We study the beam reflection from a layered structure with a left-handed metamaterial. We predict a giant lateral (Goos-Hanchen) shift and splitting of the beam due to the resonant excitation of surface polaritons with a vortex-like energy flow between the right- and left-handed materials.
We report the observation of the Goos-Hänchen effect in graphene via a weak value amplification scheme. We demonstrate that the amplified Goos-Hänchen shift in weak measurements is sensitive to the variation of graphene layers. Combining the Goos-Hänchen effect with weak measurements may provide important applications in characterizing the parameters of graphene.
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.
It is well known from quantum mechanics that weak measurements offer a means of amplifying and detecting very small phenomena. We present here the first experimental observation of the Goos-Hanchen shift via a weak measurement approach.
We demonstrate, for the first time, a scheme that generates radially-polarized light using Goos-Hanchen shift of a cylindrically symmetric Total Internal Reflection. It allows ultra-broadband radial polarization conversion for wavelengths differing >1 micron.
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.
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.
We investigate theoretically the Goos-Hänchen (GH) shift of a p-polarized terahertz beam incident on a 2D material surface with complex conductivity. Taking monolayer graphene to be the model material, we determine the dependence of GH shifts on the Fermi level and incident frequency. Both spatial and angular GH shifts are present. For both GH shifts in general, we find that increasing the Fermi level shifts the incident angle at which the maximum GH shifts arise. Moreover, we see that at higher frequencies, the amount of beam shift decreases with the Fermi level when the incident frequency is…
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.
The Goos-Hänchen (G-H) effect for neutron reflection from condensed matter is considered. An experiment to quantify the effect is proposed. The relation of G-H shift to the neutron coherence length is considered.
We study giant Goos-Hänchen (GH) shift in reflection from a near-symmetric coupled waveguide structure. We show that broken spatial symmetry can lead to GH shift with different signs for illumination from the opposite ends, a direct consequence of the nonreciprocity relations considered earlier (Opt. Lett. 27,1205 (2002)). Symmetry breaking by adding a few nm thick bio-layer to one of the guides is enough to observe the nonreciprocity. This may have far reaching implications for efficient biosensing.
We present measurements of the Goos-Hänchen shift in a two-dimensional dielectric microwave cavity. Microwave beams are generated by a suitable superposition of the spherical waves generated by an array of antennas; the resulting beams are then reflected at a planar interface. By measuring the electric field including its phase, Poynting vectors of the incoming and reflected beams can be extracted, which in turn are used to find the incoming angle and the positions where the beam hits the interface and where it is reflected. These positions directly yield the Goos-Hänchen shift. The results ar…
The analogies between optical and electronic Goos-Hänchen effects are established based on electron wave optics in semiconductor or graphene-based nanostructures. In this paper, we give a brief overview of the progress achieved so far in the field of electronic Goos-Hänchen shifts, and show the relevant optical analogies. In particular, we present several theoretical results on the giant positive and negative Goos-Hänchen shifts in various semiconductor or graphen-based nanostructures, their controllability, and potential applications in electronic devices, e.g. spin (or valley) beam splitters…
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.
We present a proposal to manipulate the Goos-Hanchen shift of a light beam via a coherent control field, which is injected into a cavity configuration containing the two-level atomic medium. It is found that the lateral shifts of the reflected and transmitted probe beams can be easily controlled by adjusting the intensity and detuning of the control field. Using this scheme, the lateral shift at the fixed incident angle can be enhanced (positive or negative) under the suitable conditions on the control field, without changing the structure of the cavity.
We study experimentally the Goos-Hanchen effect observed at the reflection of a self-collimated beam from the surface of a two-dimensional photonic crystal and describe a method for controlling the beam reflection through surface engineering. The microwave photonic crystal, fabricated from alumina rods, allows control of the output position of a reflected beam undergoing an internal Goos-Hanchen shift by changing the rod diameter at the reflection surface. The experimental data is in good agreement with the results of the finite-difference time-domain numerical calculations.
