Optical coherence encryption with structured random light

Prime number factorization and degree of coherence of speckled light beams

We discover a connection between a Gauss sum of number theory and the degree of coherence (DOC) of the field in a transverse plane of structured speckled light beams. We theoretically demonstrate and experimentally validate that prime number factorization can be achieved by manipulating the source beam's DOC in Young's double-slit experiment. The determination of whether a number can be factored is based solely on the visibility of the resulting interference patterns. Our findings offer new insights into information encryption and decryption, data compression, etc.

Partial coherence enhances parallelized photonic computing

Advancements in optical coherence control1-5 have unlocked many cutting-edge applications, including long-haul communication, light detection and ranging (LiDAR) and optical coherence tomography6-8. Prevailing wisdom suggests that using more coherent light sources leads to enhanced system performance and device functionalities9-11. Our study introduces a photonic convolutional processing system that takes advantage of partially coherent light to boost computing parallelism without substantially sacrificing accuracy, potentially enabling larger-size photonic tensor cores. The reduction of the degree of coherence optimizes bandwidth use in the photonic convolutional processing system. This breakthrough challenges the traditional belief that coherence is essential or even advantageous in integrated photonic accelerators, thereby enabling the use of light sources with less rigorous feedback control and thermal-management requirements for high-throughput photonic computing. Here we demonstrate such a system in two photonic platforms for computing applications: a photonic tensor core using phase-change-material photonic memories that delivers parallel convolution operations to classify the gaits of ten patients with Parkinson's disease with 92.2% accuracy (92.7% theoretically) and a silicon photonic tensor core with embedded electro-absorption modulators (EAMs) to facilitate 0.108 tera operations per second (TOPS) convolutional processing for classifying the Modified National Institute of Standards and Technology (MNIST) handwritten digits dataset with 92.4% accuracy (95.0% theoretically).

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.

Distribution of intensity and M2 factor for a partially coherent flat-topped beam in bidirectional turbulent atmosphere and plasma connection

This study investigates the bidirectional transmission of a partially coherent flat-topped beam in a turbulent atmosphere and plasma. Analytical formulas for the intensity distribution and M2 factor are derived based on the optical transmission matrix, Collins formula, and second moment theory with Wigner distribution function. Numerical results show that the beam order and transverse spatial coherence width can be selected appropriately to mitigate turbulence and plasma induced evolution properties. The partially coherent flat-topped beam propagation through a turbulent atmosphere and plasma of the forward transmission effect on the intensity distribution and M2 factor are smaller than that of the reverse transmission. Under the same conditions, the M2 factor of a partially coherent flat-topped beam is smaller than the Gaussian beam in bidirectional transmission. Our results can be used in long-distance free-space optical communications.

Switch of orbital angular momentum flux density of partially coherent vortex beams

We investigate the orbital angular momentum (OAM) flux density of beams which are the incoherent superposition of partially coherent vortex (PCV) beams with different topological charges and beam widths. Simulation results show that such beams can exhibit counter-rotating radial regions of the OAM flux density, and that we can "switch" the order of these regions by adjusting the topological charges and beam widths in the source plane. Furthermore, these counter-rotating regions can switch on propagation in free space without any change to the beam parameters. We discuss how these unusual OAM dynamics may find use in OAM-based applications.

Scintillation mitigation via the cross phase of the Gaussian Schell-model beam in a turbulent atmosphere

Scintillation is an important problem for laser beams in free space optical (FSO) communications. We derived the analytical expressions for the scintillation index of a Gaussian Schell-model beam with cross phase propagation in a turbulent atmosphere. The numerical results show that the quadratic phase can be used to mitigate turbulence-induced scintillation, and the effects of the turbulent strength and beam parameters at the source plane on the scintillation index are analyzed. The variation trend of the experimentally measured scintillation index is consistent with the numerical results. Our results are expected to be useful for FSO communications.

