Pulse dispersion in a lens-like medium

An analysis is given of dispersion in an optical fibre waveguide having a continuous radial variation of refractive index using the scalar wave approximation. Solutions are presented for the particular case of Selfoc fibre taking into account mode dispersion, material dispersion and group delay. It is shown that for a correctly matched input Gaussian beam the pulse dispersion is small although in practice it is likely to be 1 ns over a length of 1 km.On leave from the Nippon Sheet Glass Co., Japan.     

Pulse dispersion in a clad lens-like medium

The effects of a homogeneous cladding on the dispersion of a square-law dielectric guide are investigated using a perturbation technique. Assuming a Gaussian, band-limited input it is shown that for single mode operation the waveguide dispersion is of the order of the material dispersion. For multimode operation the effect of the cladding on the uniformly polarized modes is examined and it is shown that a significant interaction occurs only for the two modes closest to cut-off. Comparison is made between theoretical and experimental results. The perturbation technique is used to analyse the optimum index profile proposed by Okamoto and Okoshi. It is shown that this variation reduces the dispersion to below that of the infinite medium approximation.     

Beam propagation in a randomly inhomogeneous medium

An integrodifferential equation describing the angular distribution of beams is analyzed for a medium with random inhomogeneities. Beams are trapped because inhomogeneities give rise to wave localization at random locations and random times. The expressions obtained for the mean square deviation from the initial direction of beam propagation generalize the “3/2 law.”     

Beam propagation method for wide-field nonlinear wave mixing microscope

We develop a nonlinear beam propagation method for signal generation in inhomogeneous medium for wide-field nonlinear wave mixing microscope. Experimental results performed in wide-field coherent anti-Stokes Raman imaging have shown good agreement with the developed theory.     

Waveguide propagation of sound beams in a nonlinear medium

A possibility of a waveguide propagation of sound beams in the case of compensation of the diffraction divergence by the nonlinear refraction is demonstrated theoretically. A stationary (with respect to the longitudinal coordinate) solution is obtained to the nonlinear equation for a sound beam (the Khokhlov—Zabolotskaya equation); the solution describes the characteristic bow-shaped profile of the beam and the self-localized (with respect to the transverse coordinate) distribution of the peak values of this profile. The physical and mathematical features of this phenomenon belonging to nonlinear acoustics are discussed and compared with those of the well-known analog from nonlinear optics. A scheme of an experimental realization of the waveguide propagation of acoustic beams is proposed.     

Beam propagation analysis of a nonlinear dual-channel directional coupler

The dynamics of a nonlinear dual-channel directional coupler are studied numerically using a two-dimensional beam propagation method. The results are in good agreement with those of Jensen, which were based on the analytical solution of a pair of coupled-mode equations.     

Geometrical analysis of a lens-like medium with higher-order aberration

The propagation of light rays in a slab-waveguide whose dielectric constant varies radially with a quadratic law but has fourth and sixth order terms in it is described. Exact solutions consisting of Jacobi elliptic functions are shown. The exact ray trajectory and delay time of an optical pulse, therefore, can be obtained. The results show that the optimum fourth-order and sixth-order coefficients are near 2/3 and 17/45, respectively.     

Features of nonlinear wave propagation in a layer of a granular medium

Computer simulation was performed to study compression wave propagation in a granular medium in a gravity field. It is shown that in a layer with spherical granules, periodic wave structures can be formed and their parameters depend on the granule size and layer thickness. If the layer is compressed, the wave structures fail to emerge and wave attenuation is much weaker. Wave processes in a layer of granular medium with nonspherical granules were also studied. It is shown that the medium is characterized by very strong wave attenuation and by the absence of wave structure formation and is highly sensitive to its initial stress state.     

Stimulated Raman scattering in the approximation of unidirectional propagation in a medium with static dipole moments

The evolution equations of two-frequency stimulated Raman scattering in a molecular quasithree- level medium with static dipole moments have been derived in the approximations of the nondepletion of the pump field and the unidirectional propagation of the Stokes field. Completely integrable particular cases of the resulting system of equations have been found. New mechanisms of controlling the parameters of microwave pulses generated in such a system have been studied within this model. The numerical analysis and particular exact solutions demonstrate the possibility of switch between the regimes of generation of narrow Stokes field pulses and nearly rectangular pulses.     

Application of the method of minimum autonomous blocks to the problem of the propagation of radiation in a nonlinear medium

Radiophysics and Quantum Electronics -     

The propagation of a nonlinear sound wave in an unconsolidated granular medium

The propagation of a high-intensity sound wave in an unconsolidated medium is considered. Dissipation effects are taken into account on the basis of Buckingham’s theory of a relaxation mechanism of sound attenuation in a saturated sediment. The nonlinear evolution equation for the relaxing medium is obtained, and the solutions of this equation are analyzed. The second-harmonic generation in such a medium decays, as does the linear sound wave of the same frequency. The stationary weak shock profile has a specific form due to relaxation effects.     

Instability analysis of Gaussian beam propagation in a nonlinear refractive index medium

In this paper, we use a thin filament two dimensional Gaussian beam to model the self-trapping filament. The instability of the propagation of a Gaussian beam through a nonlinear refractive index media is investigated, theoretically and numerically. Specifically, the small scale instability of the beam is examined. The numerical results show that the propagation of the two dimensional Gaussian beam presents one or more nonlinear focal points.      

脉冲波在空间等离子体介质中传播的矩分析及其应用

根据随机介质波传播理论，开展脉冲波在星际空间等离子体介质中的传播特性的分析方法研究.在强起伏条件下，推导双频互相关函数的二阶矩和四阶矩方程，利用不同电子密度模型，计算双频衍射强度相关函数和闪烁指数，并应用到闪烁的动态谱观测和相关分析中，得到自相关图谱、相关带宽和相关时间等闪烁特征参数，为脉冲在等离子体中的传输特性的分析，提供必要的理论基础.