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Semiclassical theory of speckle correlations
Maxim Breitkreiz1, Piet W Brouwer1
1Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 4, 2014
Summary
Speckle patterns in random media exhibit short and long-range correlations. This study shows how ray pictures reveal these correlations, bridging the gap between ray and wave limits for wave propagation.
Area of Science:
- Physics
- Wave Phenomena
- Statistical Optics
Background:
- Coherent wave propagation in random media generates characteristic speckle patterns.
- These patterns display spatial intensity correlations with both short-range and long-range characteristics.
Purpose of the Study:
- To derive the speckle correlation function from a ray picture.
- To investigate the crossover between the ray limit and the wave limit in random media.
- To analyze the behavior of speckle correlations in different geometries like chaotic cavities and random waveguides.
Main Methods:
- Utilizing a ray picture approach to calculate the speckle correlation function.
- Analyzing two representative geometries: a chaotic cavity and a random waveguide.
- Studying the crossover regime defined by the Ehrenfest time (τ(E)) and transmission time (τ(D)).
Main Results:
- Successfully obtained the speckle correlation function using a ray picture.
- Demonstrated the crossover between the ray limit (τ(E) ≫ τ(D)) and the wave limit (τ(E) ≪ τ(D)).
- Observed that long-range speckle correlations persist even in the ray limit.
Conclusions:
- Ray pictures provide a viable method for understanding speckle correlation functions.
- The study elucidates the transition from wave to ray behavior in random media.
- Long-range correlations are a robust feature of speckle patterns, extending into the ray regime.
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