Synthesis of partially coherent beams with a prescribed conjugate-model correlation structure

Using the sum of two mutually complex conjugate functions as the integral kernel of the necessary and sufficient condition derived by Gori et al., the conjugate-model correlation structure can be constructed. Here, we introduced a general strategy for the synthesis of partially coherent beams with such correlation structures. With it, we described a specific family of such beams, called Hermite conjugate-model beams. Their focusing properties were investigated numerically and experimentally. The experimental results are consistent with the theoretical predictions, and show that the proposed beams possess novel physical features compared with well-known Schell-model beams, such as controllable intensity distributions both at the source and focal plane, which may prove useful in free-space optical communications and optical trapping.

Enhancing fiber-coupling efficiency of beam-to-fiber links in turbulence by spatial non-uniform coherence engineering

We present a general formula for the fiber-coupling efficiency of various types of non-uniformly correlated beams propagating in a turbulent atmosphere. With it, we calculate the fiber-coupling efficiency of a specific type of non-uniformly correlated beams, Laguerre non-uniformly correlated (LNUC) beams, to investigate how the non-uniform correlation structure plays a role in enhancing the fiber-coupling efficiency. Compared with conventional Gaussian Schell-model beams, the LNUC beams possess better coupling behavior, and the initial coherence length and beam order of such beams can be adjusted to further improve the fiber-coupling efficiency in turbulence. Our results demonstrate how non-uniformly correlated beams can be used for fiber-coupling applications, and demonstrate their intriguing potential for free-space optical communications.

Generating multi-focus beams with a spatial non-uniform coherence structure

We introduce a class of structured light beams, named multi-focus beams, which exhibit self-focusing at multiple propagation distances. We show that the proposed beams not only have the ability to produce multiple longitudinal focal spots, but also that the number, intensity, and position of the foci can be controlled by adjusting the initial beam parameters. Furthermore, we demonstrate that these beams still exhibit self-focusing in the shadow of an obstacle. We have experimentally generated such beams and the results are consistent with the theoretical predictions. Our studies may find application where fine control of the longitudinal spectral density is needed, such as longitudinal optical trapping and manipulation of multiple particles, and transparent material cutting.

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.

Second-order statistics of a Hermite-Gaussian correlated Schell-model beam carrying twisted phase propagation in turbulent atmosphere

We investigate the second-order statistics of a twisted Hermite-Gaussian correlated Schell-model (THGCSM) beam propagation in turbulent atmosphere, including the spectral density, degree of coherence (DOC), root mean square (r.m.s.) beam wander and orbital angular momentum (OAM) flux density. Our results reveal that the atmospheric turbulence and the twist phase play a role in preventing the beam splitting during beam propagation. However, the two factors have opposite effects on the evolution of the DOC. The twist phase preserves the DOC profile invariant on propagation, whereas the turbulence degenerates the DOC. In addition, the influences of the beam parameters and the turbulence on the beam wander are also studied through numerical examples, which show that the beam wander can be reduced by modulating the initial parameters of the beam. Further, the behavior of the z-component OAM flux density in free space and in atmosphere is thoroughly examined. We show that the direction of the OAM flux density without the twist phase will be suddenly inversed at each point across the beam section in the turbulence. This inversion only depends on the initial beam width and the turbulence strength, and in turn, it offers an effective protocol to determine the turbulence strength by measuring the propagation distance where the direction of OAM flux density is inversed.

Coherence singularity and evolution of partially coherent Bessel-Gaussian vortex beams

For a partially coherent Bessel-Gaussian (PCBG) vortex beam, information regarding the topological charge (TC) is hidden in the phase of the cross-spectral density (CSD) function. We theoretically and experimentally confirmed that during free-space propagation, the number of coherence singularities is equal to the magnitude of the TC. In contrast to the Laguerre-Gaussian vortex beam, this quantitative relationship only holds for the case with an off-axis reference point for the PCBG vortex beam. The phase winding direction is determined by the sign of the TC. We developed a scheme for CSD phase measurement of PCBG vortex beams and verified the aforementioned quantitative relationship at different propagation distances and coherence widths. The findings of this study may be useful for optical communications.

