Full-wave analysis of dielectric frequency-selective surfaces using a vectorial modal method

A novel vectorial modal method is presented for studying guidance and scattering of frequency-selective structures based on lossy all-dielectric multilayered waveguide gratings for both TE and TM polarizations. The wave equation for the transverse magnetic field is written in terms of a linear differential operator satisfying an eigenvalue equation. The definition of an auxiliary problem whose eigenvectors satisfy an orthogonality relationship allows for a matrix representation of the eigenvalue equation. Our proposed technique has been applied to the study of lossy all-dielectric periodic guiding media with periodicity in one dimension. This method yields the propagation constants and field distributions in such media. The reflection and transmission coefficients of a single layer under a plane-wave excitation can be obtained by imposing the boundary conditions. Study of the scattering parameters of the whole multilayered structure is accomplished by the cascade connection of components as characterized by their scattering parameters. Results obtained with this method for the propagation characteristics of a one-dimensional periodic dielectric medium are compared with those presented by other authors, and results for the scattering of several dielectric frequency-selective surfaces (DFSS) are compared with both theoretical and experimental results presented in the literature, finding a very good agreement. A symmetrical band-stop filter with a single waveguide grating is also demonstrated theoretically.     

The scattering and absorption characteristics of material-coatedperiodic gratings under oblique incidence

A boundary integral formulation is presented for calculating the scattering from material-coated periodic gratings under oblique incidence. Periodic boundary conditions and expansion of the fields in terms of Floquet harmonics allow the boundary integral formulation to treat just a single period of the infinite grating. Numerical results for an etched conducting grating designed for use at infrared wavelengths are presented and shown to be in good agreement with a series of measurements. Results for a number of dielectric gratings for both normal and oblique incidence also agree well with other published data. The conductor-backed coated grating is studied, and it is shown that the groove profile can be used to significantly alter the absorbing characteristics for lossy material coatings     

Analysis of the electromagnetic scattering by thick gratings usinga combined FEM/MM solution

The problem of diffraction by a thick, conducting grating situated in an inhomogeneous dielectric slab is investigated using the generalized network formulation. This formulation combines the method of moments and the finite-element method, permitting the treatment of periodic elements of arbitrary cross section and inhomogeneous profiles. Solutions are presented for both transverse electric (TE) and transverse magnetic (TM) polarizations. Transmission gratings composed of rectangular conductors filled with dielectric materials of arbitrary profiles are studied     

Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings

We demonstrate a new inverse scattering algorithm for reconstructing the structure of highly reflecting fiber Bragg gratings. The method, called integral layer-peeling (ILP), is based on solving the Gel'fand-Levitan-Marchenko (GLM) integral equation in a layer-peeling procedure. Unlike in previously published layer-peeling algorithms, the structure of each layer in the ILP algorithm can have a nonuniform profile. Moreover, errors due to the limited bandwidth used to sample the reflection coefficient do not rapidly accumulate along the grating. Therefore, the error in the new algorithm is smaller than in previous layer peeling algorithms. The ILP algorithm is compared to two discrete layer-peeling algorithms and to an iterative solution to the GLM equation. The comparison shows that the ILP algorithm enables one to solve numerically difficult inverse scattering problems, where previous algorithms failed to give an accurate result. The complexity of the ILP algorithm is of the same order as in previous layer peeling algorithms. When a small error is acceptable, the complexity of the ILP algorithm can be significantly reduced below the complexity of previously published layer-peeling algorithms.     

Improved coupled-mode formulation based on composite modes forparallel grating-assisted co-directional couplers

An improved coupled-mode formulation based on the ideal modes of the coupled waveguides (ideal composite modes) is presented. In comparison with the formulation based on the ideal modes of the individual waveguides (ideal waveguide modes), the formulation in terms of composite modes is more rigorous and yields a more accurate grating period and coupling lengths. In addition, the radiation loss due to input and output junctions can in the composite-mode formulation. A new to the coupled-mode equations is derived in which all the spatial harmonics generated by the periodic grating are taken into account. The power exchange between the waveguides is examined by considering the input and the output conditions. The phase-matching conditions and the coupling lengths are calculated and compared with the analysis in terms of the waveguide modes. The grating period predicted by the waveguide-mode formulation agrees very well with that by the composite-mode formulation; however, dramatically different coupling lengths are predicted by the two formulations     

