Anisotropic Waveguides Research Articles

Transmission and Reflection at Butt Joints between Isotropic and Anisotropic Single-Mode Slab Waveguides

Transmission and reflection properties are studied for a butt joint between an isotropic slab waveguide and an anisotropic one consisting of uniaxial crystalline material which has the optical axis in the plane defined by the propagation axis and the normal of the waveguide surface. The effects of axial displacement and angular misalignment are discussed on the basis of numerical results obtained from two different formulas: one is derived from the boundary condition together with the modal orthogonality and the other is based on the simple overlap integral of modal profiles. It is confirmed that the simple formula in terms of the overlap integral is applicable to the characterization of butt joints involving anisotropic waveguides.

Spectral problem for an anisotropic elastic waveguide

We consider the homogeneous boundary-value problem of propagation of elastic waves in a hollow anisotropic cylinder with free walls. The problem is solved by a method based on series expansion of traveling-wave amplitudes in powers of the radial coordinate. A dispersion relationship is obtained. The different types of wave motion are analyzed as a function of the degree of anisotropy of the material.

Coupling efficiency of butt-joined isotropic and anisotropic single-mode slab waveguides

Studied is the effect of axial displacement and angular misalignment on the power-coupling efficiency of a butt-joint between an isotropic and an anisotropic single-mode slab waveguide. The power-coupling coefficient is formulated by means of the boundary conditions at the interface of the butt-joint and the orthogonality relations between the modes in the outgoing waveguide. It is found from the numerical results that proper amounts of angular misalignment and axial displacement remarkably suppress transmission losses when the material coordinate system of the anisotropic waveguide is not aligned with its waveguide coordinate system in the plane defined by the propagation axis and the normal of the waveguide surface. >

Domain-integral analysis of channel waveguides in anisotropic multilayered media

A domain-integral equation method is presented to determine both propagation constants and the electromagnetic field distributions of guided surface wave modes in integrated optical waveguides. Both the waveguide and its multilayered embedding are anisotropic. The permittivity tensor of the embedding is assumed to be piecewise homogeneous. The kernels of the domain-integral equations consist of Green's tensors. The integral equations form an eigenvalue problem where the electric field strength represents the eigenvector. This problem is solved numerically by applying the method of moments. Numerical results are presented for an anisotropic ridge waveguide, embedded in an anisotropic multilayered medium.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Dispersion of guided waves in thin anisotropic waveguides

SUMMARY This paper shows that: if appropriate source mechanisms and frequency bands can be selected, thin layers in sedimentary reservoirs may act as seismic waveguides, and guided waves may be useful for reservoir characterization in cross-hole surveys; and that the dispersion of such guided waves is sensitive to crack saturations and crack orientations, and could contain important information about the level of saturation in specific thin layers in enhanced oil recovery operations. In the first part of the paper, we extend a technique, previously used for calculating the dispersion of surface waves in a plane-layered anisotropic half-space, to calculating the dispersion of guided waves in the interior of a multilayered anisotropic solid. In the second part, we demonstrate the effects of anisotropy by calculating synthetic guided waves in a thin gas-sand layer displaying crack-induced anisotropy.

Spectral representation of the electromagnetic field in anisotropic optical waveguides

The spectral representation of an electromagnetic field in a uniaxial optical waveguide excited by a line source is presented. All types of modes that can be excited and propagated in an optical waveguide are included in this representation in a natural way. Both the discrete and the continuous parts of the proper waves in the spectrum are investigated. An important contribution to the diffractional field is made by the so-called lateral wave. Lateral waves are closely associated with the phenomenon of total reflection and arise from the presence of branch-point singularities of the reflection coefficients. In the structure of uniaxial asymmetric waveguides two sets of lateral waves may propagate along two interfaces of a waveguide. A detailed wave-optical analysis of the propagation is presented.

Analysis of metal clad uniaxial waveguides

In this paper, a study of metal clad anisotropic waveguides is presented and applied to surface plasmon modes at a metal-uniaxial interface and a thick and a thin metal clad uniaxial waveguide. The effect of anisotropy on the mode propagation constant and the attenuation coefficient is investigated. The analysis should be useful in the design of metal clad polarization components in integrated optic devices based on lithium niobate and also in studies on surface plasmon measurements in anisotropic structures.

Radiation loss due to step discontinuities in symmetric biaxially anisotropic slab waveguides

This paper is an extension of previous work [1] dealing with guided wave propagation through step discontinuities in anisotropic slab waveguides which focused on the radiated fields only. As opposed to the earlier work, this paper deals with radiation power losses suered by a guided mode incident on the junction, with calculation carried out by an approximate perturbation technique. In addition, the radiation mode solutions to Maxwell's equations in a symmetric biaxially anisotropic slab waveguide are presented for both odd and even symmetries. Characteristics of anisotropic guides are discussed and compared to those of their conventional isotropic counterparts.

Nonsingular Wentzel–Kramers–Brillouin solutions for hybrid modes in Y-cut anisotropic graded-index waveguides

The wave equations describing hybrid modes of a Y-cut anisotropic graded-index planar waveguide have been solved exactly in the first- and the second-order WKB approximation. The analogous exact formulas have been derived in the vicinity of turning points. The obtained solutions have been used to discuss the-energy transmitted along the waveguide by TE and TM fields, with ordinary and extraordinary waves, and to analyze the effective thickness of the waveguide for various field components.

