Transfer-matrix approach for finite-difference time-domain simulation of periodic structures

Abstract

Optical properties of periodic structures can be calculated using the transfer-matrix approach, which establishes a relation between amplitudes of the wave incident on a structure with transmitted or reflected waves. The transfer matrix can be used to obtain transmittance and reflectance spectra of finite periodic structures as well as eigenmodes of infinite structures. Traditionally, calculation of the transfer matrix is performed in the frequency domain and involves linear algebra. In this work, we present a technique for calculation of the transfer matrix using the finite-difference time-domain (FDTD) method and show the way of its implementation in FDTD code. To illustrate the performance of our technique we calculate the transmittance spectra for opal photonic crystal slabs consisting of multiple layers of spherical scatterers. Our technique can be used for photonic band structure calculations. It can also be combined with existing FDTD methods for the analysis of periodic structures at an oblique incidence, as well as for modeling point sources in a periodic environment.

Self-interaction-free approaches for self-consistent solution of the Maxwell-Liouville equations

“…In this case, the incident field can be written as the signal evolution recorded during a preliminary FDTD simulation [42,43] or a packet of plane waves with fixed in-plane wave vector [44,45]. The last modification is used within the hybrid FDTD transfer matrix method as well [46]. The TF-SF concept can be also applied in a multigrid FDTD approach, to transfer fields between inserted (intersected) grids [47][48][49].…”

“…Note that the radiation produced by the point source is significantly distorted by the FDTD rectangular mesh in the close proximity to the source. In other words, the analytical expression for the dipole radiation (8), (9) differs from its numerical analog at the grid points close to the source (this is common problem of simulations of evanescent fields in FDTD [46]). Therefore the size of the SF region should not be too small; otherwise use of the analytical expressions (8), (9) for the incident field will result in spurious numerical signal propagating in the SF region.…”

Finite Difference Scheme for Nonlinear Finite Grating without and with Defect

“…Many researches has developed techniques (analytically or numerically) to study the propagation of light in linear periodic medium with and without defect, such as transfer matrix method [9,10], coupled mode equation [11,12], etc. These techniques are based on the assumption that the medium can be divided into a number of homogeneous layers.…”