Analytical solving of a deformed KdV equation

The celebrated Korteweg-de Vries (KdV) topics are of crucial significance in many fields of natural sciences. In this paper, a symbolic-computation-based method is applied to a perturbed form of the modified KdV equation, and one type of the analytic solutions is obtained. This work has been supported by the Out-standing Young Faculty Fellowship & the Research Grants for the Scholars Returning from Abroad, State Education Commission of China.     

The retarded solution of the scalar wave equation by means of Green's functions

A formula is obtained for the retarded solution of the scalar wave equation in a curved space-time, with boundary conditions appropriate to the case of asymptotic flatness. By means of a conformal transformation, the retarded solution is evaluated in the slow-motion expansion. It is shown that it is necessary to impose further asymptotic restrictions on the source for the usual iterative method to give the correct retarded solution to the given degree of approximation. The weak field case is briefly considered, with the same result.     

Analytical model of a corrugated optical waveguide

An analytical model of the diffraction energy exchange between the radiative and the waveguide modes in a planar optical waveguide corrugated by a waveguide grating with an arbitrary form of teeth is developed on the basis of the coupled-wave method. It is shown that the mechanism of the energy exchange between the modes is determined by the partial interaction of all components of the spatial frequency spectrum of the waveguide modes with the corresponding components of the spatial frequency spectrum of the grating. It is established that gratings with an asymmetric tooth profile providing a shift of the peak of the spatial frequency spectrum toward matching are characterized by a higher diffraction efficiency α; however, at small thicknesses δ of the waveguide grating, the efficiency is almost independent of the tooth profile. It is shown that gratings with a symmetric profile give on average a decreasing dependence α(δ), while gratings with an optimized asymmetric profile yield a monotonically increasing saturating dependence α(δ).     

Fabrication of defocus graded-index optical waveguide for evanescent wave optical amplifier

This is the first report on an evanescent wave optical amplifier with a plastic waveguide that can amplify a CW signal transmitted by a plastic optical fiber. The waveguide with a concave refractive index distribution was fabricated by an interfacial-gel polymerization technique. Since the waveguide increases the number of reflections at the boundary surface of the waveguide and the laser dye solution, the enhancement of amplification efficiency can be realized. The function of the fabricated waveguide was confirmed by calculations and experiments. The obtained results indicate that the fabricated fiber generated a larger evanescent field than the waveguide without a refractive index distribution.     

Topological optical Bloch oscillations in a deformed slab waveguide

Spatial Bloch oscillations of light waves of purely topological origin are theoretically shown to exist in weakly deformed slab waveguides. As the optical rays trapped in the deformed waveguide can roll freely, wave diffraction is strongly affected by the topology of the deformed surface, which can be tailored to simulate the effect of a tilted periodic refractive index.     

The scalar wave equation in the weak field approximation

A formula for the retarded solution of the scalar wave equation is given and is shown to differ from the usually accepted approximation.     

矢量波动方程的球面波解

利用线性变换的方法，将球坐标下矢量波动方程解的形式L、M和N变换为其他多种形式．     

Analytical solution of an equation for the pair correlation function

For the hard sphere model, an approximate analytical solution is obtained of a linear integral equation for the pair correlation function derived from the Bogolyubov equation. An equation of state is given for this system which is nearly identical to the expression obtained from the Percus-Yevick equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 28–32, August, 1984.The author thanks G. I. Nazin for proposing the problem and also acknowledges useful discussions with É. A. Arinshtein and A. F. Nyashin.     

A unified optical theorem for scalar and vectorial wave fields

The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves. Moreover, this unified theorem also holds for scattering by anisotropic elastic and piezoelectric scatterers as well as bianisotropic (non-reciprocal) EM scatterers.     

线性分段折射率分布多量子阱波导色散关系的精确分析

本文从标量Helmholtz方程出发,采用转移矩阵技术,求出了线性分段折射率分布多量子阶波导TE模色散关系的精确解,数值计算结果显示出该波导的色散特性以及与波导结构的关系,为实际制作该量子阶波导进行参数选择提供了理论依据。     

A non-relativistic wave equation of second order in time for scalar fields

In this paper a generalization of the traditional non-relativistic Schrödinger equation is considered. It is a wave equation of second order in time and fourth order in the space coordinates for scalar fields. The equation has certain features, which make it a closer analogue of the Klein-Gordon equation than the traditional Schrödinger equation. However, the equation maintains the non-relativistic relation between energy and momentum.The implications of this generalized wave equation and the quantized field theory based on it are studied. The theory can be shown to be charge symmetric and allows to introduce anti-particles and pair creation. We compare the Green functions for this theory with those of conventional non-relativistic quantum theory.The theory allows to formulate a transformation for charge conjugation. The PCT-theorem is valid for it. The usual spin-statistics connection holds.     

A numerical technique for solving the scalar wave equation for Gaussian and smoothed-out profiles

A numerical technique, based on transforming the scalar wave equation to a finite interval before discretization is applied, is proposed for the solution of the scalar wave equation defining the modal fields and propagation constants of optical fibres. It is used to compute the propagation constants and modal fields of weakly guiding fibres of circular cross-section when the refractive index profile has a Gaussian or smoothed-out form. The smoothed-out profiles are studied because they vary continuously from the Gaussian to the step profile. Results are compared with and shown to be accurately approximated by simply explicit functions, dependent only on the fibre parameter.     

Mode equation and its solution for dielectric waveguide with parabolic cross-section

The mode equation for the dielectric waveguide with parabolic cross-section is derived using both the effective index method and WKB theory, and the expression of the mode propagation constant or effective index is solved directly from this mode equation, so that the mode-propagation properties of this kind of waveguide can be analysed conveniently with comparative accuracy.     

Picosecond linear optical pulse shapers based on integrated waveguide Bragg gratings

We demonstrate a general linear pulse-shaping technique based on integrated III-V Bragg gratings (BGs). Such a technique allows for the synthesizing of complex waveforms with picosecond resolution using a compact single-waveguide design. This approach is experimentally demonstrated by fabricating and testing a series of integrated ultrafast optical pulse shapers based on BG geometries acting as time-domain code generators operating at 500 Gbits/s.     

Applicability of scalar theory for analysis of mode reflection from an optical dielectric waveguide end

Scalar and vector theories are compared for weakly guided modes reflected from a planar optical dielectric waveguide end or laser facet. By utilizing the free space radiation mode method the range of validity of the scalar theory over a wide range of reflectivities is given explicitly for the first time.     

The exact solution of an equation for the Killing spinor on a nondegenerate deformed conifold

An explicit form of the Killing spinor (generator of N = 1 sypersymmetry) is found for a nondegenerate deformed conifold [3].     

Surface acoustic wave distribution and acoustooptic interactions in silica waveguide Bragg devices

The efficiency of acoustooptic interaction in single-mode strip silica waveguide is analyzed theoretically for the first time by determining the overlap integral between the optical and acoustic field distributions. The results show that there is a good overlap of the optical and SAW fields in the low SAW frequency range. At high acoustic frequencies, the overlap integral decreases with increasing acoustic frequency. At 216 MHz, the maximum of 0.8544 for the overlap integral is obtained provided that the H/Λ equals 0.02.