Anisotropic pure-phase plates for quality improvement of partially coherent,partially polarized beams

From a theoretical point of view, the use of anisotropic pure-phase plates (APP) is considered in order to improve the quality parameter of certain partially coherent, partially polarized beams. It is shown that, to optimize the beam-quality parameter, the phases of the two Cartesian components of the field at the output of the APP plate should be identical and should exhibit a quadratic dependence on the radial polar coordinate.     

Shannon entropy of partially polarized and partially coherent light with Gaussian fluctuations

We propose to analyze Shannon entropy properties of partially coherent and partially polarized light with Gaussian probability distributions. It is shown that the Shannon entropy is a sum of simple functions of the intensity, of the degrees of polarization, and of the intrinsic degrees of coherence that have been recently introduced. This analysis clearly demonstrates the contribution of partial polarization and of partial coherence to the characterization of disorder of the light provided by the Shannon entropy, which is a standard measure of randomness. We illustrate these results on two simple examples.     

Method of direction-of-arrival estimation for uncorrelated, partially correlated and coherent sources

A new direction-of-arrival estimation method is proposed when uncorrelated, partially correlated and coherent sources coexist. These sources are estimated at two different stages. The uncorrelated and partially correlated sources are first estimated using conventional subspace methods. By exploiting the property of oblique projection, the contributions of uncorrelated and partially correlated sources are then eliminated from the covariance matrix and only the coherent sources remain. Finally, the coherent sources are estimated by the technique of spatial smoothing. The new method need not estimate the partially correlated sources repeatedly but can resolve more sources than the array elements. Simulation results demonstrate the effectiveness and efficiency of the new method.     

Modal decomposition of partially coherent beams using the ambiguity function

Phase-space representations of optical beams such as the ambiguity function or the Wigner distribution function have recently gained considerable importance for the characterization of coherent and partially coherent beams. There is growing interest in beam properties such as the beam propagation factor and the coherence and phase information that can be extracted from these phase-space representations. A method is proposed to decompose a partially coherent beam into Hermite-Gaussian modes by using the ambiguity function. The modal weights and the possible phase relations of the Hermite-Gaussian modes are retrieved. The method can also be applied for the decomposition of the Wigner distribution function. Some examples are discussed in the scope of beam characterization.     

Propagation theories of partially coherent electromagnetic fields based on coherent or separated-coordinate mode decomposition

Propagation theories of partially coherent electromagnetic fields based on coherent mode decomposition or separated-coordinate mode decomposition are proposed. With the proposed propagation theories, various powerful theories for the propagation of fully coherent electromagnetic fields can be used for the propagation of partially coherent electromagnetic fields. The proposed theories are applicable to any propagation problem of partially coherent electromagnetic fields governed by linear Maxwell equations. Some examples are provided to illustrate the validity of the proposed theories.     

Propagation properties of partially coherent radially polarized beam in a turbulent atmosphere

Based on the Huygens–Fresnel principle and the unified theory of coherence and polarization of partially coherent beams, we investigate the propagation characteristics of a partially coherent radially polarized doughnut (PCRPD) beam in a turbulent atmosphere. It is found that, after propagating through a turbulent atmosphere, the doughnut beam spot is changed into a circular Gaussian beam. Moreover, the degree of coherence, the degree of polarization and the degree of cross-polarization of the beam will change on propagation, and this change is dependent upon the degree of coherence of the source and atmospheric turbulence.     

Propagation properties of a partially coherent radially polarized beam in atmospheric turbulence

Based on the extended Huygens–Fresnel integral, second-order moments of the Wigner distribution function of a partially coherent radially polarized beam propagating through atmospheric turbulence are derived. Besides, propagation properties such as the mean-squared beam width, angular width, effective radius of curvature, beam propagation factor and Rayleigh range can also be obtained and calculated numerically. It is shown that the propagation properties are dependent on the spatial correlation length, refraction index structure constant and propagation distance.     

Polarization changes in a partially coherent radially polarized doughnut beam through turbulent ocean

On the basis of the extended Huygens–Fresnel integral principle and unified theory of coherence and polarization of light, we studied the effects of oceanic turbulence on polarization properties of a partially coherent radially polarized doughnut (PCRPD) beam. The ocean-induced fluctuations in the refractive index are assumed be driven by temperature and salinity fluctuations. Numerical examples of changes in polarization properties, such as the degree of polarization, the degree of ellipticity, and the orientation angle in the oceanic turbulence for the PCRPD beam, are given. Our analysis demonstrates how polarization of the PCRPD beam is affected by statistical properties of the source and by several parameters of oceanic turbulence. We find that the propagation of the PCRPD beam is different from that of stochastic beams in oceanic turbulence. The degree of polarization for the PCRPD beam approaches a certain steady value, and the elliptical polarized state of the fully polarized portion of the beam will become fully linear in the far field.     

Degree of polarization and heterodyne spectrum in coherent detection of partially polarized wave fields

We first study the state of polarization of the superposition of partially polarized, statistically independent optical fields with application in coherent detection systems with emphasis on heterodyne configurations and obtain the DOP of the mixture of wave fields. Next we obtain the available heterodyne power after photodetection. Finally we obtain the spectrum of the photocurrent process resulting from the coherent detection of partially polarized amplitude-stabilized fields.     

