Electromagnetic coherence theory of laser resonator modes

Experimental demonstration of ghost imaging with an electromagnetic Gaussian Schell-model beam

Recently, there has been a controversy about the dependence of the visibility of the ghost image on the degree of polarization (DOP) of a stochastic electromagnetic beam because of different definitions of the visibility. In this paper, we revisit ghost imaging with an electromagnetic Gaussian Schell-model (EGSM) beam. Through numerical examples based on the conventional definition of the visibility, we find that the visibility of the ghost image indeed increases or decreases with the increase of the DOP the beam source under certain conditions. We solve the controversy between literatures and the present paper through analyzing the r.m.s. widths of auto-correlation functions of the x component of the field and of the y component of the field. Furthermore, we carry out experimental demonstration of ghost imaging with an EGSM beam. Our experimental results verify the theoretical predictions.

Second-order moments of an electromagnetic Gaussian Schell-model beam in a uniaxial crystal

We derive the analytical expressions for the second-order moments of an electromagnetic Gaussian Schell-model (EGSM) beam propagating in a uniaxial crystal. With the help of the derived formulas, we study the evolution properties of the propagation factor, the effective radius of curvature and the Rayleigh range of an EGSM beam in a uniaxial crystal. It is found that the evolution properties of an EGSM beam in a uniaxial crystal are much different from its evolution properties in free space and are closely determined by the initial beam parameters and the parameters of the uniaxial crystal. The uniaxial crystal provides one way for modulating the properties of an EGSM beam.

Spatial coherence of broad-area laser diodes

We model the spatial coherence of broad-area laser diodes (BALDs) by representing the mutual intensity as superpositions of individually fully coherent but mutually uncorrelated fields. Consideration of spectroscopic modal structure measurements and intensity-based mode recovery shows that the standard Mercer-type coherent-mode expansion can lead to unsatisfactory results for real BALDs. However, we show that a so-called shifted elementary-field method provides a sufficiently accurate tool for spatial coherence and propagation modeling even if the modal structure of the BALD is severely distorted.

Modulation of spectral intensity, polarization and coherence of a stochastic electromagnetic beam

Analytical formula for the cross-spectral density matrix of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam truncated by a circular phase aperture propagating in free space is derived with the help of a tensor method, which provides a reliable and fast way for studying the propagation and transformation of a truncated EGSM beam. Statistics properties, such as the spectral intensity, the degree of coherence, the degree of polarization and the polarization ellipse of a truncated EGSM beam in free space are studied numerically. The propagation factor of a truncated EGSM beam is also analyzed. Our numerical results show that we can modulate the spectral intensity, the polarization, the coherence and the propagation factor of an EGSM beam by a circular phase aperture. It is found that the phase aperture can be used to shape the beam profile of an EGSM beam and generate electromagnetic partially coherent dark hollow or flat-topped beam, which is useful in some applications, such as optical trapping, material processing, free-space optical communications.

M2-factor of a stochastic electromagnetic beam in a Gaussian cavity

With the help of a tensor method, an explicit expression for the M2-factor of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam in a Gaussian cavity is derived. Evolution properties of the M2-factor of an EGSM beam in a Gaussian cavity are studied numerically in detail. It is found that the behavior of the M2-factor of an EGSM beam in a Gaussian cavity is determined by the statistical properties of the source beam and the parameters of the cavity. Thermal lens effect induced changes of the M2-factor of an EGSM beam in a Gaussian cavity is also investigated. Our results will be useful in many applications, such as free-space optical communications, laser radar system, optical trapping and optical imaging, where stochastic electromagnetic beams are required.

Partially correlated azimuthal vortex illumination: coherence and correlation measurements and effects in imaging

Correlations in the illumination field have a profound impact on the image contrast for features near the resolution limit. The pupil polarization affects these correlations. We show that a polarization vortex has a particularly dramatic effect. A theoretical model is given for the correlation matrix of a partially correlated source created by placing an azimuthal polarization vortex mode converter in the pupil plane of a critical illumination system. We then validate this model experimentally using a reversed-wavefront Young interferometer, directly show the impact that the phase of the correlation function has on image contrast.

State of polarization of a stochastic electromagnetic beam in an optical resonator

On the basis of the unified theory of coherence and polarization, we investigate the behavior of the state of polarization of a stochastic electromagnetic beam in a Gaussian cavity. Formulations both in terms of Stokes parameters and in terms of polarization ellipse are given. We show that the state of polarization stabilizes, except in the case of a lossless cavity, after several passages between the mirrors, exhibiting monotonic or oscillatory behavior depending on the parameters of the resonator. We also find that an initially (spatially) uniformly polarized beam remains nonuniformly polarized even for a large number of passages between the mirrors of the cavity.

Evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity

The interaction of an electromagnetic Gaussian Schell-model (EGSM) beam with a Gaussian cavity is analyzed. In particular, the evolution of the degree of polarization of the EGSM beam is investigated. The results show that the behavior of the degree of polarization depends on both the statistical properties of the source that generates the EGSM beam and the parameters of the cavity.

Connection between electric and magnetic coherence in free electromagnetic fields

We introduce quantitative measures for the description of the electric and magnetic coherence in a stationary, random electromagnetic field at two points, in a volume, and in the Fourier space. These quantities are applied to free electromagnetic fields, and several theorems regarding the relationship between the two types of coherences in such fields are established. Fields which are statistically homogeneous, and those which, in addition, are statistically isotropic are considered separately. Furthermore, the connection between the electric and magnetic coherence is exemplified for some specific statistically homogeneous fields.