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

Active manipulation for Goos-Hänchen shift of guided-wave via a metasurface of silicon-nanoscale semi-spheres on SOI waveguide

Goos-Hänchen shift of total internal reflection (TIR) is the light beam movement without external driving, so envisioned to have potential manipulation of optical beams. In this article, with a silicon-on-insulator (SOI) waveguide corner structure, a variable equivalent permittivity of guided wave is modelled, and then the equivalent electric polarizabilities and the Goos-Hänchen shift of guided wave are modelled. Consequently, with a 2.0-µm SOI waveguide corner structure and an abrupt phase change of ∼0.5π caused by a vertically inserted metasurface of nanoscale semi-spheres having a 450-nm radius can reach the GH shifts of 2.1 µm for TE- and TM-mode, respectively, which are verified by both the FDTD simulation results of 1.93 µm with a reflectivity of about 62% and the experimental results of 2.0 µm with ∼60%. Therefore, this work has efficiently modelled the optical feature response of semi-sphere metasurface to guided wave and the active manipulation for the GH shifts of guided-wave, opening more opportunities to develop the new functionalities and devices for Si-based photonic integrated circuit (PIC) applications.

Controllable large positive and negative Goos-Hänchen shifts with a double-Lambda atomic system

We study the Goos-Hänchen shift (GHS) of a reflected light beam from a cavity containing a double-[Formula: see text] atomic medium that is bounded by two glass slabs. Applying both coherent and incoherent fields to the atomic medium leads to positive and negative controllability of GHS. For some specific values of the parameters of the system, the amplitude of the GHS becomes large, namely, in the order of [Formula: see text] times the wavelength of the incident light beam. These large shifts are found at more than one angle of incidence with a wide range of parameters of the atomic medium.

Coherent control of spatial and angular Goos-Hänchen shifts with spontaneously generated coherence and incoherent pumping

We propose an efficient scheme to manipulate the Goos-Hänchen (GH) shift of a reflected beam from a metal-clad waveguide, where a coherent atomic medium with a Λ-type configuration is employed as the substrate. Using experimentally achievable parameters, we identify the conditions under which spontaneously generated coherence (SGC) allows us to enhance the spatial and angular GH shifts of the reflected beam. With the help of SGC, the relative phases of the probe and control fields can alter the absorption gain and refractive index of the atomic medium, thereby manipulating the magnitudes, signs, and positions of the spatial and angular shifts. Furthermore, the spatial and angular GH shifts can be coherently controlled via adjusting the incoherent pumping rate and the intensity of the control field. Our proposal provides an avenue for the manipulation of spatial and angular GH shifts and potential applications in optical switching and optical steering.

Unique interface reflection phenomena tailored by nanoscale electromagnetic boundary conditions

Local interface response effects are neglected based on the traditional electromagnetic boundary conditions (EMBCs) in an abrupt interface model. In this study, generalized nanoscale EMBCs are derived with interface response functions (IRFs) representing field inhomogeneity across the interface based on integral Maxwell's equations. They are rewritten in two different forms that correspond to the equivalent abrupt interface models with interface-induced dipoles or charges and currents. Interesting behaviors of Brewster angle shifting, non-extinction at Brewster angle, and unique absorption or gain effects are revealed based on the advanced Fresnel formula. IRFs-controlled GH-shift and angular GH-shift of a Gaussian beam near the Brewster angles are generated by the gradient interface. These unique phenomena provide some guidance for measuring the IRFs and expanding interface photonics at the nanoscale.

