A vector raytracing equation for hologram lenses of arbitrary shape

A single vector equation is given, including the effect of wavelength change, for tracing rays in the geometrical optics approximation.     

Berry effect in unmagnetized inhomogeneous cold plasmas

The propagation of electromagnetic waves in an unmagnetized weakly inhomogeneous cold plasma is examined. We show that the inhomogeneity induces a gauge connection term in wave equation, which gives rise to Berry effects in the dynamics of polarized rays in the post geometric optics approximation. The polarization plane of a plane polarized ray rotates as a result of the geometric Berry phase, which is the Rytov rotation. Also, the Berry curvature causes the optical Hall effect, according to which, rays of left/right circular polarization deflect oppositely to produce a spin current directed across the direction of propagation.     

The scattering matrix of transparent particles of random shape in the geometrical optics approximation

A numerical model that allows one to calculate elements of the scattering matrix for transparent particles of random shape in the geometrical optics approximation is presented. It is shown that a deviation from sphericity, which, in particular, is modeled by a reduction of the number of triangular facets approximating a sphere, essentially affects the magnitude, position, and width of peaks of the photometric and polarimetric indicatrices. Thus, when 1500 facets were used for the approximation, the amplitude of the polarimetric peak associated with the first rainbow, which is located close to the scattering angle 160°, decreases by a factor of two. Calculations showed that, in the region of backscattering, for particles of an arbitrary shape, the linear polarization ?F ₁₂/F ₁₁ has no negative branch, which is well observed for spherical particles. In going from spherical to nonspherical particles, the backscattering peak also disappears. The indicatrices for particles of irregular shape that were calculated for small distances from the center of a particle noticeably differ from the indicatrices at infinity. Thus, when simulating multiple scattering in dense powderlike media, the use of particle scattering indicatrices that were calculated for infinite distances is incorrect even in the geometrical optics approximation.     

Contribution of the second-order born approximation to the coherent bremsstrahlung cross section by relativistic electrons and positrons in crystals

Equations for the cross section and polarization of the coherent bremsstrahlung emitted by relativistic electrons and positrons in crystals are obtained taking into account the contribution from the second-order Born approximation. The radiation cross section and polarization in the field of the atomic plane is considered as a function of the charge sign of the particle.     

Spatial screening solitons as particles

Photorefractive spatial screening solitons are treated as rays using geometrical optics. The ray picture is transformed into a classical mechanics picture, in which solitons move self-consistently as particles in a potential created by the induced change in the refractive index. The Hamiltonian equations of motion are integrated to yield trajectories that agree with the optical center-of-mass trajectories. The motion in the transverse plane is found to be not central and the orbits are not closed, preventing the spiraling of solitons.     

Spatial-angular Mueller matrices

Arbitrary polarization changing devices are described within paraxial approximation by their action on the spatial angular Stokes parameters associated with the generalized rays of a Wigner formulation of wave optics. This approach leads to the introduction of generalized Mueller matrices being functions of the spatial and angular variables parameterizing generalized rays. We apply this approach to a polarization grating.     

Electromagnetic light rays in local dielectrics

An approach to deal with the limit of geometrical optics of electromagnetic waves which propagate in moving nonlinear local dielectric media in the context of Maxwellian electrodynamics is here developed in order to apply to quite general material media. Fresnel equations for the light rays are generically found, and its solutions are intrinsically obtained. The multi-refringence problem is addressed, and no more than four monochromatic polarization modes are found to propagate there.     

Direct simulation Monte Carlo ray tracing model of light scattering by a class of real particles and comparison with PROGRA experimental results

The Direct Simulation Monte Carlo (DSMC) model is presented for three-dimensional single scattering of natural light by suspended, randomly oriented, optically homogeneous and isotropic, rounded and stochastically rough cubic particles. The modelled particles have large size parameter that allows geometric optics approximation to be used. The proposed computational model is simple and flexible. It is tested by comparison with known geometric optics solution for a perfect cube and Lorenz–Mie solution for a sphere, as extreme cases of the class of rounded cubes. Scattering and polarization properties of particles with various geometrical and optical characteristics are examined. The experimental study of real NaCl crystals with new Progra² instrument in microgravity conditions is conducted. The experimental and computed polarization and brightness phase curves are compared.     

