Unified theory of total reflection phenomena at a dielectric interface

By utilizing a rigorous plane-wave representation, we investigate the basic wave mechanism that is responsible for both the lateral (Goos-H?nchen) shift of a gaussian light beam incident from a denser medium upon the interface to a rarer medium, and the weak radiance that accompanies the reflected beam. We thus find that the complete reflected field contains a geometric-optics component, whose domain is given by the mirror reflection of the incident beam, as well as a lateral-wave component which occupies a much larger domain. Our results show that the near field of the lateral-wave component interferes with the geometric-optics component and thereby produces the Goos-H?nchen shift of the reflected beam. The intermediate and far fields of the lateral-wave, on the other hand, are responsible for the weak radiance that trails the reflected beam. By demonstrating that both the beam shift and the trailing radiance represent two facets of the same wave process, the lateral-wave field is shown to provide a unified interpretation of two effects that have previously been regarded as separate phenomena. The dependence of these effects on beam width, angle of incidence, and polarization are also considered. Portions of this paper were presented orally at the Fall 1971 Meeting of the Optical Society of America, Ottawa, Canada; October 1971.     

Transformation and shift of a Gaussian light beam upon reflection from a resonant medium

The specific features of the transformation and shift of a Gaussian beam reflected from a resonant absorbing medium are analyzed numerically. The study is based on the expansion of the field of the incident Gaussian beam into plane-wave components by using the Fourier integral transform. The calculations are performed for a frequency range covering the resonance region. The conditions for the splitting of the profile of the reflected beam and for its negative shift are established.     

Lateral displacement of a Gaussian beam reflected from absorbing media

Lateral displacements of well-focused beams reflected from absorbing media are demonstrated in this paper. The incident beam is modeled as a tapered wave with a Gaussian spectrum. The field solutions are obtained on both sides of the interface by solving analytically from Maxwell's equations and by matching the boundary conditions at the interface. Numerical simulations are presented and the field values as well as the time-averaged power densities are computed. The influences of the polarization, the angle of incidence and the beam width on the displacement are discussed. The origin of the displacement lies in the absorption of the media, for which there is a phase shift between the incident and reflected waves. Because of this phase shift, the center of the reflected beam does not coincide with that of the incident one, similar to the Goos-Hänchen shift.     

Transformation of a Gaussian light beam reflected in the vicinity of the Brewster angle

Variations in the profile and shift of a Gaussian light beam upon reflection from a plane interface between a transparent dielectric and a medium with a complex refractive index are studied. The beam is assumed to be incident at angles close to the Brewster’s angle, where the effects of transformation of the beam profile are most substantial. Based on numerical analysis, the reflected beam profiles are obtained for different properties of the media, parameters of the incident beam, and positions of the plane of observation.     

Longitudinal shift and transformation of a Gaussian beam upon reflection from a thin film

Specific features of deformation of a Gaussian beam reflected from a thin film are studied on the basis of numerical analysis. A complex deformation of its profile is shown to be governed by three factors: by the character of behavior of the reflectance close to the angle of incidence, the Goos-Hanchen longitudinal shift, and by the shift in the direction of incidence of the beam, which is caused by the presence of the film-substrate interface. An approximate expression for the displacement of the “center of gravity” of the reflected beam is obtained.     

Reflected image of a strongly focused spot

We describe the reflection of a strongly focused beam from an interface between two dielectric media. If the beam is incident from the optically denser medium, the image generated by the reflected light is strongly aberrated. This situation is encountered in high-resolution confocal microscopy and data sampling based on solid immersion lenses and oil immersion objectives. The origin of the observed aberrations lies in the nature of total internal reflection, for which there is a phase shift between incident and reflected waves. This phase shift displaces the apparent reflection point beyond the interface, similarly to the Goos-H?nchen shift.     

Experimental study on a quasi-optical mode converter for transforming the whispering-gallery mode into a circularly polarized hollow radiation beam

An experiment was carried out for transforming the 120 GHz-TE_12.2 whispering-gallery mode (WGM) into a circularly polarized hollow radiation beam. A hollow beam was formed by reflecting the WGM, which was radiated from a 16 mm radius circular waveguide cut, with an annular mirror having suitable local normal vectors. The experimentally observed field intensity profiles of the reflected wave were in good agreement with calculated results.     

