Coherence and polarization properties of far fields generated by quasi-homogeneous planar electromagnetic sources

In studies of radiation from partially coherent sources the so-called quasi-homogeneous (QH) model sources have been very useful, for instance in elucidating the behavior of fields produced by thermal sources. The analysis of the fields generated by such sources has, however, been largely carried out in the framework of scalar wave theory. In this paper we generalize the concept of the QH source to the domain of the electromagnetic theory, and we derive expressions for the elements of the cross-spectral density matrix, for the spectral density, the spectral degree of coherence, the degree of polarization, and the Stokes parameters of the far field generated by planar QH sources of uniform states of polarization. We then derive reciprocity relations analogous to those familiar in connection with the QH scalar sources. We illustrate the results by determining the properties of the far field produced by transmission of an electromagnetic beam through a system of spatial light modulators.     

Degree of coherence for vectorial electromagnetic fields as the distance between correlation matrices

We assess the degree of coherence of vectorial electromagnetic fields in the space-frequency domain as the distance between the cross-spectral density matrix and the identity matrix representing completely incoherent light. This definition is compared with previous approaches. It is shown that this distance provides an upper bound for the degree of coherence and visibility for any pair of scalar waves obtained by linear combinations of the original fields. This same approach emerges when applying a previous definition of global coherence to a Young interferometer.     

Spatial and Temporal Coherence of Light in a Fibre Waveguide

Abstract

A general expression for the mutual coherence function of an electromagnetic field propagating in a fibre waveguide is presented by means of classical coherence formalism and the guided modes field representation. Moreover, this expression is applied to a limiting case of the fibre waveguide excitation by cross-spectrally pure, spatially coherent and quasi-monochromatic source with a symmetrical spectrum. In particular, the complex degree of both spatial and temporal coherence at the exit face of a two-mode, weakly-guiding, step-index fibre waveguide is discussed as a function of an exciting condition of guided modes, an intermodal dispersion and a temporal coherence of the source, respectively.     

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.     

Phase-space representation and polarization domains of random electromagnetic fields

The phase-space representation of stationary random electromagnetic fields is developed by using electromagnetic spatial coherence wavelets. The propagation of the field's power and states of spatial coherence and polarization results from correlations between the components of the field vectors at pairs of points in space. Polarization domains are theoretically predicted as the structure of the field polarization at the observation plane. In addition, the phase-space representation provides a generalization of the Poynting theorem. Theoretical predictions are examined by numerically simulating the Young experiment with electromagnetic waves. The experimental implementation of these results is a current subject of research.     

Ray-based propagation of the cross-spectral density

We explore the propagation of the cross-spectral density for scalar and electromagnetic fields based on generalized radiances that are exactly conserved along rays. Two formulas are derived: The first uses all rays to calculate the cross-spectral density exactly, while the second uses only the subset of those rays that pass through a single spatial point to construct an infinite series expression for the cross-spectral density. The evaluation of the truncated series is examined numerically for a variety of fields of varying angular width and coherence and is found to exhibit better convergence to the cross-spectral density when the rays through the centroid between the two observation points are used, when the fields are less coherent, and when the fields are more paraxial. In generalizing the series formula, two new cross-spectral correlations associated with the flux and energy density are examined.     

Partial spatial coherence and partial polarization in random evanescent fields on lossless interfaces

We consider partial spatial coherence and partial polarization of purely evanescent optical fields generated in total internal reflection at an interface of two dielectric (lossless) media. Making use of the electromagnetic degree of coherence, we show that, in such fields, the coherence length can be notably shorter than the light's vacuum wavelength, especially at a high-index-contrast interface. Physical explanation for this behavior, analogous to the generation of incoherent light in a multimode laser, is provided. We also analyze the degree of polarization by using a recent three-dimensional formulation and show that the field may be partially polarized at a subwavelength distance from the surface even though it is fully polarized farther away. The degree of polarization can assume values unattainable by beamlike fields, indicating that electromagnetic evanescent waves generally are genuine three-dimensional fields. The results can find applications in near-field optics and nanophotonics.     

Theory of partially coherent electromagnetic fields in the space-frequency domain

We construct the coherent-mode representation for fluctuating, statistically stationary electromagnetic fields. The modes are shown to be spatially fully coherent in the sense of a recently introduced spectral degree of electromagnetic coherence. We also prove that the electric cross-spectral density tensor can be rigorously expressed as a correlation tensor averaged over an appropriate ensemble of strictly monochromatic vectorial wave functions. The formalism is demonstrated for partially polarized, partially coherent Gaussian Schell-model beams, but the theory applies to arbitrary random electromagnetic fields and can find applications in radiation and propagation and in inverse problems.     

Electromagnetic spatial coherence wavelets

The recently introduced concept of spatial coherence wavelets is generalized to describe the propagation of electromagnetic fields in the free space. For this aim, the spatial coherence wavelet tensor is introduced as an elementary amount, in terms of which the formerly known quantities for this domain can be expressed. It allows for the analysis of the relationship between the spatial coherence properties and the polarization state of the electromagnetic wave. This approach is completely consistent with the recently introduced unified theory of coherence and polarization for random electromagnetic beams, but it provides further insight about the causal relationship between the polarization states at different planes along the propagation path.     