Lateral shifts of linearly- and radially-polarized Bessel beams scattered by a nanosphere

We report the investigation on the lateral shifts that linearly-polarized (LP) and radially-polarized (RP) Bessel beams experience during the Mie scattering by a nanosphere. A numerical procedure based on the angular spectrum theory is developed to solve the scattered electromagnetic field and subsequent lateral shifts with a high computational efficiency, which can be easily applied to an arbitrary shaped polarized beam. The influences of different factors, including conical angle, nanosphere radius and position, on the lateral shifts are systematically investigated. The results demonstrate that for on-axis scattering, a LP Bessel beam can be regarded as a plane wave with the same polarization state but an equivalent longer wavelength, while a RP Bessel beam can be regarded as a plane wave with a polarization state along the propagation direction exhibiting independence on the conical angle. The findings help deepen our understandings of lateral shifts in light scattering of vectorial non-diffractive beams.

Giant and tunable Goos-Hänchen shift with a high reflectance induced by PT-symmetry in atomic vapor

The Goos-Hänchen (GH) shifts of light beams reflected from conventional passive optical systems could be enhanced using the Brewster angle effect or resonance effect, but the maximum GH shift is located at the reflectance minima, which is difficult for experimental detection. In this paper, we present an efficient and flexible scheme to realize complex parity-time (PT)-symmetric periodic optical potentials (complex crystals) in helium atomic vapor. The GH shifts of probe light reflected from the complex crystal are theoretically investigated and large GH shifts could be obtained inside the high-reflection band. When the complex crystal is operated near the coherent perfect absorption-laser point, the maximum GH shift of probe light is exactly located at the reflectance peak. Moreover, the GH shifts could be easily controlled by adjusting the intensity of control light.

Enhancing Goos-Hänchen shift based on magnetic dipole quasi-bound states in the continuum in all-dielectric metasurfaces

Metasurface-mediated bound states in the continuum (BIC) provides a versatile platform for light manipulation at the subwavelength dimension with diverging radiative quality factor and extreme optical localization. In this work, we theoretically propose the magnetic dipole quasi-BIC resonance in asymmetric silicon nanobar metasurfaces to realize giant Goos-Hänchen (GH) shift enhancement by more than three orders of wavelength. In sharp contrast to GH shift based on the Brewster dip or transmission-type resonance, the maximum GH shift here is located at the reflection peak with unity reflectance, which can be conveniently detected in the experiment. By adjusting the asymmetric parameter of metasurfaces, the Q-factor and GH shift can be modulated accordingly. More interestingly, it is found that GH shift exhibits an inverse quadratic dependence on the asymmetric parameter. Furthermore, we theoretically design an ultrasensitive environmental refractive index sensor based on the quasi-BIC enhanced GH shift, with a maximum sensitivity of 1.5×10⁷ μm/RIU. Our work not only reveals the essential role of BIC in engineering the basic optical phenomena but also suggests the way for pushing the performance limits of optical communication devices, information storage, wavelength division de/multiplexers, and ultrasensitive sensors.

Giant Goos-Hänchen-like shifts at the merging point in strained graphene double barriers

Tunneling and the Goos-Hänchen-like (GHL) shifts of quasiparticles through double rectangular potential barriers in mono-layer graphene under uniaxial strain were considered. Expressions for the transmission coefficient and the lateral shift of the transferred beam were obtained by considering the boundary conditions and the stationary phase method, respectively. Moreover, the numerical results of the transmission probability and the lateral shifts for three values of the merging parameter,δwere presented. It was observed, for two values ofδ, very large shifts could be obtained and we found the demeanor of the GHL shift is adjustable by changing parameters and is influenced strongly byδ. Finally, our calculations were examined by the limit condition in accordance with the results obtained for a single barrier in presence of the strong uniaxial strain.

Goos-Hänchen shifts for Airy beams impinging on graphene-substrate surfaces

The spatial (Δ_GH) and the angular (Θ_GH) Goos-Hänchen (GH) shifts for an Airy beam impinging upon a weakly absorbing medium coated with the monolayer graphene are theoretically investigated. The influence of the GH shift on the incident angle, the incident wavelength, the Fermi energy, and the decay factors of Airy beams is discussed. A significant magnification of Δ_GH, which reaches its maximum of about three orders of wavelengths, is predicted. Our findings may provide a feasible tool to obtain a huge Δ_GH in experiments.

