Conical refraction of elastic waves in absorbing crystals

The absorption-induced acoustic-axis splitting in a viscoelastic crystal with an arbitrary anisotropy is considered. It is shown that after “switching on” absorption, the linear vector polarization field in the vicinity of the initial degeneracy point having an orientation singularity with the Poincaré index n = ±1/2, transforms to a planar distribution of ellipses with two singularities n = ±1/4 corresponding to new axes. The local geometry of the slowness surface of elastic waves is studied in the vicinity of new degeneracy points and a self-intersection line connecting them. The absorption-induced transformation of the classical picture of conical refraction is studied. The ellipticity of waves at the edge of the self-intersection wedge in a narrow interval of propagation directions drastically changes from circular at the wedge ends to linear in the middle of the wedge. For the wave normal directed to an arbitrary point of this wedge, during movement of the displacement vector over the corresponding polarization ellipse, the wave ray velocity s runs over the same cone describing refraction in a crystal without absorption. In this case, the end of the vector moves along a universal ellipse whose plane is orthogonal to the acoustic axis for zero absorption. The areal velocity of this movement differs from the angular velocity of the displacement vector on the polarization ellipse only by a constant factor, being delayed by π/2 in phase. When the wave normal is localized at the edge of the wedge in its central region, the movement of vector s along the universal ellipse becomes drastically nonuniform and the refraction transforms from conical to wedge-like.     

Second-harmonic conical refraction: observation of free and forced harmonic waves

Observation of second-harmonic conical refraction in KTiOPO₄ crystal is reported. Two second-harmonic conical patterns, namely forced and free harmonic waves, are identified and registered with exceptional clarity and level of details. The forced second-harmonic wave evolves into the characteristic ring intensity distribution while the free-harmonic wave gives a single ray direction, resulting in a spot.     

Second harmonic conical refraction

Second harmonic intensity patterns generated in α-iodic acid have been observed. Free and forced conical patterns occur, when the fundamental wave vector lies along a second harmonic or fundamental optic axis, respectively.     

Excitation of an elastic half-space by a buried line source of conical waves

A formal solution is obtained to the problem of a buried line source of conical waves propagating at a constant phase velocity c in an isotropic elastic half space. By applying the boundary conditions at the free surface, it is determined that the reflected field, in addition to the incident field, requires addition of a scalar potential and two components of the vector potential. The latter is in contrast to the case of cylindrical waves where only one component of the vector potential is needed. The formal solution for the conical wave source goes over to that for the two dimensional cylindrical wave case in the limit of infinite phase velocity c.     

Internal conical refraction of Bessel light beams

The internal conical refraction of a Bessel beam of arbitrary order is studied theoretically. It is shown that a beam of the order m of arbitrary polarization in the general case is partially converted to Bessel beams of the order m ± 1 with orthogonal circular polarizations. Conditions for complete conversion of a beam of the order m to a Bessel beam of the order m?1 or m+1 are determined.     

Laser with simultaneous Gaussian and conical refraction outputs

We report a double-sided two-mirror neodymium-doped KGd(WO₄)₂/Nd:KGW conical refraction laser which produces a linearly polarised output from the flat output coupler and a cone-refracted output from the curved output coupler. The linearly polarised output had a polarisation extinction ratio of 20:1 with a Gaussian beam profile and a measured M ²=1. The unpolarised output had the intensity and polarisation distribution corresponding to a cone-refracted Gaussian beam with extinction ratio of 2.7:1.     

Extremely short vector solitons under the conditions of conical refraction

Propagation of extremely short electromagnetic pulses in a biaxial crystal under the conditions of conical refraction has been considered. The system of wave equations taking into account the dispersion contribution of the crystal lattice ions to the polarization response of the medium and a nonlinearity of the polarization response of electrons has been derived. It has been shown that under certain conditions this system can be reduced to an equation which is integrable by means of the inverse scattering transformation method. The proper Lax pair has been found. Physical analysis of the steady-state pulse solution of the system of wave equations has been performed.     

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...     

Reflection and refraction of waves in oscillatory media

This paper uses the two-dimensional Brusselator model to study reflection and refraction of chemical waves. It presents some boundary conditions of chemical waves, with which occurence of observed phenomena at interface as refraction and reflection of chemical waves can be interpreted. Moreover, the angle of reflection may be calculated by using the boundary conditions. It finds that reflection and refraction of chemical waves can occur simultaneously even if plane wave goes from a medium with higher speed to a medium with lower speed, provided the incident angle is larger than the critical angle.     

Evidence of negative-index refraction in nonlinear chemical waves

The negative index of refraction of nonlinear chemical waves has become a recent focus in nonlinear dynamics researches. Theoretical analysis and computer simulations have predicted that the negative index of refraction can occur on the interface between antiwaves and normal waves in a reaction-diffusion (RD) system. However, no experimental evidence has been found so far. In this Letter, we report our experimental design in searching for such a phenomenon in a chlorite-iodide-malonic acid (CIMA) reaction. Our experimental results demonstrate that competition between waves and antiwaves at their interface determines the fate of the wave interaction. The negative index of refraction was only observed when the oscillation frequency of a normal wave is significantly smaller than that of the antiwave. All experimental results were supported by simulations using the Lengyel-Epstein RD model which describes the CIMA reaction-diffusion system.     

Polarization-tunable Yb:KGW laser based on internal conical refraction

Using internal conical refraction, we demonstrate an Yb:KGW laser where the polarization state can be arbitrarily altered without any additional cavity components. The extinction ratio can also be altered between 1:1 and 40:1. The maximum output power achieved was 8.6 W at a slope efficiency of 60.5% with respect to incident pump power. This equals the power performance of a standard Yb:KGW laser used for reference.     

Acoustooptical interaction of light beams under conditions of internal conical refraction

The collinear acoustooptical (AO) interaction of light beams under conditions of internal conical refraction is considered. The dependences of the diffraction efficiency on the ratio of radii of light and ultrasonic beams, the AO coupling length, and the ultrasound intensity are found. An analytical expression is obtained describing the diffraction efficiency of collinear AO conversion of annular beams of internal conical refraction.     

Theory of elastic waves

Wave processes in real crystals are described by covariant first-order partial differential equations. Naimi and Khzardzhyan [1] have recently shown that the second-order equations $$\Delta u^{(n)} - c_n^{ - 2} \partial ^2 u^{(n)} /\partial t^2 = 0$$ ,     

Nonlinear waves in elastic media

We ask about the possible existence of solitary waves in infinite, homogeneous, isotropic, elastic media. Namely, can a nonlinear localized wave packet propagate without altering its shape in such materials? We consider one- dimensional propagation both of body and surface waves. In the first case we show, under rather general assumptions, that if a wave packet propagates without altering its shape it must, of necessity, be a solution of a linear wave equation and in this sense, (body) solitary waves do not exist. Surface solitary waves may however exist: a model equation is derived in which nonlinear and dispersive effects balance each other to allow for waves-both periodic and solitary-of constant shape. It is conceivable they are of some relevance in seismology.     

The analogy between acoustic waves and water surface waves with refraction

The similarity between acoustic waves in an inhomogeneous medium and water surface waves with variable water depth is established. The two systems are analogous if they both are characterized by the same index of refraction field. Based on this analogy, acoustic refraction problems are treated by utilizing a surface wave simulation achieved with a water wave tank. Experimental results obtained from the wave tank for various situations are used to deduce the behavior of the corresponding acoustic systems. It is concluded that there are two major advantages in employing a water wave tank. The first is that the entire wavefront configuration can visually be observed; the second is that water surface waves can be investigated in the laboratory much more readily and more economically than acoustic waves.