Transmission Characteristics with Second Order Approximations of Elliptic-Groove Waveguide

In this paper, the transmission characteristics for the dominant mode H _{e 11} ⁽¹⁾ in the vertical-flat elliptic-groove guide are analysed by using the mode-matching method and Mathieu function. The characteristic equations with the 1st and 2nd order approximations and their solutions for the dominant mode of the elliptic-groove guide are also obtained by a great quantity of theoretical analyses and numerical computations. The cut-off, dispersion and attenuation characteristics are in good agreement with those in the relevant references under limiting conditions and are discussed in detail. The obtained results are of important significance for theoretical researches and actual applications of elliptic-groove guides for millimeter and submillimeter waves.     

Impedance Characteristics of Closed Elliptic-Groove Waveguide for Millimeter Waves

A characteristic equation and impedance characteristic for the dominant mode of closed elliptic-groove guide have been analyzed and discussed by using the mode-matching method. The reference size of the closed elliptic-groove guide for the good impedance matching with rectangular guide in actual application is given. The obtained conclusions are of important significance in theoretical studies and actual applications of closed elliptic-groove guide for millimeter waves.     

Transmission characteristics of several kinds of closed groove waveguides for millimeter waves

An advantage of closed groove guide over open groove guide is attended. In this paper, the several kinds of closed groove guides including the trapezoidal-, elliptic- and parabolic-groove guides as new types of millimeter wave transmission lines are presented. Their dispersion and cut-off characteristics of the dominant mode are analysed and compared with ones of the closed V-and circular- groove guides by using the equivalent network method. The obtained results have important meaning in theoretical studies and actual applications of groove waveguides.     

Nonlinear Study on FEM Amplifier with a Novel Elliptic-Groove Guide

FEM amplifier with a novel elliptic-groove guide is proposed and three-dimensional nonlinear theory for the elliptic-groove guide FEM amplifier is developed. A set of coupled nonlinear differential equations is derived and the characteristics of this FEM amplifier are numerically analyzed in detail including the evolution of power, efficiency and bandwidth. The effects on saturation efficiency due to electron momentum spread and wiggler taper are also studied.     

Attenuation of cutoff modes and leaky modes of dielectric slab structures

A simple formula is developed for the attenuation constant of higher order cutoff modes of a dielectric slab guide and of the modes of leaky guides. The formula is based on a perturbation analysis that reduces the problem to that of the transmission characteristic of a Fabry-Perot resonator. Under certain approximations, the formula for leaky guides reduces to that of Hall and Yeh, but the formula has a wider range of applicability.     

Theoretical analysis for dispersion characteristics of elliptic-groove waveguide with mode-matching method

In this paper, two kinds of elliptic-groove waveguides are presented. One of them has never been studied before. With the help of Mathieu function and mode-matching method, the field components and characteristic equation of the elliptic-groove waveguides are obtained for the first time. Then their dispersion characteristics for the dominant mode i.e. the mode TE _e11 ¹ are also studied. The gotten conclusions have very important values in theoretical study and actual application for the two kinds of the elliptic-groove waveguides.     

Practical microwave circuits for groove waveguides

Groove guides have been known for many years. No practical microwave circuits have yet been described although these types of transmission lines could be used in many cases. This paper discusses the physical realizability of some wide band designs such as matched load, directional coupler, hybrid coupler, bend and phase shifter. Both closed and open groove guides have been investigated. Optical type components seem to be inappropriate for groove guide transmission. The best way to design components for these guides is to adapt those of standard rectangular guides, which perturb only the Rf fields in the vicinity of the narrow walls and to optimize the dimensions of the groove structure as a function of the losses and the symmetry of the induced spurious modes.     