Orbital angular momentum spectra of twisted Laguerre-Gaussian Schell-model beams propagating in weak-to-strong Kolmogorov atmospheric turbulence

The presence of atmospheric turbulence in a beam propagation path results in the spread of orbital angular momentum (OAM) modes of laser beams, limiting the performance of free-space optical communications with the utility of vortex beams. The knowledge of the effects of turbulence on the OAM spectrum (also named as spiral spectrum) is thus of utmost importance. However, most of the existing studies considering this effect are limited to the weak turbulence that is modeled as a random complex "screen" in the receiver plane. In this paper, the behavior of the OAM spectra of twisted Laguerre-Gaussian Schell-model (TLGSM) beams propagation through anisotropic Kolmogorov atmospheric turbulence is examined based on the extended Huygens-Fresnel integral which is considered to be applicable in weak-to-strong turbulence. The discrepancies of the OAM spectra between weak and strong turbulence are studied comparatively. The influences of the twist phase and the anisotropy of turbulence on the OAM spectra during propagation are investigated through numerical examples. Our results reveal that the twist phase plays a crucial role in determining the OAM spectra in turbulence, resisting the degeneration of the detection mode weight by appropriately choosing the twist factor, while the effects of the anisotropic factors of turbulence on the OAM spectra seem to be not obvious. Our findings can be applied to the analysis of OAM spectra of laser beams both in weak and strong turbulence.

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.

Coherent mode decomposition of multiple quantum well light emission

Developing a richer understanding of the various properties of light is central to the field of photonics. One often neglected degree of freedom (DOF) is the second-order correlation of the light field, known as coherence. To make proper use of this DOF, one needs to first obtain information about the field's coherence, which may be characterized through the cross spectral density (CSD) function. We present a measurement of the CSD of a ubiquitous, partially coherent source: a multiple quantum well device in its near-field region, where a photonic structure would commonly encounter the emitted field. We show a departure from the coherence area that is expected from an incoherent source and demonstrate the application of coherent mode decomposition as a way to further analyze the measured results.

Universal orbital angular momentum detection scheme for any vortex beam

Existing methods for probing the orbital angular momentum carried by vortex beams have many limitations and are generally only applicable to specific types of vortex beam. In this work, we present a concise and efficient universal method for probing the orbital angular momentum that is applicable for any type of vortex beam. The vortex beam could range from being fully to partially coherent, with different spatial modes including Gaussian vortex beam, Bessel-Gaussian beam, Laguerre-Gaussian beam, etc., of any wavelength including x rays, matter waves such as electron vortices, and with high topological charge. This protocol only requires a (commercial) angular gradient filter, making it very easy to implement. The feasibility of the proposed scheme is demonstrated both theoretically and experimentally.

Partially coherent conical refraction promises new counter-intuitive phenomena

In this paper, we extend the paraxial conical refraction model to the case of the partially coherent light using the unified optical coherence theory. We demonstrate the decomposition of conical refraction correlation functions into well-known conical refraction coherent modes for a Gaussian Schell-model source. Assuming randomness of the electrical field phase of the input beam, we reformulated and significantly simplified the rigorous conical refraction theory. This approach allows us to consider the propagation of light through a conical refraction crystal in exactly the same way as in the classical case of coherent radiation. Having this in hand, we derive analytically the conical refraction intensity both in the focal plane and in the far field, which allows us to explain and rigorously justify earlier experimental findings and predict new phenomena. The last include the counterintuitive effect of narrowing of the conical refraction ring width, disappearance of the dark Poggendorff’s ring in the Lloyd’s plane, and shift of Raman spots for the low-coherent conical refraction light. We also demonstrate a universal power-law dependence of conical refraction cones coherence degree on the input correlation length and diffraction-free propagation of the low-coherent conical refraction light in the far field.

Generation of a higher-order Poincaré sphere beam array with spatial coherence engineering

We propose a protocol to synthesize a class of vector beam array in the far field with periodic higher-order Poincaré sphere (HOPS) polarization states by engineering the second-order spatial coherence structure of a partially coherent light source. We show that the polarization state of a single HOPS beam at the source plane can be mapped into a beam array in the far field when the spatial coherence of the beam source is engineered to have a lattice-like distribution. We demonstrate that the degree of polarization of the generated HOPS beam array can be conveniently controlled by modulating the transverse spatial coherence width of the source. Our method provides an additional way to construct the structured beam array and may find applications, e.g., in multiparticle manipulations.

