Inverse correction of fourier transforms for one-dimensional strongly scattering aperiodic lattices

Abstract

The accuracy of the Fourier transform (FT), advantageous for the aperiodic lattice (AL) design, is significantly improved for strongly scattering periodic lattices (PLs) and ALs. The approach is to inversely obtain corrected parameters from an accurate transfer matrix method for the FT. We establish a corrected FT in order to improve the spectral inaccuracy of strongly scattering PLs by redefining wave numbers and reflective intensity. We further correct the FT for strongly scattering ALs by implementing improvements applied to strongly scattering PLs and then making detailed wave number adjustments in the main band spectral region. Silicon lattice simulations are presented.

Keywords: Fourier transform algorithm; aperiodic lattice; strong scattering; Bragg resonant behavior; transfer matrix method; Riccati differential equation