Different measures of speckle and coherence at the output of a multimode optical fiber

Excitation of a multimode fiber with a focused spatially coherent light of finite bandwidth results in a partially coherent light at the output of the fiber. Here we study the properties of speckle and classical coherence of such light with analytical theory, numerical modeling, and experimentally. Of particular interest is the relationship between measures of coherence and speckle and their dependence on input source bandwidth and fiber length. Speckle contrast is easy to measure experimentally and there exist at least two different methods to generate ensembles of random speckles. We show that speckle contrast evaluated over the ensemble of external diffusers is related to the number of effective modes—one of the characteristics of beam global coherence. The other speckle contrast measure evaluated over the ensemble of random bends and twists of the fiber is related to residual coherence, which is the pedestal on the average modulus of the complex degree of the coherence function on the output endface of the fiber.