The effect of surface termination on the inverse Goos Hanchen (GH) shift of two dimensional (2D) negatively refractive photonic crystal (NRPhC) containing air holes arranged in hexagonal lattice in a dielectric background is investigated for TM polarization. Results show that the magnitude of the inverse GH shift of 2DNRPhC strongly depends on surface termination even for an incident beam with a fixed frequency and incidence angle. Further study by calculating the dispersion of surface mode of 2D-NRPhC as a function of surface termination reveals that 2DNRPhC presents large inverse Goos Hanche…
We study the giant Goos-Hanchen shift obtained from an Airy beam impinging on a nonlinear interface. To avoid any angular restriction associated with the paraxial approximation, the analysis is based on the numerical solution of the nonlinear Helmholtz equation. We report the existence of non-standard intermittent and oscillatory regimes for the nonlinear Goos-Hanchen shifts which can be explained in terms of the competition between the critical coupling to a surface mode of the reflected component of the Airy beam and the soliton emission from the refracted beam component.
We report giant Goos-Hänchen shifts [Goos and Hänchen, Ann. Phys. 436, 333 (1947)] for electron beams tunneling through graphene double barrier structures. We find that inside the transmission gap for the single barrier, the shift displays sharp peaks with magnitudes up to the order of electron beam width and rather small full-widths-at-half-maximum, which may be utilized to design valley and spin beam splitters with wide tunability and high energy resolution. We attribute the giant shifts to quasibound states in the structures. Moreover, an induced energy gap in the dispersion can increase th…
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-Hänchen 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 3-d vector beam. We briefly discuss the difficulties as…
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…
By considering an optically denser medium with a flat surface, but with natural roughness instead of abstract geometrical boundary which leads to mathematical discontinuity on the boundary of two adjacent stratified media, we have thus established the importance of considering physical surfaces; and thus we studied the Goos-Hänchen (GH) effect by ray-optics description to shed light on parts of this effect which have remained ambiguous. We replaced the very thin region of surface roughness by a continuous inhomogeneous intermediary medium. Applying Fermat's principle for the incident light ray…
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.
On total reflection from a half-space filled with an isotropic, homogeneous, weakly dissipative, dielectric-magnetic medium with negative phase-velocity (NPV) characteristics, it is shown here that a linearly polarized beam can experience either a negative or a positive Goos-Hanchen shift. The sign of the shift depends on the polarization state of the beam as well as on the signs of the real parts of the permittivity and the permeability of the NPV medium.
The law of reflection and Snell's law are among the tenets of geometrical optics. Corrections to these laws in wave optics are respectively known as the angular Goos-Hänchen shift and Fresnel filtering. In this paper we give a positive answer to the question of whether the two effects are common in nature and we study both effects in the more general context of optical beam shifts. We find that both effects are caused by the same principle, but have been defined differently. We identify and discuss the similarities and differences that arise from the different definitions.
For total reflection, the Goos-Hanchen (GH) shift is proportional to the wavelength of the laser beam. At critical angles, such a shift is instead proportional to the square root of the product of the beam waist and wavelength. By using the stationary phase method (SPM) and, when necessary, numerical calculations, we present a detailed analysis of the frequency crossover for the GH shift. The study, done in different incidence regions, sheds new light on the validity of the analytic formulas found in literature.
The Goos-Hanchen effect of light reflected from sandwich (three-layered) structures composed of a superconducting YBa2Cu3O7 film and two different dielectric films is investigated theoretically. It has been shown that optical anisotropy of YBa2Cu3O7 film, as well as its positions in the three-layer specimen, strongly effects on the lateral shift values. We have shown that, for all positions of the superconducting film in the three-layered structure, variation of temperature makes possible to control the values of the lateral shift of TE-polarized light at the incidence angles close to pseudo-B…
A theoretical analysis of the lateral displacement (Goos-Hänchen shift) of spatially limited beams reflected from Attenuated Total Reflection (ATR) devices in the Otto configuration is presented when backward surface plasmon polaritons are excited at the interface between a positive refractive index slab and a semiinfinite metamaterial with negative refractive index. First, the stationary phase approximation and a phenomenological model based on the properties of the complex poles and zeroes of the reflection coefficient are used to demonstrate that: i) the excitation of backward surface waves…
Applying Artmann's formula to the TE-polarized incident waves, we theoretically show that the Goos-Hänchen (GH) shifts near the angle of the pseudo-Brewster dip of the reflection from a slab of chiral metamaterial can be greatly enhanced. The GH shifts are observed for both parallel and perpendicular components of the reflected field. In addition, it is found that the GH shifts depend not only on the slab thickness and the incident angle, but also on the constitutive parameters of the chiral medium. In particular, when the incident angle is close to the critical angle of total reflection for L…
The lateral shift of an optical beam undergoing a Brillouin light scattering on acoustic wave in the total internal reflection geometry is studied theoretically. It is shown that the lateral shift depends on polarization (longitudinal or transversal) of the acoustic wave, as well as on the type of the scattering process: direct one, when the scattered wave undergoes a lateral shift at reflection from the interface, and cascading one, when fundamental-frequency light beam is laterally shifted at reflection and then is scattered on the acoustic wave.
