TM-mode coupling in anisotropic optical waveguides caused by periodic variation optic-axis direction

The problem of mode coupling caused by a small periodic variation of the opticaxis direction in an anisotropic optical waveguide is reduced to a pair of coupled differential equations and an expression for the coupling coefficient is given. For a periodically perturbed section of the waveguide the coupled-mode equations are solved subject to suitable boundary conditions, and the coupling between the forward TM mode and the backward TM mode is analysed. A perturbed section of an anisotropic waveguide acts as a frequency selective reflection filter for TM modes only.     

Propagation properties of elastic waves in semi-infinite phononic crystals and related waveguides

The transmission and reflection coefficients of two-dimensional semi-infinite solid-solid phononic crystal systems and fluid-fluid phononic waveguide structures have been investigated. The numerical results show that the transmission spectra for longitudinally and transversally polarized incident waves are different, and the spectra of the transmission and reflection coefficients of the semi-infinite system agree well with the band structure. The numerical results show that when a guided wave incident, localized modes are excited, and different polarities have different coupling efficiencies with the incident guided wave. At the same time, far from the cutoff frequency, the guided wave couples out of semi-infinite waveguide highly efficiently.     

Whispering-gallery mode terahertz pulses

We report what is to our knowledge the first observation of a subpicosecond terahertz (THz) pulse propagating as a superposition of the whispering-gallery modes (WGMs) of a dielectric cylinder. The WGM THz pulses are coupled into and out of a 5-mm-diameter silicon cylinder via a 100-mum -thick, single-mode silicon slab waveguide. We observed two round-trip cylindrical cavity pulses from this coupling structure, which cover a continuous frequency range from 0.4 to 1.8 THz. The coupled-mode equations are used to analyze this system and give reasonably good agreement with the experiment in both the frequency and the time domains.     

Frequency Selective Characteristics of Dielectric Periodic Structures for Millimeter Wave Application

In this paper, the frequency selective reflection characteristics of dielectric periodic structures for the oblique incidence of a plane wave are analyzed by a method which combines the multimode network theory with the rigorous mode matching method. The variations of the total reflection characteristics with the geometric dimensions of the dielectric periodic structures are systematically investigated to develop useful guidelines for the design of the dielectric frequency selective surface. Moreover, the relationship between the related wave phenomenon and the dispersion characteristics of multilayer plane dielectric structure is explained with the theory of plane dielectric waveguide.     

Asymmetric first-order Bragg interactions in an active dielectric waveguide

The asymmetric first-order Bragg interactions in an active planar dielectric waveguide are investigated for the case of even TE modes. Either the index or the gain is assumed to have a sinusoidal variation in the propagation direction. By a singular perturbation procedure using multiple space scales, the coupled-mode equations governing the nature of the Bragg interactions are systematically deduced and the characteristics of this instability are examined. For the gain-modulated waveguide having an average loss, there are two threshold values for the modulation index of the gain, one for absolute instability and the other for traveling wave amplification, and these threshold values are deduced. Representative numerical results are presented to illustrate the characteristics of the Bragg interactions.     

A New Method of Solving Multimode Coupled Equations for Analysis of Uniform and Non-Uniform Fiber Bragg Gratings and Its Application to Acoustically Induced Superstructure Modulation

A new and simple mathematical formulation that is employed to analyze numerically coupled-mode equations modeling uniform and non-uniform gratings in optical fiber is investigated. This method would be straightforward and thus beneficial to solve multimode coupled equations in comparison with a previously used fundamental matrix method, and the Runge--Kutta algorithm. The new formulation proposed in this study is applied to calculate transmission and reflection spectra of core mode and higher-order cladding modes of acoustically induced superstructure modulation caused by microbending through fiber Bragg gratings (FBGs). Co-directional and contra-directional couplings based on acoustically induced modulation in FBGs have been discussed for a variety of induced coupling coefficients.     

Analysis of Electromagnetic Waves Scattering by a Finite Size Dielectric and Metal Cylinder in a Rectangular Waveguide

The paper presents a rigorous solution of the scattering problem by a circular dielectric and perfectly conducting cylinders of any radius and any height in the rectangular waveguide oriented perpendicularly to a wall. The method is based on the representation of fields in waveguide and dielectric medium by cylindrical eigenfunctions and application of boundary conditions on surfaces of the cylinder to evaluate the fields inside and outside the cylinder. The reflection and transmission coefficients are expressed through the fields. As an example the reflection and transmission coefficients versus frequency for various dielectric and metallic cylinders are computed. The comparison of numerical with experimental data is presented.     

