A linear-operator formalism for bianisotropic waveguides

A bianisotropic waveguide can be defined as a cylindrical waveguide filled with bianisotropic materials, and all the conventional waveguides are special cases of the bianisotropic waveguide. In this paper, guided wave propagation in bianisotropic waveguide is analyzed by the theory of linear operators, and two types of adjoint waveguides and inner products are introduced respectively. Based on the concept of adjoint waveguides, the functional expressions of the field equations can be obtained, and from which the eigenvalue problem of the bianisotropic waveguide can be solved. Also, bi-orthogonality relations of guided modes are derived. These biorthogonality relations reported here can be used to expand electromagnetic fields in terms of a complete set of modes in straight bianisotropic waveguide. As an example of application, mode matching formulae for a discontinuity problem are given.     

Reverberation of Wideband Signals in Shallow Water when Using Sound Focusing

Within the framework of the normal mode approximation, expressions are obtained for calculating bottom reverberation signals recorded by a horizontal array in an inhomogeneous shallow-water waveguide in a wide frequency band. These expressions can be used to simulate bottom-scattered signals both for a monostatic and bistatic geometry, as well as in the case when sound focusing is applied. The constructed model is used to numerically study the structure of bottom reverberation in a waveguide with different parameters and characteristics of the receiver and source systems. The considered bottom inhomogeneities are the slope of the bottom, change in thermocline depth, and wind waves. The study demonstrates the promise of using sound focusing as time reversal using a single receiver–transmitter element to enhance the reverberation signal arriving from a given bottom area.     

Theoretical framework for geoacoustic inversion by adjoint method

Traditional geoacoustic inversions are generally solved by matched-field processing in combination with metaheuristic global searching algorithms which usually need massive computations. This paper proposes a new physical framework for geoacoustic retrievals. A parabolic approximation of wave equation with non-local boundary condition is used as the forward propagation model. The expressions of the corresponding tangent linear model and the adjoint operator are derived, respectively, by variational method. The analytical expressions for the gradient of the cost function with respect to the control variables can be formulated by the adjoint operator, which in turn can be used for optimization by the gradient-based method.     

掺半导体玻璃(SDG)波导非线性饱和的导波测量方法

掺半导体玻璃波导的折射率分布是通过多模波导有效折射率测量得到的.当耦合进入波导的激光功率密度变化时,可在不同模深度处,测量到波导的非线性折射率系数,并获得波导非线性折射率系数与功率密度的关系.从而得到波导的非线性饱和值为1.54×10-4.     

Atmospheric weighting functions and surface partial derivatives for remote sensing of scattering planetary atmospheres in thermal spectral region: general adjoint approach

An approach to formulation of inversion algorithms for remote sensing in the thermal spectral region in the case of a scattering planetary atmosphere, based on the adjoint equation of radiative transfer (Ustinov (JQSRT 68 (2001) 195; JQSRT 73 (2002) 29); referred to as Papers 1 and 2, respectively, in the main text), is applied to the general case of retrievals of atmospheric and surface parameters for the scattering atmosphere with nadir viewing geometry. Analytic expressions for corresponding weighting functions for atmospheric parameters and partial derivatives for surface parameters are derived. The case of pure atmospheric absorption with a scattering underlying surface is considered and convergence to results obtained for the non-scattering atmospheres (Ustinov (JQSRT 74 (2002) 683), referred to as Paper 3 in the main text) is demonstrated.     

Adjoint modeling for acoustic inversion

The use of adjoint modeling for acoustic inversion is investigated. An adjoint model is derived from a linearized forward propagation model to propagate data-model misfit at the observation points back through the medium to the medium perturbations not being accounted for in the model. This adjoint model can be used to aid in inverting for these unaccounted medium perturbations. Adjoint methods are being applied to a variety of inversion problems, but have not drawn much attention from the underwater acoustic community. This paper presents an application of adjoint methods to acoustic inversion. Inversions are demonstrated in simulation for both range-independent and range-dependent sound speed profiles using the adjoint of a parabolic equation model. Sensitivity and error analyses are discussed showing how the adjoint model enables calculations to be performed in the space of observations, rather than the often much larger space of model parameters. Using an adjoint model enables directions of steepest descent in the model parameters (what we invert for) to be calculated using far fewer modeling runs than if a forward model only were used.     

