Lateral Beam Shift Research Articles

Kekulé-modulated topological bulk cavity for intrinsic lateral beam shifting of high-purity linear-polarized light emission

Beam shaping and polarization manipulation are of great importance for the design of microcavity lasers. Recently, topological photonic cavities have emerged as excellent platforms for surface-emitting lasers. In this class of lasers, beam engineering has not thus far been extensively studied. Here, we demonstrate how to achieve an intrinsic lateral shift of the beam emitted by a topological laser. This is achieved by designing a Kekulé-modulated topological bulk cavity, in which the continuous Kekulé modulation partially lifts a set of fourfold-degenerate Dirac cones into two twofold degeneracies. The resulting photonic cavity supports a range of interesting beam emission profiles, including vector beams with polarization winding, and laterally-shifted linearly-polarized Gaussian beams. It is possible to achieve lateral beam shifts in opposite directions and orthogonal polarizations for the degenerate photonic p-/d-orbitals, a feature that may be useful for photonic sensing applications.

Lateral Beam Shifts and Depolarization Upon Oblique Reflection from Dielectric Mirrors

AbstractDielectric mirrors comprising thin‐film multilayers are widely used in optical experiments because they can achieve substantially higher reflectance compared to metal mirrors. Here, potential problems are investigated that can arise when dielectric mirrors are used at oblique incidence, in particular for focused beams. It is found that light beams reflected from dielectric mirrors can experience lateral beam shifts, beam‐shape distortion, and depolarization, and these effects have a strong dependence on wavelength, incident angle, and incident polarization. Because vendors of dielectric mirrors typically do not share the particular layer structure of their products, several dielectric‐mirror stacks are designed and simulated, and then the lateral beam shift from two commercial dielectric mirrors and one coated metal mirror is also measured. This paper brings awareness of the tradeoffs between dielectric mirrors and front‐surface metal mirrors in certain optics experiments, and it is suggested that vendors of dielectric mirrors provide information about beam shifts, distortion, and depolarization when their products are used at oblique incidence.

Spin Hall Effect of Light via Momentum-Space Topological Vortices around Bound States in the Continuum.

Optical bound states in the continuum (BICs) are exotic topological defects in photonic crystal slabs, carrying polarization topological vortices in momentum space. The topological vortex configurations not only topologically protect the infinite radiation lifetime of BICs, but also intrinsically contain many unexploited degrees of freedom for light manipulation originating from BICs. Here, we theoretically propose and experimentally demonstrate the spin Hall effect of light in photonic crystal slabs via momentum-space topological vortices around BICs. The strong spin-orbit interactions of light are induced by using the topological vortices around BICs, introducing both wave-vector-dependent Pancharatnam-Berry phase gradients and cross-polarized resonant phase gradients to the spinning light beam, which lead to spin-dependent in-plane-oblique lateral light beam shifts. Our work reveals intriguing spin-related topological effects around BICs, opening an avenue toward applications of BICs in integrated spin-optical devices and information processing.

Goos-Hänchen shift at Brillouin light scattering by a magnetostatic wave in the Damon-Eshbach configuration [Invited

The lateral shift of an optical beam undergoing Brillouin light scattering by a spin wave propagating along the interface between magnetic and dielectric media (Damon-Eshbach configuration) in the total internal reflection geometry is studied theoretically. Linear and quadratic magneto-optic terms in polarization are taken into account. It is shown that the lateral shift depends on the polarization (s- or p-) state of the scattered electromagnetic wave as well as on the frequency of the spin wave.

Measurement of net Goos–Hänchen shift and reshaping shift

We develop the concepts of net Goos–Hänchen (GH) shift and reshaping shift, and apply these concepts to lateral beam shift arising from k (wavenumber) domain dispersion. Specifically, our interest is in cases in which the traditional concept of GH shift loses its meaning. We analyzed the effects of finite beam size, complicated beam profiles, and phase modulations on GH shift. We experimentally examined the GH shift for surface plasmon polaritons and a leaky waveguide mode. The results agreed well with those from analyses based on the net GH shift and reshaping shift, indicating that these concepts are useful for extending the traditional concept of GH shift to complicated reflection systems.

