State Of Spatial Coherence Research Articles

Spectral scaling transformations of nonstationary light

We present optical systems, which transform isodiffracting nonstationary beams into fields obeying either cross-spectral purity or spectral invariance. The designs are hybrid refractive-diffractive imaging systems, which are able to perform the desired transformations over a broad spectral bandwidth and irrespective of the state of spatial coherence of the input beam.

Spatial coherence modulation using plane waves generated with a digital micromirror device

Plane waves generated and alternated using a Digital Micromirror Device (DMD) were evaluated for modulating the spatial coherence of a laser beam. The spatial coherence and its modulation can be represented as a sampling problem in the temporal domain. In this way, the integration time in the detector, the frame rate of the DMD, and the laser coherence time were properly adjusted or chosen to achieve the effect of a beam with a particular state of spatial coherence. Two methods were applied to superpose the plane waves and produce controlled visibility variations in the interferogram of a Young’s experiment. The visibility measurements show the variation of the modulus of the complex degree of spatial coherence, controlled by simple phase modulation, and between a pair of points on the wavefront. This procedure, which uses no mobile parts, could be applied in digital holography denoising, beam shaping, optical communications and optical metrology and imaging.

Linear Combinations of the Complex Degrees of Coherence

We propose a method for structuring the spatial coherence state of light via mixed linear combinations of N complex degrees of coherence (CDC) and specify the conditions under which such combinations represent a valid CDC. Several examples demonstrate that this method opens previously unknown avenues for modeling random sources, radiating to light fields with unique features.

Unified matrix representation for spin and orbital angular momentum in partially coherent beams

A matrix representation is introduced for stationary beam-like light fields that allows for simultaneous treatment of the orbital angular momentum (OAM) and the second-order state of spatial coherence. This Coherence-OAM matrix is a counterpart of the 2 x 2 beam Coherence-polarization matrix in a Cartesian polarization basis or Coherence-spin angular momentum (SAM) matrix in a circular polarization basis. The general properties of the Coherence-OAM matrix are discussed and then the Coherence-SAM-OAM matrix is introduced as a unifying entity for treating beams with any coherence, spin and orbital angular momentum states.

Correlation-induced orbital angular momentum changes

We demonstrate that the orbital angular momentum flux density of a paraxial light beam can change on propagation in free space. These changes are entirely due to the spatial coherence state of the source, and the effect is analogous to correlation-induced changes in the intensity, spectrum and polarization of a beam. The use of the source coherence state to control the width, shape, and transverse shifts of the OAM flux density is demonstrated with numerical examples.

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

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

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.

Spectrum of classes of point emitters of electromagnetic wave fields.

The spectrum of classes of point emitters has been introduced as a numerical tool suitable for the design, analysis, and synthesis of non-paraxial optical fields in arbitrary states of spatial coherence. In this paper, the polarization state of planar electromagnetic wave fields is included in the spectrum of classes, thus increasing its modeling capabilities. In this context, optical processing is realized as a filtering on the spectrum of classes of point emitters, performed by the complex degree of spatial coherence and the two-point correlation of polarization, which could be implemented dynamically by using programmable optical devices.

Spectrum of classes of point emitters: new tool for nonparaxial optical field modeling

Numerical modeling of optical fields provides valuable support to both theoretical research and technological development in many optics fields. Fourier methods have been the most widely used tools of numerical modeling. However, important limitations have restricted their application in contemporary research that involve high numerical apertures, short propagation distances, and spatially partially coherent states of light, for instance. The spectrum of classes of point emitters is introduced as a numerical tool that overcomes such limitations for the design, analysis, and synthesis of nonparaxial optical fields in arbitrary states of spatial coherence. In this context, optical processing is realized as the filtering on the spectrum of classes of point emitters performed by the complex degree of spatial coherence that could be implemented dynamically by using programmable devices.

The spatial coherence wavelets and second-order correlation

A description of the second-order spatial coherence based on the theory of spatial coherence wavelets is presented. Such description is performed in the classical context of optical fields and chaotic sources. The concepts of radiant and virtual point sources are introduced. This theory suggests that the second-order spatial coherence state of light can be described in terms of three layers of point sources; a strategy that can increase the performance of numerical algorithms. The obtained modulation in coherence is similar to that measured in Hanbury-Brown and Twiss effect for binary stars. © 2015. Acad. Colomb. Cienc. Ex. Fis. Nat. All rights reserved.

