Experimental synthesis of partially coherent sources

Measuring the orbital angular momentum of generalized higher-order twisted partially coherent beams

Recently a new family of partially coherent fields incorporating generalized inseparable cross-coupled phases named generalized higher-order twisted partially coherent beams (GHTPCBs) have been introduced. The twist factor u is a key parameter that not only quantifies the strength of the generalized cross-coupled phase for a given order, but also determines the amount of the concomitant orbital angular momentum (OAM). In this paper, we propose a simple and reliable method to measure the factor u using a two-pinhole mask. Without need of complicated optical system, it only requires to capture the far-field diffraction intensity distribution of the GHTPCB passing through the mask. By analyzing the Fourier spectrum of the intensity distribution, the value of twist factor can be derived nearly in real time. The influence of the separation distance between two pinholes and the pinholes' diameter and position on the measurement accuracy are thoroughly studied both in theory and experiment. The experimental results agree well with the theoretical results. Our methodology can also be extended to measure the sole factor of similar position dependent phases such as the topological charge of a vortex phase.

Partially coherent Pearcey-Gauss source with hyperbolic sine correlation of the spatial spectrum

By designing the intricate coherence structure, we are able to create a desired beam profile and trajectory. Our research focus lies on the Fourier plane, specifically emphasizing the coherence of spatial frequencies, and we find it can be seen as a constant system response. A theoretical framework is developed, and experimental studies are conducted to generate a light field of the spatial spectrum with a complex correlation using the pseudo-mode superposition method. We successfully produce partially coherent Pearcey-Gauss beams whose spatial spectrum is hyperbolic sine correlational. Interestingly, these beams maintain the distinctive propagation properties of the Pearcey pattern while exhibiting the remarkable ability to split the mainlobe into two separate lobes.

Virtual sources for structured partially coherent light fields

A virtual source (VS) is a hypothetical source instead of an actual physical entity, but provides a distinctive perspective to understand physical fields in a source-free area. In this work, we generalize the VS theory to structured partially coherent light fields (PCLFs) by establishing the partially coherent inhomogeneous Helmholtz equation, then demonstrate that PCLFs can be generated from the incoherent extended VS in imaginary space. Especially, we put forward an understanding of the Gaussian Schell-model beam, which consists of a group of partially coherent paraxial complex rays. The mutual coherence between these rays depends on the included angle between them. In previous studies, the analytical solution of the partially coherent Airy beam was obtained with difficulty by the Huygens-Fresnel integral; however, by applying the VS, we put forward, to our knowledge, an unprecedented analytical solution for a partially coherent Airy beam. We believe this example will qualify the VS as an important perspective to understand structured PCLFs.

Experimental generation of adjustable partially coherent optical vortices from coherent and incoherent light sources

Adjustable spatial coherence systems allow the possibility to make different intensity distributions using one source. Most common adjustable sources are based on the Collet-Wolf system. However, it is also possible to adjust the spatial coherence of the illumination field from white light sources by spatially filtering the source mutual intensity spectrum. We implement the Collet-Wolf source and the LED-based system to experimentally contrast a variety of partially coherent optical vortices that can be generated with spatial light modulation. We experimentally study the effects of changing the transverse coherence in partially coherent optical vortices, using a proposed metric of vortex contrast depth that quantifies the change of the vortex hollowness. To expand the analysis, we use a Michelson interferometer to reconstruct the spiral wavefronts using phase shifting. We found that the LED system at lower spatially correlated light produces truncated triangular distributions (a 50 µm pinhole is used), and with higher correlated light, it produces partially coherent optical vortices (a 10 µm pinhole is used). The Collet-Wolf system generates partially coherent optical vortices up to 0.5 mm of focal shift in the diffuser. Our results provide an experimental understanding and instrumental methodology capable of steering the optical transverse coherence, producing adjustable partially coherent optical vortices that can be obtained using incoherent and coherent sources.

Asymmetrical inseparable coherent structures

A novel, to the best of our knowledge, class of coherent structures of inseparability, incorporating phases asymmetrically cross-coupled by two position vectors, is introduced in theory and experiment. These phases disappear in the environment of complete coherence, but the vanishment is avoidable in the coexistent state of extreme incoherence and full coherence. The radiated beams intrinsically possess a controllable rotation but undergo an intermediate process quite different from the twisted Gaussian Schell-model beams. Analysis shows a novel association between the magnitude and the phase of the coherent structure which displays both synergy and opposition. Our work further reveals the inner mechanism of the inseparable coherent structures and extends a new horizon for the optical twist.

