Stochastic complex transmittance screens for synthesizing general partially coherent sources

Twisted sinc-correlation Schell-model array beams

We introduce a class of twisted sinc-correlation partially coherent array sources, by applying the construction theory of correlation function. Spectral density of such novel focused beam propagating in free space is analyzed. It is shown that the intensity distribution presents a good twisted effect and splitting phenomenon upon propagation. The array dimension, the intensity distribution and spatial distribution of the lobes can be flexibly regulated by altering the source parameters. We also explore the spatial evolution of multiple correlation singularities of this light field, where the phase distribution appears as a rotational spiral windmill profile during propagation. Furthermore, the coherence orbital angular momentum of the twisted source beam is investigated. These findings could be useful in the particle manipulation and free-space optical communication.

Generation of non-uniformly correlated sources with controllable beam profile by devising its statistics in the spatial frequency domain

We introduce an efficient approach to simultaneously tailor the spatial profile and the degree of coherence (DOC) of partially coherent light by devising its statistical properties in the spatial frequency domain. The relationship between the beam profile and the DOC in the source plane and the correlation function and power spectrum in the spatial frequency domain is analyzed in detail. This approach enables us to generate partially coherent sources with spatially uniform or non-uniform coherence states, and the source profiles are controlled. The condition for switching two coherence states is given through two theoretical examples. Furthermore, we validate our approach in experiment through generating two kinds of spatially non-uniform correlated sources with controllable beam profiles. The experimental results agree well with our theoretical analysis.

Simulating random optical fields: tutorial

Numerous applications-including optical communications, directed energy, remote sensing, and optical tweezing-utilize the principles of statistical optics and optical coherence theory. Simulation of these phenomena is, therefore, critical in the design of new technologies for these and other such applications. For this reason, this tutorial describes how to generate random electromagnetic field instances or realizations consistent with a given or desired cross-spectral density matrix for use in wave optics simulations. This tutorial assumes that the reader has knowledge of the fundamental principles of statistical optics and optical coherence theory. An extensive reference list is provided where the necessary background information can be found. We begin this tutorial with a brief summary of the coherent-mode representation and the superposition rule of stochastic electromagnetic fields as these foundational ideas form the basis of all known synthesis techniques. We then present optical field expressions that apply these concepts before discussing proper sampling and discretization. We finally compare and contrast coherent-mode- and superposition-rule-based synthesis approaches, discussing the pros and cons of each. As an example, we simulate the synthesis and propagation of an electromagnetic partially coherent field from the literature. We compare simulated or sample statistics to theory to verify that we have successfully produced the desired field and are capturing its propagation behaviors. All computer programs, including detailed explanations of the source code, are provided with this tutorial. We conclude with a brief summary.

Effect of optical spatial coherence on localized spin angular momentum density in tightly focused light [Invited]

Optical coherence is one of the most fundamental characteristics of light and has been viewed as a powerful tool for governing the spatial, spectral, and temporal statistical properties of optical fields during light-matter interactions. In this work, we use the optical coherence theory developed by Emil Wolf as well as the Richards-Wolf's vectorial diffraction method to numerically study the effect of optical coherence on the localized spin density of a tightly focused partially coherent vector beam. We find that both the transverse spin and longitudinal spin, with the former induced by the out-of-phase longitudinal field generated during strong light focusing and the latter induced by the vortex phase in the incident beam, are closely related to the optical coherence of the incident beam, i.e., with the decrease of the transverse spatial coherence width of the incident beam, the magnitude of the spin density components decreases as well. The numerical findings are interpreted well with the two-dimensional degrees of polarization between any two of the three orthogonal field components of the tightly focused field. We also explore the roles of the topological charge of the vortex phase on enhancing the spin density for the partially coherent tightly focused field. The effect of the incident beam's initial polarization state is also discussed.