Radially polarized cosine non-uniformly correlated beams and their propagation properties

We introduce a kind of radially polarized partially coherent (RPPC) beam with a prescribed non-uniform correlation function, called a radially polarized cosine non-uniformly correlated (RPCNUC) beam. Based on the extended Huygens-Fresnel principle, we study the propagation properties in free space and in a turbulent atmosphere. Unlike RPPC beams with uniform coherence, RPCNUC beams possess the invariance of dark hollow cores and radial polarization, and exhibit self-focusing properties. In a turbulent atmosphere, the intensity distribution demonstrates self-healing properties over a certain propagation distance. We also investigate how to adjust the beam parameters to reduce the turbulence-induced degradation in detail.

Measurement of the coherence-orbital angular momentum matrix of a partially coherent beam

The recently introduced coherence-orbital angular momentum (COAM) matrix of a partially coherent beam [Phys. Rev. A103, 023529 (2021)10.1103/PhysRevA.103.023529] is experimentally measured for the first time, to the best of our knowledge. The new methodology based on Young's interference experiment with a pair of ring-shaped slits with embedded spiral phases is thoroughly described. By introducing the phase shift of 0 and π / 2 between two ring slits, the real and imaginary parts of the elements of the COAM matrix are obtained by measuring the on-axis spectral density in the far field of the double-ring slit. We validate our protocol through measuring the COAM matrix of an elliptical Gaussian Schell-model (GSM) beam which reveals the existence of non-trivial correlations between modes with different topological indices. The experimental results agree reasonably well with the theoretical predictions.

Statistical properties of a partially coherent vector beam with controllable spatial coherence, vortex phase, and polarization

We report on a partially coherent radially polarized power-exponent-phase vortex (PC-RP-PEPV) beam with various distributions of intensity, controllable coherence width, vortex phase, and polarization. The statistical properties of the PC-RP-PEPV beam depend on topological charge, power order, polarization states, and coherence width, which differ from those of conventional radially polarized beams. Here, the initial radial polarization state will transform to complex ellipse polarization state during propagation. By modulating the topological charge of the PC-RP-PEPV beam, the intensity structure of the beam can be adjusted from circular to polygonal. Finally, PC-RP-PEPV beams were experimentally generated, and were consistent with numerical simulation results. This work has applications in optical manipulation, optical measurements, and optical information processing.

Super cosh-Gauss nonuniformly correlated radially polarized beam and its propagation characteristics

In this paper, a new kind of partially coherent vector beam termed as super cosh-Gauss nonuniformly correlated radially polarized (SCNRP) beam is introduced. Such beam source exhibits almost perfect coherence between two points that are within the beam center region or located on a ring concentric with the beam center. However, the coherence drops or even vanishes when the two points leave the central region and are located on the concentric rings with different radii. The second-order statistical properties, such as the spectral density, the state of polarization (SOP), and the degree of polarization (DOP) of such beam upon free-space propagation are studied through numerical examples. Our results reveal that the beam displays a self-focusing property during propagation. The focusing ability can be enhanced with increasing the beam index and decreasing the beam's spatial coherence width, whereas the DOP and SOP remain unchanged on propagation. Meanwhile, we establish an experimental system with the use of a radial polarization converter and a digital micro-mirror device to synthesize the SCNRP beam with controllable beam index and spatial coherence width. The spectral density and polarization properties of the synthesized beam during propagation are measured and analyzed in the experiment. The experimental results agree well with our theoretical predictions.

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.

Degree of paraxiality of a twist electromagnetic Gaussian Schell-model beam

The definition of the degree of paraxiality (DOP) for a stochastic electromagnetic field is applied to a twist stochastic electromagnetic field. As an illustrative example, DOP for a wide class of model stochastic fields, i.e., twist electromagnetic Gaussian Schell-model (TEGSM) fields, is discussed. The dependence of the DOP of the light source on its properties is also studied in detail. The numerical results show that the DOP of a TEGSM beam is determined by the rms widths of auto-correlation functions and the twist factor as well as by the degree of polarization. To explain the behavior of DOP, the far-field divergence angle of this beam source is also discussed.

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.

