Deriving real delay time statistics from the complex delay time statistics in weakly disordered optical media

TL;DR

This paper investigates the statistical relationship between real and complex delay times in weakly disordered optical media, revealing their mirrored statistical forms and the influence of reflection coefficient correlations.

Contribution

It derives the statistical connection between real and complex delay times in weak disorder regimes, highlighting their mirrored distributions and correlation effects.

Findings

Real and complex delay times share the same statistical form.

Delay times exhibit a mirror image with a time shift.

Strong correlation exists between reflection coefficient and phase.

Abstract

Considering the complex reflection amplitude R=|R|exp(i{\theta}) of a light wave, real delay time {\tau}_r (i.e., sojourn or Wigner delay time), which is the energy derivative of the real phase ({\tau}_r =d{\theta}/cdk), and complex delay time {\tau}_i , which is the energy derivative of the reflection coefficient ({\tau}_i=d{\theta}_i/cdk, |R|=r^1/2=exp(-{\theta}_i)), have the same statistical form and a mirror image with a shift in time in weak disorder and short length regime. Real delay time statistics obtained from the reflection coefficient can be attributed to the strong correlation between the reflection coefficient and its phase in this regime.