A. Aiello, J. P. Woerdman
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-Hänchen and Imbert-Fedorov shifts when the incident beam is focussed.
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Goos-Haenchen and Imbert-Fedorov shifts are diffractive corrections to geometrical optics that have been extensively studied for a Gaussian beam that is reflected or transmitted by a dielectric interface. Propagating in free space before and after reflection or transmission, such a Gaussian beam spreads due to diffraction. We address here the question how the Goos-Haenchen and Imbert-Fedorov shifts behave for a ``nondiffracting'' Bessel beam.
We present a visual interpretation of fiber mode degeneracy lifting as SOI (Imbert-Fedorov shift) of OAM modes in a ray picture, and the analytical results are verified by comparing them with eigen equation solutions.
It is shown that the spatial Goos-Hänchen shift is greatly affected by spatial coherence. A typical example is given.
We present a theoretical study of the Goos-Hänchen and Imbert-Fedorov shifts for a fundamental Gaussian beam impinging on a surface coated with a single layer of graphene. We show that the graphene surface conductibility $σ(ω)$ is responsible for the appearance of a giant and negative spatial Goos-Hänchen shift.
In this work, I present a full analytical theory for the Goos-Hänchen and Imbert-Fedorov shifts experienced by an Airy beam impinging on a dielectric surface. In particular, I will show how the decay parameter $α$ associated with finite energy Airy beams is responsible for the occurence of giant angular shifts. A comparisons with the case of Gaussian beams is also discussed.
In this work we investigate the role of the beam astigmatism in the Goos-Hänchen and Imbert-Fedorov shift. As a case study, we consider a Gaussian beam focused by an astigmatic lens and we calculate explicitly the corrections to the standard formulas for beam shifts due to the astigmatism induced by the lens. Our results show that astigmatism may enhance the angular part of the shift.
We investigate the reflection of a Gaussian beam impinging upon the surface of an epsilon-near-zero (ENZ) medium. In particular, we discuss the occurrence of Goos-Hänchen and Imbert-Fedorov shifts. Our calculations reveal that spatial shifts are significantly enhanced owing to the ENZ nature of the medium, and that their value and angular position can be tuned by tuning the plasma frequency of the medium.
We study, analytically and numerically, reflection and transmission of an arbitrarily polarized vortex beam on an interface separating two dielectric media and derive general expressions for linear and angular Goos-Hanchen and Imbert-Fedorov shifts. We predict a novel vortex-induced Goos-Hanchen shift, and also reveal direct connection between the spin-induced angular shifts and the vortex-induced linear shifts.
Weak measurements have recently allowed for the observation of the spin-Hall effect of light in reflection or transmission, which is a spin-dependent light beam shift orthogonal to the plane of incidence. We report here the observation of the Imbert-Fedorov shift via a weak value amplification scheme. The Imbert-Fedorov effect does not depend on the spin of the incident photon only, but it has richer polarization dependence. We prove that weak measurements allow for a complete experimental characterization of the polarization properties of this tiny optical effect.
