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.     

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.     

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。     

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.     

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.

     

Positively and negatively large Goos–Hänchen lateral displacements from a symmetric gyrotropic slab

A detailed study on the lateral displacements of a transverse magnetic (TM) wave transmitted and reflected from a symmetric gyrotropic slab is presented. We give the analytic formulas for the transmission coefficient and the reflection coefficient, as well as the corresponding lateral displacements. It is found that due to the external magnetic field the displacement of a transmitted beam is different from that of reflected one, even for a lossless symmetric configuration. Furthermore, within the chosen frequency band, when the incident angle is near the Brewster angle, the shift of a reflected wave can be large with nonzero reflectance, and can be positive or negative depending on the direction of the applied magnetic field and the incident wave.     

Reflection–refraction of attenuated waves at the interface between a thermo-poroelastic medium and a thermoelastic medium

Phenomenon of reflection and refraction is considered at the plane interface between a thermoelastic medium and thermo-poroelastic medium. Both the media are isotropic and behave dissipative to wave propagation. Incident wave in thermo-poroelastic medium is considered inhomogeneous with deviation allowed between the directions of propagation and maximum attenuation. For this incidence, four attenuated waves reflect back in thermo-poroelastic medium and three waves refract to the continuing thermoelastic medium. Each of these reflected/refracted waves is inhomogeneous and propagates with a phase shift. The propagation characteristics (velocity, attenuation, inhomogeneity, phase shift, amplitude, energy) of reflected and refracted waves are calculated as functions of propagation direction and inhomogeneity of the incident wave. Variations in these propagation characteristics with the incident direction are illustrated through a numerical example.     

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.     

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,     

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.     

Reflection and transmission of Laguerre Gaussian beam from uniaxial anisotropic multilayered media

Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian(LG) beam from uniaxial anisotropic multilayered media are studied. The reflected and transmitted beam fields of an LG beam are derived. In the case where the principal coordinates of the uniaxial anisotropic media coincide with the global coordinates, the reflected and transmitted beam intensities from a uniaxial anisotropic slab and three-layered media are numerically simulated. It is shown that the reflected intensity components of the incident beam, especially the TM polarized incident beam, are smaller than the transmitted intensity components. The distortion of the reflected intensity component is more evident than that of the transmitted intensity component. The distortion of intensity distribution is greatly affected by the dielectric tensor and the thickness of anisotropic media. We finally extend the application of the method to general anisotropic multilayered media.     

Goos-Hänchen shifts at the interfaces between left- and right-handed media

The Goos-H?nchen shift caused by total internal reflection at the interface between two media is analyzed. For two media of the same handedness the Goos-H?nchen phase shift opposes the phase variation associated with propagation through the incident medium. The Goos-H?nchen lateral shift is in the same direction as the horizontal component of the incident energy flux. Conversely, for two media of opposite handedness the Goos-H?nchen phase shift reinforces the phase variation associated with propagation through the incident medium. The lateral shift is in the opposite direction of the horizontal component of the incident energy flux.     

Fringed sound fields and their interaction with liquid-solid interfaces

On the one hand, it is well known that Gaussian beams possess the ability to stimulate Rayleigh waves, resulting in the Schoch effect, a lateral beam displacement. This effect, often characterized by a reflected sound pattern consisting of two anti-phase beams, is due to the re-radiation of sound because of the stimulation of leaky Rayleigh waves. On the other hand, fringed sound beams are characterized by the fact that they consist of a number of neighboring anti-phase narrow beams. They are a first approximation of a sound field originating from a phased array of harmonic vibrating crystals in which each crystal vibrates in anti-phase compared to its neighbor. The individual lobes within the fringed sound pattern diverge much less than standard Gaussian beams of the same size. The current study investigates the interaction of fringed beams with a liquid-solid interface. It is found that under certain conditions, a fringed beam, incident at the Rayleigh angle, produces a reflected sound pattern that contains a wide lobe that is not fringed. It is also shown that under other conditions, contrary to the famous forward displacement of the reflected sound for incident Gaussian beams, a strong backward displacement occurs for fringed beams.     

基于维格纳方程的电子的古斯-汉欣位移

通过求解电子的维格纳方程研究二维电子气中电子的输运性质.我们发现电子在倾斜入射到势垒界面并反射时,出现与光波类似的古斯-汉欣位移.通过维格纳方程可以得到电子的瞬态演化,不仅可以计算古斯-汉欣位移还能研究电子在势垒内部的运动轨迹以及出现稳定古斯-汉欣位移的时间.与稳定相位法得到的古斯-汉欣位移对比发现,考虑古斯-汉欣位移...     

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.     

叶绿素中用简并的四波混频产生位相复共轭后向反射波

本文报道在叶绿素溶液中用简并的四波混频得到位相复共轭后向反射波的首次实验。实验表明,转换效率在作用长度为5毫米时达22％,这是一种高效率的四能级系统。在泵浦波强度恒定的情况下,入射物波强度与复共轭反射波强度成线性关系。研究了后向反射波的位相复共轭特性。在有畸变(相位和振幅的)介质存在时,由于这种位相复共轭特性仍能获得金属丝网格高质量的再现象。 关键词：     

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.     

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.     

Spin Hall effect of light in metallic reflection

We report the first measurement of the spin Hall effect of light (SHEL) on an air-metal interface. The SHEL is a polarization-dependent out-of-plane shift on the reflected beam. For the case of metallic reflection with a linearly polarized incident light, both the spatial and angular variants of the shift are observed and are maximum for -45°/45° polarization, but zero for pure s and p polarization. For an incoming beam with circular polarization states however, only the spatial out-of-plane shift is present.