Propagation of light through a forbidden zone in chiral media

The particular features of the propagation of light in uniaxial chiral liquid crystals with a large pitch of the spiral are considered. There exist forbidden zones in these systems for fairly large angles of incidence of an extraordinary ray. On the one hand, this results in an efficient reflection of the wave from the zone boundary, and, on the other hand, this causes the wave to decay inside the zone. A case of narrow forbidden zones is studied, and it is shown that optical effects that arise upon propagation of rays near turning points are equivalent to the tunnel and over-barrier reflection effects. The angular dependences of the intensities of rays that were refracted in a forbidden zone and transmitted through it are calculated. The percolation effect is experimentally studied in a mixture of a nematic liquid crystal with a chiral addition. The intensity of a transmitted extraordinary ray is studied as a function of the angle of incidence, which determines the width of the forbidden zone. Both the over-barrier reflection and the percolation effects are observed. The calculation results are shown to agree with experiment.     

Sensitivity of ray travel times

Ray in a waveguide can be considered as a trajectory of the corresponding Hamiltonian system, which appears to be chaotic in a nonuniform environment. From the experimental and practical viewpoints, the ray travel time is an important characteristic that, in some way, involves an information about the waveguide condition. It is shown that the ray travel time as a function of the initial momentum and propagation range in the unperturbed waveguide displays a scaling law. Some properties of the ray travel time predicted by this law still persist in periodically nonuniform waveguides with chaotic ray trajectories. As examples we consider few models with special attention to the underwater acoustic waveguide. It is demonstrated for a deep ocean propagation model that even under conditions of ray chaos the ray travel time is determined, to a considerable extent, by the coordinates of the ray endpoints and the number of turning points, i.e., by a topology of the ray path. We show how the closeness of travel times for rays with equal numbers of turning points reveals itself in ray travel time dependencies on the starting momentum and on the depth of the observation point. It has been shown that the same effect is associated with the appearance of the gap between travel times of chaotic and regular rays. The manifestation of the stickiness (the presence of such parts in a chaotic trajectory where the latter exhibits an almost regular behavior) in ray travel times is discussed. (c) 2002 American Institute of Physics.     

Specific features of optical properties of helical liquid crystals with a large helix pitch

Light propagation in helical liquid crystals with the helix pitch considerably exceeding the light wavelength is studied. Using a multidimensional analog of the WKB method, the Green function of the electromagnetic field in such a medium is calculated. This function contains terms corresponding to ordinary and extraordinary waves. The behavior of the Green function in the far-field region is analyzed. It is shown that for the extraordinary ray there exists, on the surface of the wave vectors, a forbidden zone, which, due to periodic changes of the refractive index, corresponds to conditions of the beam turn with the formation of a flat wave channel. The extraordinary beam trajectory, both inside and outside the wave channel, determined by the ray vector, is not flat. The asymptotic behavior of the Green function inside and outside the wave channel is substantially different.     

Restless rays, steady wave fronts

Observations of underwater acoustic fields with vertical line arrays and numerical simulations of long-range sound propagation in an ocean perturbed by internal gravity waves indicate that acoustic wave fronts are much more stable than the rays comprising these wave fronts. This paper provides a theoretical explanation of the phenomenon of wave front stability in a medium with weak sound-speed perturbations. It is shown analytically that at propagation ranges that are large compared to the correlation length of the sound-speed perturbations but smaller than ranges at which ray chaos develops, end points of rays launched from a point source and having a given travel time are scattered primarily along the wave front corresponding to the same travel time in the unperturbed environment. The ratio of root mean square displacements of the ray end points along and across the unperturbed wave front increases with range as the ratio of ray length to correlation length of environmental perturbations. An intuitive physical explanation of the theoretical results is proposed. The relative stability of wave fronts compared to rays is shown to follow from Fermat's principle and dimensional considerations.     

Mimic Simulations of Radio-Wave Propagation in a Randomly Irregular Ionosphere

We present the technique and results of mimic simulations of radio-wave propagation in a randomly irregular ionosphere with allowance for the Earth's sphericity and the background ionosphere. Based on consideration of the probability distributions of the angle of reception and of the corresponding amplitude, eikonal, and angle of radiation, obtained by the mimic modeling, we conclude that the most probable ray path is symmetric with respect to the region of its reflection from the ionosphere and that the mean reception angle and the corresponding mean radiation angle are equal. The simulations yield the statistical characteristics of a wave, such as the variances of the reception angle and the eikonal, as well as the correlation functions of the eikonal and the field. The simulation results concerning the variances of reception angles and eikonal are compared with the results of the first approximation of the perturbation theory. It is shown that the eikonal fluctuations in the irregularity-free space, caused by fluctuations of angles of the lower rays escaping from an ionospheric layer with random irregularities, should be taken into account.     