Waveguide grating filters for dispersion compensation and pulsecompression

Dispersion compensation and pulse compression are theoretically demonstrated using aperiodic waveguide gratings. The gratings are designed to have both a flat amplitude and a quadratic phase response over the pulse bandwidth. This results in nearly transform-limited compressed pulses. The appropriate waveguide grating parameters are obtained by applying the Gel'fand-Levitan-Marchenko inverse scattering method to the coupled mode equations which describe propagation. The technique is illustrated by designing an aperiodic grating which compresses a 60-ps pulse by a factor of three. Limitations and possible extensions of the general method are discussed     

A Lossy Dielectric-Ring Loaded Waveguide With Suppressed Periodicity for Gyro-TWTs Applications

A dielectric-loaded (DL) waveguide is an attractive possibility for interaction circuits with high-power sources in the millimeter-wave regime down to tenths of millimeters, particularly for gyrotron-traveling-wave-tube amplifiers (gyro-TWTs). We present results on a systematic investigation of the influence of the periodically loaded lossy dielectric on the propagation characteristics of the operating modes, which reveals that a complex mode in the periodic system can be mapped to a corresponding mode in an empty waveguide or a uniform DL waveguide. Dielectric losses not only induce modal transitions between different modes with similar field structures and close phase velocities in the uniform system but also unify the discrete mode spectrum into a continuous spectrum in the periodic system. Since the lossy dielectric functions as a power sink, the higher order Bloch harmonic components arising from the structural periodicity are suppressed, and the mode spectrum of the lossy periodic system degenerates into that of an empty waveguide. This alleviates the potential danger of spurious oscillations induced by the higher order harmonic components, making the periodic lossy DL waveguide promising in a high-power millimeter-wave gyro-TWT.     

Improved coupled mode analysis of corrugated waveguides and lasers

Corrugated waveguides and lasers in resonant and non-resonant situations are analyzed by an improved coupled mode theory based on a set of the coupled mode equations for guided modes and radiation continuum. The distributed feedback (DFB) coefficient and the radiation loss coefficient are given in closed forms. The formulation can be applicable to arbitrarily shaped gratings and multilayer waveguide structures. The accuracy of the theory is examined by comparing it with Tamir's exact calculation for a nonresonant situation and also with Streifer's one for a DFB structure. Reasonable accuracy is obtained by the proper choice of the unperturbed waveguide parameter. The dependence of the two coefficients on the grating depth, the grating period, the guide layer thickness, and the refractive index difference between core and cladding layers is obtained for all Bragg orders up to the fourth, and for four typical grating shapes, namely, for rectangular, sinusoidal, symmetric triangular, and sawtooth gratings. Both the threshold gain of DFB lasers utilizing higher order Bragg reflection and the output coupling efficiency of grating beam couplers are also calculated for these parameters. A new multilayer structure for controlling the radiation loss is proposed and analyzed. This structure is suitable for the suppression of the radiation loss in DBR reflectors as well as for the improvement of the output coupling efficiency in grating beam couplers.     

从亚波长光栅到超构光栅:原理、设计及应用

随着纳米光子学的发展,光学结构如光学微腔、波导结构、光子晶体、亚波长光栅、超构表面等能够在微纳尺度实现对光的传输与调控,推动了光学集成化的发展。亚波长光栅由于其结构简单、成本低廉等特点得到了科学家们广泛的研究,应用在各种光学器件,逐渐形成了光栅分析模型的成熟理论体系。结合周期性结构耦合行为及超构表面中超构原子的散射调制特性,从亚波长光栅衍生出的超构光栅能够利用周期性布拉格散射提高调控光束的效率,从而避免了超构表面相位离散化带来的效率降低和能量损失。科学家们研究并设计了超构光栅,更多的物理现象及应用被探究和挖掘。文中对亚波长光栅以及超构光栅的基本理论、设计和应用进行了概述。从基本原理出发,论述了亚波长光栅和超构光栅的特性,综述了二者的理论设计及单元设计方法,并介绍了在生物传感、滤光片光谱调控和吸收薄膜等方面的应用。最后,展望了未来的发展方向。     