Pure Reflection and Refraction of a Surface Polariton by a Matched Waveguide Structure

We study the fundamental problem of reflection and refraction of a surface polariton as it strikes the interface between two waveguide structures. By making the two waveguide structures match to each other, coupling of surface polaritons to radiating modes is cancelled, and the reflected and transmitted waves consist of only surface modes. The reflection and transmission coefficients are calculated, and negative refraction of surface polaritons is demonstrated. Finite-difference time-domain numerical simulations are also performed to verify the analytical results. As one of the applications of the matched waveguide structure, a square corner reflector for phase-retardation-free reflection of surface polaritons is proposed.     

A coupled-mode sound propagation model with complex effective depth

A coupled-mode sound propagation model with complex effective depth is presented,in order to involve the effect of branch line integral for acoustic field in a range-dependent waveguide.The equations of motion and continuity are used to obtain the coupled equations,which satisfy boundary conditions in the waveguide with varying topography and contain one coupling matrix.Meanwhile,the couplings between discrete and continuous spectrum are dealt with based on complex effective depth theory.Numerical simulations show that the accuracy of transmission loss is improved by the coupled mode model when eigenvalues of trapped modes are located near the branch point.The acoustic field in a non-horizontally stratified waveguide can be calculated efficiently and accurately by this model,and the energy corresponding to trapped modes,leaky modes and branch line integral can be considered adequately.     

TE-TE mode coupling at oblique incidence in a periodic dielectric waveguide

The characteristics of reflection of a TE mode into another TE mode in a planar dielectric waveguide with a sinusoidally modulated index are investigated for the general case in which the wavevectors are not aligned with the grating vector. A singular perturbation procedure is used to deduce the asymptotically exact coupled mode equations which govern the interaction. An analysis of the coupled-mode equations has shown the existence of the Brewster phenomenon at the angle of incidence θ_iB=45°. For angles of incidence sufficiently greater than the Brewster angle, the reflection coefficient can be considerably larger than that for the normal incidence. In the spectral response curves of the reflection coefficient, a higher maximum and a smaller base bandwidth are possible for the oblique incidence as compared to that for the normal incidence. The angular sensitivity of the reflection characteristics increases as the angle of incidence changes from the normal incidence to the grazing incidence.     

钛扩散铌酸锂矩形波导中的双折射耦合对传播常数的影响

 从亥姆霍兹方程出发，得到了各向异性光波导在弱导近似下的耦合模理论。耦合系数包括偏振耦合项和双折射耦合项。并用马卡提里近似下的模式作为零级近似。用一级微扰法计算了折射率渐变分布的钛扩散铌酸锂矩形波导的传播常数。在给定参数的情况下，得到双折射项引起的传播常数的改变约为主微扰项的3%，因此双折射耦合对钛扩散铌酸锂矩形波导的性能影响不可忽略，这对设计和分析与它相关的光波导器件具有指导意义。     

Coupled-mode analysis for linear fiber Bragg grating made of metamaterial

We derive the coupled-mode equations for a metamaterial fiber Bragg gratings (FBGs). The coupled-mode theory describing wave propagation in periodic structures such as FBG is generalized for studying the transmission and reflection of electromagnetic waves through a FBG containing metamaterial layers. This approach shows that the band gap becomes broader in comparison with a conventional FBG. It is observed that the central frequency of the band gap has a shift in regard of changing metamaterial thickness. We verify this investigation through attaining the transmission and reflection spectra of a conventional FBG while we are setting related parameters. Furthermore, this proposed structure can be applied as a tunable filter.     

多波导阵列耦合研究

提出了一种求解波导阵列耦合特性的方法.采用拉普拉斯变换,将同时考虑相邻和次相邻波导耦合作用的波导阵列耦合模方程组变为一个线性方程组,利用矩阵的LU分解法(将系数矩阵分解为单位下三角阵L与上三角阵U的乘积)求出该线性方程组的解.然后根据给定的初始条件进行拉普拉斯变换反演,求出耦合模方程组的解.采用该方法研究了五波导阵列,光从中间一个波导入射和从五个波导入射时的耦合特性,给出了每个波导中光功率变化规律曲线,并将所得结果与同样条件下仅考虑相邻波导耦合的结果做了比较.采用该方法可以求出任意数目波导组成的阵列,考虑任意波导之间耦合的耦合模方程组的解.     

