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.

Dual perfect vectorial vortex beam generation with a single spin-multiplexed metasurface.

Perfect optical vortex beams (POVBs) carrying orbital angular momentum (OAM) possess annular intensity profiles that are independent of the topological charge. Unlike POVBs, perfect vectorial vortex beams (PVVBs) not only carry orbital angular momentum but also exhibit spin angular momentum (SAM). By incorporating a Dammann vortex grating (DVG) on an all-dielectric metasurface, we demonstrate an approach to create a pair of PVVBs on a hybrid-order Poincaré sphere. Benefiting flexible phase modulation, by engineering the DVG and changing the input-beam state we are able to freely tailor the topological OAM and polarization eigenstates of the output PVVBs. This work demonstrates a versatile flat-optics platform for high-quality PVVB generation and may pave the way for applications in optical communication and quantum information processing.

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.

Three-dimensional polarization effects in optical tunneling.

We consider the three-dimensional (3D) polarimetric properties of an evanescent optical field excited in the gap of a double-prism system by a random plane wave. The analysis covers the case of frustrated total internal reflection (FTIR), i.e., optical tunneling, and relies on the characteristic decomposition of the 3×3 polarization matrix. We find in particular that, for any incident partially polarized plane wave, the evanescent field inside the gap is necessarily in a nonregular, genuine 3D polarization state. We also show that the 3D polarimetric properties of the field at the second boundary are sensitive to the changes of the gap width and that the relevant effects occur for the smaller widths when the angle of incidence of the plane wave becomes larger. The results of this work uncover new aspects of the polarimetric structure of genuine 3D evanescent fields and may find applications in near-field optics and surface nanophotonics.

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.

Fast and reliable technique for spatial coherence measurement with a temporally modulated nonredundant slit array.

We propose a method of measuring the spatial coherence of light by means of a temporally modulated nonredundant slit array implemented on a digital micromirror device. We first formulate the theory of the spatial coherence measurement to incorporate a general case when the observation plane is not necessarily placed in the far field of the slit array. We then demonstrate experimentally that a single measurement determines the spatial coherence for 15 different slit separations accurately, even if background light is unavoidable, under the condition that a nonredundant array of six slits is illuminated evenly. These results clearly show that fast and highly reliable spatial coherence measurement is achievable with the proposed method without any difficulties.

100 years of Emil Wolf: introduction.

The groundbreaking research and ideas introduced by Emil Wolf continue to inspire researchers and motivate ongoing research in the wave properties of light. This special issue commemorates the legacy of Emil Wolf with research in physical optics, with specific focus on those areas where Wolf was active, such as optical coherence theory, inverse problems, singular optics, imaging, and polarization, and the intersection of these fields of study. Here we discuss the life of Emil Wolf and his influence on optical science and the optics community.

Polarization-resolved scintillations in Young's experiment.

The conventional scintillation, or intensity fluctuation, that occurs in random electromagnetic beams is just one member of a broader class of four interconnected, polarization-resolved scintillations. We examine these generalized scintillations, called Stokes scintillations, that occur when two stochastic electromagnetic beams are made to interfere in Young's experiment. We find that the magnitude of the conventional scintillation can be decreased, within certain limits, at the expense of an increase of one or more of the other Stokes scintillations. For certain applications however, it may be beneficial to suppress the latter.

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.

Probing coherence Stokes parameters of three-component light with nanoscatterers.

We establish a method to determine the spectral coherence Stokes parameters of a random three-component optical field via scattering by two dipolar nanoparticles. We show that measuring the intensity and polarization-state fringes of the scattered far field in three directions allows us to construct all nine coherence Stokes parameters at the dipoles. The method extends current nanoprobe techniques to detection of the spatial coherence of random light with arbitrary three-dimensional polarization structure.

Poincaré sphere representation of scalar two-beam interference under spatial unitary transformations.

We consider two partially correlated scalar light beams in a spatially unitary interference setup. We introduce a state vector in a Poincaré-sphere-like geometrical configuration that fully specifies such an optical system and its evolution under spatial unitary transformations. We also identify three particular unitary operations together with their geometrical representations that can be optically implemented to realize an arbitrary spatial unitary transformation. Our work forms an advantageous geometrical platform to characterize distinguishability, visibility, degree of coherence, and classical entanglement, as well as their spatial unitary evolutions, in scalar two-beam light interference.

