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.     

任意偏振态光束全反射时的侧向和横向位移

光束在电介质界面发生全反射时,实际反射光束会在入射面内相对于几何反射光束产生一侧向位移,在垂直于入射面的方向产生一横向位移。利用改进的能流法研究了任意偏振态光束发生全反射时的侧向和横向位移特性。研究表明,侧向位移的大小与入射光束的两组成部分———TE和TM偏振光的相位差无关,而与两组分的光强比密切相关,且该位移可以表示为TE和TM偏振光束各自的位移按光强的加权平均。横向位移的大小不仅与入射光束两组分的光强比相关,还与组分的相位差密切相关。另外,反射光束不仅在椭圆偏振态入射的情况下会产生横向位移,而且在TE和TM偏振态之外的其他线偏振态入射时,也会产生横向位移。     

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.     

双棱镜结构中透射光束的古斯-汉欣位移

当入射角大于全反射临界角时,双棱镜结构中透射和反射光束的古斯-汉欣(Goos-Haenchen)位移具有饱和效应,并且只有波长数量级。利用稳态相位法研究了当入射角小于全反射临界角时双棱镜结构中透射光束的古斯-汉欣位移。研究表明,传播模式下透射光束的古斯-汉欣位移是空气层厚度、入射角和双棱镜折射率的周期性函数。当透射共振时,透射光束的古斯-汉欣位移可达入射波长的几十倍,与入射角大于全反射临界角的情况相比,透射光束的位移通过边界的相互作用具有共振增强效应;在非共振点处,对称结构中的反射光束具有与透射光束相同的古斯-汉欣位移。共振增强的透射光束的位移在光开关及光耦合器中具有潜在的应用。     

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.     

Lateral beam displacements in transmitting layered structures

The lateral shift of both the reflected and the transmitted beams are examined for incidence on layered configurations. In particular, beam displacements are evaluated at a layer placed between two different semi-infinite media. We find that the reflected beam may undergo a large displacement, which occurs in either a forward or a backward direction. The transmitted beam is also substantially displaced, but its shift occurs in a forward direction only.     

Giant bistable lateral shift owing to surface-plasmon excitation in Kretschmann configuration with a Kerr nonlinear dielectric

We investigate the reflection of a TM-polarized light beam from a Kretschmann configuration with a Kerr nonlinear dielectric. It is found that there exists a hysteretic response between the lateral shift of the reflected beam and the intensity of the incident beam. In contrast to the lower switch threshold, the higher switch threshold of optical bistability is more sensitive to the variations of the angle of incidence and the thickness of metal film. It is also found that the peak value of the lateral shift is strongly dependent on the thickness of metal film.     

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.

     

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.     

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.     

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.     

Peculiarities of light beam reflection from the boundary of a 1D-photonic crystal

Typical cases of lateral shift and deformation of the profile of two-dimensional light beams reflected from the surface of a one-dimensional photonic crystal are considered. We use harmonic modulation of the spatial dependence of dielectric permeability of a crystal, which permits one to study reflectance profiles analytically. The results of numerical calculations that were performed are presented for the cases when the angular spectrum of the incident beam is split.     

Analytical model for the grazing reflection of a narrow beam

We propose an analytical model for the grazing reflection of a narrow beam. For the special incidence condition, the output field is the superposition of the incidence and reflected fields, so the incidence cutoff frequency is defined in the angular spectrum. With the definition, we deduce the effective plane-wave-reflection coefficient, together with angular spectrum of the output field. The model is verified by numerical simulation. Calculation in ordinary linear, nonabsorbing media with this model reveals some remarkable characteristics of the output fields, such as negative lateral shift and a beam-width compression effect.     

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.     

Negative and positive lateral shift of a light beam reflected from a grounded slab

We consider the lateral shift (LS) of a light beam reflecting from a dielectric slab backed by a metal. It is found that the LS of the reflected beam can be negative while the intensity of reflected beam is almost equal to the incident one under a certain condition. The explanation for the negativity of the LS is given in terms of the interference of the reflected waves from the two interfaces. It is also shown that the LS can be enhanced or suppressed under some other conditions. The numerical calculation on the LS for a realistic Gaussian-shaped beam confirms our theoretical prediction.     

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.     

Low-power laser deformation of an air-liquid interface

We report on the deformation of an air-water surface with a totally reflected low-power laser beam, inducing a convex mirror effect on the beam propagation. This bending is stronger close to the critical angle and depends on the polarization of the laser light. A model, leading to a simple dependence between the Goos-H?nchen shift and the radius of curvature of the interface, supports these observations. Bendings with radius of curvature as low as 0.10 m are demonstrated.     

Physical origin of large positive and negative lateral optical beam shifts in prism-waveguide coupling system

Large lateral beam shift in prism-waveguide coupling system is theoretically analyzed from the viewpoint of interference between multiple reflected beam constituents. It is shown that the reflected beam is a result of interference between two beams: the beam directly reflected from the prism and the total leaky beam coming from guided mode. The thickness of coupling layer determines the amplitude of the total leaky beam, and further determines the sign (positive or negative) of the reflected beam shift. Because of interference between two beams, intrinsic damping itself plays an important role in deciding the distortion of the reflected beam.     

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,     

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。