Anisotropic Waveguides Research Articles

Observation of mode selection in a radially anisotropic cylindrical waveguide with liquid-crystal cladding

Observation of mode selection in an optical fiber with nematic liquid-crystal cladding is reported. The TE01 mode is guided, while the TM01 mode leaks out. This behavior is achieved by radially oriented liquid-crystal directors in the cladding of an optical fiber with isotropic core. A theory which quantitatively accounts for the results is given.

Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides

This paper reviews numerical and approximate methods for the modal analysis of general optical dielectric waveguides with emphasis on recent developments. Six groups of methods are reviewed, covering (1) the finite-element method, (2) the finite-difference method, (3) the integral-equation method, (4) methods based on series expansion, (5) approximate methods based on separation of variables, and (6) methods that do not fit into the above groups, ranging from the specialized ones for analysing restricted classes of waveguides to the most general ones for analysing inhomogeneous, arbitrarily-shaped, anisotropic waveguides. Some suggestions with regard to the selection of methods for particular applications are given.

Coupling efficiency of two anisotropic single‐mode slab waveguides butt‐joined via a gap

AbstractThe fundamental characteristics of the coupling efficiency between two anisotropic slab waveguides with different configurations butt‐joined via a gap are analyzed in the case of a TM mode incidence by means of a single‐mode slab waveguide model made of equatorial dielectric tensor. the electromagnetic field in the gap is represented by a combination of the forward elementary plane wave propagating from the incident side to the output waveguide and the backward elementary plane wave propagating in the opposite direction.By applying the boundary conditions, the power transmission and reflection coefficients in the guided‐wave system are computed. Further, the effects of the lateral misalignment and inclination between the wave‐guides and the index of refraction and spacing of the gap on the coupling efficiency are studied based on the numerical results. an optimum condition to maximize the coupling efficiency is obtained.

On the domain integral equation method for anisotropic inhomogeneous waveguides

The domain integral equation method for anisotropic inhomogeneous dielectric waveguides is derived, and the spectral properties of the integral operator are discussed. It is explained why spurious modes do not occur when the Galerkin method is applied to the domain integral equation. Furthermore, the convergence of the method is discussed. >

Spectral method for modes excitation problem in anisotropic waveguides

In modes excitation problem of anisotropic waveguides attention should be paid to the case of excitation sources with longitudinal components. In such case the usage of the basis of membrane functions of normal modes for the solution of the excitation problem may not lead us to unequivocal results because only transverse components of modes fields form a complete set of orthonormal basis on the waveguide cross section. In this paper it is shown that in the presence of longitudinal currents it appears the additional terms in the excitation integral caused with as anisotropy of medium as the transversal derivatives of longitudinal currents.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An implementation of the vectorial finite element analysis of anisotropic waveguides through a general-purpose PDE software

This paper reports on the major progress in the development of an intelligent, interactive and automated system, based on the vector finite element method, and implemented within PDE/Protran problem solving environment. The system is known as WAVEGIDE and was originally developed by the authors for an efficient solution of inhomogeneous dielectric waveguides. In this paper, it has been further extended to the solution of anisotropic waveguiding structures. With our system, through an interactive question-and-answer session, which requires minimal knowledge of programming, the problem can be defined using high level PDE/Protran commands. It can then be simply and quickly solved by the main processor within this intelligent environment. To verify the convergence and accuracy of the present approach, numerical results (with respect to the grid density and element order) for a rectangular metallic waveguide half filled with dielectric are given and compared with other finite element methods. Numerical results for an anisotropic dielectric rectangular waveguide are also presented. These results clearly illustrate the accuracy and the ease of use of the modified WAVEGIDE program. >

A full-vectorial beam propagation method for anisotropic waveguides

An extension of the full-vectorial beam propagation method to anisotropic media is presented. Optical waveguides made of anisotropic materials can be modeled and simulated. The polarization dependence and coupling due to both the material and the geometric effects are considered.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Non-attenuated hybrid leaky guided modes in planar waveguides

A certain specific class of hybrid leaky guided modes in a step-index anisotropic planar waveguide with the optic axis in the waveguide plane is investigated. By demanding the lossy field component to vanish in the substrate, the mode attenuation coefficient can be reduced to zero. The properties of the non-attenuated leaky guided modes and the conditions making them possible to appear are discussed. The obtained mode equations are given by the exact, analytical formulae.