The influence of high-frequency fields on the order parameter in pure,type I superconductors

The behavior of the order parameter in pure, type I superconductors in the presence of high-frequency fields is discussed. It is shown that in second order in the field the order parameter is disturbed at considerably larger distances from the surface than the penetration depth and the coherence length.     

Effects of coherence and vector properties of the light on the resolution limit in stimulated emission depletion fluorescence microscopy

Stimulated emission depletion (STED) fluorescence microscopy is a diffraction-unlimited microscopy. We report a method of analyzing the intensity distribution in the focal region. The method takes both the coherence and the vector properties of the light into account. By using the Gaussian Schell model to describe the cross-spectral density function of the incident beam, we show that the coherence that exists between the electric field at any two points is one of the factors that limit further increase of the spatial resolution in STED fluorescence microscopy.     

Polarization manifestations of correlation (intrinsic coherence) of optical fields

The statement is substantiated that the experimental estimation of the degree of intrinsic coherence of statistical vector optical fields must include not only the measurement of the visibility of the interference pattern but also the degree of polarization in the resulting spatial distribution of a field.     

Changes in the polarization and coherence of a random electromagnetic beam propagating through a misaligned optical system

On the basis of the generalized diffraction integral formula for misaligned optical systems in the spatial domain, an analytical propagation expression for the elements of the cross-spectral density matrix of a random electromagnetic beam passing through a misaligned optical system is derived. Some analyses are illustrated by numerical examples relating to changes in the spectral degree of polarization and in the spectral degree of coherence of an electromagnetic Gaussian-Schell-model beam propagating through such an optical system. We find that the degree of polarization in the neighboring areas of the focal plane is oscillating, and the effect of misalignment on coherence is not so evident as that on polarization.     

Analysing the behaviour of partially coherent divergent Gaussian beams propagating through oceanic turbulence

Theoretical study of propagation behaviour of partially coherent divergent Gaussian beams through oceanic turbulence has been performed. Based on the previously developed knowledge of propagation of a partially coherent beam in atmosphere, the spatial power spectrum of the refractive index of ocean water, extended Huygens–Fresnel principle and the unified theory of coherence and polarization, analytical formulas for cross-spectral density matrix elements are derived. The analytical formulas for intensity distribution, beam width and spectral degree of coherence are determined by using cross-spectral density matrix elements. Then, the effects of some source factors and turbulent ocean parameters on statistical properties of divergent Gaussian beam propagating through turbulent water are analysed. It is found that beam’s statistical propagation behaviour is affected by both environmental and source parameters variations.     

Coherence and polarization of electromagnetic beams modulated by random phase screens and their changes on propagation in free space

The spectral degree of coherence and of polarization of some model electromagnetic beams modulated by a polarization-dependent phase-modulating device, such as a liquid-crystal spatial light modulator, acting as a random phase screen are examined on the basis of the recent theory formulated in terms of the 2 x 2 cross-spectral density matrix of the beam. The phase-modulating device is assumed to have strong polarization dependence that modulates only one of the orthogonal components of the electric vector, and the phase of the phase-modulating device is assumed to be a random function of position imitating a random phase screen and is assumed to obey Gaussian statistics with zero mean. The propagation of the modulated beam is also examined to show how the spectral degrees of coherence and of polarization of the beam change on propagation, even in free space. The results are illustrated by numerical examples.     

Efficient numerical representation of the optical field for the propagation of partially coherent radiation with a specified spatial and temporal coherence function

We propose a method to narrow the gap between the rigorous methods for the propagation of partially coherent light, which require excessive computational capacity, and the numerical methods used in practical engineering applications, where it is not clear how to handle spatial and temporal coherence in a statistically correct manner. As is the case for the latter methods, the numerical method described can deal with fields with a large spatial and temporal extent, which is necessary in practical applications such as laser fusion or optical lithography. However, the method also takes a few steps toward a more rigorous, yet efficient, representation of the optical field, which depends on detailed specified coherence properties of the radiation. The described method uses a set of independent monochromatic fields at different oscillation frequencies. The frequencies are chosen such that the statistical properties of the integrated intensity closely resemble those from a full-time trace treatment. Finally, we demonstrate the capabilities and limitations of the method with a few numerical examples of the propagation of a large field with a specified spatial and temporal coherence.     

Coherence effects in digital in-line holographic microscopy

We analyze the effects of partial coherence in the image formation of a digital in-line holographic microscope (DIHM). The impulse response is described as a function of cross-spectral density of the light used in the space-frequency domain. Numerical simulation based on the applied model shows that a reduction in coherence of light leads to broadening of the impulse response. This is also validated by results from experiments wherein a DIHM is used to image latex beads using light with different spatial and temporal coherence.     

Invariant propagation of uniform-intensity Schell-model fields

Propagation of partially coherent uniform-intensity Schell-model fields in a uniform dielectric medium is considered. It is first established that the spatial frequencies contained in such a field are non-correlated. Then it is shown that the distribution of the complex degree of spatial coherence associated with any such field is propagation invariant. An experimental set-up consisting of a diffractive beam-shaping element, a rotating diffuser, an aperture and a lens is suggested for the generation of transversely confined approximations of a large class of propagation-invariant Schell-model fields.