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

Considering the complex reflection amplitude R=|R|exp(iθ) of a light wave, real delay time τ_r (i.e., sojourn or Wigner delay time), which is the energy derivative of the real phase (τ_r =dθ/cdk), and complex delay time τ_i , which is the energy derivative of the reflection coefficient (τ_i=dθ_i/cdk, |R|=r^1/2=exp(-θ_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.

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