Diffraction properties of partially coherent electromagnetic four-petal Gaussian beams

The concept of existing scalar coherent four-petal Gaussian (FPG) beam is extended to the more general partially coherent electromagnetic four-petal Gaussian (PCFPG) beam, and the cross-spectral density matrix of the latter is derived in analytical expressions. Intensity distributions and degree of polarization in free space are investigated by numerical examples. Results show that propagation properties of the PCFPG beam are different from their scalar coherent and scalar partially coherent counterparts. Both intensity distributions and polarization strongly depend on transversal coherence lengths. When the propagation distance increases to a large value, intensity distributions of PCFPG beams convert into the Gauss profile. Polarization of PCFPG beams shows an oscillating characteristic upon propagation, and the oscillation would enhance with the increase of coherence lengths. These results may find potential applications in beam shaping and free space optical communications.     

Partially coherent multiple-beam interference

The general formula for multiple-beam interference due to regular slit arrays illuminated with partially coherent quasi-monochromatic light is derived. The correlation functions chosen for partially coherent light assume Gaussian, sinc and besinc forms of correlation. The intensity distribution in the interference patterns is presented and discussed as a function of the spatial coherence condition. It is shown that spatial coherence of the illumination largely affects the features of multiple-beam interference patterns.     

What kind of phases does one measure in usual interference experiments?

It is pointed out that in usual optical interference experiments one does not measure phases of monochromatic light beams as is usually assumed. Rather that one measures a phase of an associated correlation function of a beam; and that, when the beam is spatially fully coherent, as is usually the case, the measured phase may be identified with the phase of an average wave function of the beam.     

Spectra, coherence and polarization in Young’s interference pattern formed by stochastic electromagnetic beams

New expressions are derived that predict the change of spectral density, the spectral degree of coherence and spectral degree of polarization in Young’s interference pattern when the pinholes are illuminated by an electromagnetic Gaussian Schell-mode beam. The spectral degree of polarization in the observation plane is found, in general, to take on values different from its values at each pinhole, and it changes with position at the same spatial frequency, as does the spectral density. When the light at the pinholes is completely coherent, there are singular points in the pattern, at which the spectral degree of polarization reaches minimum value.     

Experimental determination of two-point Stokes parameters for a partially coherent broadband light beam

The generalized Stokes parameters, which are two-point extensions of conventional Stokes parameters, are determined for a pair of points in the cross-section of a partially coherent broadband light beam. For this purpose, using a two-mirror and two-beam-splitter assembly, unpolarized, linearly polarized and partially polarized electromagnetic beams are generated. This simple experimental method for determining generalized Stokes parameters establishes an analogy with the experimental scheme of determining conventional Stokes parameters, which in succession contributes to appreciable reduction in uncertainty in the measurements.     

Coherence and the statistics of the phase difference between partially polarized electromagnetic waves

Coherence between two vectorial harmonic light vibrations is analyzed in terms of the statistics of their phase difference. This provides a natural and simple extension of second-order coherence to cover more complicate situations. In particular this assigns large coherence to quantum light states providing the most accurate interferometric measurements allowed by the quantum theory, even if they are incoherent according to the standard second-order approach.     

Generalized Stokes parameters of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams

The analytical expressions for the generalized (two-point) Stokes parameters of stochastic electromagnetic Gaussian Schell-model pulsed (GSMP) beams propagating in free space are obtained. The changes in the spectral Stokes parameters in free space propagation are studied. The dependence of on-axis and transverse spectral Stokes parameters of stochastic electromagnetic GSMP beams on the pulse parameters including pulse duration and temporal coherence length is stressed and illustrated numerically. The results are interpreted physically.     

Beam criteria for propagation of electromagnetic beams in the turbulent atmosphere

A recently introduced criterion [O. Korotkova, E. Wolf, Opt. Lett. 32 (2007) 2137] for testing whether a scalar beam preserves its beam-like shape after it propagates some distance through the turbulent atmosphere is generalized to the case of electromagnetic beam propagation. The generalized criterion applies to monochromatic as well as to stochastic electromagnetic beams. The analysis is illustrated by examples.     

Polarization of completely coherent random electromagnetic beams

It is shown that the spectral degree of polarization rho(r, omega) of a fluctuating electromagnetic beam which is completely coherent throughout a domain D is necessarily the same at every point in D. It can take on any value in the range 0 < or = rho < or = 1. In particular, the fully coherent beam can be completely polarized or completely unpolarized throughout D.     

Ghost imaging with electromagnetic stochastic beams

The dependence of ghost images on polarization properties of illumination is revealed. We derive the general formulas pertaining to ghost imaging by means of electromagnetic stochastic beams and, in particular, study the case when the illumination beam belongs to the class of electromagnetic Gaussian Schell-model beams and is incident onto a soft two-dimensional aperture. We find under which conditions that source polarization may reduce/enhance the ghost image and its visibility.     

Polarization properties of stochastic electromagnetic beams

The behavior of the degree of polarization of a Gaussian Schell-model beam propagating in free space is investigated. Contour diagrams for the degree of polarization, and for the spectral density (‘intensity’) of the polarized and the unpolarized portions of the beam are presented.     

