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Resonant-state Expansion for Periodic Open Optical Systems

周期性开放光学系统的谐振态展开

基本信息

批准号：
1796606
负责人：
金额：
--
依托单位：
CARDIFF UNIVERSITY
依托单位国家：
英国
项目类别：
Studentship
财政年份：
2016
资助国家：
英国
起止时间：
2016 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=studentship-1796606
关键词：
Resonant state Expansion Periodic Open

项目摘要

The resonant state expansion (RSE) is a rigorous perturbative method recently invented in Cardiff School of Physics and Astronomy. The RSE has been developed and used for relativistic wave equations describing such open systems as planar, cylindrical and spherical optical resonators with various perturbations. The method was demonstrated to be particularly suitable for calculating high-quality modes in such open system and efficient and accurate in calculating their perturbations. It has been shown that the RSE is a few orders of magnitude quicker computational tool as compared to existing commercial software packages like ComSol or Lumerical.One of the main aims of the project is to apply the RSE to non-relativistic wave equations and develop a theory of resonant states in quantum-mechanical systems. In particular, the RSE will be applied to Schrödinger's wave equation describing an electron/exciton in various nanostructures with effectively one-, two- and/or three-dimensional potentials and various perturbations. The efficiency and the quality of the new method will be investigated and tested against the existing finite difference methods and ab initio calculations. The concept of resonant states will also be used to investigate the short and long-time behaviour of quantum states and to calculate a non-quadratic (non-exponential) decay of the survival probability of quantum states at short (long) times.The project will also consider some further applications of the RSE in relativistic problems. This may include calculation of eigenstates in optical planar waveguides and photonic crystal fibres where everlasting waveguide modes contribute to expansions of the Green's function. Finally, there will be made attempts towards generalisation of the RSE for relativistic Dirac wave equation with a potential application of the method to narrow-band semiconductor nanostructures.

共振态展开（RSE）是英国卡迪夫物理与天文学院最近发明的一种严格摄动方法。RSE已经发展并用于描述具有各种微扰的平面、圆柱和球形光学谐振器等开放系统的相对论波动方程。结果表明，该方法特别适用于此类开放系统中高质量模态的计算，并能有效准确地计算出它们的摄动。事实证明，与ComSol或Lumerical等现有商业软件包相比，RSE是一个速度快几个数量级的计算工具。该项目的主要目标之一是将RSE应用于非相对论性波动方程，并发展量子力学系统中共振态的理论。特别是，RSE将应用于Schrödinger的波动方程，该方程描述了各种纳米结构中具有有效的一维，二维和/或三维电位和各种扰动的电子/激子。新方法的效率和质量将与现有的有限差分方法和从头计算进行研究和测试。共振态的概念也将用于研究量子态的短期和长期行为，并计算量子态在短（长）时间内生存概率的非二次（非指数）衰减。该项目还将考虑RSE在相对论问题中的进一步应用。这可能包括计算光学平面波导和光子晶体光纤中的本征态，其中永久波导模式有助于扩展格林函数。最后，将尝试推广相对论狄拉克波动方程的RSE，并将该方法应用于窄带半导体纳米结构。