We present precise expressions of the spatial and angular Goos-Haenchen and Imbert-Fedorov shifts experienced by a longitudinally and transversally limited beam of light (wave packet) upon reflection from a dielectric interface, as opposed to the well-known case of a monochromatic beam which is bounded in transverse directions but infinitely extended along the direction of propagation. This is done under the assumption that the detector time is longer than the temporal length of the wave packet (wave packet regime). Our results will be applied to the case of a Gaussian wave packet and show tha…
A unified theory is advanced to describe both the lateral Goos-Hänchen (GH) effect and the transverse Imbert-Fedorov (IF) effect, through representing the vector angular spectrum of a 3-dimensional light beam in terms of a 2-form angular spectrum consisting of its 2 orthogonal polarized components. From this theory, the quantization characteristics of the GH and IF displacements are obtained, and the Artmann formula for the GH displacement is derived. It is found that the eigenstates of the GH displacement are the 2 orthogonal linear polarizations in this 2-form representation, and the eigenst…
The optical analogue of quantum weak measurements have shown considerable promise for the amplification and observation of tiny optical beam shifts, namely, the Goos-Hänchen (GH) and the Imbert-Fedorov (IF) shifts. Here, we demonstrate simultaneous weak value amplification of both the angular GH and the IF shifts in partial reflection of fundamental Gaussian beam at planar dielectric interfaces. We employ pre- and post selection schemes with appropriate linear polarization basis states for simultaneous weak measurements and amplification of both these shifts. The experimentally observed enhanc…
We present a theoretical analysis for the \GH and \IF shifts experienced by an X-wave upon reflection from a dielectric interface. We show that the temporal chirp, as well as the bandwidth of the X-wave directly affect the spatial shifts in a way that can be experimentally observed, while the angular shifts do not depend on the spectral features of the X-Wave. A dependence of the spatial shifts on the spatial structure of the X-wave is also discussed.
We consider reflection and transmission of polarized paraxial light beams at a plane dielectric interface. The field transformations taking into account a finite beam width are described based on the plane-wave representation and geometric rotations. Using geometrical-optics coordinate frames accompanying the beams, we construct an effective Jones matrix characterizing spatial-dispersion properties of the interface. This results in a unified self-consistent description of the Goos-Hänchen and Imbert-Fedorov shifts (the latter being also known as spin-Hall effect of light). Our description reve…
Second-order nonlocal shifts of scattered wave-packets: What can be measured by Goos-Hänchen and Imbert-Fedorov effects ?
研究任意色散波包在表面散射中的二阶非局域效应，提出新动量、频率位移及脉冲宽度收缩，并阐明其与介电函数测量的关系。
We study the classical optics effects known as Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts, occurring when reflecting a bounded light beam from a planar surface, by using a quantum-mechanical formalism. This new approach allows us to naturally separate the spatial shift into two parts, one independent on orbital angular momentum (OAM) and the other one showing OAM-induced spatial-vs-angular shift mixing. In addition, within this quantum-mechanical-like formalism, it becomes apparent that the angular shift is proportional to the beams angular spread, namely to the variance of the transvers…
In this paper, we present a systematic study of beam shifts and angular momenta of paraxial vortex beams at air-left-handed material (LHM) interfaces. It is shown that, compared to their counterparts at air-right-handed material (RHM) interfaces, the spatial Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts remains the same, while the angular GH and IF shifts are reversed, at air-LHM interfaces. The spatial and angular shifts of paraxial vortex beams have their respective origins in transverse angular momenta and transverse linear momenta. The spatial GH and IF shifts remain unreversed as a res…
Observation of Rydberg excitons in monolayer MoS2 at room temperature by Imbert-Fedorov shift spectroscopy
针对过渡金属二硫化物中里德伯激子研究受样品质量、背景信号及室温展宽限制的问题，本研究首次利用Imbert-Fedorov位移光谱在室温下观测到单层MoS₂的多个里德伯激子态，提取准粒子带隙并证实温度诱导红移，为相关量子应用提供了表征工具。
Enhanced opposite Imbert-Fedorov shifts of vortex beams for precise sensing of temperature and thickness
