Free-space propagation of optical coherence lattices and periodicity reciprocity

Switchable optical ring lattice in free space

Optical lattices with spatially regular structures have recently attracted considerable attention across physics and optics communities. In particular, due to the increasing emergence of new structured light fields, diverse lattices with rich topology are being generated via multi-beam interference. Here, we report a specific ring lattice with radial lobe structures generated via superposition of two ring Airy vortex beams (RAVBs). We show that the lattice morphology evolves upon propagation in free space, switching from a bright-ring lattice to dark-ring lattice and even to fascinating multilayer texture. This underlying physical mechanism is related to the variation of the unique intermodal phase between the RAVBs as well as topological energy flow with symmetry breaking. Our finds provide an approach for engineering customized ring lattices to inspire a wide variety of new applications.

Theoretical study on the diffraction-based generation of a 2D orthogonal lattice of optical beams: physical bases and application for a vortex beam multiplication

A comprehensive theoretical study on the generation of a 2D orthogonal lattice of optical beams based on the near-field diffraction and Talbot effect is presented. First we investigate the near-field diffraction of an optical beam with a finite lateral extension from an infinite 2D orthogonal grating. It is shown that the resulting diffraction patterns over the Talbot planes depend on the following parameters: the period and opening ratio (OR) of the grating, wavelength and spatial spectral bandwidth of the incident beam, and the propagation distance. In terms of these parameters, we find multiplication conditions: the certain conditions under which a 2D orthogonal lattice of the Fourier transform of the incident beam is generated on the Talbot planes. Therefore, if the incident beam is Fourier-invariant and all the established multiplication conditions are fulfilled, the intensity profile of each of the individual Talbot images resembles the intensity profile of the incident beam. We consider the Laguerre-Gaussian beams having zero radial index as an important class of the vortex beams. We explicitly show that these beams are Fourier-invariant and we calculate their spatial spectral bandwidth. As a result, in the illumination of a 2D orthogonal binary grating with this kind of vortex beam, a 2D orthogonal lattice of the incident optical vortex is generated at the Talbot planes. Considering the obtained multiplication conditions, for the first time, to our knowledge, we determine a multiplication interval. This interval covers the propagation distances at which the vortex beam multiplication occurs. Moreover, we obtain the maximum possible value of the grating's OR for the realizations of the vortex multiplication. It is shown that both the multiplication interval and the maximum value of the OR depend on the topological charge (TC) of the incident beam. With the aid of some practical examples and defining a multiplication quality factor, the mentioned results are verified quantitatively. In addition to the vortex beam multiplication effect, we consider another interesting phenomenon that results from the interference of the grating's first diffraction orders. We call this phenomenon the first diffraction orders interference (FDOI) effect. We show that both the multiplication and the FDOI effects occur simultaneously but at different propagation distances. It is also shown that the multiplication and FDOI intervals separate and distance from each other by increasing the TC of the incident beam.

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.

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.

Hollow rectangular multi-Gaussian Schell-model source

We introduced a new class of a partially coherent source that can generate a field with a hollow rectangular profile, named the hollow rectangular multi-Gaussian Schell-mode source. The dependence of distribution of far-zone spectral density on the properties of the proposed source was analyzed. The results show that one can control the distribution properties of the far-zone intensity profile, including the thickness of the hollow edge, the shape of the hollow, the size of the hollow, and the orientation of the hollow, by adjusting the corresponding structural parameters of the source.

Random sources generating hollow array beams

A novel class of partially coherent light sources that can yield stable optical lattice termed hollow array in the far field is introduced. The array dimension, the distance of hollow lobes intensity profile, the size and shape of the inner and outer lobe contours and other features can be flexibly controlled by altering the source parameters. Further, every lobe can be shaped with polar and Cartesian symmetry and even combined to form nested structures. The applications of the work are envisioned in material surface processing and particle trapping.

