Implementing structural slow light on short length scales: the photonic speed-bump

TL;DR

This paper demonstrates that significant slow-light effects and density of states enhancements in finite 1D photonic systems can be achieved with very short structures, leading to a novel 'photonic speed bump' that abruptly changes light speed without reflection.

Contribution

It introduces a new concept of a photonic speed bump that creates large DOS enhancements in short structures, differing from traditional defect-mode cavities.

Findings

Large DOS enhancement achievable with short structures scaling logarithmically with inverse group velocity.

Photonic speed bump causes abrupt light speed change without reflection.

Resonance mode differs from classical defect modes in photonic crystals.

Abstract

One-dimensional (1D) infinite periodic systems exhibit vanishing group velocity and diverging density of states (DOS) near band edges. However, in practice, systems have finite sizes and inevitably this prompts the question of whether helpful physical quantities related to infinite systems, such as the group velocity that is deduced from the band structure, remain relevant in finite systems. For instance, one may wonder how the DOS divergence can be approached with finite systems. Intuitively, one may expect that the implementation of larger and larger DOS, or equivalently smaller and smaller group velocities, would critically increase the system length. Based on general 1D-wave-physics arguments, we demonstrate that the large slow-light DOS enhancement of periodic systems can be observed with very short systems, whose lengths scale with the logarithm of the inverse of the group velocities. The understanding obtained for 1D systems leads us to propose a novel sort of microstructure to enhance light-matter interaction, a sort of photonic speed bump that abruptly changes the speed of light by a few orders of magnitude without any reflection. We show that the DOS enhancements of speed bumps result from a classical electromagnetic resonance characterized by a single resonance mode and also that the nature and the properties of the resonance are markedly different from those of classical defect-mode photonic-crystal cavities.