Self-focusing propagation characteristics of a radially-polarized beam in nonlinear media

In this study, an analytical formula for the self-focusing length of a radially polarized beam (RPB) is first derived, which has a similar behavior to the semi-empirical Marburger formula of a Gaussian beam, and is beneficial to quantitatively and qualitatively analyze practical experimental scenarios. However, the relation of the self-focusing length with the states of polarization (SoPs) was evaluated, and it was found that RPB with spatially inhomogeneous SoP at the field cross-section can retain a further self-focusing length compared to a beam with a spatially homogeneous one. The influence of the topological charge on the self-focusing length is explored, which shows that RPB with a low topological charge can achieve a high-power density at a relatively further receiver plane. Therefore, it is demonstrated that the RPB as a laser source not only extends the self-focusing length, but also improves the power density of the target. With the help of RPB, it is possible to realize a controllable self-focusing length and a high target optical power density, which may have potential applications in fine optical manipulation, optical communication, high-power long-range laser atmospheric propagation, and related areas.

Fast calculation of orbital angular momentum flux density of partially coherent Schell-model beams on propagation

Optical coherence has recently become a degree of freedom to modulate the orbital angular momentum (OAM) flux density of a partially coherent beam during propagation. However, the calculation of the OAM flux density for the partially coherent beam involves partial differential and four-dimensional integral operations, which poses drawbacks for its fast numerical calculations. In this paper, we present an efficient numerical protocol for calculating the OAM flux density of any partially coherent Schell-model beam propagating through a paraxial ABCD optical system by only adopting two-dimensional (2D) Fourier transforms. The general formalism is established in detail for the fast numerical calculation of the OAM flux density. It is found that the operation number in the developed algorithm is independent on the spatial coherence states of the beam. To demonstrate the validity of our algorithm, we calculate the OAM flux density of the partially coherent Laguerre-Gaussian beams during propagation with both the analytical and numerical methods. The obtained results are consistent well with each other. Moreover, the OAM flux density properties of two other classes of Schell-model beams, having no analytical solutions, are investigated as the specific examples. Our method provides a convenient way for studying the correlation-induced OAM density changes for any Schell-model beam propagation through a paraxial optical system.

On z-coherence in self-focusing

Both the intensity distribution and the degree of coherence between pairs of points along the propagation axis (z-coherence) are derived in closed form for a phenomenon of self-focusing produced by circularly coherent light. The first confirms results previously obtained numerically, while the second exhibits new complex features. The physical interpretation is obtained by a suitable pseudo-modal expansion that suggests an analogy with a simple two-mode structure.

Orientation-selective sub-Rayleigh imaging with spatial coherence lattices

The Rayleigh resolution criterion sets the minimum separation for two-point objects to be distinguishable in a classical optical imaging system. We demonstrate that the sub-Rayleigh resolution can be achieved in a telecentric imaging system with the help of a partially coherent illumination whose spatial coherence has lattice-like distribution. We show that the orientation-selective sub-Rayleigh imaging can be realized by controlling the spatial distribution of the coherence lattice into different symmetries. We carry out a proof-of-principle experiment to demonstrate the orientation-selective sub-Rayleigh imaging for a 1951 USAF resolution target. Our results indicate a flexible orientation-selective high-resolution imaging with spatial coherence engineering of the partially coherent light.

Radially polarized twisted partially coherent vortex beams

We introduce a new type of partially coherent vector beam, named the radially polarized twisted partially coherent vortex (RPTPCV) beam. Such a beam carries the twist phase and the vortex phase simultaneously, and the initial state of polarization (SOP) is radially polarized. On the basis of the pseudo-modal expansion and fast Fourier transform algorithm, the second-order statistics such as the spectral density, the degree of polarization (DOP) and the SOP, propagation through a paraxial ABCD optical system are investigated in detail through numerical examples. The results reveal that the propagation properties of the RPTPCV beam closely depends on the handedness of the twist phase and the vortex phase. When the handedness of the two phases is same, the beam profile is easier to remain a dark hollow shape and the beam spot rotates faster during propagation, compared to the partially coherent vortex beam or the RPTPCV beam with the opposite handedness of the two phases. In addition, the same handedness of two phases resists the coherence induced de-polarization of the beam upon propagation, and the SOP is also closely related to the handedness, topological charge of the vortex phase and the twist factor of the twist phase, providing an efficient way to modulate the beam's DOP and SOP in the output plane. Moreover, we establish an experiment setup to generate the RPTPCV beam. The average spectral density and the polarization properties are examined in the experiment. The experimental results agree reasonable well with the theoretical predictions. Our results will be useful for particle manipulating, free-space optical communications, and polarization lidar systems.

