Dispersion polaritons on metallized surfaces of optically uniaxial crystals

We have constructed a theory of dispersion polaritons (localized electromagnetic waves) on arbitrarily oriented metallized surfaces of optically uniaxial crystals. The domain of existence of polaritons is defined by the following inequalities for permittivities ε_o and ε_e of the crystal and the angle θ between the optical axis and the surface: ?ε_etan²θ < ε_o < 0. Thus, polaritons exist only in the range of wave frequencies ω ensuring negative values of ε_o(ω) for ε_e > 0. The frequency boundaries of this region are specified for the case when the ε_o(ω) dependence corresponds to the model of a single polar excitation. The azimuthal orientation φ of the optical axis projection onto the surface does not appear in the criterion for polariton existence, but affects (together with angle θ) its main dispersion characteristics, such as the refractive index and partial wave localization parameters. This effect is analytically described in detail. Anomalies in the behavior of polariton parameters are studied in the vicinity of the boundaries of the domain of its existence, where the wave fields are especially sensitive to variations in the angles θ and φ. It is shown that a polariton in the plane of propagation (sagittal plane) passing through the optical axis is transformed into a one-partial bulk wave satisfying the boundary conditions. Accordingly, the wave branch under investigation for close orientations (when the optical axis forms a small angle with the sagittal plane) describes deeply penetrating (quasi-bulk) polaritons.     

Surface polaritons on semi-infinite anisotropic media

We have investigated the nature of polaritons which propagate on the surface of semi-infinite anisotropic dielectric and magnetic media and find that the surface polaritons are regular surface waves [i.e., the penetration constant α (ω) is real] only for special orientations of the wave vector k and of the normal to the surface n relative to the principal axes. In the case of biaxial crystals, regular surface polaritons occur when k and/or n is along a principal axis of the dielectric tensor ε(ω) for dielectric media [or the magnetic permeability tensor μ(ω) for magnetic media]. When k and n are both directed along principal axes, the surface polaritons are TM with E in the saggital plane for dielectric media. One finds that surface polaritons which are coupled photon-virtual surface dipole excitation modes can exist on “surface active” anisotropic media in addition to the familiar coupled photon-real surface dipole excitation modes. When neither k nor n are along principal axes, the surface polaritons that occur are, with the exception of special orientations, “generalized” surface waves [i.e., α(ω) is complex]. The Poynting vectors of the propagating surface polaritons are always in the plane of the surface but not, in general, along k. These results, which hold for uniaxial crystals, are also applicable to gyromagnetic media and to gyrodielectric media. This theory is also applicable to surface polaritons which propagate along the interface between two media, one or both of which is anisotropic, and with one or the other serving as the “surface active” medium.     

“Right-handed” and “left-handed” polaritons in material media

The dispersion law for polariton waves is deduced from analysis of Maxwell equations in a dielectric medium characterized by the presence of resonance in the frequency range of lattice vibrations or exciton transitions. The theory considers polariton waves with right- and left-oriented vectors $\vec E,\vec H,\vec k$ , corresponding to “right-handed” and “left-handed” polaritons. Dispersion dependences of group velocity of polariton waves and effective mass are established for “right-handed” and “left-handed” polaritons. Expressions are obtained for the effective refractive index and reflection coefficient in a wide spectral range including the resonance region. The specific features of lattice reflection spectra in alkali halide crystals are explained using the proposed theory.     

振荡介质中平面波的反射

在复金慈堡-朗道方程描述的振荡介质中研究了平面波的反射.从理论上给出了产生反射的条件,导出了反射波和入射波这两个区域的分界线与两种介质分界线的夹角.发现两类反射,一类为回折射产生的反射,对于这类反射,理论上给出了反射角;另一类为纯反射,它与折射无关.理论分析与数值模拟结果均表明：只有当入射角大于临界入射角才会发生反射,而且反射角等于临界入射角;对于纯反射,反射角随波频率增大而增大. 关键词： 复金慈堡-朗道方程 平面波 反射     

光在两单轴晶体间界面的反射和透射

根据位相匹配条件和应该满足的边界方程,在光轴取向任意的条件下,得到了光在两单轴晶体界面的反射和折射的理论表达式,给出了更普遍的公式计算光能量损失以及两束折射光的能量比。数值模拟表明所得结果满足能量守恒,光轴的取向和入射角大小对晶体中折射的o光、e光的能量比有重大影响,但是对反射率影响很小。只要知道了晶体的有关参数及入射条件,利用所给表达式可以计算各光束光能量比,为晶体器件特性研究提供了有力的工具。由于对光轴取向和入射角度没有任何限制,公式具有普遍性。     

Dyakonov Plasmon–Polaritons Propagating along the Surface of a Hyperbolic Metamaterial

Optics and Spectroscopy - Plasmon–polaritons of the type of Dyakonov surface waves propagating along the plane boundary of a hyperbolic metamaterial with an arbitrary orientation of its...     

