Spatial correlations and partial polarization in electromagnetic optical fields : effects of evanescent waves

In this thesis, partial polarization and spatial correlation properties of electromagnetic optical fields are investigated. The emphasis is on near fields which exist only within the distance of the light wavelength from the emitting or scattering object. In the near-field region, the contribution of the evanescent (non-radiating) waves is overwhelming compared to the propagating waves that can be observed far from the source. Certain fundamental issues related to the optical near-fields are studied. The decomposition of the free-space Green tensor into its evanescent and propagating parts is performed. This issue is of importance in near-field optics and it has attracted considerable attention in the recent literature. Another fundamental issue investigated in the thesis concerns the three-dimensional degree of polarization needed to characterize of electromagnetic fields having arbitrary planar or non-planar wave structures. The physical interpretation of the concept is presented, and its differences in comparison with the conventional two-dimensional formulation of the degree of polarization are brought out. The theory is applied to investigate the effects of evanescent waves and resonant surface waves on the polarization state of the near fields generated by some thermal half-space sources. The thesis also includes a study of the partial polarization and spatial correlation properties of homogeneous free electromagnetic fields. The fields are modelled as an isotropic distribution of angularly uncorrelated and, in the 2D-sense, unpolarized plane waves propagating within a solid angle. When the solid angle extends over the full space, the spatial correlations are found to be determined by the imaginary part of the associated Green tensor, and the field is fully unpolarized in the 3D-sense. These results are the same as for black-body fields, although here no thermal equilibrium is assumed. The same behavior is discovered for any electromagnetic field generated by a statistically homogeneous and isotropic current distribution, which fluctuates within a medium having a vanishingly small absorption. For the fields whose electric cross-spectral density tensor is proportional to the imaginary part of the Green tensor, the degree of coherence has a universal form given by the sinc law.reviewe

Decomposition of the point-dipole field into homogeneous and evanescent parts

In near-field optics the resolution and sensitivity of measurements depend on the abundance of evanescent waves in relation to propagating waves. The electromagnetic field propagator is related to the scalar spherical wave, for which the Weyl expansion is a half-space representation containing both evanescent and homogeneous plane waves. Making use of these results, we decompose the dyadic free-space Green function into its evanescent and homogeneous parts and show that some approaches put forward in the literature are inconsistent with this formulation. We express the results in a form that is suitable for numerical computation and illustrate the field decomposition for a point dipole in some typical cases.Peer reviewe

Degree of polarization in near fields of thermal sources: effects of surface waves

We introduce the concept of degree of polarization for electromagnetic near fields. The approach is based on the generalized Stokes parameters that appear as expansion coefficients of the 3×3 coherence matrix in terms of the Gell-Mann matrices. The formalism is applied to optical near fields of thermally fluctuating half-space sources with particular interest in fields that are strongly polarized owing to resonant surface plasmons or phonons. This novel method is particularly useful when assessing the full vectorial characteristics of random evanescent fields, e.g., for near-field spectroscopy and polarization microscopy.Peer reviewe

Cross-spectral purity of the Stokes parameters in random nonstationary electromagnetic beams

We consider cross-spectral purity in random nonstationary electromagnetic beams in terms of the Stokes parameters representing the spectral density and the spectral polarization state. We show that a Stokes parameter being cross-spectrally pure is consistent with the property that the corresponding normalized time-integrated coherence (two-point) Stokes parameter satisfies a certain reduction formula. The current analysis differs from the previous works on cross-spectral purity of nonstationary light beams such that the purity condition is in line with Mandel's original definition. In addition, in contrast to earlier works concerning the cross-spectral purity of the polarization-state Stokes parameters, intensity-normalized coherence Stokes parameters are applied. It is consequently found that in addition to separate spatial and temporal coherence factors the reduction formula contains a third factor that depends exclusively on the polarization properties. We further show that cross-spectral purity implies a specific structure for the electromagnetic spectral spatial correlations. The results of this work constitute foundational advances in the interference of random nonstationary vectorial light.Comment: 5 pages, 1 figur

Polarization time and length for random optical beams

We investigate the dynamics of the instantaneous polarization state of stationary, partially polarized random electromagnetic beamlike fields. An intensity-normalized correlation function of the instantaneous Poincaré vector is introduced for the characterization of the time evolution of the polarization state. This polarization correlation function enables us to define a polarization time and a polarization length over which the polarization state remains substantially unchanged. In the case of Gaussian statistics, the polarization correlation function is shown to assume a simple form in terms of the parameters employed to characterize partial coherence and partial polarization of electromagnetic fields. The formalism is demonstrated for a partially polarized, temporally Gaussian-correlated beam, and black-body radiation. The results are expected to find a range of applications in investigations of phenomena where polarization fluctuations of light play an important role.Peer reviewe

Universality of electromagnetic-field correlations within homogeneous and isotropic sources

We investigate the structure of second-order correlations in electromagnetic fields produced by statistically stationary, homogeneous, and isotropic current distributions. We show that the coherence properties of such fields within a low-loss or nondissipative medium do not depend on the source characteristics, but are solely determined by the propagation properties, and that the degree of coherence of the field is given by the sinc law. Our analysis reproduces the known results for blackbody fields, but it applies to a wider class of sources, not necessarily in thermal equilibrium. We discuss the physics behind the universal behavior of the correlations by comparing the results with those obtained by an electromagnetic plane-wave model.Peer reviewe

Characterization of polarization fluctuations in random electromagnetic beams

Two stationary, partially polarized electromagnetic beams with equal degrees of polarization may exhibit completely different time evolutions of the instantaneous polarization state. In this work, we derive a statistical quantity that describes the rate at which the field intensity in the beam, on average, is redistributed between the beam's polarization state at any time and the state orthogonal to it. This method allows one to treat the dynamical properties of the polarization fluctuations both theoretically and experimentally. We demonstrate the method by applying it to important special cases, such as fields obeying Gaussian statistics, black-body radiation pencils and depolarized laser beams. We also prove that a geometric approach introduced earlier is closely connected with the present model.Peer reviewe

Degree of polarization for optical near fields

We investigate an extension to the concept of degree of polarization that applies to arbitrary electromagnetic fields, i.e., fields whose wave fronts are not necessarily planar. The approach makes use of generalized spectral Stokes parameters that appear as coefficients, when the full 3×3 spectral coherence matrix is expanded in terms of the Gell-Mann matrices. By defining the degree of polarization in terms of these parameters in a manner analogous to the conventional planar-field case, we are led to a formula that consists of scalar invariants of the spectral coherence matrix only. We show that attractive physical insight is gained by expressing the three-dimensional degree of polarization explicitly with the help of the correlations between the three orthogonal spectral components of the electric field. Furthermore, we discuss the fundamental differences in characterizing the polarization state of a field by employing either the two- or the three-dimensional coherence-matrix formalism. The extension of the concept of the degree of polarization to include electromagnetic fields having structures of arbitrary form is expected to be particularly useful, for example, in near-field optics.Peer reviewe

Descriptors of dimensionality for n × n density matrices

By using the recently introduced parametrization of an n-dimensional density matrix in terms of the indices of population asymmetry and the intrinsic coherences, we define descriptors in both integer and continuous forms of the effective dimension that take place for a complete description of a density matrix, thus providing accurate information beyond the rank of the density matrix. The concepts of dimensional folding, hidden dimensional purity, and dimensional entropy are introduced and discussed in view of the new approach presented. The results are applicable to any physical system represented by a density matrix, such as n-level quantum systems, qutrits, sets of interacting pencils of radiation, classical polarization states, and to transformations of density matrices, as occurs with quantum channels