Generalized form of the direct and adjoint radiative transfer equations

The main goal of this paper is to give a rigorous derivation of the generalized form of the direct (also referenced as forward) and adjoint radiative transfer equations. The obtained expressions coincide with expressions derived by Ustinov [Adjoint sensitivity analysis of radiative transfer equation: temperature and gas mixing ratio weighting functions for remote sensing of scattering atmospheres in thermal IR. JQSRT 2001;68:195-211]. However, in contrast to [Ustinov EA. Adjoint sensitivity analysis of radiative transfer equation: temperature and gas mixing ratio weighting functions for remote sensing of scattering atmospheres in thermal IR. JQSRT 2001;68:195-211] we formulate the generalized form of the direct radiative transfer operator fully independent from its adjoint. To illustrate the application of the derived adjoint radiative transfer operator we consider the angular interpolation problem in the framework of the discrete ordinate method widely used to solve the radiative transfer equation. It is shown that under certain conditions the usage of the solution of the adjoint radiative transfer equation for the angular interpolation of the intensity can be computationally more efficient than the commonly used source function integration technique.     

Relationship between different approaches to derive weighting functions related to atmospheric remote sensing problems

The paper is devoted to the investigation of the relationship between different methods used to derive weighting functions required to solve numerous inverse problems related to the remote sensing of the Earth's atmosphere by means of scattered solar light observations. The first method commonly referred to as the forward-adjoint approach is based on a joint solution of the forward and adjoint radiative transfer equations and the second one requires the linearized forward radiative transfer equation to be solved. In the framework of the forward-adjoint method we consider two approaches commonly used to derive the weighting functions. These approaches are referenced as the “response function” and the “formal solution” techniques, respectively. We demonstrate here that the weighting functions derived employing the formal solution technique can also be obtained substituting the analytical representations for the direct forward and direct adjoint intensities into corresponding expressions obtained in the framework of the response function technique. The advantages and disadvantages of different techniques are discussed.     

Propagation of soliton waves in nonlinear dielectric slab waveguides of parabolic index of refraction

The pulse propagation in a non-linear slab waveguide of parabolic index of refraction is treated by using differential equation techniques. A graded index dielectric slab waveguide free of material dispersion with a cubic order non-linearity is considered. The electromagnetic wave inside the waveguide is described in terms of a non-linear equation. Slowly varying envelope function representation is employed to develop a non-linear partial differential equation for the unknown envelope function of the electric field. An averaging method over the transverse direction is applied to reduce the unknown envelope function non-linear differential equation into a form resembling the well known non-linear Schrödinger differential equation. This equation is solved by applying the Inverse Scattering Method. The N-soliton solution is developed and presented explicitly for the practical case of the single mode dielectric slab waveguide. Numerical results presenting single and double soliton propagation are also given.     

Variational analysis of Er:Ti:LiNbO3 waveguide lasers based on Gaussian/two-half Gaussian mode field distribution

Starting with two dimensional, scalar wave equation, a variational equation was established for the fundamental TE and TM modes guided in Ti:LiNbO₃ waveguides on the basis of assuming a symmetric Gaussian mode field function in the width direction and two-half Gaussian trial functions in the depth direction. The controllable waveguide fabrication parameters, including channel width, diffusion temperature, initial Ti-strip thickness and diffusion time, dependent of fundamental mode size, effective pump area, coupling efficiency between pump and laser modes, and the coupling loss between a Ti:LiNbO₃ waveguide and a fiber were numerically calculated for Z-cut Er:Ti:LiNbO₃ channel waveguide lasers at three possible emission wavelengths 1532,1563 and 1576 nm and two possible pump wavelengths 1480 and 980 nm. The calculated results were compared with those of Gaussian/Hermite–Gaussian mode field distribution in detail.     