Reflexion und Brechung des Lichtes an einer anisotropen Schicht

Reflection and Refraction of Light by an Anisotropic Layer The linear problem of reflection and refraction of plane monochromatic electromagnetic waves by a plane-parallel homogeneous anisotropic layer between (in general different) homogeneous optically isotropic semiinfinite media is treated on the basis of MAXWELL 's equations and the boundary conditions following from them. The permittivity tensor of the anisotropic layer is assumed to be widely arbitrary and therefore asymmetric, neglecting only the spatial dispersion, i. e., the dependence on the wave vector. The electrical fields of reflected, refracted, and transmitted waves are calculated in dependence on the electric field of the incident wave. The conditions for waveguide modes of the layer in the absence of incident waves are obtained from the vanishing of a determinant. The general formulae are specialized to the cases of normal incidence and also of perpendicular and parallel polarisation, relatively to the plane of incidence, of the refracted partial waves in the anisotropic layer thus obtaining simplifications in these cases. The interesting cases of uniaxial layers, when the optic axis lies either parallel or perpendicular to the plane of incidence, belong to the last mentioned special cases of perpendicular and parallel polarisation relatively to the plane of incidence.     

Harmonic Green's functions for flexural waves in semi-infinite plates with arbitrary boundary conditions and high-frequency approximation for convex polygonal plates

This paper provides a method for obtaining the harmonic Green's function for flexural waves in semi-infinite plates with arbitrary boundary conditions and a high frequency approximation of the Green's function in the case of convex polygonal plates, by using a generalised image source method. The classical image source method consists in describing the response of a point-driven polygonal plate as a superposition of contributions from the original source and virtual sources located outside of the plate, which represent successive reflections on the boundaries. The proposed approach extends the image source method to plates including boundaries that induce coupling between propagating and evanescent components of the field and on which reflection depends on the angle of incidence. This is achieved by writing the original source as a Fourier transform representing a continuous sum of propagating and evanescent plane waves incident on the boundaries. Thus, the image source contributions arise as continuous sums of reflected plane waves. For semi-infinite plates, the exact Green's function is obtained for an arbitrary set of boundary conditions. For polygonal plates, a high-frequency approximation of the Green's function is obtained by neglecting evanescent waves for the second and subsequent reflections on the edges. The method is compared to exact and finite element solutions and evaluated in terms of its frequency range of applicability.     

Focusing of electromagnetic waves into a uniaxial crystal

We derive integral representations suitable for studying the focusing of electromagnetic waves through a plane interface into a uniaxial crystal. To that end we start from existing exact solutions for the transmitted fields due to an arbitrary three-dimensional (3D) wave that is incident upon a plane interface separating two uniaxial crystals with arbitrary orientation of the optical axis in each medium. Then we specialize to the case in which the medium of the incident wave is isotropic and derive explicit expressions for the dyadic Green's functions associated with the transmitted fields as well as integral representations suitable for asymptotic analysis and efficient numerical evaluation. Relevant integral representations for focused 3D electromagnetic waves are also given. Next we consider the special case in which (i) the incident field is a two-dimensional (2D) TM wave and (ii) the optical axis in the crystal lies in the plane of incidence, implying that we have a 2D vectorial problem, and derive dyadic Green's functions, integral representations suitable for asymptotic and numerical treatment, and integral representations for focused TM fields. Numerical results for focused 2D TM fields based on these integral representations as well as corresponding experimental results will be presented in forthcoming papers.     

Anisotropy of electrooptical interaction in LiNbO3 crystals

Results of studying the conditions for optimum electrooptical (EO) interaction in lithium niobate crystals are presented. Analytical formulas are obtained for calculating refractive indices of natural waves and their polarizations for basis X-, Y-, and Z-cuts of crystals for arbitrary orientations of the wave vector of an optical wave. Conditions are found for the appearance of intermode EO interaction causing the orientation of polarization plane of natural waves to become a function of the external electric field.     

Reflection and transmission of waves in pyroelectric and piezoelectric materials

The reflection and transmission theories of waves in pyroelectric and piezoelectric medium are studied in this paper. In general in an infinite homogeneous pyroelectric medium there are four bulk wave modes: quasi-longitudinal, two quasi-transversal and temperature waves. In an infinite homogeneous piezoelectric medium there are three bulk wave modes: quasi-longitudinal and two quasi-transversal waves. In the reflection and transmission problem there are five complex boundary conditions in the pyroelectric medium and four complex boundary conditions for the piezoelectric medium. In this paper, we find that the surface waves will be revealed in the reflection and transmission wave problem. The surface waves have the same wave vector component with the incident waves on the interface plane. The two dimensional reflection problem of waves at the interface between the semi-infinite pyroelectric medium and vacuum is researched in greater detail and a numerical example is given.     

