Formation of spatial solitons and spatial shock waves in photorefractive crystals

An analytical model, which describes the drift and diffusion mechanisms for the formation of the nonlinear response (local and nonlocal nonlinearities) of photorefractive crystals on the microscopic level, is constructed. New types of stable self-consistent distributions of the light field intensity, i.e., spatial solitons, are found. The trajectories of their motion (self-bending) are calculated, and the possibility of observing a new nonlinear-optical effect in photorefractive crystals, viz., the formation of spatial shock waves, is demonstrated. The modulation instability appearing when plane waves propagate in photorefractive crystals is analyzed, and the characteristic spatial scales of the light field distribution formed as a result of self-interaction (fanning) are determined. The results of the analysis are confirmed by computer simulation data. Zh. éksp. Teor. Fiz. 111, 705–716 (February 1997)     

Observation of shock transverse waves in elastic media

We report the first experimental observation of a shock transverse wave propagating in an elastic medium. This observation was possible because the propagation medium, a soft solid, allows one to reach a very high Mach number. In this extreme configuration, the shock formation is observed over a distance of less than a few wavelengths, thanks to a prototype of an ultrafast scanner (that acquires 5000 frames per second). A comparison of these new experimental data with theoretical predictions, based on a modified Burger's equation, shows good agreement.     

Coherent optical photons from shock waves in crystals

We predict that coherent electromagnetic radiation in the 1-100 THz frequency range can be generated in crystalline materials when subject to a shock wave or soliton-like propagating excitation. To our knowledge, this phenomenon represents a fundamentally new form of coherent optical radiation source that is distinct from lasers and free-electron lasers. The radiation is generated by the synchronized motion of large numbers of atoms when a shock wave propagates through a crystal. General analytical theory and NaCl molecular dynamics simulations demonstrate coherence lengths on the order of mm (around 20 THz) and potentially greater. The emission frequencies are determined by the shock speed and the lattice constants of the crystal and can potentially be used to determine atomic-scale properties of the shocked material.     

Observation of traveling thermoacoustic shock waves (L)

Shock waves were explored in the thermoacoustic spontaneous gas oscillations occurring in a gas column with a steep temperature gradient. The results show that a periodic shock occurs in the traveling wave mode in a looped tube but not in the standing wave mode in a resonator. Measurements of the harmonic components of the acoustic intensity reveal a clear difference between them. The temperature gradient acts as an acoustic energy source for the harmonic components of the shock wave in the traveling wave mode but as an acoustic energy sink of the second harmonic in the standing wave mode.     

Observation of collisionless plasma heating by strong shock waves

The heating of a plasma by collisionless shock waves is investigated by measuring the variation of magnetic field (with magnetic probes), density and electron temperature (from Thomson scattering of laser light) in the shock waves. The compression waves are produced in a tube of 14 cm diameter by the fast rising magnetic field (12 kG in 0.5Μsec) of a theta pinch. For shocks with Mach numbers between 2 and 3 propagating into a hydrogen or deuterium plasma with a localΒ of about 1 (Β=ratio of particle pressure to magnetic pressure) the measured jump in density and magnetic field across the front is 2 to 4, and the electron temperature increases in the front from 3 to 50 eV with a further rise to between 100 and 250 eV in the piston region. Only about 20% of the measured electron heating can be explained by adiabatic heating and resistive heating based on binary collisions, indicating a high turbulent plasma resistance. Both the observed electron heating and the width of the shock front, which is about 0.6 ·c/Ω _p, can be accounted for using an effective collision frequency close to the ion plasma frequencyΩ _p. The ion heating in the almost stationary shock fronts can be inferred indirectly from the steady state conservation relations. For shock waves with Mach numbersM<M _crit it seems to be consistent with an adiabatic heating process, whereas forM>M _crit the calculated ion temperatures exceed those one would except for a merely adiabatic heating.     

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.     

Observation of shock waves in a strongly interacting Fermi gas

We study collisions between two strongly interacting atomic Fermi gas clouds. We observe exotic nonlinear hydrodynamic behavior, distinguished by the formation of a very sharp and stable density peak as the clouds collide and subsequent evolution into a boxlike shape. We model the nonlinear dynamics of these collisions by using quasi-1D hydrodynamic equations. Our simulations of the time-dependent density profiles agree very well with the data and provide clear evidence of shock wave formation in this universal quantum hydrodynamic system.     

Hyperbolic shock waves of the optical self-focusing with normal group-velocity dispersion

The theory of focusing light pulses in Kerr media with normal group-velocity dispersion in (2+1) and (3+1) dimensions is revisited. It is shown that pulse splitting introduced by this dispersion follows from shock fronts that develop along hyperbolas separating the region of transverse self-focusing from the domain of temporal dispersion. Justified by a self-similar approach, this property is confirmed by numerical simulations using an adaptive-mesh refinement code.     

Observation of nonequilibrium radiation behind strong shock waves in low-density air

Nonequilibrium radiation phenomena behind strong shock waves in low-density air are observed by using a couple of CCD camera systems in a shock tube experiment. The simultaneous observation for total radiation and its spectral radiation is carried out in order to elucidate spaced-ependent contribution of an individual radiation spectrum to the total radiation intensity. The results are shown for the shock velocity range from 9.0 km/s to 12.1 km/s at the initial pressure 13.3 Pa. Wavelength range is selected from 300 nm to 445 nm to investigate mainly the contributions from UV radiation. It is found that the band spectra due to the molecular species N₂⁺ and CN mainly contribute to the first-peak, while the spectra due to the atomic species O⁺ and N mainly contribute to the formation of the second-peak. It is also found that the Balmer series in H spectra strongly contributes to the second-peak. The radiation along the tube wall surfaces is composed of the same constituents as those around the tube axis as well as the spectra coming from the impurities.     

Observation of optical spatial solitons in a highly nonlocal medium

We report on the observation and quantitative assessment of self-trapped pulsating beams in a highly nonlocal nonlinear regime. The experiments were conducted in nematic liquid crystals and allow a meaningful comparison with the prediction of a scalar theory in the perturbative limit, while addressing the need for beyond-paraxial analytical treatments.     

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.     

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.     

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.     

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.