Focusing of shock waves induced by optical breakdown in water

The focusing of laser-generated shock waves by a truncated ellipsoidal reflector was experimentally and numerically investigated. Pressure waveform and distribution around the first (F(1)) and second foci (F(2)) of the ellipsoidal reflector were measured. A neodymium doped yttrium aluminum garnet laser of 1046 nm wavelength and 5 ns pulse duration was used to create an optical breakdown at F(1), which generates a spherically diverging shock wave with a peak pressure of 2.1-5.9 MPa at 1.1 mm stand-off distance and a pulse width at half maximum of 36-65 ns. Upon reflection, a converging shock wave is produced which, upon arriving at F(2), has a leading compressive wave with a peak pressure of 26 MPa and a zero-crossing pulse duration of 0.1 mus, followed by a trailing tensile wave of -3.3 MPa peak pressure and 0.2 mus pulse duration. The -6 dB beam size of the focused shock wave field is 1.6 x 0.2 mm(2) along and transverse to the shock wave propagation direction. Formation of elongated plasmas at high laser energy levels limits the increase in the peak pressure at F(2). General features in the waveform profile of the converging shock wave are in qualitative agreement with numerical simulations based on the Hamilton model.     

Exponentially self-similar impact ionization waves

The existence of generalized self-similar solutions to the system of continuity and Poisson equations is analyzed for the problem of evolution of impact ionization waves (IIWs). It is shown that, for any physically reasonable electric-field dependence of the impact ionization coefficients, there exist only exponentially self-similar (“limiting”) asymptotic solutions. These solutions describe IIWs whose spatial scales and propagation velocities increase exponentially with time. Conditions are found for the existence of plane, cylindrical, and spherical waves of this type; their structure is described; analytical relations between the key parameters are derived; and effects of recombination (or attachment) and tunnel ionization are analyzed. It is shown that these IIWs are intermediate asymptotics of numerical solutions to the corresponding Cauchy problems. The most important and interesting type of exponentially self-similar IIWs are streamers in a uniform electric field. The simplest comprehensive and explicit model describing their evolution is a spherical IIW.     

Focusing of evanescent vector waves

We study focusing of two and three-dimensional evanescent vector waves, with a particular emphasis on identifying suitable intensity structures for applications in optical data storage. For two-dimensional evanescent waves large transverse spatial wave vectors result in purely circularly polarized evanescent states. We suggest that these may have applications in all-optical data storage through the inverse Faraday effect. On the other hand, for three-dimensional evanescent waves longitudinally polarized modes are observed to give the most tightly focused spot, and this may be utilized to confine light behind a solid immersion lens.     

Asymptotically self-similar propagation of spherical ionization waves

It is shown that a new type of self-similar spherical ionization waves may exist in gases. All the spatial scales and the propagation velocity of such waves increase exponentially with time. The conditions for existence of these waves are established, their structure is described, and approximate analytical relationships between the principal parameters are obtained. It is notable that spherical ionization waves can serve as the simplest, but structurally complete and physically transparent model of a streamer in a homogeneous electric field.     

Focusing effect of periodic gravitational waves

A study is made of the focusing of test particles and light rays in the field of periodic plane gravitational waves described by exact solutions of the Einstein equations. The periodicity of the focusing is investigated as a function of the type of polarization of the gravitational wave, its frequency, and intensity. The magnitude of the effect is estimated for the gravitational radiation of a pulsar.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 120–125, September, 1978.     

Gravitational shock waves

This paper reports on and summarizes some recent progress on gravitational shocks, i.e., discontinuities in the Riemann curvature tensor. It is shown how the constraint equations play a crucial rôle in determining the nature and propagation of the shocks. Existence results are stated and are illustrated by some examples from numerical relativity.     

Brane-induced-gravity shock waves

We construct exact gravitational field solutions for a relativistic particle localized on a tensional brane in brane-induced gravity. They are a generalization of gravitational shock waves in 4D de Sitter space. We provide the metrics for both the normal branch and the self-inflating branch Dvali-Gabadadze-Porrati brane worlds, and compare them to the 4D Einstein gravity solution and to the case when gravity resides only in the 5D bulk, without any brane-localized curvature terms. At short distances the wave profile looks the same as in four dimensions. The corrections appear only far from the source, where they differ from the long distance corrections in 4D de Sitter space. We also discover a new nonperturbative channel for energy emission into the bulk from the self-inflating [corrected] branch, when gravity is modified at the de Sitter radius.     

Focusing of explosion waves: Three-dimensional mathematical modeling

The propagation and focusing explosionlike waves in a cubic volume filled with a gas was considered. The wave is generated by the expansion of a small volume of a gas with enhanced parameters located at different points inside the cube. This formulation of the problem simulates the process initiated by an explosion in a volume filled with a gas and the character of loading on the walls of the volume. 3D calculations of the propagation and cumulation of explosion waves with a short positive phase were performed for the first time. The results can be used in analyzing experiments aimed at modeling the initiation of combustion by the waves generated by a primary source in closed volumes with complex geometry.     

