Coherent and incoherent polarization encoding of electromagnetic fields

We study a method generating certain distributions of the degree and state of polarization of a light field across a transverse beam cross-section. We use the introduced polarization encoding scheme to study the distribution of polarization ellipses in a cross-section of a beam generated by superposing two encoded beams, the effects of coherence relation between the input beams on this distribution were theoretically analyzed and illustrated by contour plots of the parameters representing polarization ellipses.     

Beam radiated from quasi-homogeneous uniformly polarized electromagnetic source scattering on quasi-homogeneous media

We study the coherence properties of the field generated by beam radiated from quasi-homogeneous (QH) electromagnetic source scattering on QH media. Formulas for the spectral density and spectral degree of coherence of the three dimensional scattered field are derived. The results show under assumption that the diagonal correlation coefficients of the source are proportional to each other, the far field of the scattered light satisfy two reciprocity relations analogous to that in the scalar case, that, the spectral density is proportional to the convolution of the spectral density of the source and the spatial Fourier transform of the correlation coefficient of the scattering potential; the spectral degree of coherence is proportional to the convolution of the diagonal correlation coefficients and the strength of the scattering potential.     

Changes in generalized Stokes parameters of stochastic electromagnetic beams on propagation through ABCD optical systems and in the turbulent atmosphere

Using the derived formulas for the transformation of 2 × 2 cross-spectral density matrix of the stochastic electromagnetic beams propagating through ABCD optical systems and in the turbulent atmosphere, the changes in the generalized Stokes parameters of the beams propagating under these conditions can be investigated directly. Some typical numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams passing through free space, focal system, dual-focus system, and the turbulent atmosphere with different structure parameters. Further extensions are also pointed out.     

Propagation of random electromagnetic beams through axially nonsymmetrical optical systems

When random electromagnetic beams passing through axially nonsymmetrical ABCD optical systems, the analytical formula for the transformation of the elements of 2 × 2 cross-spectral density matrix is obtained with the help of vector integration. We derive analytical expressions of the spectral degree of polarization, the spectral degree of coherence, and the spectral density in any output plane z > 0. Some numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams propagating through such optical systems.     

Parametric study of uniformly polarized stochastic electromagnetic beam and its imaging

A parametric study is performed in investigating the stochastic electromagnetic beam generated by a uniformly polarized electromagnetic Gaussian Schell-model source and passing through ABCD optical systems. Through theoretical analysis, the requirement is derived that the uniformly polarized electromagnetic field can be obtained at the output plane of the imaging optical system. Furthermore, the general imaging formula of the stochastic electromagnetic beam is derived. Numerical examples are also presented to illustrate the application.     

Statistical properties of correlated radial stochastic electromagnetic array beams on propagation

A kind of array beam named the correlated radial stochastic electromagnetic array beam that is generated by an electromagnetic Gaussian Schell-model source is introduced by use of tensor method. The analytical expression for the cross-spectral density matrix of this array beam propagating through the turbulent atmosphere and in free space is obtained after performing vector integration. Some typical numerical calculations are illustrated for the changes in the spectral density, spectral degree of polarization, and spectral degree of coherence of the beam on propagation. We find that the atmospheric turbulence can destroy the correlated effect among the beamlets.     

Change in degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence

We study the change in the degree of coherence of partially coherent electromagnetic beam (so called electromagnetic Gaussian Schell-model beam). It is shown analytically that with a fixed set of source parameters and under a particular atmospheric turbulence model, an electromagnetic Gaussian Schell-model beam propagating through atmospheric turbulence reaches its maximum value of coherence after the beam propagates a particular distance, and the effective width of the spectral degree of coherence also has its maximum value. This phenomenon is independent of the used turbulence model. The results are illustrated by numerical curves.     

Stokes parameters and degree of polarization of nonparaxial stochastic electromagnetic beams

On the basis of angular spectrum representation and the stationary-phase method, far-field expressions for generalized Stokes parameters of nonparaxial stochastic electromagnetic beams are derived, which permits us to study the changes in the ordinary Stokes parameters upon propagation, and the changes in the spectral degree of polarization of partially polarized nonparaxial stochastic electromagnetic beams. It is shown that the spectral degree of polarization changes across the section on beam propagation.     

Tensor theory of electromagnetic radiometry

A theory of electromagnetic radiometry is built on the premise that the electromagnetic generalised radiance has a tensor structure, represented by the electric, magnetic and mixed generalised radiance tensors as fundamental quantities. They allow overcoming the limitations due to the scalar generalised radiances, proposed for characterizing stationary random electromagnetic sources. Furthermore, they provide a unified framework for completely describing the energy flux and the states of spatial coherence and polarization of random electromagnetic fields. So, the fundamental quantities of both the scalar generalised radiometry and the classical radiometry or photometry are deduced as particular cases of the tensor theory. A new procedure of analysis of (second-order) correlations, subject to the accomplishment of conservation laws, is also introduced. It reveals that (1) the primary sources of the measurable radiometric quantities associated to the random electromagnetic fields in any states of spatial coherence and polarization are the individual radiators of the radiant source (the correlations of the electric and magnetic field vectors only modulate the contributions given by those radiators) and (2) there are two physical mechanisms for the transport of measurable radiometric quantities by the electromagnetic field, i.e. the propagation of the contributions from individual radiators and their redistribution over each wavefront on propagation. The term redistribution refers to the transfer of portions of the measurable quantity over the wavefronts on propagation, without change its total value over each wavefront. In this context, a physical meaning is given to the negative values of the generalised radiance, which gives new insight about the Poynting’s theory of energy transport.     

