Hanbury Brown-Twiss effect with electromagnetic waves

Relationship between Hanbury Brown-Twiss effect and spectral degree of polarization in light scattering from a collection of particles of $\mathcal {L}$ types

We consider the vectorial extension of the recently developed matrix theory for the correlation between intensity fluctuations (CIF) of the scattered field generated by a collection of particles of $\mathcal {L}$ types [Y. Ding and D. M. Zhao, Opt. Express 30 46460, 2022]. In the spherical polar coordinate system, we establish a closed-form relation that connects the normalized CIF of the electromagnetic scattered field with the pair-potential matrix (PPM), the pair-structure matrix (PSM), and the spectral degree of polarization $\mathcal {P}$ of the incident field. Based on this, we pay much attention to the dependence of the normalized CIF of the scattered field on $\mathcal {P}$. It is found that the normalized CIF can be monotonically increasing or be nonmonotonic with $\mathcal {P}$ in the region [0, 1], determined by the polar angle θ and the azimuthal angle ϕ. Also, the distributions of the normalized CIF with $\mathcal {P}$ at polar angles and azimuthal angles are greatly different. These findings are explained mathematically as well as physically, and may be of interest to some related fields, especially where the CIF of the electromagnetic scattered field plays important roles.

Generation of cross-spectrally pure electromagnetic fields using a pair of moving diffusers

In this paper, we demonstrate that the vector light field is cross-spectrally pure if it passes through two diffusers (having similar correlation properties) moving with identical linear speeds in opposite directions. To determine the spatio-temporal coherence function of cross-spectrally pure light, a double slit is placed just after the second diffuser. We show that the normalized space-time coherence Stokes parameters of emerging light can be described in the form of a reduction formula, whereas the absolute values of the normalized space-frequency coherence Stokes parameters are the same for every frequency component of the light field. These are the conditions of cross-spectral purity of Stokes parameters. We further prove that at zero time delay, the condition of strict cross-spectral purity is validated. Furthermore, we establish the conditions for cross-spectral purity for a vector light field passing through the aforesaid diffusers, when they rotate with identical angular speeds in opposite directions, offering a possibility to optimize the scheme using only a single diffuser. For the first time, to our knowledge, an additional condition for equality of the degree of cross-polarization in space-time and space-frequency domains for strict cross-spectrally pure light beams is also introduced.

Hanbury Brown and Twiss effect in spatiotemporal domain

Hanbury Brown and Twiss (HBT) effect has broad applications in optics and other branches of physics, and traditionally this effect is considered in pure spatial or temporal domain. Here we investigate the spatiotemporal HBT effect, extending this phenomenon from spatial or temporal to spatiotemporal domain. By assuming the Gaussian statistics of partially coherent spatiotemporal pulsed sources, we find the generalized analytical results for spatiotemporal HBT effect in the compact form, with the help of the matrix-optics method, which can consider the HBT effect in spatial and temporal domain simultaneously. Furthermore, for Gaussian Schell-model pulsed beams (GSMPBs) used as a spatiotemporal correlated source, we have obtained the generalized expression to calculate spatiotemporal HBT effect, which is useful for up to three-dimensional cases in any second-order linear dispersive medium. By taking a simple two-dimensional case and using air as an example of a linear dispersive medium, we numerically illustrate the properties of the spatiotemporal HBT effect by adjusting the spatial and temporal parameters of the GSMPB source, and reveal the influence of both the spatial and temporal parameters on the spatiotemporal HBT effect. This work paves the path towards the detailed study of HBT effect for a source containing spatiotemporal information with Gaussian statistics.

Measuring complex correlation matrix of partially coherent vector light via a generalized Hanbury Brown-Twiss experiment

We introduce an effective method for measuring the spatial distribution of complex correlation matrix of a partially coherent vector light field obeying Gaussian statistics by extending our recently advanced generalized Hanbury Brown-Twiss experiment. The method involves a combination of the partially coherent vector light with a pair of fully coherent reference vector fields and a measurement of the intensity-intensity cross-correlation of the combined fields. We show the real and imaginary parts of the complex correlation matrix can be recovered through a judicious control of the phase delay between two reference fields. We test the feasibility of our method by measuring the complex correlation matrix of a specially correlated radially polarized vector beam and we find the consistence between the experimental results and our general theory. We further show that our complex correlation matrix measurement can be used in reconstructing the polarization states hidden behind a thin-layer diffuser.