本文实验展示了在双棱镜谐振结构中，具有大反向轨道角动量的涡旋光束的相对伊姆伯特-费多罗夫位移显著增强，并利用该位移精确传感空气间隙的厚度和温度，灵敏度随反向OAM绝对值增大而提高。
Surface Plasmon Mediated Giant Goos-Hanchen and Imbert-Fedorov Shifts on a Corrugated Metal Surface
该研究探索波纹银界面反射时表面等离激元共振介导的光束位移增强，通过弱测量放大效应实现显著自旋霍尔位移，揭示涡旋诱导位移特征，为纳米光应用提供方法支撑。
I present calculations of reflection beamshifts, Goos-Hänchen and Imbert-Fedorov shifts, due to the presence of a monolayer graphene on a dielectric media when using a beam with wavelength in the visible range. Measuring the Goos-Hänchen and Imbert-Fedorov shifts is an alternative method to determine graphene's conductivity. I look at beamshifts for different polarization states ($p$, $s$, $45^0$, $σ^+$) and I discuss other possible experimental routes to determine these beamshifts and consequently, the graphene's optical conductivity. The Goos-Hänchen shifts for visible light I calculated are…
We predict quantized Imbert-Fedorov, Goos-Hänchen, and photonic spin Hall shifts for light beams impinging on a graphene-on-substrate system in an external magnetic field. In the quantum Hall regime the Imbert-Fedorov and photonic spin Hall shifts are quantized in integer multiples of the fine structure constant $α$, while the Goos- Hänchen ones in multiples of $α^2$. We investigate the influence on these shifts of magnetic field, temperature, and material dispersion and dissipation. An experimental demonstration of quantized beam shifts could be achieved at terahertz frequencies for moderate …
Phase-space nonseparability, partial coherence, and optical beam shifts
本文发现相空间不可分离性与光束位移的普遍联系，揭示相干古斯-亨兴和相干霍尔效应，可增强或控制位移，适用于多种波。
We have studied the effect of non-integer Orbital Angular Momentum (OAM) on OAM enhanced beam shifts, for in-plane (Goos-Hanchen) and out-of-plane (Imbert-Fedorov) shifts, using Hermite-Laguerre-Gaussian beams. Contrary to naive expectation we find, theoretically and experimentally, that the noninteger OAM beam shifts do not interpolate linearly between the integer OAM beam shifts.
Recently, the electronic analogy of the anomalous spatial shift, including Goos-Hänchen and Imbert-Fedorov effects, has been attracting widespread interest. The current research on the anomalous spatial shift in interface electronic reflection is based on the paradigm of linear approximation, under which the center position of the incident and reflected beams are obtained by expanding the phases of relevant basis states and scattering amplitudes to the first order of incident momentum. However, in a class of normal cases, the linear approximation can lead to a divergent spatial shift in reflec…
We report a unified representation of the spatial and angular Goos-Hanchen and Imbert-Fedorov shifts that occur when a light beam reflects from a plane interface. We thus reveal the dual nature of spatial and angular shifts in optical beam reflection. In the Goos-Hanchen case we show theoretically and experimentally that this unification naturally arises in the context of reflection from a lossy surface (e.g., a metal).
We investigate experimentally the role of spatial coherence on optical beam shifts. This topic has been the subject of recent theoretical debate. We consider Gaussian Schell-model beams, with different spatial degrees of coherence, reflected at an air-glass interface. We prove that the angular Goos-Hänchen and the angular Imbert-Fedorov effects are affected by the spatial degree of coherence of the incident beam, whereas the spatial Goos-Hänchen effect does not depend on incoherence. Our data unambiguously resolve the theoretical debate in favour of one specific theory.
It is known that orbital angular momentum (OAM) couples the Goos-Hanchen and Imbert-Fedorov shifts. Here, we present the first study of these shifts when the OAM-endowed LG(l,p) beams have higher-order radial mode index (p>0). We show theoretically and experimentally that the angular shifts are enhanced by p while the positional shifts are not. Since LG(l,p) modes form a complete basis set for paraxial beams, our results can be used to predict beam shifts of arbitrary modes of light.
It is well known that reflection of a Gaussian light beam ($\text{TEM}_{00}$) by a planar dielectric interface leads to four beam shifts when compared to the geometrical-optics prediction. These are the spatial Goos-Hänchen (GH) shift, the angular GH shift, the spatial Imbert-Fedorov (IF) shift and the angular IF shift. We report here, theoretically and experimentally, that endowing the beam with Orbital Angular Momentum (OAM) leads to coupling of these four shifts; this is described by a $4 \times 4$ mixing matrix.
