Eigenmode expansion

Introduction

Published in Kim Hwi, Park Junghyun, Lee Byoungho, Fourier Modal Method and Its Applications in Computational Nanophotonics, 2017

Kim Hwi, Park Junghyun, Lee Byoungho

On the other hand, in the spatial frequency domain methods, Maxwell’s equations are transformed into the algebraic Maxwell eigenvalue equations in the spatial frequency domain and the electromagnetic field distributions are represented by a Bloch eigenmode expansion. In FMM, the Bloch eigenmode is represented by a pseudo-Fourier series. The relation between a spatial domain field function and a spatial frequency domain field representation is similar to the relation between a time domain function and its temporal Fourier transform. An important feature of FMM is that, by solving the algebraic Maxwell eigenvalue equation in the spatial frequency domain, it is possible to mathematically construct a complete set of eigenmodes for an optical structure spanning all possible optical fields within the finite dimensional numerical framework.

Waves guided by metasurfaces with non-local impedance boundary conditions

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Journal Information

Published in Waves in Random and Complex Media, 2022

Sergey Bankov, Kirill Klionovski

The eigenmode expansion method uses the field representation as a set of eigenmodes. The final expression of the z-component of the magnetic field obtained using the eigenmode expansion method is as follows: Here, S is the cross-section of the waveguide and V is the volume occupied by the magnetic current. The fields E±yn, H±zn are determined through expressions (29). Waves propagating along the x-axis have a positive subscript. A negative subscript corresponds to waves propagating in the backward direction. We use the following property of the fields:

Eigenmode expansion

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Introduction

Waves guided by metasurfaces with non-local impedance boundary conditions