Spatial Goos-Hänchen and Imbert-Fedorov shifts of rotational 2-D finite energy Airy beams

Expressions of Goos-Hänchen and Imbert-Fedorov shifts of rotational 2-D finite energy Airy beams are introduced in this paper. The influences of the second-order terms of the reflection coefficient on the spatial Goos-Hänchen shift (GHS) and spatial Imbert-Fedorov shift (IFS) of rotational 2-D finite energy Airy beams are theoretically and numerically investigated at the surface between air and weakly absorbing medium for the first time. It is found that the axial symmetry of the initial field of beams has huge influences on GHS and IFS and both of the GHS and IFS can be controlled by adjusting the rotation angle of the initial field distribution.

Tunable and enhanced Goos-Hänchen shift via surface plasmon resonance assisted by a coherent medium

We present a scheme for enhancing Goos-Hänchen shift of light beam that is reflected from a coherent atomic medium in the Kretschmann-Raether configuration. The complex permittivity of the medium can be coherently controlled and has significant influence on the surface plasmon resonance (SPR) at the metal-medium interface. By tuning the atomic absorption, the internal damping of SPR system can be modulated effectively, thereby leading to giant positive and negative lateral displacements. The refractive index of medium determines the SPR angle. Thus the peak position of the beam shift becomes tunable. As the optical response of the coherent medium depends on the intensity and detuning of the controlling fields, we are able to conveniently manipulate the magnitude, the sign, and the angular position of Goos-Hänchen shift peaks.

Plasmonic-based sensitivity enhancement of a Goos–Hänchen shift biosensor using transition metal dichalcogenides: a theoretical insight

Layered transition metal dichalcogenides (TMDCs) within two dimension (2D) have been gaining widespread consideration due to their exclusive optoelectronic properties.

Tunable low-threshold bistable Goos-Hänchen shift and Imbert-Fedorov shift using long-range graphene surface plasmons within the terahertz region

An analytical exploration of bistable spatial and angular lateral shifts at terahertz radiation in a multilayered long-range graphene surface plasmon resonant configuration is proposed with a Kerr polymer at a ultra-low threshold of 200W/cm² for low Fermi energy at 1 ps relaxation time. Here, spatial Goos-Hänchen shift is observed 10 times larger than the previously reported papers. The hysteretic behavior of the spatial and angular Imbert-Fedorov shift by tuning the incident electric field and tunability of the threshold intensities is also realized, which has not been previously reported. The proposed idea explores new avenues in lateral-shift-based optical switches and optical sensors.

Giant and highly reflective Goos-Hänchen shift in a metal-dielectric multilayer Fano structure

We experimentally demonstrated a giant Goos-Hänchen (GH) shift in a metal-dielectric multilayer Fano structure. The observed GH shift was 0.176 mm, which corresponded to (GH shift/λ) = 493, where λ is the incident wavelength. A unique feature of this giant GH shift was that it occurred without attenuation, i.e., reflectivity ∼1, due to Fano interference between surface plasmon polariton and high-Q dielectric waveguide mode. The Q-value is determined by the coupling loss. Therefore, we can enhance the GH shift to an arbitrarily large value by controlling the coupling strength. The unique feature whereby the giant GH shift occurs without attenuation has great potential for real-world applications, such as optical switching, optical filters, and sensors, where the reduction of reflected beam intensity is currently a major drawback.

Giant Goos-Hänchen shift induced by bounded states in optical PT-symmetric bilayer structures

Goos-Hänchen (GH) effect is a fundamental phenomenon in optics. Here we demonstrate theoretically that the surface modes at Parity-time (PT) symmetric interfaces, can induce a giant GH shift at a specific incident angle. It is found that the amplitude of the GH shift can be tuned by adjusting the thickness of the bilayer, and as the thickness grows, its maximum value can go to infinity in theory. The physical mechanism behind this interesting feature is that the surface modes at PT interfaces are quasi-bound states in continuum (BICs), which lead to rapid variation in the phase of the scattered waves. Our work enriches the previous studies about GH effect in PT bilayer structures and provides a way in turn to explore the BICs in non-Hermitian photonic systems.