Geometric phase in a flat space for electromagnetic scalar waves

We show the existence of a fundamental geometric phase for classical electromagnetic fields arising after cyclic paths in a plane instead of a sphere. This phase is dispersive, is not related to polarization, distinguishes geometrical from wave optics, and can be easily measured in an interferometric arrangement.     

Geometrical-numerical approach to diffraction phenomena

The calculation of diffracted fields is considered by means of a geometrical analysis of the incoming wave into semiperiodic zones in the aperture plane, followed by a numerical process for addition of the contributions corresponding to the semiperiodic zones. This general approach constitutes a novel interpretation of diffraction phenomena that permits exact evaluation of the mathematical expressions of diffraction theory and overcomes the limitations of any approximation. The method is illustrated by analysis of two important configuration in optics: the pinhole camera, for which we deduce the optimum radius for imaging, and the diffraction of a spherical converging wave through a circular aperture, from which we determine the limit of the validity of the Fraunhofer approximation (i.e., of the Airy pattern) and the influence of the obliquity factor.     

Geometrical optics of moving media

The propagation of a monochromatic light wave in a medium moving at a spatially nonuniform velocity is described in terms of geometrical optics. An eikonal equation is derived to the first order in the parameter v/c (where v is the velocity of the medium and c is the velocity of light). It is shown that the nonuniformity of the motion of the medium leads to a shift and bending of the light rays and to a rotation of the plane of polarization. The estimates obtained demonstrate the feasibility of observing the revealed effects in real experiments. These effects can be used to analyze the distributions of the velocity of motion of fluids and, possibly, gases.     

The 5f localization/delocalization in square and hexagonal americium monolayers: a FP-LAPW electronic structure study

The electronic and geometrical properties of bulk americium and square and hexagonal americium monolayers have been studied with the full-potential linearized augmented plane wave (FP-LAPW) method. The effects of several common approximations are examined: (1) non-spin polarization (NSP) vs. spin polarization (SP); (2) scalar-relativity (no spin-orbit coupling (NSO)) vs. full-relativity (i.e., with spin-orbit (SO) coupling included); (3) local-density approximation (LDA) vs. generalized-gradient approximation (GGA). Our results indicate that both spin polarization and spin orbit coupling play important roles in determining the geometrical and electronic properties of americium bulk and monolayers. A compression of both americium square and hexagonal monolayers compared to the americium bulk is also observed. In general, the LDA is found to underestimate the equilibrium lattice constant and give a larger total energy compared to the GGA calculations. While spin orbit coupling shows a similar effect on both square and hexagonal monolayer calculations regardless of the model, GGA versus LDA, an unusual spin polarization effect on both square and hexagonal monolayers is found in the LDA results as compared with the GGA results. The 5f delocalization transition of americium is employed to explain our observed unusual spin polarization effect. In addition, our results at the LDA level of theory indicate a possible 5f delocalization could happen in the americium surface within the same Am II (fcc crystal structure) phase, unlike the usually reported americium 5f delocalization which is associated with crystal structure change. The similarities and dissimilarities between the properties of an Am monolayer and a Pu monolayer are discussed in detail.     

Regions of validity of geometric optics and Kirchhoff approximations for reflection from Gaussian random rough dielectric surfaces

In this paper, the effects of characteristics of incident light and the geometrical parameters to the reflectivity of dielectric Gaussian random rough surfaces are presented. The behaviors of the reflectivity vs. several parameters are quantified using approximate methods: the geometric optics approximation (GOA) and the Kirchhoff approximation (KA) and an exact method called integral method (IM). Finally, we determine the limits of validity of approximate methods by comparisons with IM results. The regions of validity of approximate methods depending of many geometrical and physical parameters: roughness, Brewster and shadowing effects, multiple reflections, surface materials, and nature of polarization. The broader domain of validity (DV) is for KA, at normal TE-polarized incident light, for the higher dielectric permittivity. However, the narrowed DV is for GOA, at normal TM-polarized incident light for lower dielectric permittivity.     