Imaging of polarimetric-phase object through scattering medium by phase shifting

Light propagating through a scattering medium generates a random field, which is also known as a speckle. The scattering process hinders the direct retrieval of the information encoded in the light based on the randomly fluctuating field. In this study, we propose and experimentally demonstrate a method for the imaging of polarimetric-phase objects hidden behind a scattering medium based on two-point intensity correlation and phase-shifting techniques. One advantage of proposed method is that it does not require mechanical rotation of polarization elements. The method exploits the relationship between the two-point intensity correlation of the spatially fluctuating random field in the observation plane and the structure of the polarized source in the scattering plane. The polarimetric phase of the source structure is determined by replacing the interference intensity in traditional phase shift formula with the Fourier transform of the cross-covariance of the intensity. The imaging of the polarimetric-phase object is demonstrated by comparing three different phase-shifting techniques. We also evaluated the performance of the proposed technique on an unstable platform as well as using dynamic diffusers, which is implemented by replacing the diffuser with a new one during each phase-shifting step. The results were compared with that obtained with a fixed diffuser on a vibration-isolation platform during the phase-shifting process. A good match is found among the three cases, thus confirming that the proposed intensity-correlation-based technique is a useful one and should be applicable with dynamic diffusers as well as in unstable environments.

Investigation of longitudinal spatial coherence for electromagnetic optical fields

For light fields, the coherence in longitudinal direction is governed by both the frequency spectra and angular spectra they possess. In this work, we develop and report a theoretical formulation to demonstrate the effect of the angular spectra of electromagnetic light fields in quantifying their longitudinal spatial coherence. The experimental results obtained by measuring the electromagnetic longitudinal spatial coherence and degree of cross-polarization of uniformly polarized light fields for different angular spectra validate the theoretical findings.

Generalized Hanbury Brown-Twiss effect for Stokes parameters

The classic experiments by Hanbury Brown and Twiss (HBT) were concerned with the correlation of intensity fluctuations at two different positions in a wave field. We generalize the HBT effect that occurs in random electromagnetic beams by examining its polarization-resolved version. This leads naturally to the concept of correlations of fluctuations of the four Stokes parameters. We calculate the correlations of such "Stokes fluctuations" for the case of Gaussian statistics. When the two points of observation coincide, these correlations reduce to "Stokes scintillations." Our work reveals a new layer of complexity in random beams by showing that the HBT effect and the scintillation coefficient are just two of many correlations that are present. We illustrate that, in general, the fluctuations of the various Stokes parameters are all correlated by studying beams and sources with different polarization states.

Application of third-order correlation between intensity fluctuations to determination of scattering potential of quasi-homogeneous medium

Within the first-order Born approximation, we introduce the third-order correlation between intensity fluctuation (CIF) of light scattered from a quasi-homogeneous (QH) medium. By utilizing the Gaussian moment theorem for describing the scattering potential statistics, analytic forms are derived for the third-order, normalized CIF and variance of intensity fluctuations (VIF) of the far-zone scattered field. It is found that the normalized CIF of the scattered field is proportional to the product of Fourier transforms of the strengths of the scattering potential, while the variance of intensity fluctuations (VIF) of the scattered field is the cube of the Fourier transform of the normalized correlation coefficient (NCC) of the scattering potential. Based on the derived formulas, we show that the correlation function of the scattering potential of the medium can be determined from the scattering equations where the third-order CIF properties of the scattered field must be known in advance.

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.

