Longitudinal Inhomogeneity Research Articles

Separation of germanium and silicon oxides by plasma-chemical deposition of germanosilicate glass in a moving plasma column

The optical transmission spectrum of germanosilicate glass deposited by surface plasma chemical vapor deposition on the inner surface of a quartz tube revealed interference resonances typical of multilayer dielectric coatings with alternating refractive indices. It is shown that this effect can be attributed to the longitudinal inhomogeneity of the plasma composition and specifically to an axial shift of the concentration maxima of germanium and silicon oxide. As a plasma having a nonuniform composition moves along the tube, a layer of glass is formed with a strong transverse germanium concentration gradient. It is established that in surface plasma chemical vapor deposition the axial separation of the regions of deposition of the silicon and germanium oxides increases if the glass is synthesized under conditions of oxygen deficiency.

Complex ABCD transformations for optical ring cavities with losses and gain

Complex ABCD field transformations are investigated for inhomogeneous optical ring cavities with losses and gain. It is shown that the sets of eigenfunctions, corresponding to counterpropagating waves, are really biorthogonal: the functions in each of these sets are really orthogonal relative to one another, and have a complex weighting factor independent of the mode number. Bidirectional and unidirectional stability conditions are formulated for such cavities. These conditions are qualitatively different from those for loss-free cavities. A simple algorithm is proposed for the evaluation of the ABCD matrix for a medium with an arbitrary longitudinal inhomogeneity along the beam.

Parametric decay of an electromagnetic pump wave in a two-dimensionally inhomogeneous plasma

The decay instability of an ordinary hf electromagnetic pump wave into quasitransversal upper hybrid (UH) and lower hybrid (LH) waves in the ionosphere is discussed. The longitudinal and transversal inhomogeneity of the medium is taken into account. It is shown that, due to the decay instability within weak plasma density enhancements, a rather broad spectrum of UH oscillations, similar to the spectrum of the downshifted maximum (DM) in stimulated electromagnetic emission (SEE) spectra, is formed. Estimates of the frequency range and characteristic k numbers of the DM spectrum are given.

The standard deviation of column ozone from the zonal mean

The standard deviation of column ozone from the zonal mean (COSDZ) provides a measure of the longitudinal inhomogeneity in ozone and dynamical wave activities in the atmosphere. Using the Total Ozone Mapping Spectrometer (TOMS) data, we obtain latitude‐season maps of COSDZ that are representative of a dynamically quiet year (1987) and a dynamically active year (1992). The spatial and temporal patterns of COSDZ show considerable similarity to the standard deviation of the 50 mb geopotential heights from the zonal mean. We point out that the simulation of this quantity by three‐dimensional (3‐D) models could provide a sensitive check of wave activities in the stratosphere that are responsible for ozone transport. Comparison between the observed COSDZ and the simulations of the GSFC 3‐D model of ozone reveals major discrepancies between data and model in the tropical stratosphere.

Beam-plasma discharge in the propagation of a long-pulse relativistic electron beam in a medium-pressure rarefied gas

A theoretical model is given, along with a numerical analysis of the evolution of beam-plasma discharge in the propagation of a long-pulse relativistic electron beam in a rarefied gas at medium pressure. It is shown that the self-stabilization of beam-plasma discharge as a result of longitudinal inhomogeneity of the density of the discharge plasma makes it possible for the beam to traverse the beam chamber with relatively low total energy losses, including ionization losses and energy losses in the generation of oscillations. During the dissociative recombination of electrons and ions of the discharge-driven plasma, heat is released and spent in raising the temperature of the gas. The investigated collective-discharge mechanism underlying heating of the gas for a relativistic beam can be more efficient than the classical heating mechanism due to ionization losses of the beam in pair collisions of its electrons with gas particles.

Experimental investigation of the coupling process in the middle atmosphere/lower thermosphere/ionosphere system

The paper briefly reviews some investigations realized mainly in Southern Spain of possible coupling between middle atmosphere, lower thermosphere and ionosphere. It draws attention to abnormal circulation changes in the winter stratosphere, detected through variations of D-region ionospheric radiowave absorption; the response of the lower ionosphere to the stratospheric warmings; quasi-periodic fluctuations in ionospheric absorption in relation to planetary wave activity in the stratosphere; the statistically significant correlations between variations of total ozone content considered as a parameter of the stratospheric changes; and radio waves absorption as an indicator of the electron density in the lower ionosphere. There is some difference in the behaviour of the lower ionosphere in relation to meteorological parameters in Southern Spain and Central and East Europe, and this is discussed as partly due to latitudinal variations of ionospheric parameters and to longitudinal inhomogeneity of lower atmosphere processes.