Radiation of Millimeter Waves from a Leaky Dielectric Waveguide with a Light-Induced Grating Layer

A theoretical analysis is presented for the radiation characteristics of millimeter waves in a periodic dielectric waveguide having a light-induced grating layer. The waveguide is assumed to be composed of an insulator (sapphire) slab whose one surface is coated with a high-resistivity semiconductor (silicon) film. A boundary-integral-equation formulation is employed to obtain characteristic solutions of the waveguide. Numerical calculations are made at 94 GHz for both TM and TE polarizations. Estimations of the illumination power required to produce the grating are given. The waveguide presented in this paper, in conjunction with a high-power semiconductor diode laser array as a light source, may be developed to operate as an electronically beam-steerable leaky-wave antenna at millimeter-wave frequencies.     

Scattering from a double-strip grating: rigorous equivalent networkformulation

An exact solution for the problem of transverse electric (TE) or transverse magnetic (TM) plane-wave scattering from a periodic, planar double-strip grating at a dielectric interface is described. The metal-strip grating is assumed to be perfectly conductive and infinite in length, with two different strips within a unit-cell. The formulation is based on a multimode equivalent network representation, and uses a rigorous solution for the relevant integral equation that extends the novel solution developed previously for the single-strip grating. Expressions for the elements of the multimode coupling matrices are given, together with a comparison of results for power transmitted through the grating, obtained by using the networks developed with the present method and a simple point-matching solution. Results are presented to illustrate the differences between single and double-strip gratings     

A transfer matrix approach based on local normal modes for coupledwaveguides with periodic perturbations

A simple transfer matrix method is used to analyze power coupling and scattering in optical waveguide structures with periodic index perturbations. The transfer matrix is determined by a mode-matching technique for the local normal modes of the structures. This approach accounts for the change in the field patterns along the waveguide axis and is more rigorous than coupled-mode theory based on ideal modes. The distinct advantages of the method are that (1) it can be applied to structures with relatively strong index perturbations caused by large grating height and/or large index difference; (2) the TM modes whose transverse electric field is perpendicular to the index interface can be properly treated; and (3) the radiation loss due to scattering at the index discontinuities along the waveguide axis can be estimated. Analytical expressions for the power coupling in a grating-assisted codirectional coupler are derived, and numerical results are shown for some typical structures     

钛扩散LiNbO_3晶体光波导长周期光栅

设计了一种钛扩散铌酸锂(LiNbO_3)晶体光波导结构,并在该基础上制作了长周期光栅.使用两步钛扩散方法在Z切LiNbO_3基片上制造了波导,它包括一个单模芯层和一个平面包层,之后用光刻胶光栅置于波导表面.实验证明用这种结构设计长周期波导光栅是可行的.对光波导制造工艺和波导结构的深入研究,为制作高速电光调制型光栅提供技术基础.     

Variational propagation constant expressions for lossyinhomogeneous anisotropic waveguides

Based on reciprocal relationships for the adjoint operator, we derive a variational formulation for the propagation constant satisfying the divergence-free condition in lossy inhomogeneous anisotropic waveguides whose media tensors have all nine components. In addition, with some advantages over previous representations, two variational formulations have been derived for waveguides with the transverse part of the media tensors decoupled from the longitudinal part. However, to obtain a variational formulation for a general lossy reciprocal problem the waveguide must be bi-directional. Each of the variational expressions results in a standard generalized eigenvalue equation with the propagation constant appearing explicitly as the desired eigenvalue. The stationarity of the formulations is shown. It is also shown that for a general lossy nonreciprocal problem the variational functional exists only if the original and adjoint waveguide are mutually bi-directional     

Lithium–Niobate Channel Waveguide for the Realization of Long-Period Gratings

We propose a special lithium-niobate (LiNbO₃) single-mode waveguide for the realization of long-period gratings, which consists of a channel core embedded in a thin slab cladding. We fabricated the waveguide on a z-cut LiNbO₃ substrate with a two-step proton-exchange process and demonstrated its suitability for grating application with a number of removable photoresist long-period gratings deposited on the waveguide surface. The waveguide fabrication process and the LiNbO₃ waveguide structure could be further explored for the development of electrooptic gratings for high-speed applications.     

