Sound propagation in inhomogeneous waveguides with sound-speed profiles using the multimodal admittance method

The multimodal admittance method and its improvement are presented to deal with various aspects in underwater acoustics,mostly for the sound propagation in inhomogeneous waveguides with sound-speed profiles,arbitrary-shaped liquid-like scatterers,and range-dependent environments.In all cases,the propagation problem governed by the Helmholtz equation is transformed into initial value problems of two coupled first-order evolution equations with respect to the modal components of field quantities(sound pressure and its derivative),by projecting the Helmholtz equation on a constructed orthogonal and complete local basis.The admittance matrix,which is the modal representation of Direchlet-to-Neumann operator,is introduced to compute the first-order evolution equations with no numerical instability caused by evanescent modes.The fourth-order Magnus scheme is used for the numerical integration of differential equations in the numerical implementation.The numerical experiments of sound field in underwater inhomogeneous waveguides generated by point sources are performed.Besides,the numerical results computed by simulation software COMSOL Multiphysics are given to validate the correction of the multimodal admittance method.It is shown that the multimodal admittance method is an efficient and stable numerical method to solve the wave propagation problem in inhomogeneous underwater waveguides with sound-speed profiles,liquid-like scatterers,and range-dependent environments.The extension of the method to more complicated waveguides such as horizontally stratified waveguides is available.

Factorization method for inverse obstacle scattering problem in three-dimensional planar acoustic waveguides

In this paper, we consider the inverse scattering problem of reconstructing a bounded obstacle in a three-dimensional planar waveguide from the scattered near-field data measured on a finite cylindrical surface containing the obstacle and corresponding to infinitely many incident point sources also placed on the measurement surface. The obstacle is allowed to be an impenetrable scatterer or a penetrable scatterer. We establish the validity of the factorization method with the nearfield data to characterize the obstacle in the planar waveguide by constructing an outgoing-to-incoming operator which is an integral operator defined on the measurement surface with the kernel given in terms of an infinite series.

ANALYSIS OF WAVEGUIDE PROBLEMS USING A RELAXED ITERATIVE DOMAIN DECOMPOSITION METHOD COMBINED WITH MULTIFRONTAL ALGORITHM

In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide problems.The relaxed algorithm is introduced to improve the iterative convergence. And the matrix equations are solved using the multifrontal algorithm. The resulting CPU time is greatly reduced.Finally, a number of numerical examples are given to illustrate its accuracy and efficiency.

A MATRIX METHOD FOR SOLVING PLANAR DIELECTRIC OPTICAL WAVEGUIDES

A matrix method used in multilayer stack of dielectric films is applied-to planar dielectric optical waveguides. A simple and applicable method for obtaining characteristic equation is presented.

VARIATIONAL METHOD TO ANALYZE THE EQUIVALENT NETWORK OF A RECTANGULAR DIELECTRIC POST IN A RECTANGULAR WAVEGUIDE

The equivalent filter modeling of a rectangular dielectric post in a rectangular waveguide is obtained through the variational expression of input impedance. The reflection coefficient expressed in components of network is in good agreement with the results given by K. Siakavara, et al. (1991), The method can be applied to design filter.

SOLUTION OF ARBITRARY CROSS-SECTION WAVEGUIDE USING METHOD OF EIGEN WEIGHTED BOUNDARY INTEGRAL EQUATION

Based on the second kind of Green’s identity,a boundary integral equation forarbitrary cross-section waveguide is transformed to a system of linear homogeneous algebraicequations by means of expansion of boundary bases and by using the eigenfunctions of a fictitiousregular boundary as weighting functions,which corresponds to less algebraic equations than BEMand simpler coefficients than the modified BEM.The numerical results for some typical metallicwaveguides are given by using the method of eigen-weighted boundary integral equation,and theyare accurate enough with fast convergence.

Revised RPS Method for Complex Solution of Multimode Slab Waveguides with Metal layers

The RPS method,which integrates the real numerical solution, the perturbation solution and the shooting solution reasonably,can obtain the complex solution of a slab waveguide with small gain/loss regions without searching the root in the entire complex plan.A revision to the RPS method is presented so that it can deal with the waveguide including large gain/loss regions.The application indicated that the simulation results are precise.

