V. N. Lyubimov

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.

Excitation of intense acoustic waves in hexagonal crystals

Resonant excitation of an intense elastic wave using reflection of a pump wave from a free surface of hexagonal crystal is described. A resonance arises in the case of specially chosen propagation geometry where the reflecting boundary slightly deviates from symmetric orientation and the propagation direction of an intense reflected wave is close to that of an exceptional bulk wave, which satisfies the free boundary condition in unperturbed symmetric orientation. It is shown that, in crystals with elastic moduli c44>c66, a resonance arises when the initial boundary is chosen parallel to the hexagonal axis 6, whereas in crystals characterized by the relation c44<c66 a resonance occurs when the initial boundary is orthogonal to this axis. The fraction of the pump energy transferred to the excited beam depends on the specific relations between the elastic moduli and can be rather significant for specially chosen crystals. Examples of crystals are presented in which the beam intensity can be increased by a factor of 5–10 at sufficiently high frequencies, with beam divergence remaining acceptable.

Dispersionless polaritons at symmetrically oriented surfaces of biaxial crystals

A set of dispersion relations is derived for surface polaritons in optically biaxial crystals at the surfaces parallel to the symmetry planes of the permittivity tensor ɛ. The domains of existence, as well as the sectors of the propagation directions of dispersionless surface polaritons which arise at positive components of the tensor ɛ, are analyzed. Three nonoverlapping domains of the dielectric-anisotropy parameters where dispersionless polaritons can exist are found for weakly anisotropic crystals. In each of these domains, polaritons exist at two different mutually orthogonal surfaces of the crystal. In optically biaxial crystals, in contrast to optically uniaxial media, polaritons arise not only in positive but also in negative crystals. The evolution of the optical-axis configuration is traced as the anisotropy parameters vary in the domains of existence of polaritons.

Resonant excitation of intense acoustic waves in crystals

The resonant excitation of an intense elastic wave through nonspecular reflection of a special pump wave in a crystal is described. The choice of the plane and angle of incidence is dictated by the requirement that the excited reflected wave be close to the bulk eigenmode with its energy flow along a free boundary. The resonance parameters have been found for a medium with an arbitrary anisotropy. General relations are concretized for monoclinic, rhombic, and hexagonal systems. A criterion is formulated for an optimal selection of crystals in which the resonant reflection is close to the conversion one, when almost all of the energy from the incident beam of the pump wave falls into the near-surface narrow high-intensity reflected beam. Estimates and illustrations are given for such crystals as an example. The intensity of the reflected beam increases with its narrowing, but its diffraction divergence also increases with this narrowing. Nevertheless, the intensity of the beam can be increased by a factor of 5–10 at sufficiently high frequencies while keeping its divergence at an acceptable level. Amplification by two orders of magnitude can be achieved by compressing the beam in two dimensions through its double reflection.

Electromagnetic waves in uniaxial crystals with metallized boundaries: Mode conversion, pure reflections, and bulk polaritons

A theory is constructed for the reflection of plane electromagnetic waves in uniaxial crystals with a positive definite permittivity tensor and an arbitrarily oriented metallized boundary. The problem is solved both for general-position orientations corresponding to three-partial reflection and for special conditions allowing two-partial reflections: mode conversions when the incident and reflected waves belong to different sheets of the refraction surface and “pure” reflections when both waves belong to the same sheet. The space of pure reflections is shown to be formed by two types of optical-axis orientations: arbitrary directions in the plane of the crystal surface and in the plane of incidence. The configurations of the conversion surface for optically positive and negative crystals are investigated. A subspace of pure reflections that transform into one-partial bulk polaritons with the energy flux parallel to the surface at grazing incidence has been found. The domain of existence of such bulk eigenmodes is bounded by two “lines” of solutions. These are any directions along the boundary containing the optical axis for ordinary polaritons and the direction along the projection of the optical axis onto the surface at an arbitrary orientation of the axis with respect to the boundary for extraordinary polaritons.

Wedge refraction of electromagnetic waves in absorbing crystals

Topological features of the self-intersection of wave surfaces near singular optical axes of an absorbing crystal are investigated. Distributions of complex polarization fields in the neighborhood of singular directions are obtained. It is shown that, when the wave normal m circumvents an optical axis, the corresponding rotation of polarization ellipses is characterized by the PoincarÉ index n=1/4. Using the example of an orthorhombic crystal, a wedge refraction of electromagnetic waves on the intersection line of the sheets of the surface of refractive indices is predicted and theoretically investigated. It is shown that the directions of the mean energy fluxes P̄± are close to the direction of normals n± to the refraction surface only in the central region of a wedge, i.e., only in the domain where the polarization is almost linear and the group velocity of waves is well defined. When m moves to singular axes, the ellipticity of the polarization increases at the ends of the edge of the wedge and the orientations of the vectors P̄± and n± gradually diverge, yet remain in the same plane that is orthogonal to the edge. The angle between P̄+ and P ̄ − monotonically decreases, and P̄+ || P̄− for the propagation along singular axes; in this case, the angle between n+ and n− increases, and they have a plane-fan-type orientational singularity along the optical axes. When m is scanned along the edge of the wedge, the unaveraged vectors P± describe per period the same conical surface that coincides with the refraction cone of a transparent crystal, while the endpoints of the vectors P± run over elliptic orbits whose shape and slope depend on m. The possibilities of observing a wedge refraction are analyzed.

Cones of optical axes in gyrotropic crystals with scalar permittivity

A theory is constructed for the degeneracy of electromagnetic waves in gyrotropic crystals near their isotropy points (in temperature and other parameters), in which permittivity ɛ becomes scalar due to dispersion and optical anisotropy is entirely determined by gyrotropy. It is shown that closed lines of intersection of sheets of the refraction surface, which correspond to the cones and, in particular, planes of the optical axes, are formed for isotropic ɛ. The polarization characteristics of wave fields experience a jump upon a transition through such lines. The conditions for the existence and geometry of the degeneracy cones under investigation are analyzed for crystals of all symmetry classes permitting optical activity. It is shown that the degeneracy lines disappear for a small deviation of ɛ from isotropy, while polarization anomalies persist. Isolated (one or two) degeneracy points may retain in place of the lines in the case when the optical axes of a perturbed crystal with “switched-off” gyrotropy belong to the initial cone.

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 εo and εe of the crystal and the angle θ between the optical axis and the surface: −εetan2θ < εo < 0. Thus, polaritons exist only in the range of wave frequencies ω ensuring negative values of εo(ω) for εe > 0. The frequency boundaries of this region are specified for the case when the εo(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.

Resonance excitation of intense acoustic beams in crystals of different syngonies

The resonance excitation of an intense elastic wave in a crystal, arising under conditions of the nonspecular reflection of an incident pump wave is described for a crystal geometry close to a cut that allows the existence of a bulk eigenwave satisfying the free boundary condition. It is shown that choosing a crystal surface parallel to the plane of symmetry optimizes reflection resonance due to the coincidence of the excited wave’s intensity maximum and the reflected (parasite) wave’s intensity minimum in the same geometry of reflection. Parameters of resonance are given for a number of crystals with monoclinic, orthorhombic, and hexagonal syngonies.

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.