Exact, dynamical analysis of the Kukhtarev equations in photorefractive barium titanate using rigorous coupled-wave diffraction theory

Rigorous coupled-wave diffraction theory is used to analyze two-wave and multiwave mixing in diffusion-controlled photorefractive barium titanate, which is modeled by the Kukhtarev equations. These equations are partially decoupled to yield a system of two equations between the electron density and the electrostatic field (and hence the induced refractive index profile). The transmitted and reflected optical fields, the dielectric modulation, the electrostatic field, and the electron density are studied for the cases in which the interfering, incident optical fields have equal and unequal amplitudes for different values of the linear refractive index mismatch and for different values of photorefractive crystal length. In each case the exact longitudinal inhomogeneity in the photorefractive medium is analyzed with the use of rigorous coupled-wave diffraction theory and an exact Kukhtarev analysis. We compare the evolution of the diffracted orders for different sample lengths to show that the nature of the steady state (oscillatory or nonoscillatory) critically depends on the sample length. Our computations study in BaTiO3 the conditions for temporal instability resulting in self-pulsation and for anisotropic diffraction contributing to significant generation of higher orders (assuming that two plane waves are incident on the photorefractive material).

A nonlinear, transient analysis of two- and multi-wave mixing in a photorefractive material using rigorous coupled-wave diffraction theory

Rigorous coupled-wave diffraction theory is used to analyze two- and multi-wave mixing in a diffusion-controlled photorefractive material which is modeled by the Kukhtarev equations. These equations are first decoupled to yield a nonlinear time-dependent differential equation for the induced refractive index profile. The transmitted and reflected field coupling coefficients are studied for the cases when the incident optical fields are coherent and partially coherent, for materials with different gain constants, and for different values of the linear refractive index mismatch. In each case, the exact longitudinal inhomogeneity in the photorefractive medium is analyzed using rigorous coupled-wave diffraction theory. Our computations predict a possible temporal instability resulting in self-pulsation and anisotropic diffraction contributing to a significant generation of higher orders when two plane waves are incident on photorefractive materials. Six-wave coupling in index mismatched barium titanate is studied.

Estimating the global ozone characteristics during the last 30 years

All available total ozone data from over 150 past and present Global Ozone Observing System (GO3OS) stations, after careful quality control and reevaluation, have been analyzed in order to deduce the basic global ozone characteristics both for pre‐ozone‐hole and during “ozone hole” time periods. Utilizing Total Ozone Mapping Spectrometer (TOMS) data, the longitudinal inhomogeneity of the total ozone distribution was estimated. That permitted the use of ground‐based data for establishing long‐term zonal as well as hemispheric and global ozone variations for the 1964–1994 period. The difference between the estimations of monthly zonal variations from ground‐based and TOMS data for the overlapping period of 1979–1993 is less than 1% in latitudes 40°S–60°N. The ozone changes are several times larger than possible errors of the estimated values; therefore the results are highly reliable. They show that the northern hemisphere average ozone was ∼312 and the southern average was ∼300 matm cm in the pre‐ozone‐hole decades (1964–1980) and that the global average for the 1984–1993 period was lower by ∼3% (from 306.4±1.0 down to 297.7±2.2 matm cm). The southern hemisphere contributed ∼64% of the overall ozone decline. The levels of annual ozone maximum have been reduced by 5.8% in the southern hemisphere and 3.2% in the northern hemisphere, and the levels of ozone minimum have been reduced by 2.1% and 1.2%, respectively. The ozone trends for midlatitudinal bands (35–65°) show a pronounced seasonal dependence varying from ∼3% to 8 % (and even more for the southern hemisphere) for the cumulative decline since 1970. The ozone decline calculated in percent per decade from 1980 is almost twice as large as the decline calculated from 1970. The cumulative year‐round global ozone decline is 4.8±0.6%; however, the cumulative year‐round decline over middle and polar latitudes is more than 7%. The advantages of establishing ozone “norms” for estimations of long‐term ozone variations from ground‐based data are emphasized.

On the structure of the middle Jovian magnetosphere

A model of the plasma distribution in the middle Jovian magnetosphere is considered. The distribution of the background plasma along the magnetic lines of force under the action of the centrifugal force and the force of gravity is analyzed in the framework of the diffusive equilibrium, taking into account the finite angle between the magnetic and rotational axes. It is shown that the dense structures of the background plasma have the form of a warped sheet located between the magnetic and centrifugal equators, and of two mirror symmetrical “petals” in the vicinity of the polar cusps. The hydrodynamic stability of the dense plasma sheet, formed under the action of the centrifugal force, is studied. The steady state radial plasma distribution at the threshold of the instability with respect to the small-scale MHD perturbations is determined. The finite conductivity of the Jovian ionosphere is taken into account. The influences of the longitudinal inhomogeneity of the perturbations, the finite ion Larmor radius, and the curvature of the magnetic field lines on the threshold of the instability are estimated. Some aspects of the formation of the energetic particle distribution in the middle Jovian magnetosphere are considered. The suggested model shows reliable agreement with the known experimental data and is also useful in describing the background plasma distribution in the magnetospheres of Neptune and Uranus.