部分相干电磁光束的焦移

 基于有效菲涅耳数的概念,给出一种简单的表达式来评估部分相干电磁光束经圆形光阑透镜后所产生的相对焦移,对部分相干电磁光束经透镜聚焦的情况进行了研究。结果表明:当交叉谱密度函数的非对角元素为零时,有效菲涅耳数不仅依赖于真实的菲涅耳数大小,而且依赖于光束的偏振分布和入射部分相干电磁光束两个偏振分量的空间相干长度;相对焦移量仅由等效菲涅耳数决定。将此方法与数值积分法进行的比较表明,等效菲涅耳数可以简单、准确地评估焦移。     

Propagation characteristics of stochastic electromagnetic array beams

A stochastic electromagnetic array beam that is generated by an electromagnetic Gaussian Schell-model source is introduced by using tensor method. An analytical expression for the cross-spectral density matrix of the stochastic electromagnetic array beam propagating in a paraxial ABCD optical system is derived after performing vector integration. Some numerical calculations are illustrated for the propagation characteristics of such an array beam in free space and fractional Fourier transform (FRFT) system as application examples.     

Partially coherent vortex beams propagating through slant atmospheric turbulence and coherence vortex evolution

Using the extended Huygens-Fresnel principle and the quadratic approximation of the phase structure function, and taking the Gaussian Schell-model (GSM) vortex beam as a typical example of partially coherent vortex beams, the explicit expressions for the cross-spectral density function and average intensity of GSM vortex beams with topological charge m=+1 propagating through slant atmospheric turbulence are derived, and used to study the propagation properties of GSM vortex beams in atmospheric turbulence along a slant path and evolution behavior of coherence vortices. It is shown that the spreading of GSM vortex beams along a horizontal path is larger than that along a slant path in the long atmospheric propagation. The propagation through horizontal atmospheric turbulence can be treated as a special case of the altitude-independent structure constant. The position of coherence vortices in slant atmospheric turbulence does not coincide with that in horizontal atmospheric turbulence, and the dependence of position of coherence vortices on the zenith angle, wavelength and reference point is illustrated by numerical examples. A comparison with the previous work is also made.     

Focal shift of the partially coherent vortex beams focused by an aperture lens

Based on the propagation law of partially coherent beams, the propagation equations of the partially coherent vortex beams focused by an aperture lens are derived. Based on these equations, the focal shift of partially coherent vortex beams is studied, and illustrative numerical results are given. It is found that the focal shift of the partially coherent vortex is dependent not only on the Fresnel number but also on the relative coherent length and the topological charge of the vortex.     

A scalar-mode representation of stochastic, planar, electromagnetic sources

A very useful theoretical tool for investigating coherence properties of stochastic scalar sources and stochastic scalar fields is the so-called coherent-mode representation. We introduce a somewhat similar new representation for planar, secondary stochastic electromag netic sources which generate beams. It consists of three expansions for the three independent elements of the 2 × 2 electric cross-spectral density matrix of the beam. The expansion of the diagonal elements of the matrix are coherent-mode representations in the sense of the scalar theory. The third one, for each off-diagonal element, is a bi-modal expansion, expressed in terms of the coherent modes of the diagonal elements.     

Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams

A 4 x 4 complex curvature tensor M>(-1) is introduced to describe partially coherent anisotropic Gaussian-Schell model (GSM) beams. An analytical propagation formula for the cross-spectral density of partially coherent anisotropic GSM beams is derived. The propagation law of M(-1) that is also derived may be called partially coherent tensor ABCD law. The analytical formulas presented here are useful in treating the propagation and transformation of partially coherent anisotropic GSM beams, which include previous results for completely coherent Gaussian beams as special cases.     

Propagation of astigmatic stochastic electromagnetic beams in oceanic turbulence

In this paper, we investigate the characteristics of astigmatic stochastic electromagnetic beams through oceanic turbulence. Taking the electromagnetic Gaussian Schell-model (GSM) beam as an example, the analytic expressions for the spectral density and the spectral degree of polarization of the beam propagating the oceanic turbulence are derived. It is indicated that the spectral density along the z-axis of the GSM beam in the oceanic turbulence is severely influenced by the source correlation properties, as well as by the sea-related parameters. We show that the characteristics of the spectral density along the x-axis, y-axis and z-axis of astigmatic electromagnetic GSM beams passing through the oceanic turbulence are qualitatively different. Furthermore, we find that as the astigmatic coefficient becomes larger, the maximum value of the spectral density along the z-axis increases rapidly and the width of the spectral density becomes shorter rapidly. Finally, the results have shown that different strengths of astigmatism have different effects on the spectral degree of polarization.     

Interference of coherent polariton beams in microcavities: polarization-controlled optical gates

We demonstrate, theoretically and experimentally, a polarization-controlled optical gate based on a degenerate polariton-polariton scattering process occurring in semiconductor microcavities. Because of the interference between coherent polaritons, this process is observed in the case of polaritons generated from two collinearly polarized coherent pump beams. On the contrary, if the beams are cross polarized, the scattering is suppressed.     

Investigation on z-scan experiment by use of partially coherent beams

Z-Scan experiment using partially coherent beams is investigated theoretically. We derive the expression for the cross-spectral density of the Gaussian Schell-model (GSM) beam passing through the nonlinear thin sample. Then the influences of the aperture radius and the spatial degree of coherence on the z-scan curves are analyzed. We find that transmittance difference ΔT_p-v between the peak and valley in z-scan curves decreases gradually with the increment of the aperture radius, which is similar to the case of the fully coherent beams. It is also shown that ΔT_p-v is getting bigger with the increment of the spatial degree of coherence α₀, and when α₀ is larger than a certain value, ΔT_p-v becomes almost unchanged. The results show that the z-scan experiment with partially coherent beams may provide a feasible method for measuring the spatial degree of coherence.