Effective degree of coherence: a second look

Effects of residual coherence on the scintillation of a partially coherent beam

Recent results show that partially coherent beams (PCB) can be conveniently generated in a multimode fiber and modulated with data at gigabit per second rates, which makes them attractive for free-space optical communication through turbulent atmosphere. An important feature of these realistic beams in contrast to model ones is the presence of residual coherence between pairs of points spatially separated by more than a few coherence radii on the beam aperture. In the present work we experimentally study the influence of this residual coherence on the scintillation of a partially coherent beam in a laboratory turbulence. It is shown that the total scintillation can be considered as a combination of scintillations of the coherent and incoherent parts of the full beam. When residual coherence is large the scintillation is mostly due to speckle motion on the detector. In the opposite case, the scintillation index settles at a low value pertaining to "ideal" homogeneous PCB.

Temporal coherence modulation of pulsed, scalar light with a Fabry-Pérot interferometer

We analyze the effect of a high-finesse Fabry-Pérot interferometer on the temporal coherence properties of scalar optical plane-wave pulse trains. We focus on the cases of single-peak and double-peak transmissions of Gaussian Schell-model (GSM) and supercontinuum (SC) pulses. For the GSM light, we show how the characteristics of the average intensity and temporal degree of coherence of the transmitted pulses depend on the coherence parameters of the incident field. Regarding the SC light, the output is found to depend specifically on the location of the transmission peak(s) within the average spectrum. The results demonstrate that a Fabry-Pérot etalon can act as a simple passive element for tailoring the temporal (and spectral) coherence properties of optical pulse trains.

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.

Temporal modes of stationary and pulsed quasistationary electromagnetic beams

We present a novel time-domain coherent-mode representation for random, stationary electromagnetic beams. We subsequently introduce random, quasistationary pulsed electromagnetic beams and develop an analogous (pseudo) mode decomposition for them as well. The former decomposition is valid provided the time window in which the field is considered is much longer than the coherence time, while the latter requires the field to vanish outside the window. For stationary beams, the theory is demonstrated by an example illustrating the role of polarization in the representation. In both cases, the data needed for the construction of the mode decomposition are straightforward to measure. The formalisms enable us to treat random vector-light beams in the time domain in terms of deterministic fields. We expect that the modal representations will find a wide range of applications in problems involving spatiotemporal propagation of temporally partially coherent light in optical systems.

Quasi-monochromatic modes of quasi-stationary, pulsed scalar optical fields

We investigate the temporal coherence of random, pulsed, quasi-stationary scalar light fields and introduce a new type of expansion for the mutual coherence function in terms of fully coherent frequency-shifted quasi-monochromatic modes of identical shape. The mode representation is valid provided the pulse length is shorter and the coherence time is much shorter than the width of the time window in which the field is considered. The construction of the expansion is particularly straightforward since information is required only on the average spectrum and the average temporal intensity. The method enables us to assess the coherence properties of quasi-stationary light by analyzing the behavior of deterministic quasi-monochromatic fields. The frequency-domain counterpart of the representation is also given. The method is illustrated by application to a pulsed free-electron laser source.

Electromagnetic theory of optical coherence [Invited]

The coherence theory of random, vector-valued optical fields has been of great research interest in recent years. In this work we formulate the foundations of electromagnetic coherence theory both in the space-time and space-frequency domains, with particular emphasis on various types of optical interferometry. Analyzing statistically stationary, two-component (paraxial) electric fields in the classical and quantum-optical contexts we show fundamental connections between the conventional (polarization) Stokes parameters and the associated two-point (coherence) Stokes parameters. Measurement of the coherence and polarization properties of random vector beams by nanoparticle scattering and two-photon absorption is also addressed.