Topological singularities and phonon focusing

The focusing directions of phonon images generated by the anisotropic propagation of ballistic phonons are interpreted as singularities of the Gauss map of the energy surface. While a linear dispersion produces only folds and cusps, a nonlinear dispersion relation generically induces singular events for critical values of the frequency. These events are classified by means of catastrophe theory and the local topology on the energy surfaces is elucidated. On reflection planes or symmetry axes new types of singularities occur. The consequences of Morse singularities in the dispersion relation for the focusing directions are discussed.     

Effect of dispersion on the phonon focusing and anisotropy of thermal conductivity of silicon single crystals in the boundary scattering regime

The effect of dispersion on the focusing of thermal phonons and on the thermal conductivity of silicon single crystals in the boundary scattering regime has been investigated. Analysis of the spectra of acoustic modes obtained for silicon single crystals from inelastic neutron scattering data has demonstrated that, upon transition from long-wavelength phonons to short-wavelength phonons, the directions of their focusing change. With an increase in temperature, this leads to a change in the anisotropy of thermal conductivity of phonons with different polarizations and, consequently, to a change in the anisotropy of the total thermal conductivity. Analysis of the temperature dependence of the thermal conductivity has revealed that the presence of extended flattened sections in the spectrum of short-wavelength transverse phonons indicates anomalously low values of the group velocity and, accordingly, a significant decrease in the contribution from these phonons to the thermal conductivity with increasing temperature. The contribution from longitudinal phonons to the thermal conductivity also significantly increases even at temperatures higher than 110 K and becomes dominant.     

Nonequilibrium phonon propagation in high-purity CdTe

Propagation of nonequilibrium acoustic phonons in samples of high-purity CdTe (impurity content ～10¹⁶ cm^?3) was studied using the heat pulse technique under pulsed photoexcitation. An analysis of nonequilibrium phonon propagation made by comparing the experimental response with Monte Carlo calculations assuming samples to be without twins provided an estimate for the spontaneous anharmonic phonon decay constant A_L=2×10^?52 s^?1 Hz^?5. The probability of free phonon transit through a twin boundary in a sample with twin structure was estimated as A_C=0.96.     

Nonlinear acoustic propagation and focusing

Two model equations of nonlinear acoustics are considered. The implications of a point transformation between forms of the generalised Burgers equation (GBE) is discussed. New exact and asymptotic solutions are obtained. The dissipative Zabolotskaya-Khokhlov (DZK) equation describing acoustic wave propagation with allowance for transverse amplitude variation is studied. By considering a transformation onto the GBE, solutions exhibiting caustic behaviour are presented. A mechanism for the control of such singularities is presented along with a comparison with shock formation time.Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, England. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 8, pp. 783–787, August, 1993.     

Caustic and anticaustic points in the phonon focusing patterns of cubic crystals

Phonon focusing patterns are dependent on the existence of concave/saddle regions and acoustic axes in the slowness surface. The main feature of the focusing patterns in cubic crystals can be characterized by the caustic and anticaustic points in the symmetry planes. By applying the Stroh formalism, the caustic and anticaustic points in the symmetry planes are investigated in relation to degeneracies in the Stroh eigenvalue equation. A set of analytical expressions for the locations of the caustic and anticaustic points is derived for cubic crystals.     

Images of the phonon propagation across twist-bonded crystals

We investigate identical but twist-bonded crystals using phonon imaging techniques. As in homogeneous crystals, very anisotropic flux patterns are observed. However, the shape of the pattern depends dramatically on the respective twist angle. The observed phonon images in wafer bonded GaAs/GaAs and Si/Si samples are essentially consistent with the predictions of the acoustic mismatch model for defect-free interfaces, with the exception of GaAs wafers twist bonded at a 45 degrees angle where modes with large shear stress are missing, which indicates strong dislocation scattering.     

Transverse electron focusing as a way of studying phonon kinetics. Turbulence of phonon flow

Novel techniques have been created for studying phonon kinetics. A supersonic conduction electron flux is used to produce a phonon flux. Transverse electron focusing (TEF) is applied for checking the electron gas affected by phonons. A turbulent regime of phonon flow-phonon flux step broadening-reveals itself as step broadening of non-equilibrium electron flux.     

Theoretical model of phonon propagation in micro- and nanostructural materials

Peculiarities of the kinetics of weakly nonequilibrium thermal phonons (λ_ph = 10−50 nm) in nanodispersed ceramics are investigated. The features of the phonon spectrum in the wavelength range λ_ph ∼ R _g (where R _g is the average size of a ceramic grain) are studied. The conditions yielding the formation of a gap in the phonon spectrum of nanodispersed materials are analyzed. It is shown that the presence of inclusions with characteristic sizes smaller than the grain size of the parent ceramic material (pores, inclusions of other phases) shifts the gap toward the high-frequency range of the phonon spectrum. Peculiarities of the transport of nonequilibrium phonons during the transition from nano- to microdispersed sizes of the ceramic structure are analyzed.     

