Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections

TL;DR

This paper demonstrates that the minimal size of localized modes at the band edge in photonic-crystal waveguides is governed by the effective photon mass rather than the group index, supported by theory, simulations, and experiments.

Contribution

It introduces a new understanding that the effective photon mass determines localized mode size, supported by theoretical, numerical, and experimental evidence.

Findings

Localized modes can be much smaller than in Bragg stacks due to larger effective photon mass.

Numerical simulations confirm the theoretical prediction about mode size.

Experimental measurements observe wavelength-scale localized modes despite minimal imperfections.

Abstract

Light localization due to random imperfections in periodic media is paramount in photonics research. The group index is known to be a key parameter for localization near photonic band edges, since small group velocities reinforce light interaction with imperfections. Here, we show that the size of the smallest localized mode that is formed at the band edge of a one-dimensional periodic medium is driven instead by the effective photon mass, i.e. the flatness of the dispersion curve. Our theoretical prediction is supported by numerical simulations, which reveal that photonic-crystal waveguides can exhibit surprisingly small localized modes, much smaller than those observed in Bragg stacks thanks to their larger effective photon mass. This possibility is demonstrated experimentally with a photonic-crystal waveguide fabricated without any intentional disorder, for which near-field measurements allow us to distinctly observe a wavelength-scale localized mode despite the smallness ($\sim 1/1000$ of a wavelength) of the fabrication imperfections.