Tailoring on-axis spectral density with circularly coherent light beams

The on-axis cross-spectral density (CSD) of a beam radiated by a stationary source with a circular coherence state and a Gaussian spectral density is obtained in the closed form. It is revealed that the on-axis CSD is expressed via the Laplace transform of the source's degree of coherence or the Hilbert transform of the corresponding pseudo-mode weighting function. Such relations enable efficient tailoring of the on-axis spectral density, as we show with a slew of numerical examples.

Phase conjugation of twisted Gaussian Schell model beams in stimulated down-conversion

Stimulated parametric down-conversion is a nonlinear optical process that can be used for phase conjugation and frequency conversion of an optical field. A precise description of the outgoing stimulated field has been developed for the case where the input pump and seed fields are coherent. However, partially coherent beams can have interesting and important characteristics that are absent in coherent beams. One example is the twist phase, a novel optical phase that can appear in partially coherent Gaussian beams and gives rise to a nonzero orbital angular momentum. Here, we consider stimulated down-conversion for partially coherent input fields. As a case study, we use twisted Gaussian Schell-Model beams as the seed and pump beams in stimulated parametric down-conversion. It is shown both theoretically and experimentally that the stimulated idler beam can be written as a twisted Gaussian Schell-Model beam, where the beam parameters are determined entirely by the seed and pump. When the pump beam is coherent, the twist phase of the idler is the conjugate of that of the seed. These results could be useful for the correction of wavefront distortion such as in atmospheric turbulence in optical communication channels, and synthesis of partially coherent beams.

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.

Generating non-uniformly correlated twisted sources

The inverse method of proving the twistability of cross-spectral density (CSD) inevitably falls into spontaneous difficulties. Based on a nonnegative self-consistent design guideline for generating genuine CSDs introduced by Gori and Santarsiero, we demonstrate a feasible way for twisting partially coherent sources by sticking a Schell-model function to CSDs, which also determines the upper bound of the twisting strength. Analysis shows that the degree of coherence of a new class of twisted pseudo-Gaussian Schell-model beam is neither shift invariant nor shift-circular symmetric. In the presence of a vortex phase, the two different types of chiral phases affect each other and together control the propagation behavior. We further carry out an experiment to generate this non-uniformly correlated twisted beam using weighted superposition of mutually uncorrelated pseudo modes. The result is beneficial for devising nontrivial twisted beams and offers new opportunities.

Three modal decompositions of Gaussian Schell-model sources: comparative analysis

Representation of the cross-spectral density (CSD) function of an optical source or beam as the incoherent superposition of mutually uncorrelated modes are widely used in imaging systems and in free space optical communication systems for simplification of the analysis and reduction of the time-consuming integral calculations. In this paper, we examine the equivalence and the differences among three modal representation methods: coherent-mode representation (CMR), pseudo-mode representation (PMR) and random mode representation (RMR) for the Gaussian Schell-model (GSM) source class. Our results reveal that for the accurate reconstruction of the CSD of a generic GSM source, the CMR method requires superposition of the least number of optical modes, followed by PMR and then by RMR. The three methods become equivalent if a sufficiently large number of optical modes are involved. However, such an equivalence is limited to the second-order statistics of the source, e.g., the spectral density (average intensity) and the degree of coherence, while the fourth-order statistics, e.g., intensity-intensity correlations, obtained by the three methods are quite different. Furthermore, the second- and the fourth- order statistics of the GSM beam propagating through a deterministic screen and dynamic random screens with fast and slow time cycling are investigated through numerical examples. It is found that the properties of the second-order statistics of the beams obtained by the three methods are the same, irrespectively of the characteristics of the screens, whereas those of the fourth-order statistics remain different.

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.

Customizing twisted Schell-model beams

Since the celebrated twist phase was proposed by Simon and Mukunda, despite the tremendous progress made in theory over the past decades, developing a simple and flexible experimental method to customize this novel phase has long been a tricky challenge. In this Letter, we demonstrate a general experimental method for generating twisted Schell-model beams by implementing the continuous coherent beam integral function in a discrete form. Experimental results based on rigorous Laguerre-Gauss modes superposition are also demonstrated, indicating that our method is more convenient and of higher quality. The twist factor is also measured using the rotation characteristics during propagation, and the results agree well with the theoretical prediction. The method could serve as a general way for customizing bona fide twisted cross-spectral densities while facilitating certain applications.