Fundamental Limit to Linear One-Dimensional Slow Light Structures

TL;DR

This paper establishes a fundamental upper limit on the delay achievable in one-dimensional linear slow light structures, based on a new approach that considers orthogonal waves generated by scattering, independent of design specifics.

Contribution

The authors introduce a general method to determine limits in optical structures, deriving a universal bound on delay that depends only on structure length and dielectric variation, not on design details.

Findings

Delay limit proportional to structure length and dielectric change

Applicable to index, absorption, or gain variations

Independent of structure design or group velocity concepts

Abstract

Using a new general approach to limits in optical structures that counts orthogonal waves generated by scattering, we derive an upper limit to the number of bits of delay possible in one-dimensional slow light structures that are based on linear optical response to the signal field. The limit is essentially the product of the length of the structure in wavelengths and the largest relative change in dielectric constant anywhere in the structure at any frequency of interest. It holds for refractive index, absorption or gain variations with arbitrary spectral or spatial form. It is otherwise completely independent of the details of the structure's design, and does not rely on concepts of group velocity or group delay.