Partially coherent sources with radial coherence

Coherence in the radial degree of freedom

Coherence quantifies the statistical fluctuations in an optical field and has been extensively studied in the space, time, and polarization degrees of freedom. In the context of space, coherence theory has been formulated between two transverse positions as well as between two azimuthal positions, referred to as transverse spatial coherence and angular coherence, respectively. In this paper, we formulate the theory of coherence for optical fields in the radial degree of freedom and discuss the associated concepts of coherence radial width, radial quasi-homogeneity, and radial stationarity with some physically realizable examples of radially partially coherent fields. Furthermore, we propose an interferometric scheme for measuring radial coherence.

Partially coherent spherical sources with spherical harmonic modes

A class of partially coherent spherical sources is introduced whose cross-spectral density across the surface has a modal expansion made up of spherical harmonics. For such sources, the solution of the propagation problem in all the outer spaces can be written through a series of the propagated modes, which maintains the spherical harmonic structure. The main features of this class of cross-spectral densities are derived illustrating their coherence properties with examples. Attention is paid to the properties of radial coherence. In particular, it is clearly shown that sources with perfect radial coherence exist with angular coherence that is only partial.

Research on NCFCP compact broadband NIR detector imaging and energy transfer function

Nonlinear crystal frequency conversion imaging with direct detection by silicon-based detectors is an effective way to break through the limitations for existing near-infrared (NIR) detectors with expensive cost and high noise. In this paper, a broadband NIR detector imaging scheme based on the principle of nonlinear crystal frequency conversion (NCFCP) was proposed. A thin film of nonlinear crystal frequency conversion material (NCFCM) combined with a silicon-based detector was used to form a broadband NIR detector. The theoretically investigated energy transfer function was used as a guidance for experiment. Meanwhile, the relationship between the imaging effect and the energy transfer of the NCFCP-based compact broadband NIR detector in the NIR band was measured experimentally. The accuracy of the theoretical study had been verified by the measured transfer results.

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.

Special correlation model sources producing a self-focusing field

We evaluate the modes for non-Schell-model sources whose degrees of spectral coherence depend on the difference of the special function values of the position coordinated of two points. It is shown that such sources modulated by various function possess different spatial coherence properties, and cause them to produce the self-focusing fields with different characteristics. The results suggest a convenient method for modeling novel classes of partially coherent self-focusing optical fields.

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.

Optical coherence encryption with structured random light

Information encryption with optical technologies has become increasingly important due to remarkable multidimensional capabilities of light fields. However, the optical encryption protocols proposed to date have been primarily based on the first-order field characteristics, which are strongly affected by interference effects and make the systems become quite unstable during light-matter interaction. Here, we introduce an alternative optical encryption protocol whereby the information is encoded into the second-order spatial coherence distribution of a structured random light beam via a generalized van Cittert-Zernike theorem. We show that the proposed approach has two key advantages over its conventional counterparts. First, the complexity of measuring the spatial coherence distribution of light enhances the encryption protocol security. Second, the relative insensitivity of the second-order statistical characteristics of light to environmental noise makes the protocol robust against the environmental fluctuations, e.g, the atmospheric turbulence. We carry out experiments to demonstrate the feasibility of the coherence-based encryption method with the aid of a fractional Fourier transform. Our results open up a promising avenue for further research into optical encryption in complex environments.

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.

Experimental synthesis of partially coherent sources

A flexible pseudo-mode sampling superposition method for synthesizing partially coherent sources has been introduced that can be thought of as an approximate discrete representation of Gori's nonnegative definiteness criterion for designing spatial correlation functions. Importantly, without performing formidable mode analysis, this method enables us to develop a convenient and efficient experimental technology to customize partially coherent sources without sacrificing theoretical accuracy. As an example, we experimentally generate a new, to the best of our knowledge, class of nontrivial pseudo-Schell model sources recently proposed by de Sande et al. Our approach opens up a useful avenue for manipulating nontrivial partially coherent beams and promotes applications for optical tweezers and photolithography.

Propagation of temporal coherence gratings in dispersive medium with a chirper

In this paper, the propagation of Temporal Coherence Grating (TCG) pulse trains in a dispersive medium with a chirp is investigated for the first time. The two-time mutual coherence function of the TCG pulse trains propagating through extended dispersive medium specified by temporal ABCD matrix is derived and the evolution of their mean intensity and temporal degree of coherence (DOC) is explored. It is shown that the distribution of the mean intensity can be modulated freely by the number of grating lobes N, grating constant a, pulse duration T₀, power distributions vn, group-velocity dispersion coefficient β₂ and the medium chirper s. Upon dispersive-medium propagation, the single pulse splits into N+1 subpulses with the same or different peak intensities which depend on power distributions vn. What's more, during the propagation the pulse self-focusing occurs being the chirp-induced non-linear phenomenon. And the distribution of temporal DOC will degenerate into Gaussian form from initial periodic coherence distribution with increasing propagation distance z or adjusting incident pulse parameters and medium dispersion. The physical explanation and numerical illustrations relating to the pulse behavior are included.