Wakefield radiation generated by an electron bunch in a rectangular dielectric waveguide

Vavilov-Cerenkov radiation generated by a relativistic electron bunch in a rectangular waveguide with a transverse-inhomogeneous dielectric filling is analyzed. A method is proposed for constructing an orthogonal basis of the transverse operator, which can be subsequently used for determining the wakefield of the relativistic bunch moving parallel to the waveguide axis. The dispersion equation for the structure is derived and the expressions for the wake field produced by such a bunch are obtained. The formalism described here forms the basis for calculating parameters of the accelerating structure for generator bunches of the Argonne Wakefield Accelerator (AWA) at the Argonne National Laboratory and the FACET complex of the SLAC accelerator. It is shown that using such structures, accelerating field gradients higher than 150 MV/m can be generated at frequencies 20?C35 GHz and exceeding 1 GeV/m in the frequency range ??1 THz.     

Numerical study of cusptron tube with an anti-coaxial-magnetron-type waveguide circuits

A new kind of mm-wave cusptron tube with anti-coaxial-magnetron-type wall structure is proposed. The dispersion equation of its RF circuit and the coupled resonant interaction equations of electrons with the waveguide mode fields are derived. A numerical simulation of the non-linear interaction process is carried out. It is found that in the cusptron tube proposed here, there may exists a new energy conversion mechanism with higher efficiency than that of conventional cusptron. Numerical results also show that the saturation efficiency for this mechanism is not sensitive to the applied dc magnetic field Bo. The saturation efficiency as the function of operation parameters, such as magnetic field Bo and electron voltage V, and the geometry of waveguide circuit is numerically illustrated. From that, the optimized design parameters for anti-coaxial-magnetron-type cusptron can be determined.     

一种基于简正波模态消频散变换的声源距离深度估计方法

针对浅海环境中传播的低频宽带水声脉冲信号,基于简正波水平波数差和波导不变量之间的关系,本文提出了一种利用距离-频散参数二维平面聚焦测距与匹配模态能量定深的目标声源定位方法.首先,通过将由频散参数和波导不变量表示的前几阶模态相速度与由环境模型计算的相速度进行对比分析,从而估计出前几阶模态的频散参数和环境的波导不变量.其次,利用估计出的频散参数值和波导不变量对接收信号进行消频散变换处理,只有当接收信号的距离参数等于目标声源距离时,各号简正波的幅度均达到最大值,在距离-频散参数二维平面上,出现声压聚焦的现象,利用此现象可以估计目标声源的距离.不仅如此,消频散变换后的接收信号,前几阶模态在时域上明显地分离开来,可以准确地估计出前几阶模态的能量,采用多模态能量匹配的方式,可以估计出目标声源的深度.最后,通过对仿真和冬季获得的气枪信号数据处理结果验证了本文方法的有效性.     

Mode field distribution of an integrated-optical waveguide generated by UV-laser radiation at the surface of a planar polymer chip

An integrated-optical strip-waveguide is directly written into the surface of a planar polymer substrate by an excimer laser beam. The mode field distribution, the surface refractive index and the refractive index depth profile of the waveguide have been examined. The intensity distribution of the mode field strongly depends on the refractive index depth profile, on the light coupling conditions and on the waveguide fabrication process parameters.     

Analysis and design of the taper in metal-grating periodic slow-wave structures for rectangular Cerenkov masers

The hybrid-mode dispersion equation of the metal-grating periodic slow-wave structure for a rectangular Cerenkov maser is derived by using the Borgnis function and field-matching methods.An equivalent-circuit model for the taper of the groove depth that matches the smooth waveguide to the metal-grating structure is proposed.By using the equivalentcircuit method,as well as the Ansoft high frequency structure simulator(HFSS) code,an appropriate electromagnetic mode for beam-wave interaction is selected and the equivalent-circuit analysis on the taper is given.The calculated results show that a cumulative reflection coefficient of 0.025 for the beam-wave interaction structure at a working frequency of 78.1 GHz can be reached by designing the exponential taper with a TE z10 rectangular waveguide mode as the input and the desired TE x10 mode as the output.It is worth pointing out that by using the equivalent-circuit method,the complex field-matching problems from the traditional field-theory method for taper design can be avoided,so the taper analysis process is markedly simplified.     