Spatial partially coherent imaging

We introduce the partial coherence response function for describing the behaviour of imaging systems under spatial partially coherent illumination in the centre and the diierence coordinates notation. It involves the impulse response of the system and the spatial coherence properties of the illumination. It is shown that this function is the image cross-spectral density for a Young's pair of pinholes attached at the object plane. Furthermore, the partial coherence response function and the partial coherence transfer function constitute a Fourier pair on which the Fourier representation of partially coherent imaging can be based.     

Propagation theories of arbitrary-order correlations of partially coherent electromagnetic fields based on separated-coordinate mode decomposition

Theories to calculate the propagation of arbitrary-order correlations of stationary or nonstationary partially coherent electromagnetic fields are proposed. The theories are based on separated-coordinate mode decomposition, and can make the well-developed propagation theories of fully coherent electromagnetic fields applicable to partially coherent electromagnetic fields governed by linear Maxwell equations. The validity of the theories is illustrated by an example.     

Beam-quality optimization of partially polarized fields

For light fields propagating through rotationally symmetric first-order optical systems, the possibility of improvement of the beam-propagation factor is shown to arise when the vectorial behavior is taken into account. For partially polarized beams, we find the optimized value of the beam-quality parameter that can be attained by using this kind of system. This value is given in terms of the beam qualities associated with the transverse polarization components of the vector field. On the basis of the so-called intensity-moment formalism, the general conditions that should be fulfilled at some plane to reach such an optimized value are determined. A procedure to experimentally get the optimization conditions is also proposed.     

Quality improvement of partially polarized beams

Improvement of the beam-quality parameter of partially polarized beams is investigated. We focus on the use of a Mach-Zehnder-type interferometric arrangement with crossed polarizers. The analysis has been carried out within the framework of the intensity moment formalism. Conditions are given under which the beam-quality parameter is optimized.     

General transfer-matrix method for optical multilayer systems with coherent,partially coherent,and incoherent interference

The optical response of coherent thin-film multilayers is often represented with Fresnel coefficients in a 2 x 2 matrix configuration. Here the usual transfer matrix was modified to a generic form, with the ability to use the absolute squares of the Fresnel coefficients, so as to include incoherent (thick layers) and partially coherent (rough surface or interfaces) reflection and transmission. The method is integrated by use of models for refractive-index depth profiling. The utility of the method is illustrated with various multilayer structures formed by ion implantation into Si, including buried insulating and conducting layers, and multilayers with a thick incoherent layer in an arbitrary position.     

Rotating correlations in partially coherent fields

Abstract

Partially coherent optical fields whose cross-spectral density functions rotate on propagation are examined. The general theory for rotating partially coherent fields in the space-frequency domain is derived for both scalar and electromagnetic approaches. Differences between the results obtained with full and partial coherence is discussed. A numerical example is given for rotating intensity distributions.     

Beam wander of partially coherent Airy beams

The beam wander of a partially coherent Airy beam in a turbulent atmosphere was investigated. By using the extended Huygens–Fresnel integral, as analytical expression is derived for the second-order moment of a partially coherent Airy beam. Based on the theory proposed by Andrews, a general expression is obtained for the beam wander of a partially coherent Airy beam. With the help of the expression, various factors which impact on the beam wander are illustrated numerically. The results show that the beam wander of a partially coherent Airy beam decreases with the increase of the characteristic scale and the decrease of the coherent length or the exponent truncation factor. The value of the beam wander is a maximum when the exponent truncation factor is 0.63, no matter what the coherent lengths are. Our results provide an effective way to control the beam wander of a partially coherent Airy beam in practice.     

Average characteristics of partially coherent electromagnetic beams

Average characteristics of partially coherent electromagnetic beams are treated with the paraxial approximation. Azimuthally or radially polarized, azimuthally symmetric beams and linearly polarized dipolar beams are used as examples. The change in the mean squared width of the beam from its value at the location of the beam waist is found to be proportional to the square of the distance in the propagation direction. The proportionality constant is obtained in terms of the cross-spectral density as well as its spatial spectrum. The use of the cross-spectral density has advantages over the use of its spatial spectrum.     

Scattering coherent and partially coherent space-time pulses through few-mode optical systems

We consider the spatiotemporal behavior of coherent and partially coherent, pulsed, few-mode optical systems. It is shown that there is some set of orthogonal space-time pulses at the input reference surface that maps in one-to-one correspondence with some set of orthogonal space-time pulses at the output reference surface; we call these pulses eigenfields. The spectrum of the coupling coefficients determines the amount of information that can be transmitted within a given period of time. The eigenfields are unique for a given system and can be used to propagate a field that is in any state of spatial and temporal coherence. They can also be used to account for the spatial and temporal coherence of internally generated noise and to calculate the powers, fluctuations, and correlations that would be recorded by multimode detectors. Our technique is ideal for modeling the behavior of pulsed imaging arrays and interferometers.