Wedge refraction of electromagnetic waves in absorbing crystals

Journal of Experimental and Theoretical Physics - Topological features of the self-intersection of wave surfaces near singular optical axes of an absorbing crystal are investigated. Distributions...     

Antiferromagnetic conical refraction of elastic waves in hematite

Conical refraction, which is due to the renormalization of the elastic moduli by the effective magnetoelastic interaction and depends on the static magnetic field, has been experimentally observed in an α-Fe₂O₃ trigonal easy-plane antiferromagnet in addition to the usual internal conical refraction of transverse elastic waves propagating along the trigonal C ₃ axis. It has been shown that the deviation angle θ_η of the energy flux from the C ₃ axis at the internal conical refraction is independent of the magnetic field applied in the basal plane (H ⊥ C ₃) and is a constant determined by the ratio of the elastic moduli C ₁₄ and C ₄₄. The deviation angle of the energy flux at the antiferromagnetic conical refraction increases with the magnetic field and approaches the value θ_η at large H values. The results are well described by the theory of this phenomenon developed by E.A. Turov and confirm its basic conclusions.     

Propagation of elastic waves in hexagonal piezoelastic crystals

The propagation of elastic waves in an arbitrary direction through a hexagonal piezoelectric crystal is investigated. Orientational relations are obtained in analytic form for the effective elastic moduli and the piezoelectric and dielectric constants, and also for the basic parameters of the elastic waves: the phase velocity, electromechanical coefficient, and the divergence between the displacement vector and the energy flux. Expressions are given for the directions in which the electromechanical coefficient takes an extremal value, and the basic parameters are calculated for cadmium sulfide.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 101–105, May, 1977.     

Theories of elastic properties and elastic waves of equal phase velocities in crystals

A survey is made of pairs of heteronormal planar elastic waves, which can propagate in an unlimited crystal medium and have equal theoretical values of the phase velocity, using Voigt elastic moduli. Such pairs are chosen for which it is possible that the theoretical equality of velocities will be disturbed when using another theory of the elastic properties of crystals with generally different tensors of material constants (for example Kuvshinskij J. V., Aero E. L.: Fiz. tv. tela5 (1963), 2591). In such a case, a comparison of the measured velocities of a suitable pair of waves can help to decide between the two theories. Pairs of waves are found for 12 non-piezoelectric crystal classes. Among such pairs it is easy to find pairs of waves of the same properties for piezoelectric crystal classes.     

Anharmonic interactions of elastic and orientational waves in one-dimensional crystals

Planar oscillations of a chain of dumbbell-shaped particles possessing three degrees of freedom are studied. This system models the dynamics of quasi-one-dimensional crystals consisting of elongated anisotropic molecules. A system of nonlinear differential equations describing the anharmonic interaction of the elastic and orientational waves in the lattice, corresponding to different degrees of freedom of the particles, is constructed assuming a cubic interparticle interaction potential. It is shown that in the low-frequency approximation the system obtained is equivalent to the equations of the moment theory of elasticity, widely employed for describing nonlinear and dispersion properties of layered crystals and phase transformations in alloys. Some types of three-wave collinear interactions are investigated, suggesting the possibility of exciting orientational waves in organic crystals because of their nonlinear interaction with acoustic waves. Fiz. Tverd. Tela (St. Petersburg) 39, 137–144 (January 1997)     

Experimental evidence of rotational elastic waves in granular phononic crystals

A generalized theory of elasticity, taking into account the rotational degrees of freedom of point bodies constituting a continuum, was proposed at the beginning of the twentieth century by the Cosserat brothers. We report the experimental observation of coupled rotational-translational modes in a noncohesive granular phononic crystal. While absent in the classical theory of elasticity, these elastic wave modes are predicted by the Cosserat theory. However the Cosserat theory fails to predict correctly the dispersion of the elastic modes in granular crystals even in the long-wavelength limit.     

Theory of elastic waves in real crystals. II.

Starting from the canonical equations of an elastic field formulated in the first part of this paper, conservation laws for an elastic field are obtained which are analogous to the energy and momentum conservation laws for an electromagnetic field. Expressions are found for the group velocity and the damping coefficient of elastic waves in a medium with space-time dispersion. A model of a continuous medium containing mobile dislocations is examined as a specific example. The question of the possibility of extending the theory to nonlinear media is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 13–20, November, 1978.     