Giant Goos-Hänchen shift in two different enantiomers' chiral molecules via quantum coherence

The Goos and Hänchen (GH) shifts in reflected and transmitted probe light through a cavity mixture of left- and right-handed chiral molecules into two enantiomer states are investigated. Due to the broken mirror symmetry of the left- and right-handed chiral molecules in the presence of cyclic population transfer, such quantum systems can be selectively excited because of the coexistence of one- and two-photon transitions. With the help of coupling Rabi frequency and damping effects due to scattering processes, the generated GH shifts accompanied by simultaneously negative and positive lateral shifts in reflected and transmitted probe lights are greatly enhanced. It is found that the large negative and positive GH shifts are available in the presence of multiphoton resonance and off-resonance conditions for two different enantiomers' chiral molecules. Moreover, the switching between superluminal and subluminal light propagation is extremely dependent on choosing the left- and right-handed chiral molecules. Furthermore, the effects of pulse shape and mode of Laguerre-Gaussian probe light on the GH shifts that lead to a switch between negative and positive shift are also studied. The negative and positive GH shifts in a reflected and transmitted probe beam for an incident Gaussian and different mode of Laguerre-Gaussian shaped beam with various widths by the use of two different enantiomers' chiral molecules are also discussed.

Giant Goos-Hänchen shifts in non-Hermitian dielectric multilayers incorporated with graphene

We theoretically investigate the Goos-Hänchen (GH) shifts of optical beam in a defective photonic crystal composed of dielectric multilayers and graphene. The system is non-Hermitian and possesses exceptional points (EPs) as the scattering matrix becomes defective at the zero points of reflection. The reflective wave at EPs experiences an abrupt phase change and there the eigenvalues of scattering matrix coalesce. The GH shifts are extremely large near EPs in parametric space composed of dielectric refractive index and incident angle. The positive and negative maxima of GH shifts could be as high as 10³ times of the incident wavelength. The direction of GH shifts switches at EPs and the EPs position can be readily controlled by the chemical potential of graphene. Moreover, the GH shifts should remarkably change as the incident waves impinge on the structure from opposite directions. The study of GH shifts in the graphene incorporated multilayers may find great applications in highly sensitive sensors.

Analysis of high-resolution electro-optical beam steering by long-range surface plasmon resonance using a ZnSe prism

A proposal on high-resolution electro-optical beam steering is conceptualized analytically using a long-range surface plasmon resonance configuration comprising a liquid crystal layer of E44 for 1550 nm wavelength. With the tuning of the refractive index of E44 through variations of applied voltage from 0 to 10 V, an optical beam steering can be attained considering the composite effect of spatial and angular Goos-Hanchen and Imbert-Fedorov shifts. As compared with the existing beam shift processes in μrad by mechanical means, here, the computed angular resolution is 3.40 nrad. The proposed idea finds a new avenue in the field of pulse generation, optical sensor applications, and atomic force microscopy, mitigating existing drawbacks.

Large and tunable lateral shifts in one-dimensional PT-symmetric layered structures

The lateral shifts of the wave reflected and transmitted from PT-symmetric one-dimensional multilayer-structures are investigated near the coherent-perfect-absorption (CPA)-laser point and the exceptional points. We predict that at the CPA-Laser point, the reflections from both sides and transmission as well as the related shifts are all very large, reaching their negative (or positive) maxima. Moreover, we show that although the reflections are direction-dependent in the PT-symmetric multilayer-structure, the related lateral shifts have same behaviors from both sides. Additionally, one may realize the reversal of the lateral shift through the suitable adjustment of the incident angle and the layer numbers. Numerical simulations for Gaussian incident beams are performed, and reasonable agreement between the theoretical results and numerical simulations is found.