离子交换LiNbO_3:Fe平面光波导中两波混合的研究

本文利用耦合波理论分析推导了单模平面光波导中两波混合的耦合波方程和弱相干光放大率的表示式.并且,在LiNbO_3:Fe单模平面光波导中进行了两波混合的实验研究,得到了与理论分析相符合的结果.     

Slow light in photonic crystals waveguide constructed with symmetrically perturbed structure

Symmetrically perturbed photonic crystal waveguide can be constructed by inserting perturbative dielectric rods into photonic crystal waveguide structure with whose rods’ radius distributed according to a certain proportion. Slow light properties in this new structure are studied by using the plane wave expansion method (PWM). In this paper, schemes of adjusting radius of perturbative dielectric rods and adjusting the dielectric constant of perturbative dielectric rods are proposed to optimize slow light properties. The result shows that the scheme for adjusting radius of perturbative rods can realize larger average slow light bandwidth and efficiently control the NDBP value of the waveguide, but it contributes little to obtain smaller group velocity. The scheme for adjusting dielectric constant of perturbative rods can realize smaller group velocity, but can only obtain smaller slow light bandwidth and cannot efficiently enlarge NDBP value of waveguide. Both optimization schemes proposed in this paper realize group velocity that is two magnitudes smaller than the vacuum speed of light meanwhile maintaining large NDBP and low GVD region. Our results provide important theoretical basis for the potential application offered by symmetrically perturbed photonic crystal in future optical networks.     

Chern-Simons Theory,Matrix Integrals,and Perturbative Three-Manifold Invariants

The universal perturbative invariants of rational homology spheres can be extracted from the Chern-Simons partition function by combining perturbative and nonperturbative results. We spell out the general procedure to compute these invariants, and we work out in detail the case of Seifert spaces. By extending some previous results of Lawrence and Rozansky, the Chern-Simons partition function with arbitrary simply-laced group for these spaces is written in terms of matrix integrals. The analysis of the perturbative expansion amounts to the evaluation of averages in a Gaussian ensemble of random matrices. As a result, explicit expressions for the universal perturbative invariants of Seifert homology spheres up to order five are presented.     

Helmholtz equation solutions corresponding to multiple roots of the dispersion equation for a waveguide with impedance walls

The Helmholtz equation solutions corresponding to multiple roots of the dispersion equation are considered for a waveguide with impedance walls. It is shown that in this case the eigenfunctions are determined by expressions that cannot be obtained by the separation of variables. In addition to exponential or trigonometric factors, such functions involve factors linear in coordinates. Equations for calculating the multiple roots are obtained, and the relationships that determine the impedance values at which the multiple roots appear are presented. The Green’s function is constructed for the case of the appearance of multiple roots. A plane waveguide and a circular waveguide with axially symmetric modes are considered.     

Adjoint sensitivity analysis of radiative transfer equation: 2. Applications to retrievals of temperature in scattering atmospheres in thermal IR

An approach to formulation of inversion algorithms for thermal sounding in the case of scattering atmosphere based on the adjoint equation of radiative transfer (Ustinov, JQSRT 68 (2001) 195, referred to as Paper 1 in the main text) is applied to temperature retrievals in the scattering atmosphere for the nadir viewing geometry. Analytical expressions for the weighting functions involving the integration of the source function are derived. Temperature weighting functions for a simple model of the atmosphere with scattering are evaluated and convergence to the case of pure atmospheric absorption is demonstrated. The numerical experiments on temperature retrievals are carried out to demonstrate the validity of the expressions obtained.