Propagation of guided elastic waves in 2D phononic crystals

The phononic band structure of two-dimensional phononic guides is numerically studied. A plane wave expansion method is used to calculate the dispersion relations of guided elastic waves in these periodic media, including 2D phononic plates and thin layered periodic arrangements. We show that, for any guided elastic wave, Lamb or generalised Lamb modes, stop bands appear in the dispersion curves, displaying a phononic band structure in both cases.     

光在吸收介质中传播的折射定律

光波在均匀非吸收介质中传播时振幅不衰减,在两种非吸收介质界面处产生折射现象,由几何光学中实数形式的光折射定律定量描述.而光波在均匀吸收介质中传播时,其振幅沿传播方向衰减,且其等振幅面与等相位面会发生分离.考虑吸收对光波传播特性的影响,本文回顾了复折射率的概念和复数形式的折射定律,据此对光波由吸收介质入射到吸收介质和光波由非吸收介质入射到吸收介质的两种情况进行了讨论,阐明了复数折射定律在具体问题讨论中的必要性和便利性,同时分析了实数形式和复数形式折射定律的关系.     

Localisation of elastic waves in two-dimensional randomly disordered solid phononic crystals

Combined with the supercell technique, the plane wave expansion method is used to calculate the band structures of the two-dimensional solid–solid phononic crystals with the random disorders in either radius or location of the scatterers. Phononic systems with plumbum scatterers embedded in an epoxy matrix are calculated in detail. The influences of the disorder degree on the band structures for both anti-plane and in-plane wave modes are investigated. It is found that, with increase of the disorder degree, the band gaps become narrower with more flat bands appearing in the gaps. Both displacement distribution and response spectra show that at the flat bands, elastic waves are localised due to the presence of the disorder. Wave localisation is more pronounced at the flat bands near the lower/upper edge for the radius/location disorder. Wave propagation and localisation in a randomly disordered system with a point defect is also studied. The influence of the disorder on the point-defect state is discussed. The results show that the disorder can tune the frequencies of the defect states. It is particularly noticed that the double degenerate mode appearing within the gap of the mixed in-plane waves is split up into two separated ones when the random disorder is introduced into the system. Generally, the influence of the disorder is more pronounced for the mixed in-plane modes than the anti-plane modes. The analysis of this paper is relevant to the assessment of the influences of manufacture errors on wave behaviours in phononic crystals as well as the possible control of wave propagation by intentionally introducing disorders into periodic systems.     

Conical refraction: Experiments and large-scale demonstrations

Results of experiments on internal and external conical refraction on a rhombic sulfur single crystal are presented. A high-transmission optical scheme is suggested with light focusing on the crystal surface which allows two fringes of internal conical refraction ∼1 m in diameter to be observed in laser radiation. Two fringes of external conical refraction with unique polarization state are first observed, and conditions of light energy concentration along the biradial are discussed. The focusing power of a plane-parallel biaxial crystal plate is measured. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 42–48, August, 2007.     

Negative refraction in photonic crystals

We demonstrate that light propagation in strongly modulated 2D/3D photonic crystals (PhCs) becomes refraction-like in the vicinity of the photonic bandgap, which is contrary to the fact that light propagation in weakly modulated PhCs is very different from refraction and thus the definition of refraction index becomes meaningless. Such a crystal behaves like a material having an effective refractive index controllable by the band structure. This situation is analogous to the effective-mass approximation in electron-band theory. The propagation states having a negative effective index exhibit unusual properties, such as mirror-like imaging effect, image-transfer effect. These properties are confirmed by finite-difference time-domain simulations.     

Collimation and enhancement of elastic transverse waves in two-dimensional solid phononic crystals

In this Letter, we numerically investigate the propagation characteristics of elastic transverse waves emitted by line sources embedded inside two-dimensional (2D) solid phononic crystals (PCs). The results show that collimation and enhancement of elastic transverse waves can be achieved at the band edge frequencies. We find that the collimation effect originates from the flat equifrequency contours (EFCs) at the band edge of appropriately designed 2D solid PCs. It is shown that, in addition to geometric symmetry, appropriate constituent material combination is essential to obtain flat EFCs at the band edge. A highly directional and enhanced elastic transverse wave source with a half power angular width of only 5.6° and an enhancement factor of 530 is realized simply by utilizing a finite-size 2D solid PC structure.