Diffuse reflection by rough surfaces: an introduction

In this introductory paper, we present with some details the (mathematically) simplest methods proposed to compute the electromagnetic field scattered by a rough surface separating two homogeneous media. These methods remain largely used both in propagation and remote sensing problems. The methods described in the paper are:

• –the geometrical optics approximation, in which the wave is considered as a set of rays obeying the laws of reflection and refraction;
• –the small perturbation method, due to Rayleigh and Rice, in which the field is given as an expansion on a set of elementary harmonic plane waves, the coefficients of which are determined so as to satisfy the boundary conditions;
• –the Kirchhoff approximation, in which the field is given as an integral on the rough surface; in this method one needs to know some components of the field on the surface, and an approximation is substituted to the unknown true value.

We end with a short discussion of some problems not adequately solved by these methods, namely self-shadowing, multiple scattering and some inadequacies of the Gaussian model for random surfaces. To cite this article: M. Sylvain, C. R. Physique 6 (2005).     

Gravitational effects on the polarization plane

We study the rotation of the polarization plane of an electromagnetic wave due to a gravitational field. An evolution law for the polarization plane is derived in the geometric optics approximation. For the particular case of a Kerr space-time, we obtain the polarization plane rotation for an incident light ray parallel to the Z axis at z = - and for a radially outgoing one. The results are compared with others which have already appeared in the literature.     

On high-frequency scattering by a strip at nearly grazing incidence

The problem of diffraction by an absolutely soft segment is considered in the high-frequency approximation. The asymptotic field decomposition is obtained, which makes it possible to trace the transition from classical asymptotics valid for grazing incidence to geometrical optics asymptotics, which describes scattering at a finite (not small) angle.     

Optical magnus effect as a consequence of Berry phase anisotropy

Presented in this work is a modified geometric optics of smoothly inhomogeneous isotropic medium, which takes into account weak anisotropy introduced by inhomogeneity. Pointed out is the common nature of two fundamental phenomena: Berry’s geometrical phase and the optical Magnus effect, that is, propagation of rays of right and left circular polarization along different trajectories. Shown is that the former phenomenon can be explained by the difference in phase velocity of waves of right-hand and left-hand polarizations, while the latter one is the result of the difference in their group velocity. This work demonstrates that the optical Magnus effect is quite a topological effect that exclusively depends on the geometry of the system’s contour in the momentum space. We predict the effect of the splitting of a ray of mixed polarization into two circularly polarized rays and propose a scheme for the experimental observation of this phenomenon.     

Geometrical optics approximation for light scattering by absorbing spherical particles

By means of geometrical optics, an approximation method is presented to compute the light scattering intensity of absorbing spherical particles illuminated by a plane wave. For absorbing particles, the effective refractive index and the effective refractive angle are related to the complex refractive index and incident angle. The formulas for calculation of the break of phases of reflection and refraction, which are different from the case of transparent particles, are exactly derived. Verification of the geometrical optics approximation (GOA) was performed by case studies and comparison of the present results with the Mie scattering. It is found that agreement between the GOA and the Mie theory is excellent in forward directions for weakly/moderately absorbing particles. Differently, for strongly absorbing particles, good agreement between the calculation methods is in the forward directions and large scattering angles. The agreement between the GOA and the Mie theory is better for larger particles.     

The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields

One of the most poorly understood subjects in physical optics is the origin of the Gouy phase (sometimes called “the phase anomaly near focus”). This is evident from the large number of publications on the subject, many of which attribute it to quite different causes. In this paper we show that the Gouy phase anomaly can be clearly understood from elementary properties of normal congruences of light rays and from the relationship between geometrical optics and physical optics. We also show that the Gouy phase anomaly may be regarded as a degenerate case of a rapid π/2 phase change that is found to occur at each focal line of an astigmatic pencil of rays. The intensity distribution in the region of the phase changes is also presented. Furthermore, symmetry relations for both the phase anomaly and the intensity distribution are derived.     

Effect of a constant electric field on mutual rectification in a graphene superlattice

The effect of a transverse dc electric field on two-wave mutual rectification in a graphene superlattice (GSL) is investigated. Two field orientations are considered: (i) the polarization plane is parallel to the GSL axis and (ii) the polarization plane is perpendicular to the GSL axis. In both cases, the constant field is perpendicular to the polarization plane. The current density is calculated within a one-miniband model using the Boltzmann equation in the approximation of constant relaxation time.