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.

     

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.     

非常偏振光在单轴晶体表面的全反射分析

利用透射波函数和由菲涅尔公式求解反射相位差并对其求导的方法,分析了非常偏振光在单轴晶体表面发生的全反射现象,求解出晶体光轴在入射面内时,非常偏振光从各向同性介质入射到晶体和从晶体出射到各向同性介质两种情况的隐失波穿透深度和Goos-Hnchen位移的一般表达式。通过计算机模拟给出了单轴晶体为方解石和水晶情况时的穿透深度和Goos-Hnchen位移图像。结果表明,对于不同的晶体,光轴的取向对穿透深度和Goos-Hnchen位移的影响是明显不同的,若选取合适的晶体、光轴取向和入射角,可以得到较大的隐失波穿透深度和Goos-Hnchen位移。     

单轴各向异性左手介质表面的Goos-H?nchen位移

分析了单轴各向异性左手介质表面的Goos-H?nchen位移，分别给出了光轴与两种介质的界面垂直和平行情形下的Goos-H?nchen位移解析表达式，并分析了Goos-H?nchen位移产生的条件以及位移的正负情况.还采用菲涅尔近似的方法给出了临界角附近的Goos-H?nchen位移表达式，结果表明临界角附近的Goos-H?nchen位移是入射光的束腰半径和入射角的函数，并且给出了临界角入射时Goos-H?nchen位移的较为简洁的近似表达式，这样就在整个角度的取值范围内都给出了Goos-H?nchen位移的表达式. 关键词： Goos-H?nchen位移 左手介质 单轴各向异性 临界角     

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.     

Large and negative Goos-Hänchen shift near the Brewster dip on reflection from weakly absorbing media

Applying Artmann's formula to a light beam in the TM state of wave polarization, we show analytically the existence of a large and negative Goos-H?nchen shift near the angle of the Brewster dip on reflection from a weakly absorbing semi-infinite medium. The shift is opposite that in the case of total internal reflection, and it can be an order of magnitude larger than a wavelength if the absorption of the reflecting medium is sufficiently weak. Examples are given, and the detectibility of the shift is discussed.     

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。     

左手材料复合双棱镜内部界面的古斯-汉森位移

设计了一种左手材料复合双棱镜,由两块各向同性左手材料棱镜与夹在其间的、其界面与光轴成一定的角度的单轴各向异性左手材料平板构成.研究了发生在其内部界面上的古斯-汉森位移.分析了发生折射的条件和古斯-汉森位移的符号.研究发现,反射波与透射波有相同的古斯-汉森位移,透射波的古斯-汉森位移随着薄层厚度的增加而振荡,整体上呈增加趋势;在透射共振点,透射波的古斯-汉森位移达到极大值,且极大值可达入射波波长的数十倍;发现入射角和光轴与界面的角度对透射波的古斯-汉森位移有很大影响.最后简单地探讨了这种双棱镜的潜在应用.     

四能级原子介质中Goos-Hnchen位移的相干控制

通过外加驱动光场的调控改变腔中四能级原子介质的色散-吸收关系,从而来调控反射光和透射光的Goos-Hanchen位移.研究表明介质可同时对探测光场进行放大和吸收,在介质对探测光的吸收和放大相互抵消(即介质呈现透明特性)的区域附近,对Goos-Hanchen位移的控制比强吸收或强放大特性下要灵敏,可以实现位移的突变和增强.     

Solution to causality paradox upon total reflection

A dispute about the existence of an additional time (named as the Goos-H?nchen time) associated with the Goos-H?nchen shift in total reflection has recently arisen. At the same time, an inconsistency between the optical ray model and the electromagnetic theory also appears in the optical planar waveguide. By analyzing light propagation in an optical planar waveguide with both the zigzag-ray model and the electromagnetic theory, this paper shows that the Goos-H?nchen time really exists, and the total time delay upon total reflection upon an ideal nonabsorbing plasma mirror is the sum of the group-delay time and the Goos-H?nchen time. The causality paradox of total reflection of a TM wave upon an ideal nonabsorbing plasma mirror is also solved taking into consideration the negative Goos-H?nchen shift. Finally, the expression of the group velocity of the guided mode in optical planar waveguide was obtained, which clearly shows that the time delay upon total reflection is the sum of the group-delay time and the Goos-H?nchen time at given any time.     

Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts

We derive the polarization-dependent displacements parallel and perpendicular to the plane of incidence for a Gaussian light beam reflected from a planar interface, taking into account the propagation of the beam. Using a classical-optics formalism we show that beam propagation may greatly affect both Goos-H?nchen and Imbert-Fedorov shifts when the incident beam is focused.     

Opposite Goos-Hänchen shifts for transverse-electric and transverse-magnetic beams at the interface associated with single-negative materials

Goos-H?nchen shifts are investigated when total reflection occurs at the interfaces associated with single-negative materials (SNMs). A general rule for judging the direction of the Goos-H?nchen lateral shift concerning lossless media is obtained: Whether the lateral shift is positive or negative depends on the sign of micro1micro2 for TE-polarized incident beams and epsilon1epsilon2 for TM-polarized incident beams. It was theoretically demonstrated that, at the interface associated with SNMs, TE- and TM-polarized incident beams experience opposite Goos-H?nchen lateral shifts. An effective and simple approach to discriminating epsilon-negative material and micro-negative material is proposed.     

Controlling the Goos-H?nchen Shift via Incoherent Pumping Field and Electron Tunneling in the Triple Coupled InGaAs/GaAs Quantum Dots

We study the controlHng of the Goos-H?nchen(GH) shifts in reflected and transmitted light beams in the triple coupled InGaAs/GaAs quantum dot(QD) nanostructures with electron tunneling and incoherent pumping Geld.It is shown that the lateral shift can become either large negative or large positive,which can be controlled by the electron tunneling and the rate of incoherent pump Geld in different incident angles.It is also demonstrated that the properties of the GH shifts are strongly dependent on the probe absorption beam of the intracavity medium due to the switching from superluminal Hght propagation to subluminal behavior or vice versa.Our suggested system can be considered as a new theoretical method for developing a new nano-optoelectronic sensor.     

Energy flux and Goos-Hänchen shift in frustrated total internal reflection

Using Yasumoto and ?ishi's energy flux method, a generalized analytical formulation for analyzing the Goos-H?nchen (GH) shift in frustrated total internal reflection is provided, from which the GH shift given by Artman's stationary phase method is shown to equal the GH calculated by Renard's conventional energy flux method plus a self-interference shift. The self-interference shift, originating from the interference between the incident and reflected beams, sheds light on the asymptotic behavior of the GH shift in such optical tunneling process in term of energy flux.     

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.     

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.     

FDTD Simulation on the Interaction Between Gaussian Beam and Biaxial Anisotropic Metamaterial Slabs

The interaction between Gaussian beam and indefinite anisotropic metamaterial (AMM) slabs are simulated with auxiliary differential equation method in finite-difference time-domain method (FDTD). The directions of wave vector and energy flow densities in three types of AMM slabs are investigated. The field intensity distributions and phases of TE-polarized wave for the interaction between Gaussian beam and AMM slabs are given. Numerical results show that the sign of x component of relative permeability tensor of AMM determines the refraction is regular or anomalous, whereas the sign of z component of relative permeability tensor of AMM determines the energy flow is positively refracted or negatively refracted. Positive or negative Goos-H?nchen shift associated with Total Cutoff media are also shown. This work was supported by National Key Laboratory of Electromagnetic Environment fund (51486030305HT0101) and (9140C08060507ZCZJ18).     

Oscillating wave displacement sensor using the enhanced Goos-Hänchen effect in a symmetrical metal-cladding optical waveguide

An oscillating wave displacement sensor based on the enhanced Goos-H?nchen (G-H) effect in a symmetrical metal-cladding optical waveguide is proposed. Since the detected signal is irrelevant to the power fluctuation of the incident light and the magnitude of the G-H shift is enhanced to hundreds of micrometers, a 40 pm resolution is demonstrated in our experiment without employing any complicated optical equipment and servo techniques.     

Negative Goos-Hänchen shift in periodic media

We show that, under certain conditions, a negative Goos-H?nchen shift-a longitudinal displacement of a totally internally reflected wave packet-occurs in periodic media such as waveguide arrays.     

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.