Electric and magnetic polarization singularities of first-order Laguerre-Gaussian beams diffracted at a half-plane screen.

Based on the vector Fresnel diffraction integrals, analytical expressions for the electric and magnetic components of first-order Laguerre-Gaussian beams diffracted at a half-plane screen are derived and used to study the electric and magnetic polarization singularities in the diffraction field for both two- and three-dimensional (2D and 3D) cases. It is shown that there exist 2D and 3D electric and magnetic polarization singularities in the diffraction field, which do not coincide each other in general. By suitably varying the waist width ratio, off-axis displacement parameter, amplitude ratio, or propagation distance, the motion, pair-creation, and annihilation of circular polarization singularities, and the motion of linear polarization singularities take place in 2D and 3D electric and magnetic fields. The V point, at which two circular polarization singularities with the same topological charge but opposite handedness collide, appears in the 2D electric field under certain conditions in the diffraction field and free-space propagation. A comparison with the free-space propagation is also made.

Method for exploring the orbital angular momentum of an optical vortex beam with a triangular multipoint plate.

An efficient method for exploring the orbital angular momentum of an optical vortex beam is provided. The method, based on a triangular multipoint plate, can easily determine both the sign and the magnitude of the topological charge of the optical vortices. We demonstrate its feasibility by measuring the orbital angular momentum of Laguerre-Gaussian laser beams.

Composite polarization singularities in superimposed Laguerre-Gaussian beams beyond the paraxial approximation.

The closed-form expression for the free-space propagation of superimposed Laguerre-Gaussian beams beyond the paraxial approximation is derived, and the composite polarization singularities formed by the transverse and longitudinal electric-field components are studied in detail. It is shown that there exist composite C-points and L-lines in vector nonparaxial fields. By suitably varying a control parameter, such as the off-axis distance, relative phase, or amplitude ratio, the motion, creation, and annihilation of composite C-points may appear, and in the process the sum of topological charge remains unchanged. The shift, deformation, combination, and disappearance of composite L-lines may take place. The topological relationship holds true. The results are compared with the previous work.

Far-field properties in two off-axis superimposed Laguerre-Gaussian beams beyond the paraxial approximation.

The analytical far-field expressions for the TE and TM terms and energy flux distributions in two off-axis superimposed nonparaxial Laguerre-Gaussian beams with azimuthal and radial indices l(1) = -l(2) = +1, p(1) = p(2) = 0 are derived and used to study the far-field properties including phase singularities and energy flux distributions of the resulting beam, where our main attention focuses on the dependence of phase singularities on the controlling parameters such as the off-axis distance, relative phase, amplitude ratio, and waist widths of superimposed beams, and the symmetry property of edge dislocations and energy flux distributions. The results are interpreted and compared with previous work.

Phase singularities and spectral changes of spectrally partially coherent higher-order Bessel-Gauss pulsed beams.

Phase singularities and spectral changes of spectrally partially coherent higher-order Bessel-Gauss pulsed beams in free-space propagation are studied, and the analytical expressions for the spectral degree of coherence and spectrum are derived. It is shown that there always exists an optical vortex at the center of the beam and the topological charge is conserved during the propagation. Some circular edge dislocations appear and the spectrum changes on propagation. A rapid spectral transition takes place. Numerical illustrative examples are given and the results are explained physically.

Polarization singularities of Gaussian vortex beams diffracted at a half-plane screen beyond the paraxial approximation.

On the basis of the vector Rayleigh-Sommerfeld diffraction integrals, the analytical expression for Gaussian vortex beams diffracted at a half-plane screen beyond the paraxial approximation is derived and used to study the polarization singularities formed by the transverse and longitudinal electric field components in the diffracted field. It is shown that there exist C-points and L-lines that depend on the off-axis parameters in the x and y directions, waist width, wavelength, and topological charge of diffracted Gaussian vortex beams, as well as on the position parameter. By a suitable variation of the off-axis and position parameters, the creation, motion, and annihilation of polarization singularities may take place, and the topological relationship holds true. Therefore, the nonparaxial beam diffraction and propagation provide a method for generating polarization singularities.

Spectral Stokes singularities of stochastic electromagnetic beams.

The spectral Stokes singularities are introduced to describe the polarization singularities of stochastic electromagnetic beams. The motion and annihilation, as well as the changes in the polarization of spectral Stokes singularities, take place in the free-space propagation. The results are illustrated by numerical examples.