Optical beam shifts from a free-standing two-dimensional atomic crystal are investigated. In contrast to a three-dimensional crystal the magnitude of the Goos-H$\rm \ddot{a}$nchen shift depends on the surface susceptibility of the crystal and not on the wavelength of the incident light beam. The surface conductivity of the atomically thin crystal is less important in this context because it enters in the expression of the shifts only as a second order parameter. In analogy to a three-dimensional crystal the magnitudes of the Imbert-Fedorov shift and of the angular shifts depend respectively on…
We demonstrate an intriguing giant optical beam shift in a tilted polarizer system analogous to the Imbert-Fedorov shift in partial reflection around the Brewster's angle of incidence. We explain this giant shift using a generalized theoretical treatment for beam shift in a tilted uniaxial anisotropic material incorporating the three-dimensional orientation of its optic axis in the laboratory frame. We further demonstrate regulated control and tunability of both the magnitude and direction of the shifts by wisely tuning the input polarization and the corresponding orientation angles. These fin…
When a beam of light is reflected by a smooth surface its behavior deviates from geometrical optics predictions. Such deviations are quantified by the so-called spatial and angular Goos-Haenchen (GH) and Imbert-Fedorov (IF) shifts of the reflected beam. These shifts depend upon the shape of the incident beam, its polarization and on the material composition of the reflecting surface. In this article we suggest a novel approach that allows one to unambiguously isolate the beam-shape dependent aspects of GH and IF shifts. We show that this separation is possible as a result of some universal fea…
The magnitudes of beam shifts (Goos-Hänchen and Imbert-Fedorov, spatial and angular) are greatly enhanced when a reflected light beam is postselected by an analyzer, by analogy with superweak measurements in quantum theory. Particularly strong enhancements can be expected close to angles at which no light is transmitted for a fixed initial and final polarizations. We derive a formula for the angular and spatial shifts at such angles (which includes the Brewster angle), and we show that their maximum size is limited by higher-order terms from the reflection coefficients occurring in the Artmann…
We analyze the paraxial beam transformation upon reflection and refraction at a plane boundary. In contrast to the usual approach dealing with the beam angular spectrum, we apply the continuity conditions to explicit spatial representations of the electric and magnetic fields on both sides of the boundary. It is shown that the polarization-dependent distortions of the beam trajectory (in particular, the "longitudinal" Goos-Hänchen shift and the "lateral" Imbert-Fedorov shift of the beam center of gravity) are directly connected to the incident beam longitudinal component and appear due to its …
We present experiments on Orbital Angular Momentum (OAM) induced beam shifts in optical reflection. Specifically, we observe the spatial Goos-Hänchen shift in which the beam is displaced parallel to the plane of incidence and the angular Imbert-Fedorov shift which is a transverse angular deviation from the geometric optics prediction. Experimental results agree well with our theoretical predictions. Both beam shifts increase with the OAM of the beam; we have measured these for OAM indices up to 3. Moreover, the OAM couples these two shifts. Our results are significant for optical metrology sin…
We show how careful control of the incident polarization of a light beam close to the Brewster angle gives a giant transverse spatial shift on reflection. This resolves the long-standing puzzle of why such beam shifts transverse to the incident plane [Imbert-Fedorov (IF) shifts] tend to be an order of magnitude smaller than the related Goos-Hänchen (GH) shifts in the longitudinal direction, which are largest close to critical incidence. We demonstrate that with the proper initial polarization the transverse displacements can be equally large, which we confirm experimentally near Brewster incid…
We investigate how beams with orbital angular momentum (OAM) behave under total internal reflection. This is studied in two complementary experiments: In the first experiment, we study geometric shifts of OAM beams upon total internal reflection (Goos-Hänchen and Imbert-Fedorov shifts, for each the spatial and angular variant), and in the second experiment we determine changes in the OAM mode spectrum of a beam, again upon total internal reflection. As a result we find that in the first case, the shifts are independent of OAM and beam focussing, while in the second case, modifications in the O…
