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Semiclassical theory of speckle correlations

Coherent wave propagation in random media results in a characteristic speckle pattern, with spatial intensity correlations with short-range and long-range behavior. Here, we show how the speckle correlation function can be obtained from a ray picture for two representative geometries: A chaotic cavity and a random waveguide. Our calculation allows us to study the crossover between a "ray limit" and a "wave limit", in which the Ehrenfest time $τ_E$ is larger or smaller than the typical transmission time $τ_D$, respectively. Remarkably, long-range speckle correlations persist in the ray limit $τ_E \gg τ_D$.