Goos-Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials

The Goos-Hänchen (GH) shifts in the reflected light are investigated both for p and s polarized partial coherent light beams incident on epsilon-near-zero (ENZ) metamaterials. In contrary to the coherent counterparts, the magnitude of GH shift becomes non-zero for p polarized partial coherent light beam; while GH shift can be relatively large with a small degree of spatial coherence for s polarized partial coherent beam. Dependence on the beam width and the permittivity of ENZ metamaterials is also revealed for partial coherent light fields. Our results on the GH shifts provide a direction on the applications for partial coherent light sources in ENZ metamaterials.

Incident-polarization-sensitive and large in-plane-photonic-spin-splitting at the Brewster angle

In this Letter, we report a phenomenon of large in-plane-photonic-spin-splitting (IPPSS) in the case of a linear polarized Gaussian light beam reflected from an air-glass interface at the Brewster angle. The IPPSS-induced displacement reaches ∼12.4  μm, which is quite larger than the previously reported value. Particularly, the IPPSS is extremely sensitive (∼70  μm/deg) to the incident polarization. We also find that the direction of the spin accumulation can be switched by adjusting the incident polarization slightly. These findings may have useful applications in spin manipulation and precise polarization metrology.

Goos-Hänchen effect in epsilon-near-zero metamaterials

Light reflection and refraction at an interface between two homogeneous media is analytically described by Snell's law. For a beam with a finite waist, it turns out that the reflected wave experiences a lateral displacement from its position predicted by geometric optics. Such Goos-Hänchen (G-H) effect has been extensively investigated among all kinds of optical media, such as dielectrics, metals, photonic crystals and metamaterials. As a fundamental physics phenomenon, the G-H effect has been extended to acoustics and quantum mechanics. Here we report the unusual G-H effect in zero index metamaterials. We show that when linearly polarized light is obliquely incident from air to epsilon-near-zero metamaterials, no G-H effect could be observed for p polarized light. While for s polarization, the G-H shift is a constant value for any incident angle.

Goos-Hänchen-like shift of three-level matter wave incident on Raman beams

When a three-level atomic wavepacket is obliquely incident on a "medium 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-Hänchen 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 transmitted wave with high transmission probability is observed, which is helpful to observe such lateral shifts experimentally. Different from the two-level atomic wave case, we find that quantum interference between different atomic states plays crucial role on the transmission intensity and corresponding lateral shifts.

Electrically controlled Goos-Hänchen shift of a light beam reflected from the metal-insulator-semiconductor structure

We proposed a scheme to manipulate the Goos-Hänchen shift of a light beam reflected from the depletion-type device via external voltage bias. It is shown that the lateral shift of the reflected probe beam can be easily controlled by adjusting the reverse voltage bias and the incidence angle. Using this scheme, the lateral shift can be tuned from negative to positive, without changing the original structure of the depletion-type device. Numerical calculations further indicate that the influence of structure parameters and light wavelength can be reduced via readjustment of the reverse bias. The proposed structure has the potential application for the integrated electronic devices.

Interferometric method to measure the Goos-Hänchen shift

We propose and demonstrate an interferometric method to measure the Goos-Hänchen (GH) shift, which is based on observing the interference between p- and s-polarized beams. In our method both p- and s-polarized beams are observed simultaneously and across the entire beam profile. To demonstrate our method, we measured the GH shift of aluminum (Al) and glass at different values of the incidence angle ranging from 20° to 70°, with a helium-neon laser as source. We compared the experimental result with theoretical calculations and found a good agreement between them. Our method also enables us to measure the GH shift at any point across the entire beam profile, for arbitrary beam profiles. This is not possible with the methods currently in use. We presented the observed values for the Gaussian mode used, which enables us to find the relative shifts between the p and s components at various points on the incident profile after reflection.