Nonreciprocal normal-incidence lateral shift for transmitted wave beams through the magnetic photonic crystal slab

Conventionally, there is no lateral beam shift (LBS) at normal incidence for a wave beam pass through a slab. However, by simultaneously breaking spatial inversion, time-reversal, and mirror symmetries of the photonic crystal slab, we realized nonreciprocal LBS for the transmitted wave beam with high transmission. We showed that the nonreciprocal LBS could be positive or negative, which could be tuned by the arrangement of a magnetic basis in the unit cell. We verified the nonreciprocal LBS at normal incidence by experiments. Our study provides a useful way to manipulate the wave propagation and wave-matter interaction by artificial materials and leads to a breakthrough in LBS, which has promising potential in optical devices, such as transducers, switches, and unidirectional couplers.

Goos-Hänchen effect for Brillouin light scattering by acoustic phonons.

The lateral shift of an optical beam undergoing Brillouin light scattering on an acoustic wave (AW) in the total internal reflection geometry is studied theoretically. It is shown that the lateral shift depends on polarization (longitudinal or transversal) of the AW, as well as on the type of scattering process: a direct one, when the scattered wave undergoes a lateral shift at reflection from the interface, or a cascading one, when a fundamental frequency light beam is laterally shifted at reflection and then scattered on the AW.

Large lateral shift in complex dielectric multilayers with nearly parity–time symmetry

We investigate the lateral shift of optical beam in complex dielectric multilayers with nearly parity–time (PT) symmetry. The gain and loss of dielectrics are modulated to achieve nearly PT symmetry. As light impinges on the multilayers, a laser point (LP) and exceptional points (EPs) appear in the parameter space composed of the incident angle and refractive index. The phase of reflection dislocates at the LP and EPs, inducing large lateral shift around these points. The shift can be positive and negative, and the polarities of the lateral shift convert at the LP and EPs. The shift, which is sensitive to the incident angle and refractive index of dielectrics, could be tuned flexibly. The study may find potential applications in highly sensitive sensors.

Theoretical large positive and negative lateral beam shift of the metal cladding waveguide in the mid-infrared region.

A large negative and positive lateral beam shift is presented in the midinfrared region based on the penetration enhancement effect of the ultrahigh order modes in the metal-cladding waveguide. The characteristics of the lateral beam shift have been discussed in theory, and the performance of the ultrahigh order modes is confirmed in an experiment at 5.4µm. The negative and positive lateral shift depends on the derivative of the imaginary part of the propagation constant.

Thermal dependence of the lateral shift of a light beam reflected from a liquid crystal cell deposited on a magnetic film

We study the influence of the thermo-optic effect and of thermal expansion on the lateral shift experienced by a Gaussian near-infrared beam upon reflection from a voltage-controlled nematic liquid crystal cell deposited on a magnetic yttrium-iron garnet film. Variations of temperature are considered in the range between room temperature and the nematic-isotropic phase transition temperature of the liquid crystal and induce changes in both the layer thicknesses and the permittivity tensor components of the constituents. We show that for all polarization configurations of the incoming and reflected beams, these changes modify the amplitude of the extrema of the lateral beam shift and their position with respect to the incidence angle of the beam and, except in the s–s polarization configuration, to the voltage applied to the liquid crystal cell. In the p–p and p–s polarization configurations, this drift can thus be controlled at some incidence angles by tuning the applied voltage. Moreover, in the p–s configuration, the lateral shift can be also controlled by a magnetization reversal in the magnetic layer. Finally, we discuss the possibility of temperature monitoring using the temperature dependence of the lateral shift in this system.