The spatial coherence wavelets and second-order correlation

A description of the second-order spatial coherence based on the theory of spatial coherence wavelets is presented. Such description is performed in the classical context of optical fields and chaotic sources. The concepts of radiant and virtual point sources are introduced. This theory suggests that the second-order spatial coherence state of light can be described in terms of three layers of point sources; a strategy that can increase the performance of numerical algorithms. The modulation in coherence found is similar to that measured in Hanbury-Brown and Twiss effect for binary stars .

Three-dimensional micro-diffraction modeling

Squared elementary cells with correlated radiant point sources are presented as basic structures for characterizing the propagation of the field emitted by two-dimensional planar sources of any shape and in arbitrary state of spatial coherence. The field is transported on a finite expansion of nonparaxial modes, whose propagation in the micro-diffraction domain is discussed under both the diffraction and the interference conditions.

Electromagnetic wave fields in the microdiffraction domain

Paraxial propagation theories are not suitable for describing the behavior of electromagnetic wave fields in any states of spatial coherence and polarization in the microdiffraction domain. The proposed nonparaxial theory overcomes such limitations by modeling (i) any planar source in terms of sets of point sources with tensor statistical behavior, and (ii) the transport of the wave field on scalar, deterministic, time-independent, and nonparaxial propagation modes, defined only by the geometry of the boundary conditions of the experimental setups. So the field emission by the source and the space structure due to the modes are independent from each other. The theory provides a unified framework for the power and the states of spatial coherence and polarization of the field, as well as for interference and diffraction, and describes the significant changes suffered by the wave fields in the microdiffraction domain.

Phase-space tomography for characterization of rotationally symmetric beams

The experimental measurement of light field correlations is a difficult problem because, even in the monochromatic scalar case, the spatial coherence state of light is described by four-dimensional functions. Additional information about the field symmetry or coherence state allows reduction of the complexity of the problem. Here, we present a simplified coherence-agnostic phase-space tomography method for the experimental characterization of the widely used class of rotationally symmetric beams, which includes as a particular case partially coherent vortices. It is based on the reconstruction of the beam ambiguity function from the intensity distributions measured in the antisymmetric fractional Fourier transform domains. The experimental data can be acquired using an optical setup consisting of four cylindrical lenses and a digital camera located in fixed positions. The feasibility of the proposed method is experimentally demonstrated.

Propagation of electromagnetic beams of any state of spatial coherence and polarization through multilayered stratified media

We present a theory of propagation of a partially coherent and partially polarized electromagnetic beam through a multilayered stratified medium. The analysis shows that spatial coherence and polarization properties of the beam change, in general, on propagation through such a medium. We illustrate the results by an example.

Diffraction of radiation of any state of spatial coherence on media with periodic structure

A general formula is derived for the spectral density distribution in the far zone, produced by the diffraction of a beam of any state of spatial coherence on a medium with a spatially periodic structure. The formula may be used to determine the structure of crystals from the diffraction of partially coherent x-ray beams.

Discreteness of the set of radiant point sources: a physical feature of the second-order wave-fronts

The non-paraxial phase-space representation of diffraction of optical fields in any state of spatial coherence has been successfully modeled by assuming a discrete set of radiant point sources at the aperture plane instead of a continuous wave-front. More than a mere calculation strategy, this discreteness seems to be a physical feature of the field, independent from the sampling procedure of the modeling.

Phase–space non-paraxial propagation modes of optical fields in any state of spatial coherence

The non-paraxial marginal power spectrum is decomposed in propagation modes, so that the zeroth-order mode is only emitted by the radiant point sources at the aperture plane, while the modes of higher orders than zero are only emitted by the virtual point sources. It allows representing the non-paraxial propagation of optical fields in arbitrary states of spatial coherence and along arbitrary distances from the aperture plane without approximations, by simply using the power distribution and the spatial coherence state at the aperture plane as entries. This modal expansion is potentially useful in micro-diffraction and spatial coherence modulation.

Analogies between classical scalar wave fields in any state of spatial coherence and some quantum states of light

The border between the descriptions of the classical optical fields in any state of spatial coherence and the quantum coherence state of light is revisited in the framework of the phase-space representation. Although it is established that such descriptions are not completely equivalent, the exact calculation of the marginal power spectrum leads to new analogies that suggest that some features exclusively attributed to quantum states of light can be also shared by classical optical fields due to their spatial coherence state.

Experimental generation of a radially polarized beam with controllable spatial coherence

We have experimentally generated a radially polarized (RP) beam with controllable state of spatial coherence by using a rotating ground-glass plate and a radial polarization converter. Furthermore, experimental and theoretical analysis of the focusing properties of a partially coherent RP beam is carried out. Our results show that we can shape the beam profile of the focused RP beam by varying its initial spatial coherence, which is useful for material thermal processing and particle trapping. The experimental results are in complete agreement with the theoretical predictions.