Optimizing Finite Structures to Suppress the Photonic Density of States

TL;DR

This paper introduces a topology-optimization framework combining density-based and level-set methods to design finite photonic structures that effectively suppress the photonic density of states, with applications in fiber-optic design.

Contribution

It presents a novel optimization approach for finite structures that identifies optimal geometries, including primitive unit cell symmetries, to minimize the photonic density of states.

Findings

Hexagonal structures best suppress the density of states.

Introducing cavities enhances suppression, especially with hexagonal cavities.

The method discovers symmetry properties of photonic crystals for optimal design.

Abstract

We propose a topology-optimization framework for optimizing finite structures of arbitrary shape by combining density-based methods with level-set approaches. We first optimize regular polygonal structures to suppress the photonic density of states and find that the best performing polygon is consistent with a tiling of space with hexagonal unit cells. We next show that introducing cavities into hexagonal structures further suppresses the photonic density of states, particularly when the cavity is also hexagonal. Such a result would find application in the design of fiber-optic cables. We then describe an approach for optimizing arbitrary x-simple or y-simple designs that can recover finite supercells of a hexagonal unit cell. Our approach can therefore discover the symmetry of photonic-crystal primitive unit cells that significantly suppress the photonic density of states for a given set of material parameters within a single optimization.