Control of direction of Goos–Hänchen shift on reflection from a weakly absorbing medium

The Goos–Hänchen effect of reflected beams at the interface between isotropic medium and weakly absorbing medium was studied. We find that there is a lateral shift when a light beam travels through the interface for reflected beam for TM wave. The influence of permeability and permittivity on the Goos–Hänchen shift was discussed, respectively. When the weakly absorbing medium is right-handed material the imaginary of magnetic permeability will control the direction and magnitude of the shift. On the contrary, when the weakly absorbing medium is left-handed material, the refractive index of the isotropic medium determines the direction and magnitude of the shift.     

Experimental observation of spin-independent transverse shift of the centre of gravity of a reflected Laguerre-Gaussian light beam

We report experimental observation of a transverse shift of the centre of gravity of partially reflected optical beam having non-zero orbital angular momentum. The results are in reasonable agreement with the theoretical predictions. Possibility of using such shift for measurement of orbital angular momentum state of photon is discussed.     

Negative and positive Goos–Hänchen shifts of a light beam transmitted from an indefinite medium slab

We study the lateral shift of a light beam transmitted from an indefinite medium slab. The analytic expressions for the transmission coefficient and the lateral shift are obtained by using the stationary-phase method, and different conditions for the occurrence of a negative lateral shift are deduced. It is shown that the thickness of the indefinite medium strongly affects the properties of the lateral shift. For a larger thickness, the sign of the lateral shift depends only on the signs of the permittivity and permeability, while, for a smaller thickness, the sign of the lateral shift is determined by the combined effect of the incident angle of the light, the signs of the permittivity and permeability, and the thickness of the indefinite medium slab. In addition, the lateral shift at the transmitted resonance points is found to be enhanced greatly, and the sign of the lateral shift around the transmitted resonance points is strongly dependent on the permittivity and permeability of the indefinite medium. Some examples are given to validate the obtained theoretical results. PACS 41.20.Jb; 42.25.Gy; 42.25.Bs; 78.20.Ci; 78.68.+m     

Goos–Hänchen shifts of a light beam reflected from the interface of colloidal ferrofluids

Controllable Goos–Hänchen shift of a light beam reflected from the colloidal ferrofluids is investigated by using the stationary-phase method. It is found that the Goos–Hänchen shift can be easily controlled by the local H_e factor and the volume factor. Using this scheme, the peak value, the peak position and the width of the Goos–Hänchen shift can all be controlled by adjusting the external magnetic field for a fixed configuration, which also provides a possibility for obtaining larger negative Goos–Hänchen shift by changing the external controlling field. Our results have potential applications in optical devices.     

Negative shift of a light beam reflected from the interface between optically transparent and resonant media

The lateral shift of a light beam reflected from the interface between an optically transparent dielectric and a medium for which the frequency dependences of the real and imaginary parts of the permittivity have a resonant form is investigated. At certain radiation frequencies and angles of incidence, a negative displacement of the reflected beam along the interface takes place.     

Transmission behavior in a photorefractive polymer film

When a p-polarized beam propagates through a high-performance photorefractive polymer composite, poly dimethyl-4-(4^′-nitrophenylazo)benzene, its transmission behavior is influenced by three effects: the electroabsorption, the photorefractive coupling with the reflected beam from the rear surface, and the amplified scattering. From the measurements on the incidence angle dependence as well as the applied-electric-field dependence of the three effects, some conclusions are obtained. At a small incidence angle with a low applied electric field, both the amplified scattering and the electroabsorption are small whereas the coupling between the incident beam and the reflected beam plays a principal role. At a large incidence angle or with a high poling electric field, the transmission is influenced mainly by the amplified scattering and the electroabsorption. A poling electric field asymmetric loss to the amplification scattering is also observed. Received: 18 November 1998 / Revised version: 10 February 1999 / Published online: 12 April 1999     

吸收介质界面上反射高斯束的角位移

给出高斯入射束反射时角位移直接计算式，适用于任意入射角和反射介质有吸收的情况。计算式在布儒斯特角上不存在发散困难，对于Ｐ偏振和Ｓ偏振均适用，只要令ｇ１＝ｎ１，ｇ２＝０计算所得即为Ｓ偏振的角位移。     