Goos-Hänchen shift of the reflected wave through an anisotropic metamaterial containing metal/dielectric nanocomposites

Goos-Hänchen (GH) shift of a transverse-magnetic (TM) wave reflected from a semi-infinite anisotropic metamaterial consisting of aligned metallic nanowires in a dielectric matrix is investigated. Based on Bruggeman effective medium theory, we obtain the conditions for realizing the negative refraction, which are dependent on both the incident wavelength and the volume fraction of metallic inclusions. Then, we investigate the GH shifts from the composite metamaterial with positive and negative refractions with the stationary-phase method. Numerical results show that the enhancement of GH shift can be achieved near the pseudo-Brewster angle for small volume fractions and at the close-to-grazing incidence for large volume fractions. We further find that for positively refractive metamaterials with weak absorption, one can realize the transition from negative GH shift to the positive one by adjusting the incident wavelength. However, for negatively refractive composite metamaterials, the reversal of the GH shifts may take place by the adjustment of the volume fraction instead of the incident wavelength. In order to demonstrate the validity of the stationary-phase approach, numerical simulations are performed for a Gaussian-shaped beam. In the end, by using COMSOL simulation, a comprehensive understanding is given and the above analysis is confirmed.

Nearly three orders of magnitude enhancement of Goos-Hanchen shift by exciting Bloch surface wave

Goos-Hanchen effect is experimentally studied when the Bloch surface wave is excited in the forbidden band of a one-dimensional photonic band-gap structure. By tuning the refractive index of the cladding covering the truncated photonic crystal structure, either a guided or a surface mode can be excited. In the latter case, strong enhancement of the Goos-Hanchen shift induced by the Bloch-surface-wave results in sub-millimeter shifts of the reflected beam position. Such giant Goos-Hanchen shift, ~750 times of the wavelength, could enable many intriguing applications that had been less than feasible to implement before.

Direct experimental observation of giant Goos-Hänchen shifts from bandgap-enhanced total internal reflection

Giant Goos-Hänchen (GH) shifts are experimentally demonstrated from a prism-coupled multilayer structure incorporating a one-dimensional photonic crystal (PC) through a bandgap-enhanced total internal reflection scheme. By combining the large phase changes near the bandgap of the PC and the low reflection loss of the total internal reflection, 2 orders of magnitude enhancement of the GH shift is realized with rather low extra optical loss, which might help to open the door toward many interesting applications for GH effects.

Large positive and negative lateral shifts near pseudo-Brewster dip on reflection from a chiral metamaterial slab

The lateral shifts from a slab of lossy chiral metamaterial are predicted for both perpendicular and parallel components of the reflected field, when the transverse electric (TE)-polarized incident wave is applied. By introducing different chirality parameter, the lateral shifts can be large positive or negative near the pseudo-Brewster angle. It is found that the lateral shifts from the negative chiral slab are affected by the angle of incidence and the chirality parameter. In the presence of inevitable loss of the chiral slab, the enhanced lateral shifts will be decreased, and the pseudo-Brewster angle will disappear correspondingly. For the negative chiral slab with loss which is invisible for the right circularly polarized (RCP) wave, we find that the loss of the chiral slab will lead to the fluctuation of the lateral shift with respect to the thickness of the chiral slab.The validity of the stationary-phase analysis is demonstrated by numerical simulations of a Gaussian-shaped beam.

Propagation behavior of incoherent beams in one-dimensional photonic crystals

The propagation properties of Gaussian Schell-model spatially incoherent beams through a one-dimensional photonic crystal (1DPC) are investigated. The dynamical evolution of incoherent beams in 1DPC and the Goos-Hänchen lateral shift of the transmitted beams are obtained. The mutual effects of coherence and bandgap of the PC on the evolution of incoherent beams are analyzed. The incidence angle of the incoherent beam also has an influence on the incoherent electric field and the lateral shift.