Generation of novel partially coherent truncated Airy beams via Fourier phase processing

We propose theoretically and numerically, for the first time, the generation of novel partially coherent truncated Airy beams (NPCTABs) with Airy-like distributions for both intensity and degree of coherence via Fourier phase processing. We demonstrate a clear link between the magnitude and frequency of intensity and degree of coherence distributions oscillations of generated beams, and the source coherence and the phase screen parameter. Thus, the source coherence and phase can serve as convenient parameters to control the intensity and degree of the coherence of NPCTABs. Furthermore, we discover that NPCTABs are more stable than the fully coherent truncated Airy beams (FCTABs) during their propagation in free space and can maintain their Airy-like profile for an extended propagation distance. The interesting and tunable characteristics of these novel beams may find applications in particle trapping, phase retrieval, and optical imaging.

Vortex preserving statistical optical beams

We establish a general form of the cross-spectral density of statistical sources that generate vortex preserving partially coherent beams on propagation through any linear ABCD optical system. We illustrate our results by introducing a class of partially coherent vortex beams with a closed form cross-spectral density at the source and demonstrating the beam vortex structure preservation on free space propagation and imaging by a thin lens. We also show the capacity of such vortex preserving beams of any state of spatial coherence to trap nanoparticles with the refractive index smaller than that of a surrounding medium.

Statistical properties of a controllable partially coherent radially and azimuthally polarized rotating elliptical Gaussian optical coherence lattice in anisotropic ocean turbulence

The optical coherent lattice (OCL) with periodic reciprocity has been previously proposed for free-space information transfer and optical communications. Here, a new class of partially coherent radially and azimuthally polarized rotating elliptical Gaussian optical coherent lattice (PCRPREGOCL and PCAPREGOCL) is introduced. Based on the extended Huygens-Fresnel principle and the spatial power spectrum of the anisotropic ocean turbulence, the analytical expressions of the average intensity of the PCRPREGOCL and the PCAPREGOCL through the anisotropic ocean turbulence are obtained. The effects of elliptical coefficients, lattice constants, the number of lattice lobes, wavelengths and anisotropic ocean turbulence parameters on the statistical properties of the PCRPREGOCL and the PCAPREGOCL are studied in detail. It is found that each sub-pattern in the PCRPREGOCL maintains a controllable rotation within a certain distance, which plays an important role in resisting the influence of turbulence. When the propagation distance increases, the PCRPREGOCL and the PCAPREGOCL gradually change from two elliptical Gaussian patterns into a coherent array with periodic reciprocity and eventually evolves into a Gaussian-like pattern. Our work provides new thoughts in applying OCL to overcome turbulence influence in underwater optical communication and underwater laser radar.

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.

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 and Propagation of a Hermite-Gaussian Correlated Schell-Model LG0l Beam

A partially coherent beam under the combined action of a Hermite-Gaussian correlated function and vortex phase, named the HGCSMLG0l beam has been explored both theoretically and experimentally. The statistical properties, such as the intensity and distribution of the degree of coherence (DOC) on propagation are analyzed in detail, based on the deduced equations. We find that the intensity is determined dominantly by the non-conventional correlated function when the coherence length is comparatively small and by vortex phase when the coherence length is large. The modulus of the DOC is not vulnerable to coherence width, rather, it is affected by both non-conventional correlated function and vortex phase. Our results are verified well by the experiment results.

Measuring spatial coherence by using a lateral shearing interferometry

A modified lateral shearing interferometry is proposed to measure the spatial coherence of partially coherent light beams. This interferometry based on a 4f system consists of a diffraction grating and a spatial light modulator (SLM). In this system, the diffraction grating splits the partially coherent wave into two copied waves, forming a shearing interferogram on the observation plane. The period of the composite blazing grating generated by the phase-modulated SLM is flexibly tuned for controlling the lateral displacement of the two copied waves. The complex degree of spatial coherence of the partially coherent field is obtained through measurements and Fourier analysis of the fringe pattern.

