Linear algebraic theory of partial coherence: continuous fields and measures of partial coherence

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.

Coherence and speckle contrast at the output of a stationary multimode optical fiber

We relate classic coherence properties of light at the output of a multimode optical fiber excited by a spatially coherent broadband source to speckle contrast measured by two different methods. Speckle contrast measured with an external diffuser is related to the effective number of modes, while that measured over the ensemble of random bends and twists of the fiber is related to the residual coherence defined as a spatial average of the modulus of the classic complex degree of coherence between pairs of widely separated points at the fiber output.

Partially coherent diffraction-free vortex beams with a Bessel-mode structure

A new family of partially coherent beams carrying optical vortices is introduced. Any member of this family represents an incoherent superposition of fully coherent orthogonal Bessel modes with the same helical wavefront and is notable for its diffraction-free propagation. It is shown analytically and experimentally that such beams can be approximately generated in the Fourier-transforming optical system with a computer-controlled liquid-crystal spatial light modulator.