Scattering of Partially Coherent Vector Beams by a Deterministic Medium Having Parity-Time Symmetry

We study the scattering properties of the partially coherent vector beams with the deterministic media having the classic symmetric and parity-time (PT) symmetric scattering potential functions. The closed-form expressions for the intensity and polarization matrix of the far-zone scattered field are obtained, under first-order Born approximation, when the partially coherent vector beams are taken to be radially polarized and the deterministic media are assumed as the four-point scatterers. We demonstrate both analytically and numerically that the far-zone scattered field becomes noncentrosymmetric and the directionality appears in the scattering pattern when the scattering potential function is switched from classic symmetry to PT symmetry. We show the effect of spatial coherence of the incident partially coherent vector beam on the directionality in scattering. We find that by turning the symmetry property of the spatial coherence function of the incident beam, i.e., into PT symmetry, the directionality in the far-zone scattering can be suppressed or enhanced, depending on the joint effect from the symmetry of the scattering potential and the symmetry of the spatial coherence. Our findings may be useful in the application of dynamic control of the directionality in light scattering.

Enhanced fiber-coupling efficiency via high-order partially coherent flat-topped beams for free-space optical communications

The fiber-coupling efficiency of signal beams is crucial in free space optical (FSO) communications. Herein, we derived an analytical expression for the fiber-coupling efficiency of partially coherent flat-topped beams propagating through atmospheric turbulence based on the cross-spectral density function. Our numerical calculation results showed that the fiber-coupling efficiency of partially coherent flat-topped beams in a turbulent atmosphere could be enhanced by increasing the beam order. Under the same conditions, the fiber-coupling efficiency of the high-order partially coherent flat-topped beams was larger than those connected to the Gaussian and Gaussian Schell-model (GSM) beams. Our results will improve the quality of partially coherent beams used in FSO communications.

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.

Analysis and experimental demonstration of propagation features of radially polarized specific non-uniformly correlated beams

With the development of the unified theory of coherence and polarization, the novel physical properties generated by different correlation structures of vector partially coherent beams (PCBs) have attracted much attention. Recently, a new class of structured beams have been proposed [Opt. Lett.45, 3824 (2020)10.1364/OL.397316], called vector specific non-uniformly correlated beams. These beams combine non-uniform polarization and non-uniform correlation, and they exhibit propagation features not seen in conventional vector PCBs. In this Letter, we continue the analysis of the previous work, taking radially polarized Hermite non-uniformly correlated (RPHNUC) beams as an example, and focus on the physical interpretation of the peculiar propagation features of such beams. We verify the predicted behavior of RPHNUC beams through experiment.

Second-order statistical properties of conjugate mode "double-H" partially coherent beams in turbulence

We present an analysis of the propagation properties of a recently introduced class of conjugate mode partially coherent beams (called "double-H" beams) in a turbulent atmosphere using the extended Huygens-Fresnel integral. We investigate how the phase constant φ₀ between the modes plays a role in controlling the evolution of the intensity distribution and resisting the degradation effects of the atmosphere. Our results indicate that this new class of structured beams provides a new degree of freedom for controlling the shape of the beams and improves turbulence resistance, with potential application in free-space optical communications.

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.

Simultaneous measurement of orbital angular momentum spectra in a turbulent atmosphere without probe beam compensation

In free-space optical (FSO) communications, the orbital angular momentum (OAM) multiplexing/demultiplexing of Bessel beams perturbed by atmospheric turbulence is of great significance. We used the Gerchberg-Saxton algorithm without a beacon beam to compensate for the aberrant helical phase of the Bessel beam distorted by the turbulent atmosphere. The optical vortex Dammann axicon grating was applied for the simultaneous measurement of the intensities of the demodulated spectra of the OAM modes of the Bessel beams disturbed by atmospheric turbulence. The experimental results demonstrate that the distorted phase of the Bessel beam can be compensated and the mode purity of the target OAM mode is enhanced from 0.85 to 0.92 in case of weak turbulence. Our results will improve the quality of the OAM modes of Bessel beam (de)multiplexing in FSO communication systems.

