Efficient method for lasing eigenvalue problems of periodic structures

In this paper, an accurate and efficient method is presented for analyzing the dynamic response of two-dimensional (2D) periodic structures. The algebraic structure of the corresponding matrix exponential is analyzed and, based on its special structure, an accurate and efficient method for its computation is proposed. Accuracy is maintained using the precise integration method (PIM), and great efficiency is achieved in the computational effort using the periodic properties of the structure and the energy propagation features of the dynamic system. The proposed method is compared with the conventional Newmark and Runge–Kutta (R–K) methods, and it is shown to be accurate, efficient and extremely frugal in its memory requirements.

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Efficient Method for Full-Wave Analysis of Large-Scale Finite-Sized Periodic Structures

Journal of Electromagnetic Waves and Applications ◽

10.1163/156939307783152812 ◽

2007 ◽

Vol 21 (14) ◽

pp. 2157-2168 ◽

Cited By ~ 7

Author(s):

W. B. Lu ◽

T. J. Cui

Keyword(s):

Efficient Method ◽

Large Scale ◽

Periodic Structures ◽

Wave Analysis ◽

Full Wave ◽

Full Wave Analysis

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Efficient Operator Marching Method for Analyzing Crossed Arrays of Cylinders

Communications in Computational Physics ◽

10.4208/cicp.100614.270315a ◽

2015 ◽

Vol 18 (5) ◽

pp. 1461-1481

Author(s):

Yu Mao Wu ◽

Ya Yan Lu

Keyword(s):

Electromagnetic Field ◽

Efficient Method ◽

Periodic Structures ◽

Three Dimensional ◽

Circular Cylinders ◽

Geometric Features ◽

Spatial Direction ◽

Number Of Layers ◽

Crossed Arrays ◽

Marching Method

AbstractPeriodic structures involving crossed arrays of cylinders appear as special three-dimensional photonic crystals and cross-stacked gratings. Such a structure consists of a number of layers where each layer is periodic in one spatial direction and invariant in another direction. They are relatively simple to fabricate and have found valuable applications. For analyzing scattering properties of such structures, general computational electromagnetics methods can certainly be used, but special methods that take advantage of the geometric features are often much more efficient. In this paper, an efficient method based on operators mapping electromagnetic field components between two spatial directions is developed to analyze structures with crossed arrays of circular cylinders. The method is much simpler than an earlier method based on similar ideas, and it does not require evaluating slowly converging lattice sums.

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Higher-order sensitivity analysis of periodic 3-D eigenvalue problems for electromagnetic field calculations

Advances in Radio Science ◽

10.5194/ars-15-215-2017 ◽

2017 ◽

Vol 15 ◽

pp. 215-221 ◽

Cited By ~ 2

Author(s):

Philipp Jorkowski ◽

Rolf Schuhmann

Keyword(s):

Sensitivity Analysis ◽

Discrete Model ◽

Eigenvalue Problems ◽

Periodic Structures ◽

Higher Order ◽

Integration Technique ◽

Periodic Boundaries ◽

Eigenvalue Derivatives ◽

Eigenvector Derivatives ◽

Eigenvalue And Eigenvector

Abstract. An algorithm to perform a higher-order sensitivity analysis for electromagnetic eigenvalue problems is presented. By computing the eigenvalue and eigenvector derivatives, the Brillouin Diagram for periodic structures can be calculated. The discrete model is described using the Finite Integration Technique (FIT) with periodic boundaries, and the sensitivity analysis is performed with respect to the phase shift φ between the periodic boundaries. For validation, a reference solution is calculated by solving multiple eigenvalue problems (EVP). Furthermore, the eigenvalue derivatives are compared to reference values using finite difference (FD) formulas.

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