Effects of orientational and positional randomness of particles on photonic band gap

TL;DR

This study investigates how positional and orientational randomness in self-assembled 2D photonic crystals affect photonic band gaps, revealing that each type of randomness influences TE and TM gaps differently, aiding PBG engineering.

Contribution

It provides a detailed analysis of the separate effects of positional and orientational randomness on photonic band gaps in self-assembled systems.

Findings

Orientational randomness reduces TE band gap, no effect on TM gap.

Positional randomness significantly decreases TE gap and variably affects TM gap.

Understanding randomness effects aids in photonic crystal PBG engineering.

Abstract

A recent work [PRL, 126, 208002 (2021)] has explored how thermal noise-induced randomness in a self-assembled photonic crystal affects photonic band gaps (PBGs). For the system of a two-dimensional photonic crystal composed of a self-assembled array of rods with square cross sections, it was found that its PBGs can exist over an extensive range of packing densities. Counterintuitively, at intermediate packing densities, the transverse magnetic (TM) band gap of the self-assembled system can be larger than that of its corresponding perfect system (rods arranged in a perfect square lattice and having identical orientations). Due to shape anisotropicity, the randomness in the self-assembled system contains two kinds of randomness, i.e., positional and orientational randomness of the particles. In this work, we further investigate how PBGs are influenced solely by positional or orientational randomness. We find that compared to the perfect situation, the introduction of only orientational randomness decreases the transverse electric (TE) band gap while having no obvious effects on the transverse magnetic (TM) band gap. In contrast, the introduction of only positional randomness decreases the TE band gap significantly, while it can widen or narrow the TM band gap, depending on the parameter range. We also discuss the thermal (i.e., self-assembled) system where two kinds of randomness are present. Our study contributes to a better understanding of the role orientational randomness and positional randomness play on PBGs, and may benefit the PBG engineering of photonic crystals through self-assembly approaches.