Spatial distributions of the energy and energy flux density of partially coherent electromagnetic beams in atmospheric turbulence.

The formulas of the energy and energy flux density of partially coherent electromagnetic beams in atmospheric turbulence are derived by using Maxwell's equations. Expressions expressed by elements of electric cross spectral density matrixes of the magnetic and the mutual cross spectral density matrix are obtained for the partially coherent electromagnetic beams. Taken the partially coherent Cosh-Gaussian (ChG) electromagnetic beam as a typical example, the spatial distributions of the energy and energy flux density in atmospheric turbulence are numerically calculated. It is found that the turbulence shows a broadening effect on the spatial distributions of the energy and energy flux density. Some interesting results are obtained and explained with regard to their physical nature.

Dynamic evolution of an edge dislocation through aligned and misaligned paraxial optical ABCD systems.

The closed-form propagation expressions of an edge dislocation nested in a general elliptical Gaussian beam through aligned and misaligned paraxial optical ABCD systems are derived and used to study the dynamic evolution behavior of the edge dislocation propagating in free space and through a misaligned lens. It is shown that the noncanonical vortex and dynamic inversion of the topological charge, as well as a new edge dislocation may appear under certain conditions. The results are illustrated analytically and numerically.

Effects of astigmatism on spectra, coherence and polarization of stochastic electromagnetic beams passing through an astigmatic optical system.

Analytical formulas for the cross-spectral density matrix of stochastic electromagnetic Gaussian Schell-model (EGSM) beams passing through an astigmatic optical system are derived. We show both analytically and by numerical examples the effects of astigmatism on spectra, coherence and polarization of stochastic electromagnetic EGSM beams propagating through an astigmatic lens. A comparison with the aberration-free case is made, and shows that the astigmatism has significant effect on the spectra, coherence and polarization.

Comparative study of the beam-width spreading of partially coherent Hermite-sinh-Gaussian beams in atmospheric turbulence.

Taking the partially coherent Hermite-sinh-Gaussian (H-ShG) beam as a more general type of partially coherent beams, a comparative study of the beam-width spreading of partially coherent H-ShG beams in atmospheric turbulence is performed by using the relative width, normalized beam width, and turbulence length. It is shown that the relative width versus the beam parameters, such as the spatial correlation length sigma(0), beam orders m, n, Sh-part parameter Omega(0), and waist width w(0), provides a simple and intuitive insight into the beam-width spreading of partially coherent H-ShG beams in turbulence, and the results are consistent with those using the turbulence length. The validity of our results is interpreted physically.

Effect of dispersion on the spectrum of partially coherent beams.

Taking the Gaussian Schell-model (GSM) beam as a typical example of partially coherent beams, the analytical expressions of the spectrum of GSM beams propagating in dispersive media are derived, and the spectral properties are studied in detail. It is shown that, in comparison with propagation in free space and in turbulence, whether or not GSM beams satisfy the scaling law, the normalized spectrum of GSM beams in dispersive media changes on propagation in general, because the dispersive medium affects different spectral components differently. As compared with the free-space propagation, for the scaling-law GSM beams the dispersion results in spectrum change, and for the nonscaling-law GSM beams the dispersion gives rise to a further increase in spectral changes. The structure constant of the dispersive property of the media, the transverse coordinate of the observation point, the spatial correlation length of the source, and the propagation distance affect the spectral behavior of GSM beams; this effect is illustrated numerically.

Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence.

The propagation of partially coherent Hermite-cosh-Gaussian (H-ChG)beams through atmospheric turbulence is studied in detail. The analytical expression for the angular spread of partially coherent H-ChG beams in turbulence is derived. It is shown that the angular spread of partially coherent H-ChG beams with smaller spatial correlation length sigma0, smaller waist width w0, smaller beam parameter Omega0, and larger beam orders m, n is less affected by turbulence than that of partially coherent H-ChG beams with larger sigma0, w0, Omega0, and smaller m, n. Under a certain condition partially coherent H-ChG beams may generate the same angular spread as a fully coherent Gaussian beam in free space and also in atmospheric turbulence. The angular spread of partially coherent Hermite-Gaussian (H-G), cosh-Gaussian (ChG), Gaussian Schell-model (GSM) beams, and fully coherent H-ChG, H-G, ChG, Gaussian beams is studied and treated as special cases of partially coherent H-ChG beams. The results are interpreted physically.

Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence.

