Rigorous electromagnetic analysis of volumetrically complex media using the slice absorption method

Abstract

There is tremendous demand for numerical methods to perform rigorous analysis of devices that are both large scale and complex throughout their volume. This can arise when devices must be considered with realistic geometry or when they contain artificial materials such as photonic crystals, left-handed materials, nanoparticles, or other metamaterials. The slice absorption method (SAM) was developed to address this need. The method is fully numerical and able to break large problems down into small pieces, or slices, using matrix division or Gaussian elimination instead of eigensystem computations and scattering matrix manipulations. In these regards, the SAM is an attractive alternative to popular techniques like the finite-difference time domain method, rigorous coupled-wave analysis, and the transfer matrix method. To demonstrate the utility of the SAM and benchmark its accuracy, reflection was simulated for a photonic crystal fabricated in SU-8 by multiphoton direct laser writing. Realistic geometry was incorporated into the model by simulating the microfabrication process, which yielded simulation results that matched experimental measurements remarkably well.

Nonadiabatic switching of a photonic band structure: Ultrastrong light-matter coupling and slow-down of light

“…The dynamics is characterized by an opening of a pronounced anticrossing, a dramatic flattening of the photonic bands, and a 13-fold slow-down of the group velocity. While at late delay times the measured band structure is well reproduced by a finite-difference frequency domain (FDFD) simulation, 22 the system exhibits an intriguing asymmetry of the ultrafast build-up dynamics of the lower and upper polariton branches, suggesting a novel class of nonadiabatic quantum interference. Figure 1(a) illustrates the design of our device.…”

Simple Implementation of Arbitrarily Shaped Total-Field/Scattered-Field Regions in Finite-Difference Frequency-Domain

“…In these cases, iterative algorithms [19,20] or alternate techniques like the slice absorption method [21,22] are recommended.…”

“…It is useful to create a separate function that constructs these matrices because it will make the FDFD code cleaner and the same function can also be used in other numerical methods that use finite-differences like the method of lines [24,25], beam propagation method [26,27], and more [18,21,28]. Given the derivative operators and the diagonal materials matrices, the wave matrix A is calculated using an equation from Table 1. Step 3 -Calculate the source vector b…”

Convergence improvement of the Fourier modal slice absorption method for crossed gratings

“…Fourier modal slice absorption method (FMSAM) [7] is a combination of Rumpf's formulation [8] and the RCWA's formulation. The key point of FMSAM's formulation is to build the Fourier space's difference wave equation sets in the longitudinal direction, and then solve the block tridiagonal systems formed by these wave equation sets by the Gaussian elimination method.…”