Modeling and optimization of photonic crystal devices based on transformation optics method

Abstract

In this paper, we propose a method for designing Photonic Crystal (PhC) devices that consist of dielectric rods with varying size. In the proposed design method, PhC devices are modeled with the Transformation Optics (TO) approach, and then they are optimized using the gradient method. By applying the TO technique, the original device model is transformed into an equivalent model that consists of uniform and fixed-sized rods, with parameterized permittivity and permeability distributions. Therefore, mesh refinement around small rods can be avoided, and PhC devices can be simulated more efficiently. In addition, gradient of the optimization object function is calculated with the Adjoint-Variable Method (AVM), which is very efficient for optimizing devices subject to multiple design variables. The proposed method opens up a new avenue to design and optimize a variety of photonic devices for optical computing and information processing.

Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale

“…The earliest application of computational methods in nanophotonic inverse design dates back to the late 1990s, with the attempts to optimize the performance of dielectric waveguides [40] and to engineer the bandgaps of PhCs [41]. Since then, continuous progress has been made along these lines [42][43][44][45][46][47][48][49][50][51][52][53], and some previously unattainable functionalities have been made possible by using advanced algorithms and hardware [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]. Among the pioneers who introduced various computational techniques into nanophotonic inverse design, Sigmund and coworkers conducted a systematic study using the tool of topology optimization, which was originally developed for structural design [36,37] but has been applied to many other applications [25].…”

Transformation Optics: From Classic Theory and Applications to its New Branches

“…In addition to the above aspects, TO has many other applications, such as calculating the optical force, designing gratings, designing spontaneous emissions, reverse ray tracings, designing perfect matched layers in numerical simulations, etc. In recent years, more and more new branches are emerging from TO, such as TO with graphene, TO with photonic crystals, TO with meta‐surfaces, TO with Fourier optics, TO for lossy media by complex coordinate transformations, etc. Such a coordinate transformation method that can link physical quantities in two spaces will lead the trends in future optical design and multiphysical fields design …”

“…branches are emerging from TO, such as TO with graphene, [238] TO with photonic crystals, [239] TO with meta-surfaces, [240] TO with Fourier optics, [241,242] TO for lossy media by complex coordinate transformations, [243][244][245] etc. Such a coordinate transformation method that can link physical quantities in two spaces will lead the trends in future optical design and multiphysical fields design.…”

Efficient Computational Design and Optimization of Dielectric Metamaterial Structures

“…Optimization of photonic crystal devices with circular inclusions was performed in [20] by means of transformation optics. Spatial optimization of circular dielectric rods in the radio-frequency regime was performed in [21,22] using a finite differences discretization and both gradient-based and gradient-free algorithms.…”