A Modified Residue-Calculus Technique for Solving a Class of Boundary Value Problems-Part II: Waveguide Phased Arrays, Modulated Surfaces, and Diffraction Gratings

The modified residue-calculus technique (MRCT) described in a companion paper may be combined with scattering matrix, multiple-reflection techniques to provide solutions in scattering matrix form to thick-wall waveguide phased array, modulated surface, and strip grating geometries. Each of these geometries may be regarded as a periodic array of thin plates modified by dielectric fillings, waveguide steps, and terminations. Solutions to the modified geometries are found by combining the exact solution to the thin-wall array problem with approximate solutions to certain waveguide discontinuity problems found by the MRCT. In particular, a value of the dominant mode reflection coefficient versus scan angle for the thick-wall array may be found accurate to two or three significant figures without need for matrix inversion. In general, reduction of matrix size by a factor of 5 or more over conventional methods with equivalent accuracy may be realized.     

Theory of line-source radiation from a metal-strip gratingdielectric-slab structure

This paper describes the fundamental theory of line source radiation from a source on a dielectric slab backed by a metal-strip grating. A continuous phased-array (CPA) method is applied to treat the analytic and numerical problems of antenna interaction with periodic structures. Both TE and TM mode cases for a one-dimensional strip grating are investigated. It is found that the strip grating on the dielectric surface may result in surface wave elimination and may also be used to support leaky waves. It is shown that high-efficiency and high-gain antennas on a dielectric substrate are possible with such metal-strip gratings     

Scattering from stacked gratings and dielectrics for various anglesof wave incidence

The theory of scattering matrices and microwave network analysis is used to solve the problem of scattering from cascaded infinite periodic gratings. The total reflection and transmission coefficients are calculated as functions of angle of incidence, wire spacing for each grating separation, wire thickness, and number of gratings that comprise the cascaded structure. The problem of stacking dielectric slabs with periodic gratings is also formulated and solved. In all cases, the secant corrector spectral iteration approach is used as a numerical method for calculating the desired currents and fields. Finally, the calculated values of the reflection and transmission coefficients are presented and compared with reported experimental and theoretical data     

Characteristics of a hollow-core distributed feedback CO2laser

Using perturbation theory and a plane wave analysis, the scattering amplitudes and coupling coefficients for a planar, hollow-core, double grating distributed feedback (DFB) waveguide laser are derived. Waveguide reflectivity has been compared for a single and double grating waveguide configuration. For a waveguide dimension of 100 μm over a 10 cm length, reflectivity is enhanced from 75 percent for a single grating to 98 percent using a double grating configuration. Included in this analysis is the effect of phase relationship between the two gratings. Using this analysis a means has been devised whereby reflectivity of the DFB waveguide may be optimized during operation of the laser. With the double grating configuration, coupling is enhanced such that a greater plate separation is possible in nearly all cases. Use of a double grating allows the plate separation of the waveguide to be increased from 80 to 100 μm, reducing total waveguide loss from 15.9 to 8.1 dB/m. These results have led to a method of solving heretofore prohibitive characteristics of single grating hollow-core DFB waveguides. Formal relationships for the waveguide parameters where a double grating configuration is used have been presented for designing hollow-core DFB waveguide lasers operating at 10.6 μm.     

一种用于合成光纤布拉格光栅的全时域算法

基于离散的光纤布拉格光栅(FBG)模型,推导了时域内的传输矩阵和散射矩阵;根据因果分析,提出了一种全时域的FBG合成算法,它能直接在时域内计算已知FBG的冲激响应.这种算法在迭代求解的过程中仅使用了简单的变换和移位操作,并考虑了光在FBG中多个反射点间的来回反射,能适用于高反射率FBG的重构.FBG合成的数值模拟,证实了这种全时域算法的优越性.