Pulse-quality metric for nonstationary partially coherent fields

This paper generalizes a pulse-quality metric referred to as P², i.e., the time analogue of Siegman's beam quality factor M², to include pulsed (nonstationary) random fields of any state of coherence. The analysis begins with the derivation of a general P² relation, which we then specialize to the important cases of coherent and Schell-model pulsed beams. As examples, we derive the P² for two stochastic sources: (1) a cosine Gaussian-correlated Schell-model pulsed beam and (2) a nonuniformly correlated pulsed beam. For both of these sources, we generate (in simulation) random instances of each and compare the simulated (Monte Carlo) P², i.e., computed directly from its definition, to the theoretical quantity. The agreement is excellent, thereby validating our P² analysis.

Complex and phase screen methods for studying arbitrary genuine Schell-model partially coherent pulses in nonlinear media

Partially coherent pulses, especially those with non-Gaussian correlated functions, have rarely been explored in nonlinear media because of the demanding procedure of the widely used coherent-mode representation method. This study develops temporal analogues of the complex screen and phase screen methods, which were recently introduced for the spatial counterpart of a partially coherent beam. These methods were employed to study the beam propagation properties of partially coherent pulses, and the obtained results show that they both are highly precise, convenient, and powerful. We believe that these protocols can effectively provide useful insight into the behavior of many coherence-related phenomena in nonlinear media.

Compact generation of robust Airy beam pattern with spatial coherence engineering

We present a class of partially coherent light sources having Airy-type amplitude and Airy-correlated spatial coherence. We show that the light beam generated by such sources can preserve the Airy beam pattern well during its propagation from source to far field. We demonstrate the robustness of the Airy beam pattern by introducing a hard aperture to largely block the beam source. We find that the coherence-induced Airy beam pattern can still be well reconstructed during propagation. We successfully synthesize such partially coherent source using the principle of complex random modes decomposition by using a single phase-only spatial light modulator. The proposed robust Airy beam pattern may find applications in information transmission through complex media.

Rotation of degree of coherence and redistribution of transverse energy flux induced by non-circular degree of coherence of twisted partially coherent sources

It is known that a twisted Gaussian Schell-model (TGSM) beam with elliptical Gaussian amplitude will rotate its beam spot upon propagation because of the vortex structure of the transverse energy flux. In this paper, we study a special kind of twisted partially coherent beams named twisted Hermite-Gaussian correlated Schell model (HGCSM) beam whose degree of coherence (DOC) is non-circularly symmetric but the source amplitude is of the circular Gaussian profile. Our results reveal that the beam spot (average intensity distribution) does not rotate during propagation even if the circular symmetry of the beam spot is broken. However, the DOC pattern shows the rotation under propagation. From the investigation of the transverse energy flux and OAM density flux, we attribute the nontrivial rotation phenomenon to the redistribution of the transverse energy flux by non-circular DOC. Furthermore, based on Hyde's approach [J. Opt. Soc. Am. A37, 257 (2020)10.1364/JOSAA.381772], we introduce a method for the generation of this class of twisted partially coherent sources. The non-rotation of the beam spot and rotation of the DOC are demonstrated in experiment.

Twisted sinc-correlation Schell-model beams

We introduce a new class of twisted sinc-correlation Schell-model (TSCSM) beams and analyze the statistical characteristics of such novel sources during propagation. Several typical examples are given to specifically explore the distribution and twist effect of spectral density and degree of coherence (DOC). It is shown that the irradiance profile of light intensity always rotates to 90 degree. With appropriate light field adjustment, twist effect of DOC would be diverse. DOC can exhibit unidirectional or non-unidirectional rotation during propagation. Besides, the twist factor can make the spot show a tendency to split. And beam width and coherence length also have an impact on this splitting phenomenon of spectral density.

Modal Analysis of Pseudo-Schell Model Sources

All pseudo-Schell model sources have been shown to possess the same continuous set of circularly symmetric modes, all of them presenting a conical wavefront. For keeping energy at a finite level, the mode amplitude along the radial coordinate is modulated by a decreasing exponential function. A peculiar property of such modes is that they exist in the Laplace transform’s realm. After a brief discussion of the near-zone, we pass to the far-zone, where the field can be evaluated in closed form. The corresponding features of the intensity distribution are discussed.