Propagation of Optical Coherence Vortex Lattices in Turbulent Atmosphere

Propagation properties in the turbulence atmosphere of the optical coherence vortex lattices (OCVLs) are explored by the recently developed convolution approach. The evolution of spectral density distribution, the normalized M 2 -factor, and the beam wander of the OCVLs propagating through the atmospheric turbulence with Tatarskii spectrum are illustrated numerically. Our results show that the OCVLs display interesting propagation properties, e.g., the initial Gaussian beam distribution will evolve into hollow array distribution on propagation and finally becomes a Gaussian beam spot again in the far field in turbulent atmosphere. Furthermore, the OCVLs with large topological charge, large beam array order, large relative distance, and small coherence length are less affected by the negative effects of turbulence. Our results are expected to be used in the complex system optical communications.

Evolution properties of the radially polarized multi-Gaussian Schell-model beam in uniaxial crystals

The evolution properties of the normalized intensity distribution, the spectral degree of coherence (SDOC), and the spectral degree of polarization (SDOP) of the radially polarized multi-Gaussian Schell-model (MGSM) beam in uniaxial crystals are illustrated. Numerical results show that the intensity distribution of the radially polarized MGSM beam gradually evolves from a doughnut shape into an elliptical symmetric flattop shape and retains its elliptical flattop shape on further propagation in anisotropic crystals. The evolution behavior of the SDOC and SDOP for the radially polarized MGSM beam is quite different from that of the linearly polarized one. In addition, the influences of the spatial coherence length δ₀, beam index M, and the ratio of the extraordinary refractive index to the ordinary refractive index n_e/n_o of the uniaxial crystals on the evolution properties of the normalized intensity distribution, the SDOC, and the SDOP of the radially polarized MGSM beam are discussed in detail.

Rectangular Hermite non-uniformly correlated beams and its propagation properties

We introduce a new class of non-uniformly correlated beams that are called rectangular Hermite non-uniformly correlated (RHNUC) beams, which possess rectangular symmetry in their degree of coherence. It is shown that, in free space and in turbulence, these beams possess self-focusing properties and that the position of the focus can be adjusted in 3-D space by manipulating the correlation properties of the source. Furthermore, it is demonstrated that, by choosing different mode orders and correlation lengths along two transverse directions, one creates astigmatic beams that can be designed to have a high and near-constant intensity over an extended propagation range.

Propagation Characteristics of a Twisted Cosine-Gaussian Correlated Radially Polarized Beam

Recently, partially coherent beams with twist phases have attracted growing interest due to their nontrivial dynamic characteristics. In this work, the propagation characteristics of a twisted cosine-Gaussian correlated radially polarized beam such as the spectral intensity, the spectral degree of coherence, the degree of polarization, the state of polarization, and the spectral change are investigated in detail. Due to the presence of the twisted phase, the beam spot, the degree of coherence, and the state of polarization experience rotation during transmission, but the degree of polarization is not twisted. Meanwhile, although their rotation speeds closely depend on the value of the twist factor, they all undergo a rotation of π / 2 when they reach the focal plane. Furthermore, the effect of the twist phase on the spectral change is similar to the coherence, which is achieved by modulating the spectral density distribution during transmission. The twist phase opens up a useful guideline for manipulation of novel vector structure beams and enriches potential applications in the field of beam shaping, optical tweezers, optical imaging, and free space optical communications.

Coherence lattices in surface plasmon polariton fields

We explore electromagnetic coherence lattices in planar polychromatic surface plasmon polariton (SPP) fields. When the SPP constituents are uncorrelated-and thus do not interfere-coherence lattices arise from statistical similarity of the random SPP electromagnetic field. As the SPP correlations become stronger, the coherence lattices fade away, but the lattice structure reemerges in the spectral density of the field. The polarization states of the structured SPP lattice fields are also investigated. Controllable plasmonic coherence and spectral density lattices can find applications in nanophotonics, such as nanoparticle manipulation.

High-quality partially coherent Bessel beam array generation

We propose a protocol for generating high-quality, partially coherent (quasi-)Bessel beam arrays with controllable beam order and spatial distributions. Our protocol involves, apart from beam intensity shaping, coherence engineering of recently introduced optical coherence lattices. Our theoretical results are validated with the experimental realization of partially coherent Bessel beam arrays. The novel beam arrays are anticipated to be useful for multi-particle trapping and micromanipulation, optical metrology and microscopy, as well as for 3D imaging.