We report the first observation of the Goos-H$\rm \ddot{\textbf{a}}$nchen shift of a light beam incident on a metal surface. This phenomenon is particularly interesting because the Goos-H$\rm \ddot{\textbf{a}}$nchen shift for $p$ polarized light in metals is negative and much bigger than the positive shift for $s$ polarized light. The experimental result for the measured shifts as a function of the angle of incidence is in excellent agreement with theoretical predictions. In an energy-flux interpretation, our measurement shows the existence of a backward energy flow at the bare metal surface w…
We have investigated that the Goos-Hänchen (GH) shifts in frustrated total internal reflection (FTIR) studied with wave packet propagation. In the first-order approximation of the transmission coefficient, the GH shift is exactly the expression given by stationary phase method, thus saturates an asymptotic constant in two different ways depending on the angle of incidence. Taking account into the second-order approximation, the GH shift always depends on the width of the air gap due to the modification of the beam width. It is further shown that the GH shift with second-order correction increa…
We show in which conditions optical gaussian beams, propagating throughout an homogeneous dielectric right angle prism, present an asymmetric Goos-Hänchen (GH) effect. This asymmetric behavior is seen for incidence at critical angles and happens in the propagation direction of the outgoing beam. The asymmetric GH effect can be also seen as an amplification of the standard GH shift. Due to the fact that it only depends on the ratio between the wavelength and the minimal waist size of the incoming gaussian beam, it can be also used to determine one of these parameters. Multiple peaks interferenc…
We theoretically predict a giant quantized Goos-Hänchen (GH) effect on the surface of graphene in quantum Hall regime. The giant quantized GH effect manifests itself as an angular shift whose quantized step reaches the order of mrad for light beams impinging on a graphene-on-substrate system. The quantized GH effect can be attributed to quantized Hall conductivity, which corresponds to the discrete Landau levels in quantum Hall regime. We find that the quantized step can be greatly enhanced for incident angles near the Brewster angle. Moreover, the Brewster angle is sensitive to the Hall condu…
We have investigated the tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals, based on the Pockels effect. The positive and negative lateral shifts could be easily controlled by adjusting the permittivity tensor, which is modulated by the external applied electric field. An alternative way to realize the polarization beam splitter was also proposed by the polarization-dependent lateral shifts. Numerical simulations for Gaussian-shaped incident beam have demonstrated the above theoretical results obtained by stationary phase method.…
The longitudinal and the transverse beam shifts, namely, the Goos-Hänchen (GH) and the Spin-Hall (SH) shifts are usually observed at planar interfaces. It has recently been shown that the transverse SH shift may also arise due to scattering of plane waves. Here, we show that analogous in-plane (longitudinal) shift also exist in scattering of plane waves from micro/nano systems. We study both the GH and the SH shifts in plasmonic metal nanoparticles/ nanostructures and dielectric micro-particles employing a unified framework that utilizes the transverse components of the Poynting vector of the …
We perform a theoretical investigation on the Goos-Hächen (GH) shift in one-dimensional photonic crystals (1DPCs) containing left-handed metamaterials (LHMs). We find an unusal effect of the GH shift near the photonic band-crossing structure, which is located at the condition, $% -k_{z}^{(A)}d_{A}=k_{z}^{(B)}d_{B}=mπ$ $(m=1,2,3...)$, under the inclined incident angle, here A denotes the LHM layer and B denotes the dielectric layer. Above the frequency of the band-crossing point (BCP), the GH shift changes from negative to positive as the incident angle increases, while the GH shift changes rev…