Application of the FDTD technique to periodic problems in scattering and radiation

The finite-difference-time-domain (FDTD) technique is applied to two-dimensional periodic problems in scattering and radiation. This method allows the direct and complete treatment of periodic scatterers and arrays having transverse or longitudinal inhomogeneities, and several examples are presented to illustrate the versatility of the technique. The FDTD grid needs only to be applied to a unit cell of the periodic structure, making the analysis very efficient from a computational point of view. The method is presently limited to broadside incidence, however.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Control of Mode Structure in Active or Passive Graded-index Waveguides with Large-scale Periodic Longitudinal Inhomogeneities

Abstract The mode structure of both active and passive graded-index waveguides with a parabolic-index profile and large-scale (in comparison with wavelength) periodic variations of the profile in the longitudinal direction is investigated analytically in the paraxial approximation of the scalar wave equation. Quasimode solutions which periodically reconstruct themselves up to some phase factor characterizing quasi-propagation constants are investigated in detail using a quantum-theoretical formalism. The possibility of effective control of the quasi-mode structure in such waveguides is shown and possible practical applications to different waveguide components and lasers are discussed. The spontaneous emission K factor for the quasi-modes in active and passive periodic waveguides is also evaluated.

X-mode generation mechanism of the auroral kilometric radiation in the inhomogeneous plasma

A study is made of the influence of plasma and geomagnetic field inhomogeneities (longitudinal and transverse) upon the X-mode generation process of auroral kilometric radiation (AKR) due to cyclotron maser resonance. It is shown that the generation of AKR by auroral electron beams of typical energies 1–10 keV takes effect only in those local regions of a discrete arc where the regular longitudinal inhomogeneity of the geomagnetic field is compensated by the longitudinal inhomogeneity of magnetospheric plasma. Outside of such regions, waves recover too rapidly from cyclotron maser resonance as a consequence of a decrease of the longitudinal component of the wave vector. A critical study is made of an earlier solution to this problem through wave generation, with the transverse component of the refractive index being close to unity. The analytical approach to solving the problem of AKR generation in an inhomogeneous medium suggested in this paper relies on an in-depth study of the phase synchronism condition with the use of a full system of canonical equations of motion for wave packets. A logical consequence of the proposed mechanism for X-mode AKR generation implies the observed fine structure of the AKR frequency spectrum.

Classical nonlinear dynamics and chaos of rays in problems of wave propagation in inhomogeneous media

We discuss the geometrical theory of wave propagation in regularly inhomogeneous waveguide media from the point of view of nonlinear Hamiltonian dynamics. We consider ray dynamics in waveguides with periodic longitudinal inhomogeneities, including the phenomenon of spatial nonlinear resonance of rays, which leads to the formation of an effective waveguide channel in the neighborhood of the ray in resonance with the periodic inhomogeneities. We consider different properties of spatially resonant rays: the optical path length and propagation velocity of a signal along rays trapped in a separate nonlinear resonance; the fractal properties of rays, such as the devil's staircase form of the dependence of the spatial oscillation frequency of the ray and the propagation time of a signal along the rays. The trajectory of sound rays in a model of the ocean with transverse flow is considered using the adiabatic invariant method and the transverse drift of a ray with respect to the main propagation direction of sound is described. We consider the conditions for dynamical chaos of rays in a waveguide with longitudinal periodic inhomogeneities. We examine the conditions for internal spatial nonlinear resonance and chaos of rays in waveguides with an irregular cross section and their effect on the propagation velocity of a signal. We study the connection between the structure of the wave front and the dynamics of rays in waveguide channels with regular inhomogeneities. Finally, we discuss the applicability of geometrical optics in waveguides under the conditions of nonlinear resonance and chaos of rays, and the relation between this problem and quantum chaos.

Classical chaos and nonlinear dynamics of rays in inhomogeneous media.

An investigation is made of the classical nonlinear resonance and the classical stochastic dynamics of rays in waveguide media with irregular inhomogeneities. Analytic and numerical methods are used to study the characteristics of the ray trajectories, their confinement in a nonlinear resonance, and the development of chaotic behavior in waveguides with longitudinal periodic inhomogeneities. It is established that the localization of the rays has fractal properties; in particular, the cycle length of a ray and the time and velocity of propagation of a signal depend on the initial parameters of the ray in the form of a "devil's staircase." A waveguide with an inhomogeneous index of refraction and a periodically corrugated wall is considered.

