A Fourier (k-) space design approach for controllable photonic band and localization states in aperiodic lattices

Abstract

In this paper we present a systematic study of photonic bandgap engineering using aperiodic lattices (AL's). Up to now AL's have tended to be defined by specific formulae (e.g. Fibonacci, Cantor), and theories have neglected other useful AL's along with the vast majority of non-useful (random) AL's. Here, we present a practical and efficient Fourier space-based general theory to identify all those AL's having useful band properties, which are characterized by well-defined Fourier (i.e. lattice momentum) components. Direct control of field localization comes via control of the Parseval strength competition between the different Fourier components characterizing a lattice. Real-space optimization of AL's tends to be computationally demanding. However, via our Fourier space-based simulated annealing inverse optimization algorithm, we efficiently tailor the relative strength of the AL Fourier components for precise control of photonic band and localization properties.

Switchable Aperiodic Distributed Feedback Lasers: Time Domain Modelling and Experiment

“…(c) ADFB spectral reflectivity response, calculated using ref. [2]. (d) Illustrative single-pass ADFB phase spectra ψ(k) (red), with two global phase shifts (green, blue); ψ(k) = mπ, m = integer defines the possible laser oscillation frequencies.…”

“…In this paper, we report an aperiodic distributed feedback (ADFB) cavity designed applying an SA algorithm (Fig. 1b) [2]. Unlike single-mode DFB lasers, the ADFB grating does not possess a regular or uniform periodicity in real space; instead it contains a multitude of phase-shifts with precise locations and sizes set in such a way that they operate collectively to provide a well-defined set of spatial frequency components, leading to three Bragg reflection bands centered around a frequency f B (Figs.…”

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

“…The simulated annealing (SA) optimization algorithm is one of the design theories developed based on the FT [7]. Fig.…”

“…The FT algorithm is particularly useful for inversely calculating an aperiodic grating design from a target reflective spectrum. Some algorithms based on the FT algorithm, such as the Fourier (k-) space design approach, have been investigated for this purpose [7]. Unfortunately, the FT formula suffers from inaccuracy as the scattering strength increases due to phase-accumulation error and predicts a narrower photonic bandgap.…”

K-space design of methods for optical and imaging hardware

“…Also, being Fourier-based, it permits the easy incorporation of well-known methods for dealing with limited noisy sampled data [1]. We note that some work related to our approach was recently published by Chakraborty et al [4]. …”