On the Theory of Randomly Misaligned Beam Waveguides

A straightforward method for the determination of the expected attenuation in misaligned beam waveguides is presented. It applies to confocal guides and assumes that the misalignment consists of random displacements of the lenses in directions perpendicular to the beam axis. Reiterative fields, as they are present in perfectly aligned beam waveguides, do not exist in misaligned guides. However, it can be shown that there are beams whose expected field distribution is repeated from lens to lens. These "statistical modes" are determined by the eigenfunctions of a homogeneous integral equation of the second kind. The corresponding eigenvalues determine the expected attenuation per iteration. The absolute squares of the eigenvalues yield an upper bound for the expected power loss per iteration. The integral equation is solved for small mean square displacements of the lenses by a perturbation method. For infiitely extended lenses, the equation can be solved in closed form. In both cases the expected attenuation of the lower-order statistical modes has been calculated; the results are shown as function of the mean square displacement of the lenses.     

Characteristics of double-groove guide for 100 GHz operation

There are two types of possible transmission modes in double-groove guides. They are:

1. modes with a concentration of energy in the groove regions (region A), and
2. modes with a concentration of energy in the region between the two grooves (region S).

Attention had been concentrated on the first type of modes[1]. This paper gives the theoretical and experimental work on the second type of modes.     

Limitations on power-transfer efficiency in three-guide optical couplers

The eigenvalue equations for a slab three-guide coupler were solved and the power-transfer efficiency was calculated when the coupler is used as 1) a power divider and 2) to transfer power from one outside guide to another. In the first case, two modes take part in the power transfer, and unless the guides are very tightly coupled, periodic beats with high power transfer are obtained at multiples of the coupling length as in a two-guide coupler. In the second case, three modes take part in the power transfer, and periodic beats and high power-transfer efficiency can only be obtained if the propagation velocities of the three modes are related to each other in a simple way. This condition will occur only if the guides of a three-guide coupler made up of identical guides are much more loosely coupled than guides generally used in a two-guide coupler.     

Modes of propagation in optical fibres

Light propagates along optical fibres in form of normal modes. As long as fibres are uniform in axial direction, these modes follow as solutions of the eigenvalue problem which Maxwell’s equations together with the boundary conditions of the particular fibre represent. Such modes propagate independently from each other and transmit and distort signals according to their respective delay, dispersion and attenuation. Imperfections of the fibre couple its modes with each other and change its signal attenuation and transmission characteristics. When a randomly imperfect fibre guides many modes, the random coupling leads to a new set of statistical modes which again propagate independently from each other and describe the average power in each of the perfect fibre modes. Interaction between statistical modes occurs only at points along the fibre where the statistics of imperfections change such as at connectors or splices.     

Analysis for a Novel Cocoon-Shaped Groove Guide with Method of Lines

An arbitrarily cross-sectional groove guide is analyzed by using the method of lines and its characteristic equations are gives for TE and TM modes. Some numerical results show that correctness of the method of lines compared with the relevant results in the references is verified, and it is convenient to solve groove guide with arbitrary shape in practical application problems. A novel cocoon-shaped groove guide is firstly presented and its transmission characteristics are analyzed and discussed. The new type of cocoon-shaped groove guide has the good performances. The obtained results are of important application values in theoretical studies and practical applications of groove guides for millimeter waves.     

Tapered, both in dimension and in index, velocity coupler: theoryand experiment

The authors consider a tapered velocity coupler (TVC) that meets the adiabatic invariance condition with sufficiently strong coupling between the fundamental modes of individual guides in the middle region of the coupler while permitting individual excitation at the input end and sorting of the modes at the output end. This approach helps reduce the device length considerably by permitting much higher taper angle. A TVC consisting of one tapered and another straight, graded index waveguide is modeled using the normal modes of the entire, composite TVC structure. The analytical results are in excellent agreement with experimental results for a TVC fabricated in Ti:LiNbO₃. It is shown that the representation of the local normal modes as the superposition of the modes of the uncoupled guides leads to erroneous results     

Finite-Difference Analysis of Rectangular Dielectric Waveguide Structures

A class of dielectric waveguide structures using a rectangular dielectric strip in conjunction with one or more layered dielectrics is analyzed with a finite-difference method formulated directly in terms of the wave equation for the transverse components of the magnetic field. This leads to an eigenvalue problem where the nonphysical, spurious modes do not appear. Moreover, the analysis inclndes hybrid-mode conversion effects, such as complex waves, at frequencies where the modes are not yet completely bound to the core of the highest dielectric constant, as well as at frequencies below cutoff. Dispersion characteristic examples are calculated for structures suitable for millimeter-wave and optical integrated circuits, such as dielectric image lines, shielded dielectric waveguides, insulated image guides, ridge guides, and inverted strip, channel, strip-slab, and indiffused inverted ridge guides. The numerical examples are verified by results available from other methods.     