The simple reflection of a light beam of finite transverse extent from a homogenous interface gives rise to a surprisingly large number of subtle shifts and deflections which can be seen as diffractive corrections to the laws of geometrical optics [Goos-Hänchen shifts] and manifestations of optical spin-orbit coupling [Imbert-Fedorov shifts], related to the spin Hall effect of light. We develop a unified linear algebra approach to dielectric reflection which allows for a simple calculation of all of these effects and lends itself to an interpretation of beam shifts as weak values in a classica…
On anomalous optical beam shifts at near-normal incidence
本文发展了近正入射条件下的光束位移理论，揭示了异常位移增强源于Berry相位奇点，并提出利用四分之一波片同时观测巨光束位移的实验方案。
The linear birefringence of uniaxial crystal plates is known since the 17th century, and it is widely used in numerous optical setups and devices. Here we demonstrate, both theoretically and experimentally, a fine lateral circular birefringence of such crystal plates. This effect is a novel example of the spin-Hall effect of light, i.e., a transverse spin-dependent shift of the paraxial light beam transmitted through the plate. The well-known linear birefringence and the new circular birefringence form an interesting analogy with the Goos-Hänchen and Imbert-Fedorov beam shifts that appear in t…
We present a solution to the problem of partial reflection and refraction of a polarized paraxial Gaussian beam at the interface between two transparent media. The Fedorov--Imbert transverse shift of the centers of gravity of the reflected and refracted beams are calculated. Our results differ in general case from ones derived previously by other authors. In particular, they obey general conservation law for the beams' total angular momentum but do not obey one-particle conservation laws for individual photons, which have been proposed by Onoda et al. [Phys. Rev. Lett. 93, 083901 (2004)]. We a…
A single paraxial beam reflection at a plane dielectric interface, configured appropriately, can lead to the formation of a polarization singularity in the inhomogeneously polarized output beam-field for any central angle of incidence. In this paper we derive the necessary condition to realize this effect. We explore the phase singularity characteristics associated to this polarization-singular field; and explore the dynamics of the singularities due to controlled variations of the input polarization. The simulation-generated exact field information lead to the exploration of the unique Goos-H…
In periodic media, despite the close relationship between geometrical effects in the bulk and topological surface states, the two are typically probed separately. We show that when beams in a Weyl medium reflect off an interface with a gapped medium, the trajectory is influenced by both bulk geometrical effects and the Fermi arc surface states. The reflected beam experiences a displacement, analogous to the Goos-Hänchen or Imbert-Fedorov shifts, that forms a half-vortex in the two-dimensional surface momentum space. The half-vortex is centered where the Fermi arc of the reflecting surface touc…
The geometric Spin Hall Effect of Light (geometric SHEL) amounts to a polarization-dependent positional shift when a light beam is observed from a reference frame tilted with respect to its direction of propagation. Motivated by this intriguing phenomenon, the energy density of the light beam is decomposed into its Cartesian components in the tilted reference frame. This illustrates the occurrence of the characteristic shift and the significance of the effective response function of the detector. We introduce the concept of a tilted polarizing interface and provide a scheme for its experimenta…
Confocal microscopy is an essential imaging tool for biological systems, in solid-state physics and nano-photonics. Using confocal microscopes allows performing resonant fluorescence experiments, where the emitted light has the same wavelength as the excitation laser. Theses challenging experiments are carried out under linear cross-polarization conditions, rejecting laser light from the detector. In this work we uncover the physical mechanisms that are at the origin of the yet unexplained high polarization rejection ratio which makes these measurements possible. We show in both experiment and…
Enhanced beam shifts mediated by Bound States in Continuum
本研究基于角谱分解开发通用理论，揭示了连续域束缚态（BIC）谐振可引发巨大的 Goos-Hanchen 偏移和显著的 Imbert-Fedorov 偏移，并阐明了反射光束因光谱干涉产生畸变与卫星光斑的机制。
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