Goos-Hänchen shifts of the reflected waves from a cold, inhomogeneous, and magnetized plasma slab

We discuss theoretically the Goos-Hänchen (GH) shifts of the reflected waves from a cold, inhomogeneous, and magnetized plasma slab by using the invariant imbedding approach. Aiming at the linear and parabolic electron-density profiles, we demonstrate numerically the dependences of the co- and cross-polarized GH shifts on the angle of incidence, external static magnetic field, and the thickness of the plasma slab. The results show that the different electron-density profiles of plasma can result in the very different dependences of the GH shifts on the angle of incidence, external magnetic field, and the slab's thickness; the GH shifts can be switched between the considerably large positive and negative values under certain conditions. Particularly, without altering the structure of the plasma slab, the GH shifts can be manipulated by modifying the angle of incident or the external static magnetic field.

Temperature-dependent Goos-Hänchen shift on the interface of metal/dielectric composites

The temperature-dependent Goos-Hänchen shift (GHS) for an electromagnetic wave reflected from a metal/dielectric composite material is investigated. With the stationary-phase method, we theoretically show that the effect of the temperature on GHS is significant near the Brewster angle for the dielectric composites and at the grazing angle for the metallic composites. For dielectric composites, the lateral shift can be negative as well as positive. And GHS may become much negative, much positive, and nonmonotonic variation with increasing the temperature under different conditions. Moreover, through the suitable adjustment of the temperature, one may realize the reversal of the GHS. To support the above results, numerical simulations for Gaussian incident beams based on the momentum method and COMSOL Multiphysics software are provided, and reasonable agreement between the theoretical results and numerical simulations is found.

Propagation-dependent beam profile distortion associated with the Goos-Hanchen shift

The propagation-dependent profile distortion of the reflected beam is studied via deriving the theoretical model of the optical field distribution in both the near and far field. It is shown that strong and fast-varying beam distortions can occur along the propagation path, compared to the profile on the reflecting surface. Numerical simulations for the case of a typical SPR configuration with a sharp angular response curve reveal that, when the phase distribution in the angular range covered by the input beam becomes nonlinear, previous theories based on the linear phase approximation fail to predict the Goos-Hanchen shift and its propagation-dependent variations precisely. Our study could shed light on more accurate modeling of the Goos-Hanchen effect's impact on the relevant photonic devices and measurement applications.

Error analysis and compensation method of focus detection in exposure apparatus

An original approach to measurement accuracy of a typical focus sensor in conventional integrated circuit lithographic equipment is introduced. Causes of measurement error in the focus sensor are theoretically analyzed and found to be generated mainly from interactions between imperfections of the optical system and the actual surface of processed wafers. We derive mathematical formulations describing these errors, which are confirmed by the experimental results performed by using an optical setup composed of the focus sensor and samples on which the wafer surface condition is reproduced. Furthermore, several novel techniques that are intended to reduce those measurement errors are successfully demonstrated.

Geometrical approach in physical understanding of the Goos-Haenchen shift in one- and two-dimensional periodic structures

The Goos-Haenchen shift of a totally reflected beam at the planar interface of two dielectric media, as if the incident beam is reflected from beneath the interface between the incident and transmitted media, has been geometrically associated with the penetration of the incident photons in the less-dense forbidden transmission region. This geometrical approach is here generalized to analytically calculate the Goos-Haenchen shift in one- and two-dimensional periodic structures. Several numerical examples are presented, and the obtained results are successfully tested against the well-known Artman's formula. The proposed approach is shown to be a fast, simple, and efficient method that can provide good physical insight to the nature of the phenomenon.

Optical temperature sensing based on the Goos-Hänchen effect

The possibility of constructing an optical sensor for temperature monitoring based on the Goos-Hänchen (GH) effect is explored using a theoretical model. This model considers the lateral shift of the incident beam upon reflection from a metal-dielectric interface, with the shift becoming a function of temperature due mainly to the temperature dependence of the optical properties of the metal. It is found that such a sensor can be most effective by using long wavelength p-polarized incident light at almost grazing incidence onto the metal, where significant variation of negative GH shifts can be observed as a function of the temperature.