Surface Wave Propagation In A Slowly Varying Anisotropic Waveguide

SUMMARY We present a JWKB theory which describes the propagation of seismic surface waves in a laterally heterogeneous, anisotropic waveguide. We introduce a local dispersion relation and local vertical eigenfunctions which depend explicitly on the direction of the local wavevector as a consequence of the anisotropy. the variation of amplitude along a surface wave ray path is determined by a conservation law for the surface wave energy. Apart from the usual dynamical phase, which is the integral of the local wavevector along a ray path, there is an additional variation in phase in a general anisotropic waveguide. This additional phase, which is an analogue of the Berry phase in adiabatic quantum mechanics, vanishes in a waveguide with a local vertical two-fold symmetry axis or a local horizontal mirror plane.

Anisotropic dielectric waveguides

The guided modes of anisotropic waveguides are known to be leaky when degenerate radiation modes of the orthogonal polarization exist. These losses can be quite large when the principal axes of the dielectric tensor are not aligned with the waveguide axis. We calculate the leakage rate in waveguides that have arbitrarily oriented dielectric tensors, using a perturbation expansion that is valid for weak guidance and weak anisotropy A relatively simple expression for the loss is obtained and is applied to model cases drawn from planar and fiber waveguides with step- and graded-index profiles. The scaling of the loss with profile height and anisotropy is discussed, including the practical case of strongly asymmetric planar waveguides.

Analysis of biaxially anisotropic dielectric waveguides with gaussian—gaussian index of refraction profiles by the finite-difference method

A rigorous, versatile and general formulation for the analysis of propagation characteristics of rectangular biaxial anisotropic dielectric waveguide structures with arbitrarily varying indices of refraction profiles is presented. In this formulation the finite-difference method is used for the numerical solution of the wave equation, written in terms of the transverse components of the magnetic field. As a result, a conventional eigenvalue problem is obtained without the presence of the spurious modes (observed in previous formulations), due to the implicit inclusion of the divergence of the magnetic field equal to zero. The theoretical development was used to solve particular problems and the results have shown agreement with those available using other methods.

Rigorous boundary integral equation solution for general isotropic and uniaxial anisotropic dielectric waveguides in multilayered media including losses, gain and leakage

Bounded and leaky eigenmodes of arbitrary shaped polygonal dielectric waveguides embedded in a multilayered medium are determined based on a rigorous full-wave analysis. The dielectric waveguides consist of isotropic or uniaxial anisotropic material. Losses and gain inside the layers and the waveguides are allowed. The eigenmodes are determined with a boundary integral equation technique in conjunction with the method of moments. Results for the propagation constants are presented for a number of waveguides and, where possible, compared with published data. Special attention is devoted to the transition from a dielectric waveguide to a perfectly conducting waveguide when the loss tangent of the waveguide material changes from zero to infinity. >

Two-dimensional problems of determination of mode spectra of anisotropic diffusion waveguide

Spectral problems of determination of the mode propagation constants and electromagnetic fields of a two-dimensional optical waveguide with a diagonal permittivity tensor are formulated mathematically and solved numerically. The results for some refractive-index profiles in the isotropic case are in good agreement with the solutions of other authors. A specific calculation is made for an anisotropic diffusion waveguide. Some physical aspects of the obtained equations are discussed.

