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Updated: Jun 8, 2026

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
Published on: November 30, 2012
Number of propagating modes of a diffusive periodic waveguide in the semiclassical limit
Felipe Barra1, Agnes Maurel, Vincent Pagneux
1Departamento de Física y CIMAT, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile.
Abstract:
We study the number of propagating Bloch modes N(B) of an infinite periodic billiard chain. The asymptotic semiclassical behavior of this quantity depends on the phase-space dynamics of the unit cell, growing linearly with the wave number k in systems with a non-null measure of ballistic trajectories and going like ∼square root of k in diffusive systems. We have calculated numerically N(B) for a waveguide with cosine-shaped walls exhibiting strongly diffusive dynamics. The semiclassical prediction for diffusive systems is verified to good accuracy and a connection between this result and the universality of the parametric variation of energy levels is presented.
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