Average intensity and beam quality of optical coherence lattices in oceanic turbulence with anisotropy

Based on the extended Huygens-Fresnel principle, we have derived the analytical expression of the average intensity of optical coherence lattices (OCLs) in oceanic turbulence with anisotropy, and then the beam quality parameters including the Strehl ratio (SR) and the power-in-the-bucket (PIB) are obtained. One can find that the OCLs will eventually evolve into Gaussian shape with the periodicity reciprocity gradually breaking down when propagating through the anisotropic ocean water, and that the trend of evolving into Gaussian can be accelerated for increasing the ratio of temperature and salinity contributions to the refractive index spectrum ω, the lattice constant a and the rate of dissipation of mean square temperature χT or decreasing the anisotropic factor ξ and the rate of dissipation of turbulent kinetic energy per unit mass of fluid ε. Further, the SR and PIB in the target plane under the effects of oceanic parameters are discussed in detail, and the SR and PIB can be increased for the larger ξ and ε or the smaller χT and ω, namely, the beam quality becomes better. Our results can find potential application in the future optical communication system in an oceanic environment.

Optical coherence grids and their propagation characteristics

A novel class of partially coherent light sources termed optical coherence grids (OCGs) are introduced that can yield stable optical grids in the far field. The optical grids, of which the light distributes in a network of straight lines crossing each other to form a series of hollow cages, can be seen as a better controlled optical lattice. Propagation properties of OCG beams in free space, including spectral density, transverse coherence, and M² factor, are investigated in detail. It is interesting that a periodic grid pattern is produced at a distance and remains stable on further propagation, and we stress that the structure of far-field optical grids can be flexibly tuned by modulating the correlation parameters of the source. In addition, by performing convolution of degree of coherence, we also propose perfect optical coherence grids (POCG). The far-field grid pattern of POCG is in a fully controllable fashion. This work is expected to find applications in cooling atoms, trapping microscopic particles, or assembling cells, etc.

Complex Gaussian representations of partially coherent beams with nonconventional degrees of coherence

We adopt the recently introduced complex Gaussian function to expand the partially coherent beams with nonconventional degrees of coherence, and derive detailed representations of Hermite-Gaussian correlated Schell-model beam, elliptical Laguerre-Gaussian correlated Schell-model beam, and multi-Gaussian correlated Schell-model beam. Complex Gaussian representation of a partially coherent beam provides a convenient way for treating its propagation. As an application example, we explore the self-splitting properties of a Hermite-Gaussian correlated Schell-model beam propagating in a uniaxial crystal with the help of the complex Gaussian representation, and it is found that the uniaxial crystal can be used to control the splitting properties.

Propagation of multi-cosine-Laguerre-Gaussian correlated Schell-model beams in free space and atmospheric turbulence

We introduce a class of random stationary, scalar source named as multi-cosine-Laguerre-Gaussian-correlated Schell-model (McLGCSM) source whose spectral degree of coherence (SDOC) is a combination of the Laguerre-Gaussian correlated Schell-model (LGCSM) and multi-cosine-Gaussian correlated Schell-model (McGCSM) sources. The analytical expressions for the spectral density function and the propagation factor of a McLGCSM beam propagating in turbulent atmosphere are derived. The statistical properties, such as the spectral intensity and the propagation factor, of a McLGCSM beam are illustrated numerically. It is shown that a McLGCSM beam exhibits a robust ring-shaped beam array with adjustable number and positions in the far field by directly modulating the spatial structure of its SDOC in the source plane. Moreover, we provide a detailed insight into the theoretical origin and characteristics of such a ring-shaped beam array. It is demonstrated that these peculiar shaping properties are the concentrated manifestation of the individual merits respectively associated with the Laguerre- and multi-cosine-related factors of the whole SDOC. Our results provide a novel scheme to generate robust and controllable ring-shaped beam arrays over large distances, and will widen the potentials for manipulation of multiple particles, free-space optical communications and imaging in the atmosphere.