Coupled-mode analysis of leaky waves in channel waveguides consisting of anisotropic material

A study of leaky waves in anisotropic circular channel waveguides consisting of uniaxial crystalline material, in which the optical axis is on the plane defined by the propagation axis and one of the transverse coordinates axes, is discussed. The analysis is based on the theory of coupled modes. Mathematical discretization of the continuum of radiation modes offers satisfactorily accurate solutions of the coupled-mode equations. The characteristics of leakage losses and the field distributions of leaky waves in a LiNbO/sub 3/ waveguide are discussed on the basis of the numerical results. >

Design of multielement acircular waveguide lens systems in anisotropic media

We discuss the evaluation and design of wide-field-angle acircular lens systems in anisotropic planar waveguides. After a short summary of the applied ray and wave optical relations, we examine the aberrations of systems that were optimized for an isotropic waveguide but are embedded in an anisotropic one. We show that effects of anisotropy must be taken into account in the design of wide-field-lens systems. We present a four-element acircular lens that was optimized using a merit function computed for uniaxially anisotropic media.

Photoelectrochemical etching of high aspect ratio submillimeter waveguide filters from n+ GaAs wafers

A 200 μm high-pass filter has been fabricated using the photoelectrochemical (PEC) etch process to form a series of waveguides through a Si-doped n+ GaAs (1×1018 cm−3) substrate. A metal mask on the sample surface with 100 μm square openings and 41 μm spaces was used to locally prevent PEC etching. The sample was etched in a (4:1:50) HCl:HNO3:H2O electrolyte for 1.5 h using an argon ion laser (514 nm) at an intensity of 0.7 W/cm2, and an applied bias of 0.35 V. The result was a series of highly anisotropic waveguides with a (3:1) aspect ratio. The transmittance curve had a cutoff of 45 cm−1 and a transmittance of 20% just above the cutoff.

Rigorous analysis of a step discontinuity in a dielectric planar anisotropic waveguide

Using a discretizing procedure for the continuous spectral amplitude of the radiation modes and the least-squares boundary residual method a rigorous analysis of a step discontinuity in a dielectric planar anisotropic waveguide is presented. The numerical examples clearly show the effect of the medium anisotropy on the scattering characteristics—namely on the radiation pattern—of a uniaxial dielectric step. © 1992 John Wiley & Sons, Inc.

Aplanatic waveguide Fresnel lenses

A new modification of waveguide Fresnel lenses is proposed. The phase-shifting zones in these lenses are located on a curvilinear contour. It is shown that the coma aberration can be eliminated by selecting the contour shape as a circle in an isotropic waveguide and as part of an ellipse in an anisotropic waveguide. Results of a numerical simulation are presented. These demonstrate that the optical characteristics of lenses having a curvilinear contour are improved considerably. It is noted that hybrid planar optical systems free of the lowest-order aberrations can be constructed.

Leaky mode propagation in planar multi-layer inhomogeneous birefringent waveguides: polar dielectric tensor configuration

The lightwave propagation characteristics in planar inhomogeneous multi-layered anisotropic waveguides having a polar dielectric tensor configuration are investigated. The transition from guided modes to leaky modes is found to be dependent on the azimuth angle theta and on the type and thickness of the embedded metal and buffer layers. The guided mode losses assume the lowest values (about 10dB cm-1) for a Ag layer. The leaky mode losses exhibit a peak near the critical angle theta c and then decrease with increasing azimuth angle. This effect can be advantageously exploited to build integrated optical devices such as angle deviation detectors. For a structure with a Ni layer the authors find theta c approximately=25.5 degrees and the loss value is the highest calculated to date ( alpha approximately=1280 dB cm-1).

Field Excited by Plane Waves in Anisotropic Optical Waveguide

Displacing a linear source exciting the waveguide along an arbitrary fixed direction to infinity one can create the conditions in which the waveguide is excited by a plane wave. The nature of the excited field in a waveguide is complicated. On the upper plane of the waveguide x +l one always deals with the radiation mode whereas on the lower boundary of the waveguide x = -l one can deal with the radiation mode or the surface-type wave.