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.     

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.     

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.     

Radiation efficiency of partially coherent electromagnetic beams.

We present a general definition of the radiation efficiency of stationary electromagnetic fields and prove that it is bounded between zero and unity for beams of any state of coherence and polarization. The radiation efficiency may be interpreted as a measure of how directed the radiated fields are, and therefore it can be used to assess the allowed spatial coherence and intensity variations across a beam. We consider a class of partially coherent electromagnetic fields that were recently introduced in the literature and evaluate the radiation efficiencies for two particular examples, namely, the azimuthally polarized symmetric beams and the dipolar beams that are nearly linearly polarized in the central region. The results show that the radiation efficiency is fairly insensitive to the state of polarization and that it differs appreciably from unity for only small values of source and correlation widths.     

Rotational frequency shifts in partially coherent optical fields

We study the frequency shifts taking place when a random, stationary optical field rotates with respect to an observer. The field is expanded in terms of fully coherent Laguerre-Gaussian basis modes, for which the rotational frequency shifts have been studied previously. We demonstrate the formalism by considering the spectrum of a Gaussian Schell-model field, and show that for a spatially highly incoherent field, significant spectral changes can be expected.     

Generation of partially coherent diffraction-free fields with tunable geometry

The synthesis of diffraction-free fields with different profiles is described. The synthesis is done by illuminating a screen containing a circular slit with a cosine beam. The treatment is equivalent to the modulation of the slit transfer characteristics and makes possible a tunable interference interaction of Bessel beams with noncommon axes. These results are generalized, and it is shown that coherent diffraction-free fields with arbitrary profiles can be expressed as the superposition of shifted zero-order Bessel beams and temporary parametric representations of the shifted functions. Diffraction-free fields with partially coherent features can be obtained. Experimental results are shown for each case.     

Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere

We study the changes in the degree of polarization of an electromagnetic Gaussian Schell-model beam, as the beam propagates through the turbulent atmosphere. We demonstrate that, within the framework of the Tatarskii model of the turbulent atmosphere, the degree of polarization of the beam changes appreciably at relatively short propagation distances in the atmosphere. In the long-propagation distance limit, however, we find that the degree of polarization of the beam tends to the value that it has in the source plane.     

Power coupled between partially coherent vector fields in different states of coherence.

A procedure is described for calculating the power coupled between collimated, partially coherent vector fields that are in different states of coherence. This topic is of considerable importance in designing submillimeter-wave optical systems for astronomy. It is shown that if the incoming field S has coherence matrix A, and the outgoing field D has coherence matrix B, then the power coupled is simply Ps = Tr(ATBT), where the elements of T project the basis functions of B onto those of A. A similar technique can be used to calculate the power coupled from the background of S to D. The scheme is illustrated by calculating the power coupled between two scalar, Gaussian Schell-model beams. The procedure can be incorporated into optical design software.     

Propagation-invariant electromagnetic fields: Theory and experiment

Abstract

The vector concept of the propagation invariance is formulated to be applied to the stationary electromagnetic fields. The analysed exact solutions of the Maxwell equations are obtained on the basis of general propagation-invariant solutions of the scalar Helmholtz equation. A possible classification of the propagation-invariant fields based on quantities which appear in the complex Poynting theorem is proposed. The longitudinal periodicity of the electromagnetic field obtained due to the superposition of two Bessel beams is verified by a simple experiment.     

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.     

Theory of the heating of dielectrics by high-power electromagnetic fields

The self-consistent problem of determining the interacting electromagnetic and temperature fields in a semi-infinite medium when a plane electromagnetic wave is incident normally on it is solved in the adiabatic approximation. The parameters of the medium are arbitrary functions of the temperature, thus enabling the WKB method to be used.     

Coherent-mode decomposition of partially polarized,partially coherent sources

It is shown that any partially polarized, partially coherent source can be expressed in terms of a suitable superposition of transverse coherent modes with orthogonal polarization states. Such modes are determined through the solution of a system of two coupled integral equations. An example, for which the modal decomposition is obtained in closed form in terms of fully linearly polarized Hermite Gaussian modes, is given.     

Irreversible effects of random unitary transformations on coherence properties of partially polarized electromagnetic fields

We demonstrate monotonic, irreversible effects on the entropy, the degree of polarization, and different degrees of coherence when random, energy-preserving unitary transformations are applied to vectorial electromagnetic fields.     

Spreading of partially coherent beams in random media

Some published computational work has suggested that partially coherent beams may be less susceptible to distortions caused by propagation through random media than fully coherent beams. In this paper this suggestion is studied quantitatively by examining the mean squared width of partially coherent beams in such media as a function of the propagation distance. The analysis indicates under what conditions, and to what extent, partially coherent beams are less affected by the medium.     

Theory of domain wall motion induced by microwave magnetic fields

A general theory is developed that applies to arbitrary polarization and takes account of damping and of the dipolar interaction between domains. The effect of the microwave field on the domain structure can be characterized by a pressure on the domain walls and by an alignment energy, both of which are proportional to the square of the rf magnetic field and become large in the vicinity of a resonance. For circular polarization the pressure tends to decrease the Larmor-domains (domains in which the imposed sense of polarization coincides with the sense of the natural spin precession) for frequencies outside the resonance region. Inside the resonance region, however, the pressure tends to increase the Larmor-domains. A linearly polarized field also exerts a pressure on the domain walls, with the polarity dependent upon the orientation of the field to the wall normal. In a linearly polarized magnetic field the domain walls tend to become aligned parallel to the rf field at frequencies ω near the low-frequency resonance (ω =γHa, γ = gyromagnetic ratio, Ha= anisotropy field) and perpendicular to the rf field at frequencies near the high-frequency resonance (ω = γ[Ha(Ha+ 4πM0)]^1/2, M0= saturation magnetization).     

Propagation of partially coherent fields through planar dielectric boundaries using angle-impact Wigner functions I. Two dimensions

We examine the angle-impact Wigner function (AIW) as a computational tool for the propagation of nonparaxial quasi-monochromatic light of any degree of coherence past a planar boundary between two homogeneous media. The AIWs of the reflected and transmitted fields in two dimensions are shown to be given by a simple ray-optical transformation of the incident AIW plus a series of corrections in the form of differential operators. The radiometric and leading six correction terms are studied for Gaussian Schell-model fields of varying transverse width, transverse coherence, and angle of incidence.     

Propagation-induced polarization changes in partially coherent optical beams

Propagation of a partially coherent optical beam inside a linear, nondispersive, dielectric medium is studied, taking into account the vector nature of the electromagnetic field. Propagation-induced polarization changes are studied by using the Gaussian-Schell model for the cross-spectral-density tensor. The degree of polarization changes with propagation and also becomes nonuniform across the beam cross section. The extent of these changes depends on the coherence radius associated with the cross-correlation function. For optical beams with symmetric spectra, the bandwidth of the source spectra is found to play a relatively minor role.     

The effect of phase modulation of scattered radiation on the asymptotic behavior of the contrast ratio of partially coherent speckle fields

We analyze the influence of a weak phase modulation of multiply scattered partially coherent light fields on the variance of fluctuations of the scattered field intensity. It is suggested to perform diagnostics of scattering media by analyzing the probing radiation scattered from a “modulating” medium and determining the speckle intensity index (or contrast ratio) upon introduction of an object studied into the scheme of measurements. The proposed method is experimentally verified on model scattering media.