Motivated by the realization of the Dirac point (DP) with a double-cone structure for optical field in the negative-zero-positive index metamaterial (NZPIM), the reflection, transmission, and Goos-Hänchen (GH) shifts inside the NZPIM slab are investigated. Due to the linear Dirac dispersion, the transmission as the function of the frequency has a gap, thus the correspond reflection has a frequency or wavelength window for the perfect reflection, which is similar to the Bragg reflection in the one-dimensional photonic crystals. Near the DP, the associated GH shifts in the transmission and refle…
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…
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…
The spatial and the angular variants of the Goos-Hänchen (GH) and the Imbert-Federov (IF) beam shifts contribute in a complex interrelated way to the resultant beam shift in partial reflection at planar dielectric interfaces. Here, we show that the angular GH and the two variants of the IF effects can be decoupled, amplified and separately observed by weak value amplification and subsequent conversion of spatial$\leftrightarrow$angular nature of the beam shifts using appropriate pre and post selection of polarization states. We experimentally demonstrate such decoupling and illustrate various …
It is well-known that the variations of Goos-Hänchen shifts (GHSs) are closely associated with the enengy-flux provided by evanescent states in the case of total internal reflection. However, when the frustrated internal total reflection (FTIR) is realized with a Polymethyl Methacrylate (PMMA) double-prism system operated in the microwave frequency range of 8.2 GHz to 12.4 GHz, we observe that the GH shifts for the reflected beam show periodic resonances with varying the operation frequency or the air layer thickness, which is different from the variation of the corresponding reflected energy.…
The influence of the misfit strain on the lateral shift (Goos-Hanchen effect) experienced by a near-infrared electromagnetic wave upon reflection from the surface of a bilayer consisting of a magnetic, gyrotropic (i.e., whose permittivity tensor elements depend upon magnetization) yttrium-iron garnet film deposited on a nonmagnetic gadolinium-gallium garnet substrate is investigated theoretically. In the geometry of the transverse magneto-optical Kerr effect, it is shown that the mechanical strain near the geometrical film/substrate interface can induce a significant lateral shift of the beam …
The energy flux patterns of inverse Goos-Hanchen (GH) shift around the interface between air and negatively refractive photonic crystal (NRPhC) with different surface terminations is investigated. Results show that NRPhC exhibits inverse GH shift in TM and TE polarization, and the localization and pattern of energy flux differ in TM and TE polarizations and are strongly affected by surface termination. This is different to the condition of negative permittivity materials (i.e., metal), which only presents inverse GH shift in TM polarization. In the case of TE polarization, the energy flux patt…
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…
Goos-Hanchen-Shift Photonic Sensor for Nanometer-Scale Delayering and Tamper Detection in Semiconductor Packages
Bangladesh Army International University of Science and Technology(孟加拉国陆军国际科学技术大学);James C. Wyant College of Optical Sciences, University of Arizona(亚利桑那大学詹姆斯·C·怀恩特光学科学学院)
When a three-level atomic wavepacket is obliquely incident on a "edium slab" consisting of two far-detuned laser beams, there exists lateral shift between reflection and incident points at the surface of a "medium slab", analogous to optical Goos-Hanchen effect. We evaluate lateral shifts for reflected and transmitted waves via expansion of reflection and transmission coefficients, in contrast to the stationary phase method. Results show that lateral shifts can be either positive or negative dependent on the incident angle and the atomic internal state. Interestingly, a giant lateral shift of …
We study theoretically the influence of the surface plasmon excitation on the Goos-Hänchen lateral shift of a $p$-polarized Gaussian beam incident obliquely on a dielectric-metal bilayer in the Otto configuration. We find that the lateral shift depends sensitively on the thickness of the metal layer and the width of the incident beam, as well as on the incident angle. Near the incident angle at which surface plasmons are excited, the lateral shift changes from large negative values to large positive values as the thickness of the metal layer increases through a critical value. For wide inciden…
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…