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.     

Total reflection of a light beam at a dielectric interface: A comparative study

A rigorous plane-wave integral representation is employed to investigate the reflected field of a light beam, having a Cauchy profile, which is incident from a denser medium upon the interface to a rarer medium. Explicit analytical and graphical results are obtained for both the lateral (Goos-Hänchen) shift of the actual reflected beam from the position predicted by geometric optics, and the lateral-wave-produced trailing radiance that accompanies the reflected beam and persists for distances large compared to the beamwidth, to the right of that beam. Those results are compared analytically and graphically with prior results obtained for a Gaussian beam. That comparison demonstrates strikingly close correspondence between the two sets of results, and serves to point to the generality of features of the beam shift and lateral-wave field produced by symmetric beams having a spectral density concentrated about the symmetry axis.

     

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.     

Negative Goos-Hanchen Effect in Thin-Film Fabry-Perot Filter

We investigate the Goos-Hgnchen effect of a Gaussian light beam reflected by the thin-film Fabry-Perot filter. It is shown that the Goos-Hanchen shift can be either negative or positive, The Gaussian-beam analysis and stationary phase method are introduced to calculate the lateral shift between the incident beam and the reflected beam at different wavelengths and to analyse the Goos-Hgnchen effect in the thin-film Fabry-Perot filter, The effect of the incident beam diameter is also discussed,     

Beam Displacement in a Layered Configuration due to Formation of Standing Waves

We obtain a large positive lateral shift of a light beam reflected from a layered configuration due to the formation of the unusual standing wave, which acts like the forward surface wave. An explicitly analytic condition to obtain the large lateral shift is presented. Finally we present a numerical simulation for the lateral displacement of a Gaussian beam.     

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.     

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。     

Analysis of the positive or negative lateral shift of the reflected beam in Otto configuration under grazing incidence

We investigate the lateral shift of a TM-polarized light beam reflected from Otto configuration under grazing incidence. It is found that the lateral shift is strongly dependent on the thickness of the air-gap layer. By employing the pole-null representation, we demonstrate that the lateral shift is closely related to the null of the reflection function. The numerical simulations for a Gaussian beam are performed to demonstrate the validity of our theoretical analysis.     

Non-geometrical effects on Gaussian beams transmitting through a thin dielectric slab

It is shown that a Gaussian light beam transmitting through a planar thin dielectric slab in the air undergoes four different effects, i.e. lateral Goos-Hanchen-like （GHL） displacement, angular deflection, width modification and longitudinal focal shift as compared with the results predicted by geometrical optics. According to the Taylor expansion of the exponent of transmission coefficient when expressed as an exponential form, the lateral GHL displacement and the angular deflection are the first-order effects and can be negative or positive. The width modification and the longitudinal focal shift are the second-order effects and can also be positive or negative. Owing to the waist-width dependent term, the non-geometrical effects of transmitted beam are not identical with the non-specular effects of reflected beam. The conditions for the validity of those effects are suggested and numerical simulations are also given.     

左手材料平板对傍轴高斯光束聚焦特性分析

在傍轴近似下,推导出了左手材料平板聚焦系统的传输矩阵,并利用ABCD定律得到了高斯光束在左手材料中和经过平板透镜聚焦后的传输公式。高斯光束在左手材料内部和像空间的传输公式的研究表明:像高斯光束和物高斯光束束腰大小一致,即左手材料平板透镜实际上对高斯光束没有聚焦作用。研究同时表明左手材料平板对高斯光束的聚焦与几何光学成像规律完全一致,而不存在一般透镜聚焦时的焦移效应。     

Spectral shift of a stochastic electromagnetic Gaussian Schell-model beam in a Gaussian cavity

Spectral changes of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam interacting with a Gaussian cavity are investigated. It is shown that the spectral shift is mainly determined by the degree of polarization of the initial beam and by the parameters of the cavity. Generically the blue shift occurs at on-axis points, while the red shift can occur at off-axis points. The condition under which the relative spectral shift is independent of the degree of polarization of the initial beam is analyzed.     

Total internal reflection of a Gaussian light beam

An approximate theoretical model for calculating the reflected and refracted fields of a Gaussian light beam at a plane interface between two isotropic media is formulated on the basis of a Fourier integral. In the vicinity of the critical angle of incidence (for total internal reflection) the model predicts the presence of two refracted beams, one displaced along the interface by an amount equal to the Goos-Hänchen shift; curvature of the phase fronts and nonalignment of the effective directions of energy and phase propagation occur for each beam, as in an anisotropic medium.     