The closed-form expression for the mean-squared beam width of partially coherent Hermite-Gaussian (H-G) beams propagating through atmospheric turbulence is derived. The influence of turbulence on the spreading of partially coherent H-G beams is studied quantitatively by examining the mean-squared beam width. It is found that the smaller the coherence length sigma(0) of the source is, and the larger the beam order m and the wavelength lambda are, the less partially coherent H-G beams are affected by the turbulence, although the beams with smaller sigma(0), larger m, and larger lambda have greater spreading in free space. In addition, it is shown that two partially coherent H-G beams may generate the same angular spread and that there exist equivalent partially coherent H-G beams that may have the same directionality as a fully coherent Gaussian beam in free space and also in turbulence. The results are illustrated by examples, and a comparison with previous work is also made.

Influence of atmospheric turbulence on the spatial correlation properties of partially coherent flat-topped beams.

The analytical expression for the spectral degree of coherence of partially coherent flat-topped beams propagating through the turbulent atmosphere is derived, and the spatial correlation properties are studied in detail. In particular, we find that the oscillatory behavior and phase singularities of the spectral degree of coherence may appear when partially coherent flat-topped beams propagate through the turbulent atmosphere; this behavior is very different from the behavior of Gaussian Schell-model beams. But the oscillatory behavior becomes weaker with increasing turbulence and even disappears when the turbulence is strong enough. The width of the spectral degree of coherence is always smaller than that of the spectral density in the far field when the turbulence is strong enough, whereas the width of the spectral degree of coherence in free space can be either larger or smaller than that of the spectral density in the far field.

Three-dimensional calculation of high-power, annularly distributed, laser-beam-induced thermal effects on reflectors and windows.

Based on the three-dimensional transient heat conduction equation and the elastic stress-strain equation, the temperature rise, distortion, and equivalent stress distributions of a high-reflectivity silicon reflector and a white bijou window irradiated by a high-power sloped annularly distributed laser beam are simulated using a three-dimensional finite element model (FEM). The effects of laser intensity, output duration, beam obscure ratio, and laser intensity spatial gradient on the results are especially investigated. The effects of mirror and window thermal distortion on laser beam phase aberrations are also evaluated. This noncylindrosymmetric three-dimensional FEM can be used to evaluate high-power, high-energy, laser beam-induced thermal effects on optical components.

Propagation of Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation.

On the basis of the vectorial Rayleigh-Sommerfeld formulas and by means of the relation between Hermite and Laguerre polynomials, the analytical expressions for the propagation of the Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) beams beyond the paraxial approximation are derived, with the corresponding far-field propagation expressions and that for the Gaussian beams being given as special cases of the results. Some detailed comparisons of our results with the expansion series and paraxial expressions are made, which show the advantages of our results over the expansion series. With the results obtained, some typical intensity patterns of nonparaxial HG and LG beams are shown.

Polarization properties of vectorial nonparaxial Gaussian beams in the far field.

The polarization properties of vectorial coherent nonparaxial Gaussian beams are studied. It is shown that, when the source of a nonparaxial Gaussian beam is completely polarized, the degree of polarization of the propagation field maintains a constant value of 1. However, when the source is completely unpolarized, the degree of polarization does not maintain a constant value of 0. In the far field, vectorial nonparaxial Gaussian beams can become partially polarized, except on the propagation axis, and are spatially nonuniform across a typical cross section of the beam even though the source field is completely unpolarized.

Improved diffraction integral for studying the diffracted field of a spherical microlens.

By introducing a new kind of Green function, we formulate an improved diffraction integral, which can be used to numerically evaluate the diffracted field of a microlens of plane-convex shape. Analytical expressions for the diffracted field of microlens are derived for the case where the curvature radius of the convex surface is larger than the dimension of the microlens aperture. The validity of the results and the diffracted field of the microlens are illustrated with numerical examples. The focal shifts of the diffracted field are found to depend mainly on the Fresnel number N of the microlens.

Propagation of the Wigner distribution function for partially coherent nonparaxial beams.

On the basis of the Rayleigh-Sommerfeld diffraction integral, a closed-form propagation expression for the Wigner distribution function of partially coherent nonparaxial beams in free space is derived for what is to our knowledge the first time. The propagation of spatially fully coherent nonparaxial beams is treated as a special case of our general result. Application of the result is illustrated with the nonparaxial propagation of partially coherent anisotropic Gaussian-Schell-model beams and TEM11-mode Hermite-Gaussian beams.