Coherence Switching with Metamaterials.

We demonstrate, theoretically, how the insertion of an enhanced epsilon-near-zero (EENZ) mirror in a laser cavity grants exceptional control over the coherence properties of the emitted light beam. By exploiting the peculiar sensitivity to polarization of EENZ materials, we achieve superior control over the spatial coherence of the emitted laser light, which can be switched at will between nearly incoherent and fully coherent, solely by means of polarization optics. Our EENZ cavity design is expected to be an efficient, compact, reconfigurable, and easily scalable source of light for illumination and speckle contrast imaging, as well as any other application that benefits from controlled spatial coherence.

Spatial coherence measurement via a digital micromirror device based spatiotemporal light modulation.

We propose a method for measuring the spatial coherence of light by means of temporal modulation of a double slit displayed on a digital micromirror device. It is demonstrated theoretically and experimentally that the technique is generally insensitive to background light, and thus its suppression or subtraction is not necessary. Moreover, the visibility of the interference fringe pattern can be enhanced by modulating only either one of the two slits. These favorable features enable one to measure the spatial coherence of even faint light more conveniently and accurately.

Complete coherence of random, nonstationary electromagnetic fields.

Despite a wide range of applications, the coherence theory of random, nonstationary (pulsed or otherwise) electromagnetic fields is far from complete. In this work, we show that full coherence of a nonstationary vectorial field at a pair of spatiospectral points is equivalent to the factorization of the cross-spectral density matrix, and full pointwise coherence over a spatial volume and spectral band leads to a factored cross-spectral density throughout the domain. We further show that in the latter case, the time-domain mutual coherence matrix factors in the spatiotemporal variables, and the field is temporally fully coherent throughout the volume. The results of this work justify that certain expressions of random pulsed electromagnetic beams appearing in the literature can be called coherent-mode representations.

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.

Correlated and uncorrelated parts of scalar fields in two-beam optical interferometry.

We show that in the interference of two partially correlated scalar light beams, the fields can be divided into parts that are mutually completely correlated (coherent) and parts that are fully uncorrelated with the correlated parts and with each other. Such correlated and uncorrelated parts cannot, in general, be unambiguously specified, but with a certain additional constraint, the partition becomes unique and can be determined. We demonstrate experimentally that the uncorrelated contribution can be physically isolated with the help of a spatial unitary transformation, such as a nonabsorbing beam splitter. Our findings constitute foundational results on optical two-beam interferometry.

Blackbody far-field coherence.

We revisit the spectral coherence properties of far-field radiation emanating from an aperture in a blackbody cavity on the basis of Kirchhoff's boundary conditions. We point out that the far zone cross-spectral density matrix derived earlier in the literature by separately propagating all three aperture-field components does not show transversality of the field at nonparaxial directions. This is not the case when Luneburg's diffraction integrals are applied on the transverse source field components to determine the entire far field. We compare the electromagnetic degrees of coherence for the two methods and show that over important angular separations their values coincide with high accuracy. The results of this work and of others concerning the far-field intensity, polarization, and paraxial angular coherence are in full agreement.

Mirror-based scanning wavefront-folding interferometer for coherence measurements.

We demonstrate a modification to the traditional prism-based wavefront-folding interferometer that allows the measurement of spatial and temporal coherence, free of distortions and diffraction caused by the prism corners. In our modified system, the two prisms of the conventional system are replaced with six mirrors. The whole system is mounted on a linear XY-translation stage, with an additional linear stage in the horizontal arm. This system enables rapid and exact measurement of the full four-dimensional degree of coherence, even for relatively weak signals. The capabilities of our system are demonstrated by measuring the spatial coherence of two inhomogeneous and non-Schell model light sources with distinct characteristics.

Ghost polarimetry using Stokes correlations.

We present here a novel ghost polarimeter based on Stokes parameter correlations and a spatially incoherent classical source with adjustable polarization state and Gaussian statistics. The setup enables extracting the four amplitudes and three phase differences related to the spectral $ 2 \times 2 $2×2 complex Jones matrix of any transmissive polarization-sensitive object. Our work extends the ghost imaging methods from the traditional intensity correlation measurements to the detection of polarization state correlations.