Separation Method in the Problem of a Beam-Plasma Interaction in a Cylindrical Warm Plasma Waveguide

The stabilization effect of a strong HF electric field on beam-plasma instability in a cylindrical warm plasma waveguide is discussed. A mathematical technique “separation method” applied to the two-fluid plasma model to separate the equations, which describe the system, into two parts, temporal and space parts. Plasma electrons are considered to have a thermal velocity. It is shown that a HF electric field has no essential influence on dispersion characteristics of unstable surface waves excited in a warm plasma waveguide by a low-density electron beam. The region of instability only slightly narrowing and the growth rate decreases by a small parameter and this result has been reduced compared to cold plasma. Also, it is found that the plasma electrons have not affected the solution of the space part of the problem.

Wavelet Beam Propagation Method for Study the Integrated Optical Waveguide

A new numerical technique based on the wavelet derivative operator is presented as an alternative to BPM to study the integrated optical waveguide. The wavelet derivative operator is used instead of FFT/IFFT or finite difference to calculate the derivatives of the transverse variable in the Helmholtz equation. Results of numerically simulating the injected field at z =0 are exhibited with Gaussian distribution in transverse direction propagating through the two dimensional waveguides (with linear and/or nonlinear refractive index) , which are similar to those in the related publications. Consequently it is efficient and needs not absorbing boundary by introducing the interpolation operator during calculating the wavelet derivative operator. The iterative process needs fewer steps to be stable. Also, when the light wave meets the changes of mediums, the wavelet derivative operator has the adaptive property to adjust those changes at the boundaries.

Numerical Analysis of 3mm Ferrite Dielectric Waveguide Through Galerkin’s Method

With the development of long range missile early warning radar,MMW phased array antenna is strongly needed. The phase shifter (PS) with high power capability and low insertion loss is a key technology in this kind of radar. Ferrite dielectric waveguide is introduced in this paper to manufacture PS,the cross section can be enlarged to 4 times of that of the conventional PS,which facilitates the engineering realization with reduced insertion loss. A novel vector base function of Galerkin method is proposed in calculating the eigenvalue of ferrite dielectric waveguide. The field distribution of main mode,power density and efficiency of 94 GHz difference phase shifter are also given.

Analysis of circular-to-circular groove waveguide junction

Mode matching method is used to analyze the scattering characteristics of thecircular-to-circular groove waveguide junction. Matching the electric fields and magnetic fields atthe boundary of the junction, and multiplying the mode functions of the circular waveguide andcircular groove waveguide on both sides of the boundary equation, the scattering matrix equation isobtained, the scattering coefficients can be obtained from the equation. Then the scatteringcharacteristics of the iris with circular window in circular groove waveguide are analyzed. At lastthe convergent problem is discussed; when choosing a suitable mode group, convergent numericalresults are obtained, and the frequency response of the iris' scattering coefficients is also given.

Modelling of graded index waveguide fabricated by ion exchange on Er^(3+) doped glass

A general numerical tool, based on thermal diffusion equation and full-vectorial eigen-mode equation, has been presented for the systematic analysis of graded index channel waveguide fabricated by ion exchange on Er^3＋ doped glass. Finite difference method with full-vectorial formulation （FV-FDM） is applied to solving the full-vectorial modes of graded index channel waveguide for the first time. The coupled difference equations based on magnetic fields in FV-FDM are derived from the Taylor series expansion and accurate formulation of boundary conditions. Hybrid nature of vectorial guided modes for both pump （980 nm） and signal light （1550 nm） are demonstrated by the simulation. Results show that the fabrication parameters of ion exchange, such as channel opening width and time ratio of second step to first step in ion exchange, have large influence on the properties of waveguide. By optimizing the fabrication parameters, maintenance of monomode for signal light and improvement of the gain dynamics can be achieved in Er^3＋ doped waveguide amplifier （EDWA） fabricated by ion exchange technique. This theoretical model is significant for the design and fabrication of EDWA with ion exchange technique. Furthermore, a single polarization EDWA, which operates at wavelength from 1528 nm to 1541 nm for HE polarization, is numerically designed.

Scattering loss in optical waveguide with trapezoidal cross section

To get the scattering loss of the trapezoidal core waveguide,a new analysis model is presented based on the perturbation equivalent method and modified effective-index method.Firstly,the trapezoidal core waveguide is successfully equivalent to the rectangular one with both restricting the same optical field energy by adopting the perturbation method,Then,the equivalent rectangular core waveguide is decomposed into two slab waveguides by employing the modified effective-index method,The trapezoidal core waveguide scattering theory model is established based on the slab waveguide scattering theory.With the sidewalls surface roughness in the range from 0 to 100 nm in the single model trapezodial core waveguide,optical simulation shows excellent agreement with the results from the scattering loss model presented.The relationship between the dimension and side-wall roughness with the scattering loss can be determined in the trapezoidal core waveguide by the scattering loss model.