Electromagnetic wave scattering from a random medium layer with a random interface

Abstract

The problem of electromagnetic wave scattering from a random medium layer with a random interface is considered. The layer has planar boundaries on average. Assuming that both the random perturbations of the interface and the random fluctuations of permittivity of the medium are small, a first-order perturbation solution to the scattered field is obtained. Using this solution, the bistatic scattering coefficients γ_αβ are calculated and expressed in a compact and meaningful form. The various terms that constitute γ_αβ are identified with distinct scattering processes. Since it is often of particular interest, the special case of backscattering is considered. Finally, the results are compared with those of others.     

光抽运小型铯束频标中光频移的测量与分析

在弥漫激光场抽运斜入射光检测小型铯原子束频标实验系统上 ,对弥漫激光场产生的散射光所引起的光频移 (主要是交流斯塔克移动 )以及光抽运区产生的荧光引起的光频移对铯束频标准确度的影响作了仔细的实验测量 ,并与理论计算结果作了比较分析。测量结果表明在正常工作条件下 ,散射光引起的光频移小于 - 2× 10 -13 ,荧光引起的光频移值在 0 8× 10 -13 左右 ,这样的光频移对小型光抽运铯束频标来说是可以接受的。     

Reflection and transmission of an Airy beam in a dielectric slab

The reflection and transmission of a finite-power Airy beam incident on a dielectric slab are investigated by an analytical method. Based on the plane-wave angular spectrum expansion and Fresnel approximation, the analytical expressions of the reflected field, internal field as well as transmitted field in each region are obtained. Through numerical simulations, the intensity distributions of the incident beam, reflected beam, internal beam as well as transmitted beam are presented at oblique incidence. Besides, we also compare the intensity distributions of the geometrical-optics beam field, the first order beam mode field and the actual beam field, which indicates that the contribution of each order beam mode field to the actual beam field is related to the refractive index of the dielectric slab. Meanwhile, the reflection characteristics of the Airy beams in the special cases of Brewster incidence and total reflection are investigated. Finally, the effects of the optical thickness and refractive index of the dielectric slab on the peak intensity distributions and beam shifts of the reflected and transmitted beams are also discussed in detail. The analytical and numerical results will be useful to analyze the propagation dynamics of Airy beam in the dielectric slab and provide some theoretical supports to the design of optical film.     

Finite thickness lens model for self-focusing (defocusing) in Kerr medium

A “finite thickness lens” model for self-focusing (defocusing) in Kerr medium is presented. An on-axis normalization transmittance formula is presented for arbitrary nonlinear phase shift for the finite thickness Kerr medium by introducing a nonlinear ABCD-matrix for the transition of a Gaussian beam from linear to non-linear medium, without complex calculation for the beam radius at the far field aperture. The variation of the peak and valley transmittance difference is found to enhance linearly as the phase shift at the focus increases by increasing the thickness of the medium. If the ratio of the Rayleigh istance divided by the thickness of the medium (d/z0) is constant and small enough, the peak and valley transmittance difference stays constant. Finally, a qualitative formula is presented to express the relationship between the system parameters and the on-axis phase shift at the focus.      

Scattering and diffraction of a plane wave from a randomly rough strip*

Abstract

This paper deals with plane wave scattering and diffraction from a randomly rough strip using a combination of three tools: the perturbation method, the Wiener-Hopf technique and a group-theoretic consideration based on the shift-invariant property of the homogeneous random surface. The D ^a -Fourier transformation associated with the shift invariance is defined instead of the conventional complex Fourier transformation. For a slightly rough case, Wiener-Hopf equations for the zero-, first- and second-order perturbed fields are derived. They are reduced to a common Wiener-Hopf equation, an exact solution of which is obtained formally by means of the Wiener-Hopf technique. Using the inverse D ^a -Fourier transformation, the scattered wavefield is obtained as a stochastic field. When the strip width is large compared with the wavelength, a uniformly asymptotic representation of the scattered far field is obtained by the saddle point method. For a Gaussian roughness spectrum, several numerical results are calculated and illustrated in figures, based on which the characteristics of scattering and diffraction are discussed.