Self-modulation of Bessel-Gaussian wave beams in a medium with cubic nonlinearity

A semi-discrete dynamic model has been developed for the formation of the spatial structure of wave fields in a medium with cubic nonlinearity. The characteristic features of self-focusing and conical modulation of intense Bessel-Gaussian light beams of different orders have been studied in different stages of their evolution during propagation. It has been shown that as a result of nonlinear refraction, in the far zone wave structures are formed consisting of three spatially separated conical beams. Increasing the cone angle of the wave vectors leads to a decrease in the effect of conical modulation of the radiation, and improves the structural stability of the beam. The considered self-modulation effects can be used for passive limiting of the laser radiation power. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 5, pp. 626–630, September–October, 2006.     

The parametric Doppler effect in a medium with Lorentz dispersion

The frequency conversion under the parametric Doppler effect, which occurs when weak probe radiation reflects off from a refractive index inhomogeneity induced in a nonlinear medium by intense pumping, has been analyzed. Under these conditions, the frequency dispersion of the medium is assumed to correspond to the single Lorentz oscillator model. It is shown that the presence of resonance and a spectral range forbidden for propagation may lead to a complex Doppler effect, where the incident radiation is single-frequency but the reflected radiation consists of two or three monochromatic waves, one of which has a phaseconjugated wavefront.     

A justification for the use of approximate transition amplitudes in semiclassical surface hopping

Recent work has shown that a certain surface hopping form of the wave function is capable of obtaining highly accurate transition probabilities for nonadiabatic problems. It has also been found that it is necessary to include hops in classically forbidden regions in order to obtain this level of accuracy at low energies. The amplitude for the hops in this surface hopping expansion of the wave function has the typical p^?1/2 semiclassical divergence at the turning points in the classical motion. While this singularity is an integrable divergence, the divergent behavior complicates the numerical evaluation of the integrals over hopping points that is present in the surface hopping expressions. Numerical evidence has shown that only small errors are incurred at most energies if these singular hopping amplitudes are replaced with a nonsingular approximation. This agreement is surprising, since the exact and approximate amplitudes differ greatly in the turning point region, and this region is expected to make important contributions to the transition probability at low energies. A numerical analysis is presented in this work that provides a justification as to why this numerically useful approximation works as well as it does.     

Light propagation in a strong external magnetic field with regard to quantum corrections

Linearized motion equations for electromagnetic wave field in the external magnetic field have been solved for the PVLAS experiment configuration within the low-energy approximation of quantum electrodynamics. It has been shown that the wave propagation velocity depends on the initial direction of the plane of wave polarization. Dispersion laws corresponding to the waves with mutually perpendicular directions of polarization have been established. The dependence of ellipticity of laser radiation field on initial polarization and the value of the external magnetic field has been obtained. The ellipticity parameter for the configuration of the system used in the PVLAS experiment has been found.     

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.     

Planar waveguide‐resonator: a new device for x‐ray optics

Systematic investigations of the width dependence on the x‐ray beam propagation mechanism for a narrow extended slit formed by two plane dielectric plates are presented. It is shown that the mechanism of a multiple consecutive total reflection for Cu Kα radiation dominates in a slit width range s ≥ 3 µm. At the same time the manner of Cu Kα radiation propagation for super‐narrow slits s ≤ 0.1 µm is very different from the multiple total reflection mechanism. The x‐ray beam intensity proves to be constant for all this range of magnitude. This gives grounds to expect that the super‐narrow slit area is characterized by a specific type of mechanism of x‐ray beam propagation: waveguide‐resonance. A simple model for the waveguide‐resonance propagation mechanism based on the formation of a uniform x‐ray standing wave interference field in the total space of a narrow extended slit was developed. The design of a new x‐ray optical device, namely a planar x‐ray waveguide‐resonator, is proposed based on the waveguide‐resonance mechanism. Some properties of the composite planar x‐ray waveguide‐resonator are discussed. It is shown that under specific conditions the composite waveguide can demonstrate a partial tunneling effect of the x‐ray beam. The main applications of the new technique are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

The problem of surface wave propagation in a reduced Cosserat medium

This article continues a series of publications devoted to the study of waves in the framework of the asymmetric theory of elasticity, where the deformed state of the medium is characterized by independent vectors of translation and rotation. The problem of acoustic Rayleigh wave propagation in half space is considered within a model of the reduced Cosserat medium. A general analytic solution of this problem is obtained. The analysis of this solution is compared with the corresponding solution for a classical elastic medium and full linear Cosserat medium. It is shown that the Rayleigh wave is characterized by a range of forbidden frequencies, where this wave cannot propagate. The dispersion curve consists of two branches. One of them has a cut-off frequency and cut-off wavenumber.     

Four-wave mixing of quasi-monochromatic waves and few-cycle pulses

Four-wave coherent mixing models for two quasi-monochromatic pumping fields and pulses of a two-component Stokes field with an elliptic polarization and a duration on the order of the period of oscillations have been derived for a two-level medium with a forbidden dipole transition. It is shown that, under the unidirectional wave propagation conditions and in the absence of depletion of pumping, the system of Maxwell-Bloch equations can be reduced to a new completely integrable system of equations. Nonsoliton radiation dynamics of generation of Stokes field pulses is studied in the framework of the integrable reduction of this model. The apparatus for the inverse problem algorithm corresponding to the solvable problem is developed. An approximate asymptotic expression for the leading front of the pulse packet being generated is obtained for various initial and boundary conditions. The application of these results for describing parametric processes involving various types of waves is discussed.     