The effect of phonon focusing on the electron-phonon relaxation and electron transport in potassium crystals

The influence of anisotropy of elastic energy on electron-phonon relaxation and the role of shear waves in the electrical resistance of potassium crystals are investigated. It is shown that, at temperatures much lower than the Debye temperature (T<< θ_D), the contribution of slow quasi-transverse phonons to the electrical resistance of potassium crystals exceeds that of longitudinal phonons by an order of magnitude. Earlier, the Bloch-Grüneisen theory left aside this component under the above conditions. At the same time, at high temperatures(T>>θ_D), the contribution of longitudinal phonons to the electrical resistance turns out to be 4 times greater than the total contribution of electron relaxation by fast and slow transverse modes. The role of shear waves in the electrical resistance of potassium crystals is analyzed. It is shown that, at low temperatures, this mechanism provides 32% of the total electrical resistance. It is 4 times higher than the contribution of longitudinal phonons to the electrical resistance and should be taken into account when analyzing the electrical resistance of alkali metals. The distribution function of the most effective phonons for electrical resistance is defined, and the inelasticity of electron-phonon scattering is analyzed. It is shown that the calculated results of the electrical resistance of potassium in the temperature range from 40 to 400 K, taking into account the anisotropy of elastic energy, are in good agreement with the experimental data without the use of fitting parameters.     

Dispersive anisotropic ballistic phonon propagation in [100] GaAs

We report experimental observations of the phonon focusing pattern in [100] GaAs using low temperature electron beam scanning for phonon generation. The typical dispersive effects for high-frequency phonons expected from the calculations by Tamura have clearly been observed using PbIn tunnel junctions for phonon detection. The quantitative comparison of our experimental results with the frequency dependent calculations by Tamura allowed to determine the dominant phonon frequencies contributing to the detector signal in our different experiments. Above the temperature of the -point the dominant phonon frequencies appear to be shifted considerably to lower values, which could be explained by a heating effect in the liquid-He layer adjacent to the tunnel junction detector. By comparing the observed magnitude of the detector signal with different theoretical treatments of the detector response, we have found satisfactory agreement for a model where the perturbation due to the high-frequency phonons is restricted to the base electrode of the detector reached first by the phonons following their passage through the crystal.     

About the regime of unidirectional propagation of radiation in nonlinear media

The generation of counterpropagating waves with low frequencies by pump copropagating waves in a weakly nonlinear medium is analyzed. The generation is shown to be efficient in the presence of intervals with anomalous and normal dispersion in the spectrum. Under these conditions, the approximation of unidirectional propagation, which is widely used in the literature, is incorrect and the nonlinear propagation of radiation should be described by the full wave equation.     

The multiwave regime of light diffraction and focusing effect in volume phase gratings

Some pecularities of multiwave light diffraction in optically thin and thick phase unslanted gratings have been considered. An approximate solution of the wave equation is derived by the eiconal method. The solution is valid for gratings which are both optically thin and thick. This is verified by comparison of approximate solutions with numerical calculations. A range of parameters is found where the solution gives a reliable result. It has been found that the phase grating has the property of focusing light in planes with a maximum value of refractive index if the grating thickness is close to the focal distance introduced.     

On the focusing limit of high-power femtosecond laser pulse propagation in air

Focused propagation of high-power femtosecond laser radiation in air is considered. Based on numerical solution of the nonlinear Schr?dinger equation for complex envelope of light wave electric field, evolution of the beam effective radius is studied. The dependence of the effective (rms) size of a focal spot and the maximally achievable intensity of laser radiation at focal waist on the initial pulse power is established. It is shown that focal spot of tightly focused intensive ultrashort laser radiation can change its size during the pulse passage through the beam waist. This is the consequence of pulse intensity clamping in region of beam focusing caused by gas photoionization and plasma producing. This may prevent laser intensity from its further growth in the focal region and arrest the transversal compression of the beam in the linear focus as a whole.     

Microwave propagation in two dimensional structures using lossy cylindrical glass rods

Two dimensional microwave band gap structures have been constructed using lossy cylindrical glass samples ( and ). The power transmission spectra observed between 10 and 20 GHz for both square and triangular structures with three different lattice spacing (2.5, 1.4 and 0.9 cm) are explained in terms of the lattice spacing, filling fraction and loss tangent. The experimental results and the theoretical values agree well for the structures having higher filling fraction. Also, the values predicted from the scaling procedure agree well with the experimental values. The appearance of acceptor modes due to the introduction of defects in these structures is also reported.Received: 26 April 2004, Published online: 12 October 2004PACS: 41.20.Jb Electromagnetic wave propagation; radiowave propagation - 42.25.Fx Diffraction and scattering     

光束在强湍流区中传播的到达角起伏

 基于修正Rytov理论，导出了适用于强湍流区的无限平面波和球面波的到达角起伏方差表达式及其功率谱表达式，分析了散射盘对到达角起伏的影响。研究结果表明：导出的方差表达式在弱湍流区也适用，随着Rytov方差的增加到达角起伏趋于饱和；高频功率谱的下降速度随着散射盘尺度的增加而增加。