Anisotropic Optical Waveguides Research Articles

Approximate scalar finite-element beam-propagation method with perfectly matched layers for anisotropic optical waveguides

The perfectly matched layer boundary condition for arbitrary anisotropic media is incorporated into the approximate scalar beam propagation method. The procedure is based on a finite-element method for three-dimensional anisotropic optical waveguides with off-diagonal elements in a permittivity tensor. In order to treat a wide-angle beam propagation, the Pade approximant operator is employed. To show the validity and usefulness of this approach, numerical results are presented for Gaussian beam propagation in free space and Gaussian beam excitation on a three-dimensional anisotropic optical waveguide.

Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides

Perfectly matched layer (PML) boundary conditions are incorporated into the full-vectorial beam propagation method (BPM) based on a finite element scheme for the three-dimensional (3-D) anisotropic optical waveguide analysis. In the present approach, edge elements based on linear-tangential and quadratic-normal vector basis functions are used for the transverse field components. To show the validity and usefulness of this approach, numerical examples are shown for Gaussian beam propagation in proton-exchanged LiNbO/sub 3/ optical waveguides. Numerical accuracy of the present PML boundary condition is investigated in detail by comparing the results with those of the conventional absorbing boundary condition (ABC).

Complex FEM modal solver of optical waveguides with PML boundary conditions

A full-wave modal analysis of two-dimensional, lossy and anisotropic optical waveguides using the finite element method (FEM) is presented. In order to describe the behavior of radiating fields, anisotropic perfectly matched layer boundary conditions are applied for the first time in modal solvers. The approach has been implemented using high order edge elements. The resulting sparse eigenvalue algebraic problem is solved through the Arnoldi method. Application to an antiresonant reflecting optical waveguide is reported.

Full-vector finite-element beam propagation method for anisotropic optical device analysis

A finite-element full-vectorial beam-propagation method is presented, for the first time, for the analysis of 3-D anisotropic optical waveguides. Full 3/spl times/3 permittivity and permeability tensors are considered. The formulation takes into account the polarization dependence and the component coupling due to the waveguide geometry and the medium anisotropy without any analytical approximations. The perfectly matched anisotropic absorber is introduced to eliminate the influence of the computational border on the numerical solutions. The correctness of the proposed approach is verified by analyzing several kinds of anisotropies. For the first time, a full vectorial finite-element propagation analysis is presented for diffuse waveguides and magnetooptic devices.

Interaction of a guided wave with space charge waves in anisotropic waveguides with the inclusion of a leaky wave

The conversion of an optical guided wave into a leaky mode in a film anisotropic optical waveguide resulting from its interaction with a space charge wave is considered. It is shown that this conversion mechanism may be more efficient than the acoustooptic conversion.

Finite element analysis of anisotropic optical waveguide with arbitrary index profile

This work presents the application of a scalar finite element formulation for E/sup x/ (TE-like) modes in anisotropic planar and channel waveguides with diagonal permittivity tensor, diffused in both transversal directions. This extended formulation considers explicitly both the variations of the refractive index and their spatial derivatives inside of each finite element. Dispersion curves for E/sup x/ modes in planar and channel waveguides are shown, and the results compared with solutions obtained by other formulations.

Finite element beam propagation method for anisotropic optical waveguides

A finite element beam propagation method (BPM) for anisotropic optical waveguides is newly formulated. In order to treat a wide-angle beam propagation, a Pade approximant operator is employed and to avoid nonphysical reflection from computational window edges, a transparent boundary condition is extended to anisotropic materials. To show the validity and usefulness of this approach, the numerical results for an anisotropic planar waveguide and a magnetooptic channel waveguide are presented.

Stress analysis method considering piezoelectric effects and its application to static strain optic devices

A stress analysis method considering piezoelectric effects based on the finite-element method (FEM), which can be applied to arbitrarily anisotropic material-based optical waveguide devices, is newly formulated. To produce a two-step analysis of static strain optic (SSO) and electrooptic (EO) modulations of optical waveguide devices, this stress analysis is linked to the guided mode analysis and the beam propagation analysis taking into account the refractive index changes. Numerical examples are shown for strain-induced optical waveguides and strain-induced polarization mode converters on LiNbO/sub 3/ substrates.

Efficient finite-element analysis of tilted open anisotropic optical channel waveguides

An iterative method to analyze open anisotropic dielectric waveguides with arbitrary dielectric tensor /spl epsi/~ such as tilted channel waveguides is presented. The proposed /spl beta/ formulation approach reduces significantly the computational resources compared to previously proposed other choices.

Stress analysis method for elastically anisotropic material based optical waveguides and its application to strain-induced optical waveguides

A numerical approach for the stress analysis of elastically anisotropic material-based optical waveguides is newly formulated with the finite element method (FEM). The stress analysis method developed here is linked to the guided mode analysis method to produce a two-step analysis of acoustooptic modulation of optical waveguides. Numerical examples are shown for strain-induced optical waveguides on LiNbO/sub 3/ substrates.