Inhomogeneity and nonlinearity effects on stop bands of Alfvénic ion cyclotron waves in multicomponent plasma

We study the existence of stop bands for left‐handed Alfvénic ion cyclotron waves propagating in the direction of magnetic field in a multicomponent plasma. Three effects are discussed: finite ion temperature, inhomogeneous magnetic field, and nonlinear wave amplitude. All of them affect the existence of stop bands and set critical bounds on the relevant physical parameters, particularly on the density of heavy ions. Using the model of a linearly varying, longitudinally inhomogeneous magnetic field, we calculate the critical lower bound on heavy ion density as a function of longitudinal inhomogeneity, and we discuss the difference between the truly inhomogeneous and essentially homogeneous situations. Typical values for the wave vector in the resonance region are derived. We also find the upper bound on the wave amplitude for the linear theory to be applicable, and we derive the condition for stop band formation in the nonlinear case. The obtained results are applied to the magnetospheric environment and are shown to lead to relevant modifications. For example, the formation of stop bands by thermal heavy ions is strongly dependent on the local inhomogeneity of the magnetic field.

Resonance excitation of standing Alfven waves in an axisymmetric magnetosphere (monochromatic oscillations)

A theoretical study is made of the phenomenon of standing Alfven wave resonance excitation by a monochromatic fast magnetosound in an axisymmetric model of the magnetosphere. A theory is developed which includes the Alfven and magnetosound wave relationship, transverse and longitudinal inhomogeneities of the medium, the weak transverse dispersion of Alfven waves and their dissipation on the ionosphere. General formulae are derived which describe the spatial structure of a monochromatic Alfven wave. These formulae are specified for all physically differing cases of the behaviour of magneto-spheric parameters. An analysis is made of the back influence of an Alfven wave on a magnetosound field.

Casimir forces between plates with periodic longitudinal inhomogeneity

A method is proposed for computing the Casimir forces between plates with longitudinal inhomogeneities based on utilization of the modified impedance boundary condition. Corrections are found to the Casimir forces between flat plates in first and second order perturbation theory with respect to the relative degree of the inhomogeneity.

Longitudinal spatial inhomogeneities in intrinsic optical bistability due to induced absorption

Longitudinal spatial effects in the nonlinear medium are analyzed in a model for mirrorless optical bistability due to induced absorption that treats heat conduction, electromagnetic field propagation, and temperature-dependent absorption. We consider two specific cases: the temperature-induced shift of the absorption peak of bound I2 excitons in CdS single crystals and the temperature-induced shrinkage of the band gap in GaAs/GaAlAs quantum-well material. For both cases it is shown that the inhomogeneous spatial distribution of the nonlinear absorption profile along the direction of propagation of the electric field undergoes a first-order-like phase transition commensurate with the transition of the output intensity from one value to another for fixed input intensity. Stability conditions are presented for the steady states of the output intensity as a function of the input intensity for the cases treated. There is a multiplicity of bistability curves, and the stability analysis produced the expected branches of stable solutions.

Dynamic stiffness measured in central segment of excised rabbit papillary muscles during barium contracture.

The dynamic mechanical behavior of excised rabbit papillary muscles that had been tonically activated by replacing bathing Ca2+ with Ba2+ was studied. Steady activation was used to visualize the dynamic behavior of cardiac myofilaments more clearly than is possible during twitches, which are complicated by the kinetics of excitation-contraction coupling. To avoid artifacts due to damaged ends of the muscle, the length of a central segment, which was defined by 2 tungsten pins inserted through the muscle, was measured. To test the mechanical behavior of the contractured muscles (at 24 degrees C), the central segment length was sinusoidally oscillated (amplitude 1%) at 15 different frequencies (0.05-30 Hz). The dynamic stiffness of the central segment was calculated from the ratio of force response amplitude to length perturbation amplitude. At low frequencies (below 0.4 Hz), stiffness was approximately constant and reflected the force-length relation. However, in a localized range near 1 Hz, there was a distinct drop in the magnitude of dynamic stiffness to approximately half its low-frequency baseline. This range may reflect the dynamics of attachment and detachment of force generators. The frequency of minimum stiffness was consistent among all muscles (1.3 +/- 0.3 Hz). Moreover, no significant change in this frequency was found over the examined range of lengths (90-100% of the segment length that produced maximal developed force) and activation levels (Ba2+ concentration 0.3-1.0 mM). From 2 to 8 Hz, dynamic stiffness appeared to reflect force-velocity properties, but at higher frequencies, another elastic property emerged. At 30 Hz, stiffness was proportional to force, with an apparent series elasticity less than 1.8%. Even though the muscles had only moderate longitudinal inhomogeneity, quantitatively significant (35%) errors would have been introduced had the study relied on total muscle length instead of central segment length.