Tailored plasmon-induced transparency in attenuated total reflection response in a metal\u2013insulator\u2013metal structure

We demonstrated tailored plasmon-induced transparency (PIT) in a metal (Au)–insulator (SiO2)–metal (Ag) (MIM) structure, where the Fano interference between the MIM waveguide mode and the surface plasmon polariton (SPP) resonance mode induced a transparency window in an otherwise opaque wavenumber (k) region. A series of structures with different thicknesses of the Ag layer were prepared and the attenuated total reflection (ATR) response was examined. The height and width of the transparency window, as well as the relevant k-domain dispersion, were controlled by adjusting the Ag layer thickness. To confirm the dependency of PIT on Ag layer thickness, we performed numerical calculations to determine the electric field amplitude inside the layers. The steep k-domain dispersion in the transparency window is capable of creating a lateral beam shift known as the Goos–Hänchen shift, for optical device and sensor applications. We also discuss the Fano interference profiles in a ω − k two-dimensional domain on the basis of Akaike information criteria.

Goos-Hänchen effect in light transmission through biperiodic photonic-magnonic crystals

We present a theoretical investigation of the Goos-H\"anchen effect, i.e., the lateral shift of the light beam transmitted through one-dimensional biperiodic multilayered photonic systems consisting of equidistantmagnetic layers separated by finite size dielectric photonic crystals. We show that the increase of the number of periods in the photonic-magnonic structure leads to increase of the Goos-H\"anchen shift in the vicinity of the frequencies of defect modes located inside the photonic band gaps. Presence of the linear magnetoelectric coupling in the magnetic layers can result in a vanishing of the positive maxima of the cross-polarized contribution to the Goos-H\"anchen shift.

Spin- and valley-dependent Goos–Hänchen effect in silicene and gapped graphene structures

We investigate the Goos–Hänchen shift for ballistic electrons (i) reflected from a step-like inhomogeneity of the potential energy and (or) effective mass, and (ii) transmitted through a ferromagnetic barrier region in monolayer silicene or gapped graphene. For the electrons reflected from a single interface we found that the Goos-Hänchen shift is valley-polarized for gapped graphene structure, and valley- and spin-polarized for silicene due to the spin-valley coupling. In contrast, for example, to gapless graphene the lateral beam shift in gapped structures occurs not only in the case of total, but also of partial, reflection, i.e. at the angles smaller than the critical angle of total reflection. We have also demonstrated that the valley- and spin-polarized displacement of the electron beam, transmitted through a ferromagnetic silicene barrier, resonantly depends on the barrier width. The resonant values of the displacement can be controlled by adjusting the electric potential, the external perpendicular electric field, and the exchange field induced by an insulating ferromagnetic substrate.

3-D Gaussian beam scattering from a gyromagnetic perforated layer: Quasi-static approach

This paper is devoted to the study of the scattering of a three-dimensional (3-D) Gaussian beam with the circular cross section from a double periodic perforated gyromagnetic layer with polarization independent unit-cell, in the quasi-static approximation. We used the plane-wave spectrum representation for Gaussian beam field representation and reduced it to a single integral representation. The phenomena of the lateral beam shift influenced by Faraday rotation and the nearly total beam transmission when passing through gyromagnetic slab biased with an external static magnetic field in the Faraday configuration were considered.

Nonlocal optical effects on the Goos–Hänchen shifts at multilayered hyperbolic metamaterials

The lateral beam shift of light incident on a multilayered hyperbolic metamaterial (HMM) is investigated using a theoretical model which emphasizes the nonlocal optical response of the indefinite material. By applying an effective local response theory formulated recently in the literature, it is found that nonlocal effects only affect p polarized light in this Goos–Hänchen (GH) shift of the incident beam; leading to a blue-shifted peak for positive shifts at high frequencies and red-shifted dip for negative shifts at low frequencies in the GH shift spectrum. An account for the observed phenomenon is given by referring to the ‘Brewster condition’ for the reflected wave from the HMM. This observation thus provides a relatively direct probe for the nonlocal response of the HMM.

Design method for compensating lateral beam shift of ground-plane cloak

This paper demonstrates a method to improve the accuracy of the ground-plane cloak by compensating for the lateral beam shift. The lateral beam shift can be compensated by increasing the height of the bump with the upper boundary of the cloak and shifting the reference ground plane downwards in the cloaking region. Moreover, the asymmetric ground-plane cloak, which represents not only the lateral beam shift but also an error of the reflection angle, is also compensated by generating the initial grids unequally. The accuracy of the proposed method is verified via ray tracing simulation.