Linear and nonlinear coupling properties of a novel multicore circular dielectric waveguide

In this work we investigate the linear and nonlinear coupling properties of a novel multicore circular dielectric waveguide. The proposed device consists of a circular central core and many circular sectoral cores at the periphery, while the whole structure can be considered as a nonlinear multicore composite optical coupler. Hybrid guided modes in a circular sectoral dielectric waveguide are derived using circular harmonic expansion for the electromagnetic fields and the Point Matching Method (PMM) for the application of boundary conditions. Several cases are investigated varying some of the parameters of the geometry and the optical frequency in order to produce dispersion diagrams. In advance, the electric and magnetic field distributions for the fundamental guided modes are produced, while linear and nonlinear coupling coefficients as well as the sectoral waveguide mode effective area are derived.     

Mode Coupling in a Partially Filled Plasma Waveguide With a Dielectric Liner

The stimulated Raman scattering of a perturbed TM mode in a dielectric loaded partially filled plasma waveguide is considered. The radiation is the result of the scattering of pump electromagnetic wave, which is an EH waveguide mode, off of a space-charge wave. A nonlinear wave equation for a three-wave interaction is used to investigate the coupling of the space-charge and waveguide modes. Dispersion relations for electromagnetic modes are solved numerically to study the frequency characteristics of the interaction of the EH waveguide modes with the space-charge modes. Formulas for the growth rates of the backscattered wave near the electron cyclotron frequency are derived, and the effect of a dielectric liner on the growth rates is investigated. Numerical studies show that the presence of the dielectric liner has an effect on the phase-matching condition and leads to rather larger growth rates close to electron cyclotron resonance.      

Optimized overmoded TE01-to-TM11 mode converters for high-power millimeter wave applications at 70 and 140 GHz

Mode coupling in bent, oversized, smooth-wall circular waveguides was studied by means of numerical integration of coupled-mode differential equations in order to optimize high-power TE01-to-TM11 mode transducers at 70 GHz and 140 GHz. Such mode transformers are used in the mode conversion sequence TEOn to TE01 to TM11 to HE11 for generating the almost perfectly linearly polarized Gaussian-like HE11 mode from circular electric TEOn gyrotron modes. This quasi-optical HE11 hybrid mode is in many respects ideal for electron cyclotron resonance heating (ECRH) of magnetically confined plasmas in thermonuclear fusion research and for other technical applications. Curvature and ellipticity coupling as well as ohmic attenuation of 6 coupled modes (TE01, TM11, TE11, TE12, TE21, TM21) are included in the coupling matrices. Integral expressions were used for deriving the coupling coefficients for arbitrary modes in bent, smooth-wall waveguide. Lowest level of unwanted spurious modes together with highest transmission efficiency (shortest arc length) is achieved with sinusoidal curvature distribution instaed of constant curvature. The calculated conversion efficiencies of 98.0% at 70 GHz and 95.2% at 140 GHz (interior waveguide diameter D=27.8 mm for 200 kW transmission lines) are in excellent agreement with the measured values of (97.6±0.4)% and (95±1)%, respectively.     

复等效深度耦合简正波模型

为了考虑海底地形随距离变化的非水平分层介质中割线积分对声场的贡献,提出了复等效深度耦合简正波模型。该耦合简正波模型由介质运动方程和连续性方程推导得到了耦合微分方程组,此方程组满足海底地形随距离变化情况下的边界条件且仅包含一个耦合矩阵,并通过引入复等效深度理论处理连续谱和离散谱之间的相互耦合。仿真计算表明,复等效深度耦合简正波模型提高了波导简正波本征值位于割线枝点附近情况下声传播损失的计算精度,充分考虑了波导简正波、非波导简正波和割线积分对声场的贡献,可快速而准确地计算非水平分层介质中的声场。      

Multi-wavelength filtering in side-coupled cascaded-cavities systems

We theoretically investigate an optical system, which consists of a waveguide side-coupled to a cascade of cavities, the filtering properties by the time domain coupled-mode theory. In such a system, the filter operating bandwidth and the width of transmission peaks are completely determined by the mutual coupling coefficients between the cavities. The characteristics are numerically demonstrated in photonic crystals by the finite-difference time-domain method.     

A computation of the reflection and transmission coefficients for dielectric coated waveguides

A previously developed variational technique for finding the approximate solution to the electromagnetic field inside waveguides of varying shapes and containing non-uniform dielectric and magnetic materials is applied to the specific case of an axisymmetric waveguide containing three layers of different dielectric materials. The magnetic permeability is taken equal to unity. The method enables the problem to be reduced to a two point boundary value problem for a pair of second order, linear, ordinary differential equations. The values of the reflection and transmission coefficients obtained by this method are in good agreement with those derived from solving the partial differential equations for the field.