Multiple Fano resonances in metal–insulator–metal waveguide with umbrella resonator coupled with metal baffle for refractive index sensing

A single baffle metal–insulator–metal(MIM)waveguide coupled with a semi-circular cavity and a cross-shaped cavity is proposed based on the multiple Fano resonance characteristics of surface plasmon polaritons(SPPs)subwavelength structure.The isolated state formed by two resonators interferes with the wider continuous state mode formed by the metal baffle,forming Fano resonance that can independently be tuned into five different modes.The formation mechanism of Fano resonance is analyzed based on the multimode interference coupled mode theory(MICMT).The finite element method(FEM)and MICMT are used to simulate the transmission spectra of this structure and analyze the influence of structural parameters on the refractive index sensing characteristics.And the transmission responses calculated by the FEM simulation are consistent with the MICMT theoretical results very well.The results show that the figure of merit(FOM)can reach 193 and the ultra-high sensitivity is 1600 nm/RIU after the structure parameters have been optimized,and can provide theoretical basis for designing the high sensitive refractive index sensors based on SPPs waveguide for high-density photonic integration with excellent performance in the near future.

Theoretical investigation of hierarchical sub-wavelength photonic structures fabricated using high-order waveguide-mode interference lithograph

This paper presents the theoretical investigation of hierarchical sub-wavelength photonic structures with various periods and numbers of layers, which were fabricated using a high-order waveguide-mode interference field. A 442-nm laser was used to excite high-order waveguide modes in an asymmetric metal-cladding dielectric waveguide structure. The dispersion curve of the waveguide modes was theoretically analyzed, and the distribution of the interference field of high-order waveguide modes was numerically simulated using the finite-element method. The various dependences of the characteristics of hierarchical sub-wavelength photonic structures on the thickness and refractive index of the photoresist and the waveguide mode were investigated in detail. These hierarchical sub-wavelength photonic structures have various periods and numbers of layers and can be fabricated by a simple and low-cost method.

STUDY OF GROOVE NONRADIATIVE DIELECTRIC WAVEGUIDE AND LEAKYWAVE ANTENNA

A new structure of dielectric waveguide for millimeter waveband namedgroove nonradiative dielectric(GNRD)waveguide and a leakywave antenna based on thisstructure are developed in this paper.The GNRD structure overcomes the difficulty of as-sembling precisely the dielectric strip in the nonradiative dielectric(NRD)structure.Thedispersion characteristics of the GNRD waveguide,and the propagation and radiationcharacteristics of the GNRD leakywave antcnna have been analysed by the use of thetransverse rcsonance mcthod.The theoretical results are in good agreement with the exper-imental data.

AN INVESTIGATION OF BANDWIDTH IN DIELECTRIC SLAB LOADED RECTANGULAR WAVEGUIDE

Several technical problems of numerical method in TLM procedures arediscussed.The bandwidth of single mode in four kinds of dielectric slab loaded rect-angular waveguides is investigated,and the optimum bandwidth which is related tothe dimensions and dielectric constants is obtained.These results are useful to the de-sign of dielectric slab loaded rectangular waveguide.

Variational analysis of the disc-loaded waveguide slow-wave structures

The variational method is applied to calculate the dispersion characteristics of disc-loaded waveguide slow-wave structures. The parameters describing the waveguide discontinuities in disc-loaded waveguide are calculated by the variational method. Then the dispersion characteristics of slow-wave structures are obtained using lossless microwave quadrupole theory. Good agreement was observed between results of the Variational method and those of field matching method and high frequency structure simulator. In the case of broad band, results of the variational method are better than those of field matching method.

ANALYSIS OF CLOSED DIELECTRIC WAVEGUIDES——MULTIMODE NETWORK APPPOACH

The dispersion characteristics of a class of closed dielectric waveguides are investigated by themethod which combines the building-block approach of multimode network theory with the rigorous modematching procedure.Several numerical examples for difrerent guiding structures have been given by the ap-proach.The same structures are also analyzed with the finite element method and the EDC method forcomparison.The calculations show that the present approach yields as highly accurate results as the finite ele-ment method while almost retaining the simplicity of the EDC method,and justify the utility of the presentmethod.