Transversal symmetry breaking and axial spreading modification for gaussian optical beams

For a long time, it was believed there was no reason to include the geometrical phase in studying the propagation of gaussian optical beams through dielectric blocks. This can be justified by the fact that the first-order term in the Taylor expansion of this phase is responsible for the lateral shift of the optical beam which is also predicted by ray optics. From this point of view, the geometrical phase can be seen as a purely auxiliary concept. In this paper, we show how the second-order term in the Taylor expansion accounts for the symmetry breaking of the transversal spatial distribution and acts as an axial spreading modifier. These new effects clearly show the importance of the geometrical phase in describing the correct behavior of light. To test our theoretical predictions, we briefly discuss a possible experimental implementation.

Arbitrary positive and negative lateral shift of Gaussian beam reflected from an anisotropic grounded slab

Both positive and negative lateral shifts are demonstrated in this paper for a Gaussian beam reflected from an anisotropic grounded slab, whose constructive parameters are determined by the optical transformation approach. The incident wave is modeled as a tapered wave with a spatial Gaussian shape. Layered structures with alternating isotropic materials are applied to model the parameters of such an anisotropic grounded slab and good agreements are obtained when the positive lateral shifts caused by ideal anisotropic slab are compared with those of the equivalent isotropic layered slab.

Coupling of spatially partially coherent beams into planar waveguides.

The second-order coherence theory of partially spatially coherent light and the overlap integral method are applied to study the end-coupling of stationary multimode light beams into planar waveguides. A method is presented for the determination of the cross-spectral density function of the guided field. Examples are given on the effects of spatial coherence, lateral shift, angular tilt, and defocusing of the incident beam on the coupling efficiency, spatial coherence, and propagation characteristics of the guided field.

132: Monitoring of carbon ion beams using secondary ions: investigations in inhomogeneous targets

Purpose: Radiation therapy with ion beams provides highly conformal dose distributions. These are sensitive to possible variations of the beam settings and changes of the tissue in the beam path, which can deteriorate the dose distribution in the patient. To monitor the ion beam, it was suggested in [Amaldi et al. NIM A 617, 2010] to exploit the information carried by prompt secondary ions produced within the patient during irradiation. Our initial experimental investigations of monitoring the beam position, width and energy in a homogeneous phantom have been published in [Gwosch et al. PMB 58, 2013]. In this contribution we address the performance of the method in phantoms with inhomogeneities. Materials and Methods: The experiments were performed at the Heidelberg Ion-Beam Therapy Center using beam energies and widths typical for therapy. Secondary charged particles emerging from phantoms during irradiation were registered by the pixelated semiconductor detector Timepix [Llopart et al. NIM A 581, 2007], which was developed by the Medipix Collaboration at CERN. Its multi-layered version (3D voxel detector) [Soukup et al. JINST 6, 2011] was used to determine the direction of single particles. Using an anthropomorphic head phantom containing real bones, it was tested whether the distributions of secondary ions around the phantom are sensitive to variations of the beam parameters. In a plastic slab phantom it was studied how changes of its structure affect the secondary ion distribution. Experiments and Results: The measured particle directions were projected to the vertical beam plane. An example of such a projection is shown in figure 1 (inset). Changes of this projection with the beam parameters and phantom structure were analysed. This new imaging modality [Jakubek IEEE, 2011] was found to be capable of detecting lateral beam shifts, changes of the beam energy (affecting the range) and beam width (see figure 1) of a few millimeters in the head phantom. In a homogeneous plastic phantom, missing slabs of 1cm thickness were found to influence the distribution of secondary ions significantly. Conclusion: The presented experimental investigations demonstrate that measurements of charged particle tracks around phantoms irradiated with carbon ion beams enable to detect missing slices of 1cm thickness in an otherwise homogeneous phantom. In the head-phantom it was shown that the method provides an attractive source of information on the actual beam delivery, despite the inherent tissue inhomogeneities.