On the attenuation coefficient of monomode periodic waveguides

TL;DR

This paper challenges the common assumption that guided mode transmission in monomode periodic waveguides always decays exponentially with length, especially at low group velocities, based on theoretical and numerical analysis.

Contribution

It demonstrates that the exponential damping law does not hold universally for periodic monomode waveguides, particularly as group velocity decreases.

Findings

Exponential decay law is invalid at low group velocities.

Numerical results show contrasting damping behaviors in different waveguide geometries.

Theoretical analysis supports the deviation from exponential damping.

Abstract

It is widely accepted that, on ensemble average, the transmission T of guided modes decays exponentially with the waveguide length L due to small imperfections, leading to the important figure of merit defined as the attenuation-rate coefficient alpha = -<ln(T)>/L. In this letter, we evidence that the exponential-damping law is not valid in general for periodic monomode waveguides, especially as the group velocity decreases. This result that contradicts common beliefs and experimental practices aiming at measuring alpha is supported by a theoretical study of light transport in the limit of very small imperfections, and by numerical results obtained for two waveguide geometries that offer contrasted damping behaviours.