Dispersionless Media Research Articles

Inertial nonlinearity and chaotic motion of particle fluxes.

A brief review is given of the nonlinear phenomena arising in the evolution of random perturbations in particle fluxes of the hydrodynamical type, the velocity field of which is described by equations similar to the Riemann and Burgers equations. It is shown that a nonlinearity of the inertial type deforming the fluxes owing to the inertia of the motion of their constituent particles leads to the formation of singularities in the realizations of the velocity and density fields, and, consequently, to the appearance of universal asymptotes in their spectra and probability distributions. Methods are presented for the statistical description of waves in dispersionless media. A brief discussion is given of the laws of evolution of the statistical characteristics of the velocity and density fields of particle fluxes, both without interactions and with a contact interaction. In particular, the analogy between the solution of the Burgers equation and a particle flux with adhesion is studied. Diverse physical applications are discussed: to the dynamics of particles and mixtures, intensity fluctuations of an optical wave which has passed through a phase screen and in a randomly nonuniform medium, gravitational instability, and acoustical turbulence.

The phase, spectral shape and frequency shift of a self-phase modulated pulse

We show that, due to self-steepening, the phase of the self-phase modulated (SPM) signal, generated in a X (3) dispersionless medium i.e. thin sample, is asymmetrical in the time domain; that the SPM spectral distribution anti-Stokes extent is larger than the Stokes extent and that the spectral maximum is shifted to the Stokes side.

Supercontinuum generated by six-photon mixing

We obtain the shape, phase, and spectral distribution of an ultrafast pulse propagating in a chi((5)) medium (six-photon mixing). The calculation is performed in the plane-wave approximation for a dispersionless medium but with self-steepening present.

Distortion of finite amplitude ultrasound in tissue

A form of Burgers' equation is used to derive an algorithm for calculation of harmonic content versus range for a plane sound wave of finite amplitude propagating in a lossy, dispersionless medium. Amniotic fluid, liver, cerebrospinal fluid, and blood plasma are investigated using common biomedical frequencies and intensities. It is shown that shock front formation is possible in tissue having a sufficiently low infinitesimal amplitude attenuation coefficient. A criterion is given to determine if shock front formation is possible in any tissue for a given initial sound frequency and intensity. The implications of this distortion include effects on imaging capabilities of diagnostic systems, measurement of attenuation coefficients of tissues, and biological effects mechanisms.

Nonlinear interactions of two ultrasonic waves in a dispersionless liquid medium

Nonlinear interactions of two ultrasonic waves, propagating collinearly in a dispersionless liquid medium, are investigated experimentally for both degenerate and nondegenerate cases. Results are described of the first experimental observation of parametric amplification of the signal wave for the degenerate case. For the nondegenerate case, no such amplification of the amplitude of the signal wave is observed. These experimental results are found to be in good agreement with the results of the theoretical analysis presented in the paper.

Theory of temporal pump stochasticity in stimulated Raman scattering in dispersionless media

A diagrammatic formalism is presented which gives exact results for the forward Stokes wave in dispersionless media in the field of a temporally stochastic pump. Both pump and Stokes waves are assumed to be plane waves, but transient effects are treated exactly. Results are derived in the Bourret approximation for the n-point functions (n≳2) but are exact to all orders in the mean pump field and its two-point function. The generalization to treat general n-point functions within this formalism is possible and the method of doing so is indicated. The partial summation of diagrams corresponding to previous treatments is identified and the next order terms are evaluated. It is found that for high gain systems, approximations made in previous work may be quite poor.

Optimal primary spectra for parametric transmitting arrays

The use of more than two spectral components in the primary signal of a parametric endfire array is considered. Equations are developed for the spectra of N components which maximize the farfield SPL for shock-free primaries in dispersionless media. Effects of the variation of attenuation with frequency are shown to have a considerable influence on the shape of the optimal spectra. For the case of attenuation proportional to the square of the frequency, the optimal spectra are functions only of the downshift ratio R and the number of components N, and not functions of the absolute value of the frequencies. The optimal spectra and waveforms for several sets of R and N values are shown. It is found that a 3-dB increase over a two-component primary can be obtained with three or four components for a wide range of downshift ratios. At extremely high primary powers, an increased tendency toward shock formation may negate this gain. Beamwidths were found to be essentially unaffected. Subject Classification: 25.35; 60.10.

Velocity modulation of propagating waves

Propagation in a dispersionless linear medium whose dielectric constant varies slowly in space and time is analyzed. The medium is represented as a series of small and moving dielectric constant discontinuities, with a uniform medium between adjacent moving steps. In the simplest approximation the reflections generated at the steps are ignored but the change in transmitted amplitude is taken into account. This extends earlier work by Tsai and Auld and shows that the electric field is proportional to (ωk/ε)1/2 as ω, k, and ε vary along the path taken by a given phase of the propagating wave. This amplitude variation is shown to be equivalent to the conservation of photon numbers. The neglected higher-order multiple reflections are discussed in an evaluation of the validity of the approximation. We also review the solution for the truly nonlinear problem. In this case, the same nonlinearities which couple a large pump wave and a small signal cause different portions of the pump wave to travel with different velocities. A given portion of the small signal stays with a particular value of the dielectric constant and therefore no reflections are generated. The E∼(ωk/ε)1/2 result then becomes exact. Finally, a novel amplifying device called ``radiation klystron'' is discussed. In this device the small signal to be amplified controls the propagation of a high-level high-frequency signal.

Experimental Investigation of Transient Stimulated Raman Scattering in a Linearly Dispersionless Medium

The results of numerical calculations of the transient stimulated Raman scattering reported previously have been verified experimentally under conditions where both linear dispersion and self-focusing effects were negligible. The existence of a delay between maxima of the laser and Stokes pulses is experimentally demonstrated for the first time, while the pulse shortening in time via Raman scattering is established more firmly than in previous work. The incident-laser-pulse duration, generated-Stokes-pulse duration, and delay between intensity maxima for the laser and Stokes pulses were measured with the two-photon absorption-fluorescence technique. The effective phonon-dephasing time is determined via spontaneous Raman scattering. By using these measured quantities, inferences are made as to the magnitude of the transient gain and the shape of the exciting picosecond laser pulse.