Focusing of waves in an anisotropic plane-layered medium

The problem of propagation of electromagnetic waves in an inhomogeneous uniaxial anisotropic medium is discussed. Analytic solutions of Maxwell's equations are found for two particular cases of a plane-layered dielectric. The effect of different parameters of an inhomogeneous distribution of refractive indices on the propagation characteristics of wave beams is analyzed. The corrections of the first approximation of perturbation theory to the propagation constants of natural waves are obtained for a plane-layered focusing medium of general type. This has permitted solving the problem of a distribution of the refractive index which provides for optimal focusing.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 21, No. 12, pp. 1812–1821, December, 1978.In conclusion, the author expresses his gratitude to I. V. Ivanov and N. A. Morozov for their attention to this paper.     

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.     

On gravitational shock waves

The discontinuity planes of the Riemann curvature tensorR _klm ⁱ in the Einsteinian vacuumR _kl =0 are isotropic hypersurfaces. These surfaces are to be conceived as being constructed of lightlike geodesics, which form, in the eikonal approximation, gravitational radiation. The discontinuity planes themselves describe the wave fronts of disturbances of the metricg _ik , propagating with the velocity of light. By successively applying continuity conditions for the derivatives of theg _ik that follow from Einstein's equations, we obtain the universal expression of gravitational wave fields in space-time strips (or representations) of arbitrarily selected Einstein spaces.     

Thermal diffusion shock waves

The Ludwig-Soret effect or thermal diffusion, which refers to the separation of liquid mixtures in a temperature gradient, is governed by a nonlinear, partial differential equation in space and time. It is shown here that the solution to the nonlinear differential equation for a binary mixture predicts the existence of shock waves completely analogous to fluid shocks and obeys an expression for the shock velocity that is an exact analogue of the Rankine-Hugoniot relations. Direct measurements of the time dependent, spatial absorption profile of a suspension of nanometer sized particles subjected to a sinusoidal temperature field generated by a pair of continuous laser beams, as well as self-diffraction experiments, show motion of the particles in agreement with the predictions of nonlinear theory.     

Analysis of propagation of ionization waves in nonuniform channels with noncircular cross sections

We investigate the propagation of ionization waves in nonuniform channels of a dc glow discharge. The dependences of the distances between adjacent strata on the cross-sectional area of the channel are measured using the method of image visualization and processing. It is found that the form of the dependences is determined to a considerable extent by the channel geometry: for a specific channel, the dependence can be increasing, decreasing, or nonmonotonic with a local peak.     

Interactions of dispersive shock waves

Collisions and interactions of dispersive shock waves in defocusing (repulsive) nonlinear Schrödinger type systems are investigated analytically and numerically. Two canonical cases are considered. In one case, two counterpropagating dispersive shock waves experience a head-on collision, interact and eventually exit the interaction region with larger amplitudes and altered speeds. In the other case, a fast dispersive shock overtakes a slower one, giving rise to an interaction. Eventually the two merge into a single dispersive shock wave. In both cases, the interaction region is described by a modulated, quasi-periodic two-phase solution of the nonlinear Schrödinger equation. The boundaries between the background density, dispersive shock waves and their interaction region are calculated by solving the Whitham modulation equations. These asymptotic results are in excellent agreement with full numerical simulations. It is further shown that the interactions of two dispersive shock waves have some qualitative similarities to the interactions of two classical shock waves.     

Novel exact self-similar solitary waves in graded-index media with Kerr nonlinearity

A broad class of exact self-similar solitary wave solutions to the nonlinear Schrdinger equation (NLSE) are found by using the extended mapping deformation method. These novel waves can propagate inside planar, graded-index nonlinear waveguide amplifiers with self-focusing and self-defocusing Kerr nonlinearities, respectively. Furthermore, we analyze the features of the self-similar waves and their evolution. Our results in this paper include some in the literature [S.A. Ponomarenko, G.P. Agrawal, Phys. Rev. Lett. 97 (2006) 013901].     

Stationary one-dimensional dispersive shock waves

We address shock waves generated upon the interaction of tilted plane waves with negative refractive index defects in defocusing media with linear gain and two-photon absorption. We found that, in contrast to conservative media where one-dimensional dispersive shock waves usually exist only as nonstationary objects expanding away from a defect or generating beam, the competition between gain and two-photon absorption in a dissipative medium results in the formation of localized stationary dispersive shock waves, whose transverse extent may considerably exceed that of the refractive index defect. One-dimensional dispersive shock waves are stable if the defect strength does not exceed a certain critical value.     

Turbulence in argon shock waves

Irregular density fluctuations with turbulent-like behaviors are found in ionizing shock fronts produced by our arc driven shock tube. We use electric probes as the primary diagnostic. Spectral analyses show statistical patterns which seem frozen-in and characterizable by a dominant mode and its harmonics.