Random source for generating Airy-like spectral density in the far field

A stationary beam forming an Airy-like spectral density in the far field is analyzed theoretically and experimentally. The Schell-model source that radiates such a beam is an extended version of a recently introduced source [O. Korotkova, et al., Opt. Lett.43, 4727 (2018)10.1364/OL.43.004727; X. Chen, et al., Opt. Lett.44, 2470 (2019)10.1364/OL.44.002470, in 1D and 2D, respectively]. We show, in particular, that the source degree of coherence, being the fourth-order root of a Lorentz-Gaussian function and having linear and cubic phase terms, may be either obtained from the Fourier transform of the far-field Airy-like pattern or at the source using the sliding function method. The spectral density of the beam is analyzed on propagation through paraxial ABCD optical systems, on the basis of the generalized Collins integral, by means of the derived closed-form expression. We show that the distribution of the side lobes in the Airy beam spectral density can be controlled by the parameters of the source degree of coherence. Further, an experiment involving a spatial light modulator (SLM) is carried out for generation of such a beam. We experimentally measure the complex degree of coherence of the source and observe the gradual formation of a high-quality Airy-like spectral density towards the far field. In addition, the trajectory of the intensity maxima of the beam after a thin lens is studied both theoretically and experimentally. The random counterpart of the classic, deterministic Airy beam may find applications in directed energy, imaging, beam shaping, and optical trapping.

Besinc Pseudo-Schell Model Sources with Circular Coherence

Partially coherent sources with non-conventional coherence properties present unusual behaviors during propagation, which have potential application in fields like optical trapping and microscopy. Recently, partially coherent sources exhibiting circular coherence have been introduced and experimentally realized. Among them, the so-called pseudo Schell-model sources present coherence properties that depend only on the difference between the radial coordinates of two points. Here, the intensity and coherence properties of the fields radiated from pseudo Schell-model sources with a degree of coherence of the besinc type are analyzed in detail. A sharpening of the intensity profile is found for the propagated beam by appropriately selecting the coherence parameters. As a possible application, the trapping of different types of dielectric nanoparticles with this kind of beam is described.

Self-steering partially coherent vector beams

We introduce a class of self-steering partially coherent vector optical beams with the aid of a generalized complex Gaussian representation. We show that such partially coherent vector beams have mobile guiding centers of their intensity and polarization state distributions on the beam free space propagation that could be employed to generate far-field polarization arrays. Further, we introduce theoretically and realize experimentally a class of vector beams with inhomogeneous statistical and nontrivial far-field angular distributions, which we term cylindrically correlated partially coherent (CCPC) vector beams. We find that such novel beams possess, in general, cylindrically polarized, far-field patterns of an adjustable degree of polarization. The steering control of the intensity and polarization of the self-steering CCPC vector beam is also demonstrated in experiment. Our findings can find important applications, such as trapping of neutral microparticles and excitation of novel surface waves.

Experimental realization of dark and antidark diffraction-free beams

We report the first, to the best of our knowledge, experimental realization of high-quality dark and antidark diffraction-free beams, first theoretically proposed by Ponomarenko et al. [Opt. Lett.32, 2508 (2007)OPLEDP0146-959210.1364/OL.32.002508]. Our method employs a single spatial light modulator (SLM) and is based on superposing mutually uncorrelated but spatially coherent in the time domain Bessel modes with modal weights proportional to the SLM display times of the corresponding modes. We also experimentally verify diffraction-free properties of the generated beams upon their free space propagation.

Hyperbolic sine-correlated beams

An explicit expression is given for the cross-spectral density that characterizes a new family of partially coherence sources with hyperbolic sine correlated function. Beam conditions for such sources are established. The propagation properties of such partially coherent beams are studied by numerical simulations. It is demonstrated that, unlike the reciprocity theorems relating to radiation from classical Schell-model sources, such beams possess both the invariance of coherent distribution and of hollow intensity shape.

Pseudo-Schell model sources

Partially coherent pseudo-Schell model sources are introduced and analyzed. They present radial symmetry and coherence characteristics depending on the difference between the radial distances of two points from the source center. As a consequence, all points belonging to circles centered on the symmetry center of the source are perfectly correlated. We show that such sources radiate fields with peculiar behaviors in paraxial propagation. In particular, when compared to beams produced by Gaussian Schell-model sources with comparable coherence parameters, their irradiance can present sharper profiles and higher peak valuesmono and a better beam quality parameter. Furthermore, when a pseudo-Schell model source presents a vortex, the propagated beam preserves a null of the intensity along its axis.

Generation of an Adjustable Optical Cage through Focusing an Apertured Bessel-Gaussian Correlated Schell-Model Beam

An adjustable optical cage generated by focusing a partially coherent beam with nonconventional correlation function named the Bessel–Gaussian correlated Schell-model (BGCSM) beam is investigated in detail. With the help of the generalized Huygens–Fresnel integral and complex Gaussian function expansion, the analytical formula of the BGCSM beam passing through an apertured ABCD optical system was derived. Our numerical results show that the generated optical cage can be moderately adjusted by the aperture radius, the spatial coherence width, and the parameter β of the BGCSM beam. Furthermore, the effect of these parameters on the effective beam size and the spectral degree of coherence were also analyzed. The optical cage with adjustable size can be applied for particle trapping and material thermal processing.

Propagation characteristics of partially coherent circular Airy beams

The abruptly autofocusing properties of partially coherent circular Airy beam (CAB) with different spatial coherent length are theoretically investigated in this paper. It is found that, as spatial coherent length decreases, the size of the focal spot would increase and the focal intensity would decrease. But the abruptly autofocusing property for partially coherent CAB is still quite obvious, when comparing with the common partially coherent Gaussian beam under the same conditions; and its autofocusing position is less easily influenced by coherence. The influences of initial radius r₀ and decaying parameter a on the autofocusing property have also been investigated in the end.