Ultrashort coherence times in partially polarized stationary optical beams measured by two-photon absorption

We measure the recently introduced electromagnetic temporal degree of coherence of a stationary, partially polarized, classical optical beam. Instead of recording the visibility of intensity fringes, the spectrum, or the polarization characteristics, we introduce a novel technique based on two-photon absorption. Using a Michelson interferometer equipped with polarizers and a specific GaAs photocount tube, we obtain the two fundamental quantities pertaining to the fluctuations of light: the degree of coherence and the degree of polarization. We also show that the electromagnetic intensity-correlation measurements with two-photon absorption require that the polarization dynamics, i.e., the time evolution of the instantaneous polarization state, is properly taken into account. We apply the technique to unpolarized and polarized sources of amplified spontaneous emission (Gaussian statistics) and to a superposition of two independent, narrow-band laser beams of different mid frequencies (non-Gaussian statistics). For these two sources femtosecond-range coherence times are found that are in good agreement with the traditional spectral measurements. Although previously employed for laser pulses, two-photon absorption provides a new physical principle to study electromagnetic coherence phenomena in classical and quantum continuous-wave light at extremely short time scales.

Synthesis of statistical properties of a randomly fluctuating polarized field

An experimental technique for the synthesis of statistical properties of a randomly fluctuating polarized field is investigated and experimentally demonstrated. The technique offers the controlled synthesis of coherence and polarization and subsequent analysis of the synthesized field is carried out by making use of two-point intensity correlation and the speckle holographic technique. The controlled synthesis is achieved by using an aperture of specific size at the source plane and generating a vortex in one of the orthogonal polarization components of the polarized field, thereby producing a singularity in off-diagonal elements of the coherence-polarization matrix.

Experimental determination of generalized Stokes parameters

A new technique to determine generalized Stokes parameters by making use of the speckle holographic technique and the two-point intensity correlation is proposed and experimentally demonstrated. Assuming Gaussian statistics and spatial stationarity, a speckle hologram is generated prior to the fourth-order correlation, i.e., the two-point intensity correlation. This measurement technique offers a complete retrieval of complex generalized Stokes parameters. The application of the proposed technique is experimentally demonstrated for two different, random source structures.

Correlation of intensity fluctuations in beams generated by quasi-homogeneous sources

We derive expressions for the far-zone correlation of intensity fluctuations (the Hanbury Brown-Twiss effect) that occurs in electromagnetic beams that are generated by quasi-homogeneous sources. Such sources often have a radiant intensity pattern that is rotationally symmetric, irrespective of the source shape. We demonstrate how from the far-zone correlation of intensity fluctuations the spectral density distribution across the source plane may be reconstructed.

Hanbury Brown-Twiss effect with partially coherent electromagnetic beams

We derive expressions that allow us to examine the influence of different source parameters on the correlation of intensity fluctuations (the Hanbury Brown-Twiss effect) at two points in the same cross section of a random electromagnetic beam. It is found that these higher-order correlations behave quite differently than the lower-order amplitude-phase correlations that are described by the spectral degree of coherence.

Complete characterization of partially coherent and partially polarized optical fields

We suggest a method to access the second-order, or two-point, Stokes parameters of a partially coherent and partially polarized Gaussian model optical field from an intensity interferometry experiment. Through a remarkably simple experimental arrangement, it is possible to measure the two-point and one-point Stokes parameters simultaneously, allowing the reconstruction of the coherence matrix and the polarization matrix, thus completely characterizing the optical field both statistically and locally on the observation plane. Developments, automation, and applications are pointed out.

Topological reactions of correlation functions in partially coherent electromagnetic beams

It was recently shown that so-called coherence vortices, singularities of the two-point correlation function, generally occur in partially coherent electromagnetic beams. We study the three-dimensional structure of these singularities and show that in successive cross sections of a beam a rich variety of topological reactions takes place. These reactions involve, apart from vortices, the creation or annihilation of dipoles, saddles, maxima and minima of the phase of the correlation function. Since these reactions happen generically, i.e., under quite general conditions, these observations have implications for interference experiments with partially coherent, electromagnetic beams.

Correlation singularities in partially coherent electromagnetic beams

We demonstrate that coherence vortices, singularities of the correlation function, generally occur in partially coherent electromagnetic beams. In successive cross sections of Gaussian Schell-model beams, their locus is found to be a closed string. These coherence singularities have implications for both interference experiments and correlation of intensity fluctuation measurements performed with such beams.

Coherence and polarization properties in speckle of totally depolarized light scattered by totally depolarizing media

When a totally unpolarized light is scattered by a medium that spatially totally depolarizes incident polarized light, the scattered field presents an increase of the order described by the temporal degree of polarization. We analyze the behavior of some polarization and coherence properties in such a physical situation.