Modes in anisotropic optical waveguides formed by diffusion

Solutions of the wave equation are obtained for planar guides whose dielectric constant ε is anisotropic and decreases exponentially in the direction perpendicular to that of wave propagation. Although for TE modes the solutions are quite similar to those obtained earlier for exponentially varying but isotropic ε, there are some singificant differences for TM modes. The condition for single-mode operation and the number of modes of such guides are given in terms of the exponential decay rate, the difference between the surface and bulk values of ε, and the wavelength. The results are illustrated for the cases of Se-diffused CdS and out-diffused LiNbO3.     

Coupled mode theory of parallel waveguides

A new coupled mode formulation for parallel dielectric waveguides is described. The results apply to any guided modes (TE, TM, or hybrid) in waveguides of arbitrary cross-section, dissimilar index, and nonidentical shape. Additional index perturbations not included within the waveguides are encompassed by the theory. Propagation constants and mode patterns for the coupled modes computed according to this theory are shown to agree very well with numerical solutions for the system modes when the latter can be determined. Moreover, the new results are more accurate than those obtained from prior coupled mode formulations. It is shown that even for Iossless guides the coupling coefficients from waveguide"b"to"a"and from"a"to"b,"described by kaband kbarespectively, are not related by their complex conjugates if the guides are not identical.     

Variational coupled-mode theory of optical couplers

A scalar coupled-mode theory is developed from the variational principle. The formulation is variational in the sense that the mode parameters are adjustable and can be optimized subject to the coupling between the guides. The theory is applied to slab and fiber couplers. In comparison with the conventional scalar coupled-mode theory in which only the amplitudes of the modes in the individual guides are adjustable, the variational scalar coupled-mode theory predicts more accurate propagation constants and field patterns of the normal modes of the couplers     

Cutoff Wavelengths of Ridged, Circular, and Elliptic Guides

Cutoff wavelengths of TE and TM modes in doubly ridged guides of elliptical cross section have been calculated using an exact method. Closed-form expressions in terms of Mathieu functions have been obtained for the cutoff frequencies and eigenfunctions describing the field distribution for different modes. These solutions are further extended to include the case of doubly and quadruply ridged guides of circular cross section and to calculate the slot coupling of two waveguides with semielliptical or circular cross sections. The dual problem of the coaxial strip guide has also been treated using the same method.     

Transmission of horizontally polarized waves and trapped waveguide modes in inhomogeneous media

A generalized Wentzel-Kramer-Brillouin (WKB) approach is used to obtain full wave solutions for horizontally polarized waves in inhomogeneous media when no closed form analytic solutions are known. This approach is suitable for complex permittivity profiles with critical coupling regions even when the permittivity gradient approaches zero. The transmission and reflection coefficients and the characteristic surface impedance for inhomogeneous layers of finite thickness are computed for several permittivity profiles. Excitation of propagating and evanescent waves is considered and the results are shown to satisfy the realizability and reciprocity relationships in electromagnetic theory. Sinusoidal permittivity profiles for which closed form analytical solutions are known are also considered to provide an additonal check on the generalized WKB solutions. For permittivity profiles with several spatial periods, transmission windows with very narrow beamwidths are found to exist. When conditions for total internal reflection in the inhomogeneous dielectric layer are satisfied, the reciprocal of the reflection coefficient vanishes and propagating waves are trapped in the layer. For these trapped waveguide modes the inhomogeneous dielectric is characterized by a surface reactance.     

Propagation in cylindrical fibres with anisotropic crystal cores

Expressions for the fields and propagation constants in cylindrical dielectric waveguides with umaxial crystal cores are found. The propagation constants of biaxial-crystal-cored guides are then deduced from a coupled-mode analysis, using the uniaxial solutions as ideal modes.