Dispersionless surface polaritons in the vicinity of different sections of optically uniaxial crystals

The sectors of propagation directions of dispersionless polaritons localized at the optically uniaxial crystal-optically isotropic medium interface are determined. The region of possible orientations of the crystal surface containing these sectors is revealed. The boundaries of the sector of possible propagation directions are analytically described as functions of the crystal surface orientation with respect to the optical axis of the crystal. Consideration is given to the optimum ratios of permittivities at which the width of the propagation sectors appears to be maximum. It is found that the boundaries of the sectors of polariton propagation along different surfaces change drastically in the limit of small dielectric anisotropy of the crystal.     

Total reflection in a uniaxial crystal–uniaxial crystal interface

Considering an interface between two uniaxial birefringent crystals, four reflected and four refracted waves for each incidence direction are obtained. Along this direction can propagate an ordinary wave and an extraordinary wave. Here, we present the analytic expressions for the four critical angles, from which each refracted wave no more exists as propagating wave. We show the variation in these critical angles for different interfaces varying the orientation of the incidence plane with respect to the optical axes. When both principal refractive indices of the second medium are smaller than those of the first medium, then the four critical angles exist for each incidence plane and for any direction of the optical axes. But, when one of the indices has an intermediate value between the values of the indices of the other crystal, we can chose the optical axes directions in such a way that certain critical angles do not exist. Therefore, we can select the refracted wave that is eliminated by total reflection.     

Photonic crystal sensor based on surface waves for thin-film characterization

A new sensor based on optical surface waves in truncated one-dimensional photonic crystals is proposed for use in determining the optical properties of metallic or dielectric thin films and bulk media. Specifically, the method of optical characterization takes into account the changes that the surface waves of a layered structure undergo when either a thin film of arbitrary material is added at the surface or the optical properties of transmission medium change. For the surface-wave excitation the Kretschmann configuration used in attenuated total reflectance is employed.     

Resonance compression of an acoustic beam in a crystal

The resonance excitation of an intense acoustic beam in a crystal is described for a special geometry of pump-wave reflection from the crystal surface. The resonance appears in the vicinity of the total internal reflection angle under the condition that the wave field in a compressed reflected beam propagating almost parallel to the surface is close to the volume eigenmode satisfying the free boundary condition. Criteria for the existence of such modes are considered in detail. Conversion conditions are analyzed under which a “parasitic” reflected wave of the same branch as the incident wave is absent and entire energy from the incident wave falls within a narrow intense acoustic beam of another branch. It is shown that, when the surface is chosen parallel to the crystal symmetry plane, the conversion criterion is reduced to the sole condition on the elastic moduli of the medium. Analysis is performed by analytic and numerical methods for skew cuts of monoclinic, rhombic, trigonal, and hexagonal crystals, when the boundary is the symmetry plane, while the sagittal plane has no symmetry. A number of crystals are found in which resonance excitation is very close to conversion.     

Reflection of elastic waves in a crystal of Heusler alloy Ni<Subscript>2</Subscript>MnGa in the phase transition range

The reflection of longitudinal and transverse acoustic waves from the free surface of the ferromagnetic shape memory alloy Ni₂MnGa that is located in the ranges of the premartensite and martensite phase transformations is considered. The propagation directions and amplitudes of the waves reflected in the (001) plane of the crystal are determined. They acquire the character of substantially quasi-longitudinal and quasi-transverse vibrations rather than being pure modes. The angles of wave reflection and conversion are shown to be effectively controlled by temperature and a magnetic field due to the colossal acoustic anisotropy of the crystal over the wide range of its phase transitions. Beginning from a certain critical angle of incidence of a quasi-transverse wave, the quasi-longitudinal wave having appeared upon reflection becomes an accompanying surface vibration, and it can be emitted into the bulk of the crystal when the phase transition point is approached. Two angles of full conversion of an incident quasi-longitudinal wave into a quasi-transverse wave are established, and their temperature dependences are found. Trivisonno’s experimental data for the ultrasound velocity and absorption in an Ni₂MnGa crystal are used to numerically estimate these acoustic effects.     

Theory of surface polaritons in n-type silicon in the presence of a dc current,including the electron thermal pressure gradient

A theoretical investigation has been made of the effect of a drift current, including the electron thermal pressure gradient, on surface polaritons in n-type Si. The polariton propagation and drift current directions are taken to be either parallel or antiparallel. Retardation is included, but damping is neglected. The specular reflection approach of Kliewer and Fuchs is used to obtain the polariton dispersion relation. The results show that the drift current and surface polaritons interact, leading to evanescent waves for certain frequencies. However, no wave amplification is obtained.     

Light propagation in anisotropic metamaterials. II. Reflection from the half-space

We consider reflection of light from half-space of anisotropic metamaterial at arbitrary direction of optical axis in the plane of light incidence. We obtain conditions at which total reflection and refraction do not depend on the polarization of incident light and the reflection does not depend on also the angle of incidence. We also study the possibilities and conditions for using the considered system as beam splitter, omnidirectional reflector, phase retarder, and so on.