Interfering optical coherence lattices by use of a wavefront-folding interferometer

We investigate the properties of an interfering optical coherence lattice, which is generated by passing an optical coherence lattice through a wavefront-folding interferometer. Two symmetrical lattices are formed in the far-field. Changing the phase difference between the two optical paths causes the interference pattern, and thus the far-field intensity profile to change. In addition, we have shown that in the non-uniform case, the intensity pattern can also be changed by varying the weight distribution parameter. Our results may be applied in free-space communications and periodic trapping of micro-particles.

Vector optical coherence lattices generating controllable far-field beam profiles

We introduce partially coherent vector sources with periodic spatial coherence properties, which we term vector optical coherence lattices (VOCLs), as an extension of recently introduced scalar OCLs. We derive the realizability conditions and propagation formulae for radially polarized VOCLs (i.e., a typical kind of VOCLs). We show that radially polarized VOCLs display nontrivial propagation properties and generate controllable intensity lattices in the far zone of the source (or in the focal plane of a lens). By adjusting source coherence, one can obtain intensity lattices with bright or dark nodes. The latter can be employed to simultaneously trap multiple particles or atoms as well as in free-space optical communications. We also report the experimental generation of radially polarized VOCLs and we characterize VOCLs propagation properties.

Self-steering partially coherent beams

We introduce a class of shape-invariant partially coherent beams with a moving guiding center which we term self-steering partially coherent beams. The guiding center of each such beam evolves along a straight line trajectory which can be engineered to make any angle with the x-axis. We show that the straight line trajectory of the guiding center is the only option in free space due to the linear momentum conservation. We experimentally generate a particular subclass of new beams, self-steering Gaussian Schell beams and argue that they can find applications for mobile target tracing and trapped micro- and/or nanoparticle transport.

Complex degree of coherence measurement for classical statistical fields

We propose a new method for measuring real and imaginary parts of the complex degree of coherence of a classical field obeying Gaussian statistics. Our method is based on mixing incoherently a coherent Gaussian beam, a local oscillator, and the statistical field. We stress that our approach is especially beneficial for revealing the complex degree of coherence of inhomogeneous two-dimensional fields. As an illustration, we report the complex degree of the coherence measurement of a complex Gaussian-correlated beam. Our method can find applications in image transmission and recovery.

Self-reconstruction of partially coherent light beams scattered by opaque obstacles

Self-reconstruction refers to an ability of certain fully coherent optical beams to recover their spatial profiles after scattering by obstacles. In this communication, we extend the self-reconstruction concept to partially coherent beams. We show theoretically and verify experimentally that any partially coherent beam can self-reconstruct its intensity profile and state of polarization upon scattering from an opaque obstacle provided the beam coherence area is reduced well below the obstacle area. We stress that our self-reconstruction technique is independent of the obstacle shape and it is scalable to the case of multiple obstacles or even of inhomogeneous media as long as a characteristic obstacle area or a medium inhomogeneity scale is well in excess of the beam coherence area or length, respectively. We anticipate the technique to be instrumental in applications ranging from beam shaping to image transfer and trapped particle manipulation in turbid media.

Propagation of optical coherence lattices in the turbulent atmosphere

We explore the propagation of recently introduced optical coherence lattices (OCLs) in the turbulent atmosphere. We show that the lattice intensity profile and the spatial degree of coherence will display periodicity reciprocity over long propagation distances even though the lattices are affected by the turbulence. The lattice periodicity reciprocity has been previously conjectured to be advantageous for free-space information transfer and optical communications. We then show how one can increase the distance over which the lattice periodicity reciprocity is preserved in the turbulent atmosphere by engineering input lattice beam parameters. We also show that the OCLs have scintillation indices lower than those of Gaussian beams.