Focusing of a wave beam in an underwater sound channel

The use of a vertical radiating antenna array for generation of a wave beam propagating in an underwater sound channel along the reference ray trajectory is discussed. The method for selecting the starting field in the antenna aperture for maximum compression of a beam in the specified vicinity of the reference ray is proposed. The estimates showing up to what distances a beam can propagate while remaining narrow as compared to the range of depths between the rotation horizons have been obtained. The problem concerning the distances from the antenna array at which a beam can still be effectively focused in the vicinity of the selected reference ray point is investigated.     

Interbranch scattering of an X-ray wave field in a strongly distorted region of the elastic field around a dislocation

The case of a diffraction image of screw dislocations arranged parallel to the surface of a specimen has been studied experimentally and by methods of computer simulation. Special features of scattering of an X-ray wave field in a strongly distorted region near the dislocation core have been considered. It has been shown that the diffraction image in the vicinity of the defect is formed due to a superposition of new wave fields generated at each point of the elastic field around a dislocation with the existing fields.     

A high‐accuracy complex‐phase method of simulating X‐ray propagation through a multi‐lens system

The propagation of X‐ray waves through an optical system consisting of many X‐ray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finite‐difference method is applied. The error of simulation is analytically estimated and investigated. It was found that a very detailed difference grid is required for reliable and accurate calculations of the propagation of X‐ray waves through a multi‐lens system. The reasons for using a very detailed difference grid are investigated. It was shown that the wave phase becomes a function, very quickly increasing with increasing distance from the optical axis, after the wave has passed through the multi‐lens system. If the phase is a quickly increasing function of the coordinates perpendicular to the optical axis, then the electric field of the wave is a quickly oscillating function of these coordinates, and thus a very detailed difference grid becomes necessary to describe such a wavefield. To avoid this difficulty, an equation for the phase function is proposed as an alternative to the equation of the electric field. This allows reliable and accurate simulations to be carried out when using the multi‐lens system. An equation for the phase function is derived and used for accurate simulations. The numerical error of the suggested method is estimated. It is shown that the equation for the phase function allows efficient simulations to be fulfilled for the multi‐lens system.     

Drift mechanism caused by a nonlinear wave and the Cassini Division and Uranian rings formation

The mechanism leading to the observed coexistence of gaps and narrow ringlets in the planetary rings is found. It is based upon the quasi-stationary radial drift of the matter under action of two forces in the disk plane: the Coriolis force and the Reynolds stresses. To an accuracy of the factor of 2 the first force coincides with the Lorentz force, therefore the radial drift in rings is similar to the gradient drift of plasma in the magnetic field. The second force is produced by the wave generated by the nearby satellite in the resonance position. In inertial systems, the second force alone causes a matter flow in its direction, called acoustic streaming. Since the radial drift is caused by nonlinear time-averaged force of high-frequency harmonic interactions in the wave, it exists in the wave propagation zone: from the birth place of the wave-the resonance position, up to the reflection point of the wave, where its group velocity vanishes. Our estimations show that the size of the density wave propagation zone corresponding to the density wave which had been formerly generated the 2:1 orbital resonance with Mimas is consistent with the width of the Cassini Division. In our case the nature of the radial drift is such that first of all it clears out the farthest from the resonance position; later, the closer areas also get affected by the drift. The zone closest to the resonance position itself is the last to be involved in the process. The matter carried away by the drift is partially accumulated near the resonance position forming a narrow dense ringlet. (c) 1996 American Institute of Physics.     

Conformal scalar propagation and Hawking radiation

The construction of the conformal scalar propagator which has been obtained in the preceding two projects as an analytic function of the Schwarzschild black-hole space-time is completed with a boundary condition imposed by the physical context through contour integration in the exterior vicinity of the event horizon. It is shown that, as a consequence of the semi-classical character which the emitted quanta have in that exterior vicinity, the particle production by the Schwarzschild black hole which was formally established in the preceding project is identical to thermal Hawking radiation. By extension, it is established that such a particle production corresponds to a spectrum which detracts from thermality by the amount predicted by Parikh and Wilczek if energy conservation is properly imposed as a constraint on scalar propagation. The results obtained herein support the case made by Hawking on the relation between quantum propagation and observation of particles produced by a black hole.     

Observation of surface-avoiding waves: a new class of extended states in periodic media

Coherent time-domain optical experiments on GaAs-AlAs superlattices reveal the existence of an unusually long-lived acoustic mode at approximately 0.6 THz which couples weakly to the environment by evading the sample boundaries. Classical as well as quantum states that steer clear of surfaces are generally shown to occur in the spectrum of periodic structures, for most boundary conditions. These surface-avoiding waves are associated with frequencies outside forbidden gaps and wave vectors in the vicinity of the center and edge of the Brillouin zone. Possible consequences for surface science and resonant-cavity applications are discussed.