Deep diamond single-photon sources prepared by a femtosecond laser

Nitrogen-vacancy color centers (NVs) in diamond have several potential applications ranging from quantum computing to data storage. However, artificial NVs are often close to the surface, which limits their spatial density and applicability. Here we demonstrate an effective and precise method for preparing deep single NVs in diamond. The method is based on a spatial-shaped femtosecond laser to overcome laser defocus in high-refractive materials, and realizes the preparation of single NVs at 95 µm. In addition, owing to the good energy distribution of the shaped laser focus, the single NVs exhibit a statistic yield of 56%±11% with excellent qualities. This processing method will contribute to the integration of color centers with emerging optical elements and high-density data storage.

Photopolymerization strategy for the preparation of small-diameter artificial blood vessels with micro-nano structures on the inner wall

Although large diameter vessels made of polyurethane materials have been widely used in clinical practice, the biocompatibility and long-term patency of small diameter artificial vessels have not been well addressed. Any technological innovation and advancement in small-diameter artificial blood vessels is of great interest to the biomedical field. Here a novel technique is used to produce artificial blood vessels with a caliber of less than 6 mm and a wall thickness of less than 0.5 mm by rotational exposure, and to form a bionic inner wall with a periodically micro-nano structure inside the tube by laser double-beam interference. The polyethylene glycol diacrylate used is a widely recognized versatile biomaterial with good hydrophilicity, biocompatibility and low cytotoxicity. The effect of the bionic structure on the growth of hepatocellular carcinoma cells and human umbilical vein endothelial cells was investigated, and it was demonstrated that the prepared vessels with the bionic structure could largely promote the endothelialization process of the cells inside them.

Airy beams on incoherent background

We present a class of diffraction-free partially coherent beams, each member of which comprises a finite-power, non-accelerating Airy bump residing on a statistically homogeneous, Gaussian-correlated background. We examine free-space propagation of soft apertured realizations of the proposed beams and show that their evolution is governed by two spatial scales: the coherence width of the background and the aperture size. A relative magnitude of these factors determines the practical range of propagation distances over which the novel beams can withstand diffraction. The proposed beams can find applications to imaging and optical communications through random media.

Synthesis of vector nonuniformly correlated light beams by a single digital mirror device

We present a stable and flexible way to generate the vector nonuniformly correlated (NUC) beams with a compact optical system that involves only a single digital mirror device and a common-path interferometer. The system provides near real-time generation and accurate control of the phase difference between the orthogonal field components of the vector NUC beams. We discuss the methodology based on the vectorial pseudo-mode decomposition of the cross-spectral density matrix of the beam. The method is validated by experimentally generating a class of vector NUC beams, named electromagnetic cosh-Gauss NUC beams, which have not been previously synthesized. Such beams display self-focusing feature on propagation and can reduce to different types of scalar NUC beams by selecting out the linearly polarized components at different polarization angles.

Propagation properties of phase-locked radially-polarized vector fields array in turbulent atmosphere

Owing to the increasing demand for information transmission, the information capacity of free-space optical communications must be increased without being significantly affected by turbulence. Herein, based on a radially-polarized vector field array, analytical formulae for three parameters are derived: average intensity, degree of polarization, and local states of polarization (SoPs). Propagation properties varying with propagation distance, strength of turbulence, beam waist, and beamlet number are investigated. In particular, the results show that the sign of local SoPs on different receiver planes is consistent with that of the source field, and that the SoPs remain constant at specific locations as the propagation distance increases; hence, the effect of turbulence on local SoPs is slight. Meanwhile, three different SoPs, i.e., linear, right-handed, and left-handed rotation polarizations, appear at corresponding locations, thereby enabling the channel capacity to be increased. This study may not only provide a theoretical basis for vector beam array propagation in a turbulent environment, but also propose a feasible solution for increasing the channel capacity and reliability to overcome challenges in a free-space link. Additionally, this study may benefit potential applications in laser lidar and remote sensing.