Vector Hermite-Gaussian correlated Schell-model beam

A new kind of partially coherent vector beam named vector Hermite-Gaussian correlated Schell-model (HGCSM) beam is introduced as a natural extension of recently introduced scalar HGCSM beam. The realizability and beam conditions for a vector HGCSM beam with uniform state of polarization (SOP) or non-uniform SOP are derived, respectively. Furthermore, analytical formulae for a vector HGCSM beam propagating in free space are derived, and the propagation properties of a vector HGCSM beam with uniform SOP or non-uniform SOP in free space are studied and analyzed in detail. We find that the behaviors of a vector HGCSM beam on propagation are quite different from those of a conventional vector partially coherent beam with uniform SOP or non-uniform SOP, and modulating the structures of the correlation functions cannot only modulate the intensity distribution, but also the state of polarization, the degree of polarization and the polarization singularities of a partially coherent vector beam on propagation. Furthermore, we report experimental generation of a radially polarized HGCSM beam for the first time. Our results provide a novel way for polarization modulation.

Second-order statistics of a radially polarized cosine-Gaussian correlated Schell-model beam in anisotropic turbulence

Recently, we introduced a new class of radially polarized cosine-Gaussian correlated Schell-model (CGCSM) beams of rectangular symmetry based on the partially coherent electromagnetic theory [Opt. Express23, 33099 (2015)]. In this paper, we extend the work to study the second-order statistics such as the average intensity, the spectral degree of coherence, the spectral degree of polarization and the state of polarization in anisotropic turbulence based on an extended von Karman power spectrum with a non-Kolmogorov power law α and an effective anisotropic parameter. Analytical formulas for the cross-spectral density matrix elements of a radially polarized CGCSM beam in anisotropic turbulence are derived. It is found that the second-order statistics are greatly affected by the source correlation function, and the change in the turbulent statistics induces relatively small effect. The significant effect of anisotropic turbulence on the beam parameters mainly appears nearα=3.1, and decreases with the increase of the anisotropic parameter. Furthermore, the polarization state exhibits self-splitting property and each beamlet evolves into a radially polarized structure in the far field. Our work enriches the classical coherence theory and may be important for free-space optical communications.

Electromagnetic Schell-model sources generating far fields with stable and flexible concentric rings profiles

A class of electromagnetic sources with multi-cosine Gaussian Schell-model correlation function is introduced. The realizability conditions for such sources and the beam conditions for the beams generated by them are established. Analytical formulas for the cross-spectral density matrix of such beams propagating in free space are derived and used to examine their statistical properties by numerical simulations. The results demonstrate that such beams possess invariant far-field concentric rings-like intensity patterns, uniform polarization state on all rings, and generally different degree of polarization values on different rings. By changing the summation index and other source parameters, the number of rings along with the behavior of various beam characteristics can be tuned at will.

Gaussian Schell-model arrays

We introduce a novel class of planar, quasi-homogeneous Schell-model source for producing far fields with optical lattice average intensity patterns and derive the corresponding beam conditions. The array dimension, lobes intensity profile, and periodicity of the optical lattice can be flexibly tuned by changing the correlation parameters of the source field. It is also found that, with an appropriate choice of the source parameters, the radiant intensity may possess flat-topped intensity patterns.

Coherent pseudo-mode decomposition of a new partially coherent source class

We introduce a new class of Schell-model temporal sources that admit a closed-form analytical decomposition in terms of coherent pseudo-modes. We explore the source mode and the corresponding eigenvalue structure and demonstrate that the lowest-order mode profile reflects the distribution of the source intensity as a function of time. We also examine the global degree of coherence of the class and show that it is virtually independent of the pulse intensity profile particulars at the source.

Shape-invariant difference between two Gaussian Schell-model beams

The difference between two Gaussian Schell-model cross-spectral densities can give a new genuine correlation function if suitable conditions are met. Generally speaking, the structure of such cross-spectral density changes in a complicated way upon propagation. We consider here the notable exception of shape-invariant beams, and we investigate their intensity and coherence properties. The modal analysis of this class of cross-spectral densities is exploited to devise a synthesis scheme for this type of beam.

Self-imaging of partially coherent light in graded-index media

We demonstrate that partially coherent light beams of arbitrary intensity and spectral degree of coherence profiles can self-image in linear graded-index media. The results can be applicable to imaging with noisy spatial or temporal light sources.