Independently Controlling Stochastic Field Realization Magnitude and Phase Statistics for the Construction of Novel Partially Coherent Sources

In this paper, we present a method to independently control the field and irradiance statistics of a partially coherent beam. Prior techniques focus on generating optical field realizations whose ensemble-averaged autocorrelation matches a specified second-order field moment known as the cross-spectral density (CSD) function. Since optical field realizations are assumed to obey Gaussian statistics, these methods do not consider the irradiance moments, as they, by the Gaussian moment theorem, are completely determined by the field’s first and second moments. Our work, by including control over the irradiance statistics (in addition to the CSD function), expands existing synthesis approaches and allows for the design, modeling, and simulation of new partially coherent beams, whose underlying field realizations are not Gaussian distributed. We start with our model for a random optical field realization and then derive expressions relating the ensemble moments of our fields to those of the desired partially coherent beam. We describe in detail how to generate random optical field realizations with the proper statistics. We lastly generate two example partially coherent beams using our method and compare the simulated field and irradiance moments theory to validate our technique.

Young's interference experiment for generating light with non-uniform coherence states

Up to now, methods for generating non-uniformly correlated light have been of two kinds: one is based on the use of specially designed random phase screens, and the other relies on the coherent-mode superposition, both being very complex experimental procedures. In this Letter, we show both theoretically and experimentally that in Young's interference experiment with light having a sufficiently large transverse coherence width, as compared with the width of the slits, the initially uniformly correlated partially coherent light converts to a non-uniformly correlated light. Such a non-uniform correlation is induced by the interference of light fields originating from the two slits. Our results point to the possibility of using diffraction by specially tailored deterministic aperture arrays for generating light with exotic coherence states.

Twisted space-frequency and space-time partially coherent beams

We present partially coherent sources that are statistically twisted in the space-frequency and space-time domains. Beginning with the superposition rule for genuine partially coherent sources, we derive source plane expressions for the cross-spectral density (CSD) and mutual coherence functions (MCFs) for twisted space-frequency and space-time Gaussian Schell-model (GSM) beams. Using the Fresnel approximation to the free-space Green's function, we then paraxially propagate the CSD and MCF to any plane [Formula: see text]. We discuss the beams' behavior as they propagate, with particular emphasis on how the beam shape rotates or tumbles versus z. To validate our analysis, we simulate the generation and subsequent propagation of twisted space-frequency and space-time GSM beams. We compare the simulated moments to the corresponding theoretical predictions and find them to be in excellent agreement. Lastly, we describe how to physically synthesize twisted space-frequency and space-time partially coherent sources.

Fast calculation of tightly focused random electromagnetic beams: controlling the focal field by spatial coherence

Focusing of a vectorial (electromagnetic) optical beam through a high numerical aperture can be investigated by means of the Richards-Wolf diffraction integral. However, such an integral extends from two-dimensional to four-dimensional, greatly increasing the computation time and therefore limiting the applicability, when light with decreased spatial coherence is considered. Here, we advance an effective protocol for the fast calculation of the statistical properties of a tightly focused field produced by a random electromagnetic beam with arbitrary state of spatial coherence and polarization. The novel method relies on a vectorial pseudo-mode representation and a fast algorithm of the wave-vector space Fourier transform. The procedure is demonstrated for several types of radially (fully) polarized but spatially partially coherent Schell-model beams. The simulations show that the computation time for obtaining the focal spectral density distribution with 512 × 512 spatial points for a low coherence beam is less than 100 seconds, while with the conventional quadruple Richards-Wolf integral more than 100 hours is required. The results further indicate that spatial coherence can be viewed as an effective degree of freedom to govern both the transverse and longitudinal components of a tightly focused field with potential applications in reverse shaping of focal fields and optical trapping control.