Second-harmonic generation by off-axis propagation in an anisotropic optical waveguide

Second-harmonic generation (SHG) by means of radiation modes (the Čerenkov-type radiation scheme) in an anisotropic optical waveguide by off-axis propagation has been studied theoretically. If the second-harmonic wave is a leaky wave of the waveguide, the Čerenkov-type SHG efficiency may be comparable with the efficiency of the guided-mode–guided-mode SHG without critical control of the wave-vector-matching condition. The model presented predicts a strong modification of the radiation field by a change of the interaction length. A numerical simulation of the proposed type of SHG in a graded-index waveguide on the X-cut surface of LiNbO3 is made.

Analysis of anisotropic channel optical waveguide using an equivalent transformation of the index profile

An analysis method for anisotropic channel optical waveguides using an equivalent transformation of the index profile is proposed here. This method transforms the anisotropic channel waveguide into an equivalent isotropic symmetric waveguide by taking into account the effects of both (1) field leakage of eigenmodes into the air and (2) permittivity anisotropy on the propagation constant as the perturbation of index profile. This technique permits an accurate solution to be obtained using conventional weakly guiding analytical methods. In this paper, the equivalent transformation rules are derived theoretically. It is shown to be effective for analyzing the Ti-diffused LiNbO3 waveguide with good accuracy. The analysis results using the present method is described for the Ti-diffused LiNbO3 waveguide. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80 (1): 14–23, 1997

Radiation modes of an anisotropic optical waveguide with arbitrary refractive index profile

A direct numerical procedure is presented to evaluate the field distribution of radiation modes in an anisotropic optical waveguide with arbitrary ordinary and extraordinary index profiles.

Vectorial eigenmode calculation for anisotropicplanar optical waveguides

A newly derived spurious-mode-free finite-difference-method for computing the eigenmodes of anisotropic planar optical waveguides is presented. For solving the linear eigensystem, a powerful multi-grid-method is used. An application of the method is given.

A new technique of analysis of anisotropic channel optical waveguides using the propagating beam method

A new technique of analysis of anisotropic channel optical waveguides using the propagating beam method

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.

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.

Improved coupled-mode theory of anisotropic optical waveguides

A coupled-mode equation for anisotropic waveguide systems of arbitrary cross section and general dielectric distribution is derived. Numerical results comparing the exact calculations to those of the method of Hardy et al. (Opt. Lett., vol.11, 742-4, 1986) show that the same accuracy can be obtained not only for TE, but also for TM mode coupling in the case of anisotropic waveguides, and the improved coupled-mode theory is applicable to the situation when moderately strong coupling occurs under the condition where the edge-to-edge separation of two coupled guides D/sub 2/ is about 0.1 mu m. >

Waveguide dispersion in anisotropic optical waveguides

The method of shift formulas is employed to obtain approximate analytic expressions which can be used to calculate?with sufficient accuracy for practical applications?the waveguide and polarization dispersion of the dominant orthogonally polarized modes in anisotropic optical fiber waveguides. It is shown that the anisotropy of a dielectric in the transverse cross section and the ellipticity of the shape of this cross section (shape anisotropy) alter the waveguide dispersion of modes in such waveguides compared with an isotropic waveguide. In the case of waveguides which conserve the state of polarization of the transmitted signal the changes in the waveguide dispersion due to the transverse anisotropy of the refractive index are considerably greater than the changes due to the ellipticity of the shape of the transverse cross section of the waveguide. In a waveguide with a transverse anisotropy of the refractive index the maximum waveguide dispersion of two mutually orthogonal modes occurs at different frequencies.

Vector variational analysis of the guided modes in the three‐dimensional anisotropic optical waveguides

AbstractThe guided wave characteristics in a three‐dimensional dielectric optical waveguide containing anisotropic materials must be investigated by vectorial analysis. Such analyses are extremely complicated if non‐diagonal terms are contained in the dielectric tensor or more than two anisotropic materials are involved. In this paper the guided modes are analyzed by a variational method in the case where the dielectric tensor contains nondiagonal elements of the transverse components. First, a new variational expression and trial functions suitable for analysis of the guided mode in these waveguides are derived. Next, numerical calculations are performed for a rectangular dielectric waveguide in which both the core and the substrate are made of anisotropic materials. With these calculations, we investigate the effects of the directions of the multiple principal axes on accuracy of the propagation constant near the lower limit, coupling of the guided modes and directions of the electromagnetic vectors. It is found that there are tight hybrid modes and weak hybrid modes. In the case of weak hybrid modes the electromagnetic vectors are straight and almost parallel to the principal axes. On the other hand, in tight hybrid modes the electromagnetic vectors bend significantly and the vector direction is rotated as the normalized frequency is varied.