Polarimetric measurement of temporal coherence in electromagnetic light beams.

We present a method to determine the degree of temporal coherence of a quasimonochromatic vectorial light beam by polarimetric measurements. More specifically, we employ Michelson's interferometer in which the polarization Stokes parameters of the output (interference) beam are measured as a function of the time delay. Such a measurement enables us to deduce the magnitudes of the coherence (two-time) Stokes parameters, and hence the degree of coherence, of the input beam. Compared to existing methods the current technique has the benefits that neither optical elements in the arms of the interferometer nor visibility measurements are needed. The method is demonstrated with a laser diode and a filtered halogen source of various degrees of polarization.

Nonstationary optics: tutorial.

Over the past several decades, nonstationary optics has risen as a key enabling technology for a multitude of novel applications. These include areas of research such as micromachining and ultrafast optics, as well as the Nobel awarded research in femtochemistry, optical frequency combs, and attosecond physics. This tutorial aims to present some of the main concepts required to analyze nonstationary fields, with an emphasis on pulsed beams. The work begins from the fundamental building blocks of such fields, and builds up to some of their main properties. The spatiotemporal properties and stability of such fields are discussed in length, and some common measurement schemes are reviewed.

Cross-spectral purity of the Stokes parameters in random nonstationary electromagnetic beams.

We consider cross-spectral purity in random nonstationary electromagnetic beams in terms of the Stokes parameters representing the spectral density and the spectral polarization state. We show that a Stokes parameter being cross-spectrally pure is consistent with the property that the corresponding normalized time-integrated coherence (two-point) Stokes parameter satisfies a certain reduction formula. The current analysis differs from the previous works on cross-spectral purity of nonstationary light beams such that the purity condition is in line with Mandel's original definition. In addition, in contrast to earlier works concerning the cross-spectral purity of the polarization-state Stokes parameters, intensity-normalized coherence Stokes parameters are applied. It is consequently found that in addition to separate spatial and temporal coherence factors the reduction formula contains a third factor that depends exclusively on polarization properties. We further show that cross-spectral purity implies a specific structure for electromagnetic spectral spatial correlations. The results of this work constitute foundational advances in the interference of random nonstationary vectorial light.

Reduction formula for cross-spectral purity of nonstationary light fields.

We examine cross-spectral purity of random, nonstationary (pulsed), scalar light fields with arbitrary spectral bandwidth. In particular, we derive a reduction formula in terms of time-integrated coherence functions, which ensures cross-spectral purity of interfering fields having identical normalized spectra. We further introduce fields that are cross-spectrally pure in either a global or local sense. Our analysis is based on an ideal field superposition realizable with all-reflective wavefront-shearing interferometers. Such devices avoid certain problems related to Young's interferometer, which is the framework customarily employed in assessing cross-spectral purity. We show that any partially coherent beam can be transformed into a locally cross-spectrally pure beam whose cross-spectral density is specular. On the other hand, lack of space-frequency (and space-time) coupling ensures cross-spectral purity in the global sense, i.e., across an entire transverse plane, regardless of the spectral bandwidth or the temporal shape of the pulses.

Singular-value decomposition and electromagnetic coherence of optical beams.

We investigate the implications of the singular-value decomposition of the cross-spectral density (CSD) matrix to the description of electromagnetic spectral spatial coherence of stationary light beams. We show that in a transverse plane any CSD matrix can be expressed as a mixture of two CSD matrices corresponding to beams which are fully polarized but in general spatially partially coherent. The polarization and coherence structures of these constituent beams are specified, respectively, by the singular vectors and singular values of the full CSD matrix. It follows that vector-beam coherence, including the coherence Stokes parameters and the degree of coherence, can be formulated in terms of only two correlation functions. We further establish two-point analogs of the spectral and characteristic decompositions of the polarization matrix and show that in the case of a Hermitian CSD matrix their composition is specified by the so-called degree of cross-polarization.

Poincaré sphere of electromagnetic spatial coherence.

We introduce a Poincaré sphere construction for geometrical representation of the state of two-point spatial coherence in random electromagnetic (vectorial) beams. To this end, a novel descriptor of coherence is invoked, which shares some important mathematical properties with the polarization matrix and spans a new type of Stokes parameter space. The coherence Poincaré sphere emerges as a geometric interpretation of this novel formalism, which is developed for uniformly and nonuniformly fully polarized beams. The construction is extended to partially polarized beams as well and is demonstrated with a field having separable spatial coherence and polarization characteristics. At a single point, the coherence Poincaré sphere reduces to the conventional polarization Poincaré sphere for any state of partial polarization.