Far‐field radiation from step junctions in biaxially anisotropic slab waveguides

AbstractIn this article far‐field radiation properties of step discontinuities on biaxially anisotropic slab waveguides are examined. The stationary phase method is applied to obtain the asymptotic form of the far‐field expressions, which are derived based on the transmission coefficient of the radiation mode. The analysis yields data that agree well with those previously published for special cases of isotropic slabs. The newly calculated results for far‐field radiation patterns of step junctions between biaxially anisotropic waveguides are presented for several combinations of tensor element parameters.

An efficient finite-element formulation without spurious modes for anisotropic waveguides

A numerically efficient finite-element formulation is presented for the analysis of lossless, inhomogeneously loaded, anisotropic waveguides of arbitrary shape. The electromagnetic field is described either by the three components of a magnetic vector potential and an electric scalar potential or by the three components of an electric vector potential and a magnetic scalar potential. The uniqueness of the potentials is ensured by the incorporation of the Coulomb gauge and by proper boundary conditions. Owing to the implementation of the solenoidality condition for the vector potential even in the case of zero wavenumber, no spurious modes appear. Variation expressions suited to the finite-element method are formulated in terms of the potentials. Standard finite-element techniques are employed for the numerical solution, leading to a generalized eigenvalue problem with symmetric, sparse matrices. This is solved by means of the bisection method with the sparsity of the matrices fully utilized. Dielectric- and ferrite-loaded waveguides with closed and open boundaries and including both isotropic and anisotropic materials are presented as examples.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Integral-equation approach for the analysis of anisotropic channel waveguides

A general technique is presented for treating propagation in anisotropic channel waveguides. The proposed method is based on the use of Green’s function theory in conjunction with integral-equation techniques. The unknown mode propagation constants are determined by solving a homogeneous integral equation on the cross-sectional area of the channel waveguide. The method of moments is employed in order to transform this integral equation into a homogeneous linear set of equations. The propagation constant is determined by truncating this set and setting its determinant equal to zero. The validity of the numerical procedure is examined, and several characteristic cases are presented.

Vector spatial soliton: trapped TM light pattern in planar geometry

The existence of the stable TMl wave in the selfinduced anisotropic planar waveguide is demonstrated for the first time. The modal field profile of this trapped wave pattern is shown to depend on the modal propagation constant, in contrast to the TE1 (optical spatial soliton) case where the field profile is characterised by a hyperbolic function independent of the modal propagation constant.

Spectral representation of self-adjoint problems for layered anisotropic waveguides

Layered waveguides with lossless anisotropic layers in the polar configuration are analyzed through the unifying concept of a real self-adjoint operator. For a suitable definition of two-vector transverse eigenfunctions, general properties such as orthogonality and completeness relations are derived. The linear operator formalism is applied to closed waveguides inhomogeneously filled with anisotropic materials, including crystals and gyrotropic media. As an extension of the former theory to open waveguides, a grounded uniaxial dielectric slab with a coplanar optic axis is also analyzed: as for open isotropic waveguides, a complete spectral representation including the surface (proper eigenfunctions) and the pseudosurface modes (improper eigenfunctions) is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Overexcitation of modes in an anisotropic earth-ionosphere waveguide on transequatorial paths in the presence of two close degeneracy points

Overexcitation of modes in an anisotropic earth-ionosphere waveguide on transequatorial paths in the presence of two close degeneracy points

Anisotropic waveguides with an elliptic stress-inducing cladding and a circular core

A technology of fabrication of anisotropic single-mode fiber waveguides with an elliptic stress-inducing cladding and a circular core was developed. This technology was used to make fiber waveguides with a birefringence (1–3) × 10 − 4, a coefficient representing the coupling between the polarization modes h = (5–7) × 10 − 5 m − 1, and optical losses a = 0.5 dB/km in the vicinity of 1.6 μm. A comparison was made of the experimental data with the results of a theoretical analysis. It was found that certain mechanisms restricted the ability of these waveguides to maintain a constant polarization of the injected linearly polarized radiation.

Bound modes in anisotropic multilayer thin film waveguides

We discuss the construction of field transfer matrices and derive expressions for the modal condition and elliptically polarized fields of anisotropic multilayer waveguides.

Leaky modes in multilayer uniaxial optical waveguides

The propagation characteristics of the leaky modes in planar anisotropic waveguides with a multilayer structure have been investigated by means of a compact rigorous formalism. The leakage losses and leaky transition angle have been studied for the fundamental and first hybrid modes. An inhomogeneous waveguide and buffered step index type structure have been discussed. Particular attention has been devoted to the variation of the loss coefficient of the leaky modes as a function of buffer thickness and buffer refractive index. A notably different behavior has been obtained for various configurations.

Plasmon dispersion relation of a quasi-one-dimensional electron gas.

The plasmon dispersion relation of a quantum wire is derived by solving Maxwell's equations for an anisotropic dielectric waveguide including retardation effects. In the long-wavelength limit, and for the extreme quantum limit, the group velocity of the one-dimensional electron gas is found to be finite and given by the Fermi velocity.

Polarization characteristics of anisotropic single-mode fiber waveguides

An experimental investigation was made of the polarization characteristics of anisotropic fiber waveguides with an elliptic stress-inducing cladding, operating in a wide spectral range. The maximum birefringence amounted to 3.4 × 10 − 4, the minimum mode coupling parameter was 2.5 × 10 − 5 m − 1 (λ = 1.1 μm), and the minimum losses were 0.7 dB/km (λ = 1.5 μm). A qualitative comparison was made with the theoretical data.