Spatial coherence properties of monochromatic electromagnetic beams and of laser modes

It is shown that, contrary to common belief, monochromatic light beams are, in general, not spatially completely coherent, i.e., they will, in general, not produce fringes of unit visibility in a Young's double pinhole interference experiment. We cite experiments with laser modes which confirm this result.     

Precision of degree of polarization estimation in the presence of additive Gaussian detector noise

We address the problem of degree of polarization (DOP) estimation in images limited by additive Gaussian detector noise. We derive and analyze the probability density function (PDF) of the pixelwise DOP estimate, which is shown to have significantly different statistical properties than when noise is Gamma distributed (speckle). We then determine the Cramer-Rao Lower Bound and the maximum likelihood estimator of the DOP. We deduce from this study practical solutions for characterizing and reducing the noise in these images.     

Stochastic electromagnetic vortex beam and its propagation

The recent theory formulated in terms of the 2×2 cross-spectral density matrix and the propagation law of cross-spectral density are employed to investigate the stochastic electromagnetic vortex beam and its propagation characterization. Based on these, we derived the general formulae for the intensity distribution, degree of coherence and degree of polarization for stochastic electromagnetic vortex beam while propagating in free space. It is shown that the intensity distribution and the degree of polarization of the stochastic electromagnetic vortex beam propagating in free space depend on the correlation length and the topological charge of the vortex beam.     

Coherence, polarization, and entanglement for classical light fields

We examine a classical version of entanglement between spatial and polarization degrees of freedom for classical light. We examine the relation between classical entanglement, polarization, and several recently introduced measures of coherence for vectorial waves. We show that there is no definite relation between quantum and classical entanglement.     

Changes in the coherence of quasi-monochromatic electromagnetic Gaussian Schell-model beams propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the mutual coherence function of quasi-monochromatic electromagnetic Gaussian Schell-model (EGSM) beams propagating through turbulent atmosphere is derived analytically. By employing the lateral and the longitudinal coherence length of EGSM beams to characterize the spatial and the temporal coherence of the beams, the behavior of changes in the spatial and the temporal coherence of those beams is studied. The results show that with a fixed set of beam parameters and under particular atmospheric turbulence model, the lateral coherence of an EGSM beam reaches its maximum value as the beam propagates a certain distance in the turbulent atmosphere, then it begins degrading and keeps decreasing along with the further distance. However, the longitudinal coherence length of an EGSM beam keeps unchanging in this propagation. Lastly, a qualitative explanation is given to these results.     

Partially coherent anomalous hollow beam and its paraxial propagation

Anomalous hollow beam is extended to the partially coherent case. Analytical propagation formulae for a partially coherent anomalous hollow beam passing through a paraxial ABCD optical system are derived. The propagation properties of a partially coherent anomalous hollow beam in free space and the focusing properties of a partially coherent anomalous hollow beam are studied numerically. It is found that the propagation and focusing properties of the partially coherent anomalous hollow beam are closely related to its initial coherence.     

Analytical structure of an apertured vector Gaussian beam in the far field

Based on the angular spectrum representation of the Maxwell’s equations and the complex Gaussian expansion of the aperture function, the structure of an apertured vector Gaussian beam in the far field is presented in the integral form. By means of the method of stationary phase, the analytical vectorial structures are obtained. According to the analytical expressions, the characteristics of vectorial structure of an apertured Gaussian beam are investigated in the far field. The influence of a linearly polarized angle on the vectorial structure is also studied in the far field. This research provides a novel approach to further comprehend the vectorial property of an apertured Gaussian beam.     

Resonant amplification of frustrated evanescent waves by single dielectric coating

Resonant amplification and enhancement of evanescent wave’s frustration across an optical barrier by using single dielectric coating is numerically demonstrated in this article. With further tuning of the thickness values of the second and the third medium (optical barrier) of the proposed stratified four-media configuration, it is shown that it may be possible to achieve unity transmittance at discrete, but closely spaced incident angles within the full range defined by the theoretical cut-off limit. The designed configuration may have other potential applications than lithography and waveguide design is one such example.     

Beams of electromagnetic radiation carrying angular momentum: The Riemann-Silberstein vector and the classical-quantum correspondence

All beams of electromagnetic radiation are made of photons. Therefore, it is important to find a precise relationship between the classical properties of the beam and the quantum characteristics of the photons that make a particular beam. It is shown that this relationship is best expressed in terms of the Riemann-Silberstein vector - a complex combination of the electric and magnetic field vectors - that plays the role of the photon wave function. The Whittaker representation of this vector in terms of a single complex function satisfying the wave equation greatly simplifies the analysis. Bessel beams, exact Laguerre-Gauss beams, and other related beams of electromagnetic radiation can be described in a unified fashion. The appropriate photon quantum numbers for these beams are identified. Special emphasis is put on the angular momentum of a single photon and its connection with the angular momentum of the beam.     

Focal field computation of an arbitrarily polarized beam using fast Fourier transforms

In this work the vectorial diffraction theory of Richards and Wolf is extended to compute the focal field components of an arbitrarily polarized beam using fast Fourier transform (FFT) operations. Here the arbitrarily polarized pupil function is written as the vector sum of two mutually perpendicularly polarized pupil functions. The FFT based focal field expressions are particularly useful to compute the focal field components of pupil functions without a simple analytical form. We have then applied these expressions to simulate the effects of Zernike mode aberrations on the point spread functions of a number of important cylindrical-vector beam profiles such as radially and azimuthally polarized and helical light beams.     

A temporal-coherence anisotropy of unpolarized light

We analyze the anisotropic behavior of unpolarized, temporally partially coherent light. We demonstrate that unpolarized light with different intrinsic degrees of coherence can present an anisotropic behavior which is experimentally observable while it is not the case if both intrinsic degrees are equal. This behavior is analyzed in comparison with the standard anisotropy property of partially polarized light.