvement of the second harmonic generation process. A preliminary linear analysis has been performed by using the finite-difference time-domain method, which includes the dispersive response of the material, modeled using the well-known one-pole pair Lorentzian function.     

Frequency domain optical tomography using a conjugate gradient method without line search

A conjugate gradient method without line search (CGMWLS) is presented. This method is used to retrieve the local maps of absorption and scattering coefficients inside the tissue-like test medium, with the synthetic data. The forward problem is solved with a discrete-ordinates finite-difference method based on the frequency domain formulation of radiative transfer equation. The inversion results demonstrate that the CGMWLS can retrieve simultaneously the spatial distributions of optical properties inside the medium within a reasonable accuracy, by reducing cross-talk between absorption and scattering coefficients.     

Unconditionally Stable Complex Envelope Wave Equation PML Algorithm for Band Limited FDTD Simulations

Unconditionally stable complex envelope (CE) perfectly matched layer (PML) absorbing boundary conditions (ABCs) are presented for truncating the scalar wave-equation finite difference time domain (WE-FDTD) grids. The formulations are based on incorporating the alternating direction implicit (ADI) scheme into the CE FDTD implementations of the scalar wave-equation derived in the PML region at the domain boundaries. Numerical example carried out in two dimensional domain shows that the proposed formulations are more accurate than the classical ADI scalar wave equation PML formulations when it is used for modelling band limited electromagnetic applications.     

波前编码系统成像特性的空间域分析

波前编码技术在大幅度地增加光学系统景深的同时,可以抑制各种离焦类型的像差。目前波前编码系统的成像特性分析大多是基于空间频率域的分析,在应用稳定相法导出三次型相位板波前编码系统的点扩展函数近似解析式的基础之上,描述了点扩展函数的边界、带宽与振荡等特性,分析了波前编码系统对离焦、像散、彗差等常见像差的敏感性,从空间域进一步分析了波前编码系统的成像特性。     

基于表面等等离波子的新型Y分支波导

新型高效的纳米光波导器件的研制纳米集成光学的核心技术之一。Y分支波导作为最基本的分光和光路连接元件是纳米光学器件设计与制备的基础。运用时域有限差分(FDTD)法,模拟计算了基于表面等等离波子(SPP)的纳米Y分支波导的传输特性。结果表明,该新型Y分支波导在光通信波段可以实现大角度的分光功能,且在180°分支情况下,传输效率仍高达92.8%以上。另外,该波导还具有导波性能良好、对分叉处间隙缺陷大小不敏感及制作容差较大和器件尺寸在纳米量级等特点。对该新型光波导器件的研究为未来纳米集成光学器件的研制和应用有一定的指导意义。