Observation of large positive and negative lateral shifts of a reflected beam from symmetrical metal-cladding waveguides

Both large positive and negative lateral shifts were observed for the reflected light beam on a symmetrical metal-cladding waveguide. The positive and negative shifts approach about 480 and 180 microm, respectively, which to our knowledge are the largest experimental results ever reported. The experiment also proves that the positive or the negative shift depends on sign of the difference between the intrinsic and radiative damping.

Nonspecular effects on reflection from absorbing media at and around Brewster's dip

We show that, for a TM (or p-state) Gaussian beam incident onto an absorbing medium at and around Brewster's dip, the reflected beam always remains Gaussian and undergoes a Goos-Hänchen-like (GH) shift, an angular shift, a focal shift, and a beam-waist modification, provided that the beam is sufficiently collimated that the third-order change of the (logarithmic) reflection coefficient can be ignored in the angular range of beam divergence. For weak absorption, not only are a large negative GH shift and an odd-functioned-like focal shift with greater magnitude found but also the angular shift, though small by itself, is shown to give an even larger lateral net shift at a distance beyond the Rayleigh range.

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.

Large positive and negative lateral optical beam shift in prism-waveguide coupling system

In this paper, the lateral beam shift in a prism-waveguide coupling system at wavelengths ranging from visible to near infrared is theoretically examined. A simple theoretical formula is derived to analyze the behavior of the beam shift. We demonstrate that large positive and negative lateral optical beam shifts can be obtained when guided modes are excited. It is also found that the magnitude of the beam shift is closely related to the intrinsic and radiative damping. When the intrinsic damping is larger than the radiative damping, negative lateral beam shift occurs. Numerical calculations confirm the theoretical analysis and show that a beam shift of the order of millimeters is possible.

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.

Giant lateral shift of a light beam at the defect mode in one-dimensional photonic crystals

It is found that when a light beam is incident on a one-dimensional photonic crystal (1DPC) containing a defect layer, the lateral shifts of both the reflected and the transmitted beams are greatly enhanced near the defect mode of the 1DPC, whose location depends on the angles at a fixed frequency. The effect was studied by use of a Gaussian beam. The giant lateral displacement is due to the localization of the electromagnetic wave.

Large negative Goos-Hänchen shift from a weakly absorbing dielectric slab

It is theoretically shown that the negative Goos-Hänchen shifts near resonance, Re[k(z)d] = m pi, can be an order of magnitude larger than the wavelength for both TE- and TM-polarized beams reflected from a weakly absorbing dielectric slab if the absorption of the slab is sufficiently weak, which is different from the case for a lossless dielectric slab [Phys. Rev. Lett. 91, 133903 (2003)].

Prediction of simultaneously large and opposite generalized Goos-Hänchen shifts for TE and TM light beams in an asymmetric double-prism configuration

It is predicted that large and opposite generalized Goos-Hänchen (GGH) shifts may occur simultaneously for TE and TM light beams upon reflection from an asymmetric double-prism configuration when the angle of incidence is below but near the critical angle for total reflection, which may lead to interesting applications in optical devices and integrated optics. Numerical simulations show that the magnitude of the GGH shift can be of the order of beam's width.

Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects

It is found that when a light beam travels through a slab of optically denser dielectric medium in air, the lateral shift of the transmitted beam can be negative. This is a novel phenomenon that is reversed in comparison with the geometrical optic prediction according to Snell's law of refraction. A Gaussian-shaped beam is analyzed in the paraxial approximation, and a comparison with numerical simulations is made. Finally, an explanation for the negativity of the lateral shift is suggested, in terms of the interaction of boundary effects of the slab's two interfaces with air.

Goos-Hänchen shift in negatively refractive media

The Goos-Hänchen shift is calculated when total internal reflection occurs at an interface between "normal" and negatively refractive media. The shift is negative, consistent with the direction of energy flow in the negatively refractive medium.