Implications of spectral hole burning on the manipulation of spatial Goos–Hänchen shift in an atomic cell

We present a new scheme to report on Goos–Hänchen (GH) shift experienced by the Gaussian light beam interacting with an optical cavity filled with four-level sodium atomic medium in the spectral hole burning region with and without Doppler broadening effect. Theoretical atomic density-matrix formalism is employed to obtain the susceptibility of atomic medium while the stationary-phase-theory is used to compute the GH shift in the reflected and transmitted probe beams subjected to control fields. A steep normal slope of dispersion is observed with a maximum and zero probability of transmission and reflection coefficients, respectively, at the regions of the spectral holes burning. In the normal dispersion spectrum at the region of spectral hole burning, positive and negative GH shift is observed, respectively, in the transmitted and reflected light beams. However, at anomalous dispersive regions negative GH shift in the transmission beam and positive GH shift in the reflection beam is observed. The reflection and transmission coefficients as well as the spatial GH shift are the functions of probe detuning, collective phase of control fields, beam incident angle and inverse Doppler broadening effect in the spectral hole burning region. The position and number of spectral holes also depend on the same spectral parametrs as stated above. The study is expected to be useful for optoelectronic devices and optical-clocking applications.     

Transmission Characteristics of a Gaussian Electromagnetic Beam by a Cylindrcal Wire Grid

In this paper, the scattering formulae of a Gaussian electromagnetic beam by a cylindrical wire grid are derived. For the summation of Hankel functions, we adopt an integral form of lattice sums, which is developed by Yasumoto and Yoshitomi, to speed up convergence. The reflected and transmitted characteristics of a Gaussian beam by an actual wire grid are thoroughly investigated. Detailed simulation results are presented.     

高斯光束对标准硅球直径测量的影响分析

针对高精度硅球直径测量系统的特点,分析平面波反射光的多光束干涉和双光束干涉,以及正入射时高斯光束反射光中心的多光束干涉和双光束干涉,对不同条件下的高斯光束反射光中心的干涉光强进行了数值模拟.对采用五步相移算法时高斯多光束干涉的影响进行了研究,给出了特定参数条件下不同束腰ω0和传播距离z时的最大相位误差,当ω0=5 mm,z=2000 mm时的最大相位误差达0.08%.     

会聚高斯光束焦点附近的三维光分布状态

根据惠更斯 菲涅耳原理 ,推导出了会聚高斯光束经圆形孔径衍射后焦点附近的三维光分布状态级数表达式 ,并与经典的均匀光波理论进行了比较。讨论了会聚高斯光束焦移与光学系统及高斯光束参数的关系。给出了会聚高斯光束焦点附近的等照度线图。结果表明 ,对于大菲涅耳数系统来说 ,其光强分布具有对称性     

Large negative Goos-H(a)nchen shift from a wedge-shaped thin film

The analytical expression for the complex amplitude of light reflected from a wedge-shaped thin film is derived.For plane wave incidence,a simple ray tracing approach is used to calculate Goos-H(a)nchen(GH)shifts;and for non-plane wave incidence,for example,a Gaussian beam,the angular spectrum approach of plane wave is used in simulation.The two approaches predict that a wedge-shaped thin film can produce large negative longitudinal GH shifts.Although the reflectivity is small near the condition of resonance,the large negative GH shifts can be more easily detected in comparison with the shift from a plane-paxallel film in vacuum.     

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.     

Goos–Hänchen shift for higher-order Hermite–Gaussian beams

We study the reflection of a Hermite–Gaussian beam at an interface between two dielectric media. We show that unlike Laguerre–Gaussian beams, Hermite–Gaussian beams undergo no significant distortion upon reflection. We report Goos–H?nchen shift for all the spots of a higher-order Hermite–Gaussian beam near the critical angle. The shift is shown to be insignificant away from the critical angle. The calculations are carried out neglecting the longitudinal component along the direction of propagation for a spatially finite, s-polarized, full 3D vector beam. We briefly discuss the difficulties associated with the paraxial approximation pertaining to a vector Gaussian beam.     

Spectral shift of a twisted electromagnetic Gaussian Schell-model beam focused by a thin lens

Spectral changes of a twisted electromagnetic Gaussian Schell-model (EGSM) beam focused by a thin lens are investigated by using a tensor method. It is shown that the spectral shift is mainly determined by the degree of polarization, twist phase and correlation coefficients of the initial beam. Generically the blue shift occurs at on-axis points, while the red shift can occur at off-axis points.