Frozen mode in an asymmetric serpentine optical waveguide

TL;DR

This paper demonstrates the existence of a frozen mode in an asymmetric serpentine optical waveguide, characterized by zero group velocity and enhanced field amplitude, with practical design equations and analysis of symmetry conditions.

Contribution

It introduces a numerical demonstration of the frozen mode in asymmetric waveguides and derives simple design equations for its realization.

Findings

Frozen mode associated with stationary inflection point (SIP) of dispersion.

Enhanced field amplitude and zero group velocity in the frozen mode.

Analysis of symmetry conditions for exceptional points of degeneracy.

Abstract

The existence of a frozen mode in a periodic serpentine waveguide with broken longitudinal symmetry is demonstrated numerically. The frozen mode is associated with a stationary inflection point (SIP) of the Bloch dispersion relation, where three Bloch eigenmodes collapse on each other, as it is an exceptional point of order three. The frozen mode regime is characterized by vanishing group velocity and enhanced field amplitude, which can be very attractive in various applications including dispersion engineering, lasers, and delay lines. Useful and simple design equations that lead to realization of the frozen mode by adjusting a few parameters are derived. The trend in group delay and quality factor with waveguide length that is peculiar of the frozen mode is shown. The symmetry conditions for the existence of exceptional points of degeneracy associated with the frozen mode are also discussed.