Anisotropic Waveguides Research Articles

Fields in anisotropic hard surface waveguide with application to polarisation transformer

Electromagnetic fields inside a circular axially corrugated waveguide, also called a hard surface waveguide, are considered. The waveguide is filled with uniaxial anisotropic material. The eigenfields in this kind of waveguide are TE and TM fields which propagate with different propagation factors. Polarisation properties of reflected and transmitted fields are studied. This kind of waveguide component can be used for changing handedness, as a polarisation transformer, and a mode filter element for hard surface waveguides. As a practical example, the polarisation transforming effect of a sapphire filled hard surface waveguide is considered.

Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers

A new method to determine the reflection of substrate modes in finite substrate planar circuits is proposed. The perfectly matched layer (PML) concept is used to transform the open problem into a closed one. The discrete set of substrate, evanescent, and Berenger modes of the resulting anisotropic waveguides are then used in a mode-matching scheme to deduce the scattering coefficients of the substrate modes for oblique incidence on the edge of the substrate. We show results for single- and double-layered substrates and compare with finite-difference time-domain (FDTD) results. The combined perfectly matched layer (PML) mode-matching technique turns out to be very efficient.

Propagation, dispersion, and localization of elastic waves in low-symmetric anisotropic waveguides

The results of a theoretical investigation into ultrasonic linear normal wavefields in anisotropic three-dimensional bodies with mechanical orthorhombic symmetry are presented. A detailed study is made of the dispersion dependencies for higher normal wave modes in a single-layered orthorhombic plate-type waveguide. Moreover, the distribution of complex branches corresponding to the edge standing wave modes is studied and their role in the transformation of the entire spectrum upon a change in the travel direction in the waveguide plane is analyzed. A new type of localization of the higher modes of high-frequency short-range normal waves in a crystal layer is described. An efficient method is developed for studying the spectrum of ultrasonic normal waves in a circular cylindrical waveguide made of an orthorhombic monocrystal

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.

On the theory of wave propagation in anisotropic plates

A theoretical framework is developed which describes wave propagation in infinite homogeneous elastic plates of unrestricted anisotropy. The approach exploits the propagator matrix which is the exponential of the fundamental elasticity matrix underlying Stroh9s formalism of anisotropic elastodynamics. The matrices of plate impedance and admittance are introduced, and their analytical properties are established, which appear fruitful for computing and analysing the plate wave spectra. On this basis, the dispersion equation can be cast into the form of a real equation involving the monotonic function, whose zeros and poles are the wave velocities in a given plate subjected to different boundary conditions (traction–free or clamped faces). It is proved that three fundamental wave branches exist for any orientation of wave propagation in an anisotropic plate with traction–free faces, and that those branches are missing if one or both faces are clamped. The intrinsic symmetry of the wave motion in an arbitrary plate is revealed. The general formalism is applied to elaborate the long–wavelength low–frequency approximation for a (thin) free plate of unrestricted anisotropy. The frequency–dispersive wave velocities, displacements and tractions at the onset of the fundamental wave branches are derived explicitly. The conditions for the extreme velocity values and some other useful universal connections are determined for an arbitrary thin plate, and exemplified for specific anisotropy cases.

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.

Efficient β-formulation for the FEM analysis of leaky modes in general anisotropic channel waveguides

An efficient method to model guided and leaky modes of anisotropic dielectric waveguides with arbitratry dielectric tensor e¯¯ is presented. This method takes advantage of a particular β-formulation approach of the finite element method (FEM), leading to an optimized use of the computational resources.

Anisotropic surface relief diffraction gratings under arbitrary plane wave incidence

A modal method is used for the analysis under oblique incidence of a diffraction grating made of anisotropic material. The problem is studied viewing the structure as the cascade of junctions between periodic arrays of anisotropic slab waveguides with the same period and different heights. This diffraction problem is formulated in terms of an integral equation that enforces the continuity of the transverse magnetic field at the junction. The unknown is the transverse electric field at the junction. It is possible to use also another formulation, where the role of the two fields is exchanged. The kernels of these equations are the relevant Green's functions, which are expressed in terms of eigenfunction expansions. The determination of the modes of the various regions composed of arrays of anisotropic dielectric slabs has been carried out by the method of spectral elements, whereby the field components are represented in a polynomial basis and the original differential eigenvalue problem is converted into an algebraic one. The integral equation is solved numerically by the method of moments and each junction is characterized by its generalized scattering matrix (GSM). Finally, the diffraction efficiencies of the grating are obtained by combining the various GSM's.

Excitation of the Earth-Ionosphere Waveguide by VLF Radiators Situated in the Lower Ionosphere and at Satellite Heights

Structural peculiarities of the electromagnetic fields excited in the Earth-ionosphere waveguide by VLF antennas situated in the lower ionosphere and at satellite heights are discussed. A model of a spherical anisotropic waveguide anisotropic in two dimensions is used. The antennas are simulated by arbitrarily oriented magnetic dipoles. The problem is solved by the cross-section method extended to the case of a two-dimensional irregularity. Within the limits of applicability of the quasi-longitudinal approximation, simple relationships between the electric and magnetic components of the fields formed by different dipoles are obtained. In the framework of a model taking into account the geomagnetic and geographic coordinates, the sun zenith angle, the azimuth, the Earth's surface properties etc., results illustrating the influence of different irregularities on the VLF field structure are obtained.

Performance enhancement of nonlinear lithium niobate couplers via double titanium and magnesium diffusion

The effects of double Ti and Mg diffusion into lithium niobate couplers exploiting cascaded second-order nonlinearity are theoretically investigated. We demonstrate that this technology may be employed to optimize the performance of a new type of coupler made by uniaxial crystal having an unusual dielectric tensor configuration, i.e. equatorial. An extended version of the simple effective index method is developed in order to take into account the complex nature of hybrid modes. A home-made computer code is utilized in the electromagnetic analysis of rotated anisotropic channel waveguides. As an example, the simulation results show that a magnesium diffusion, made in the external region of a Ti : LiNbO 3 coupler which induces negative extraordinary and ordinary changes of the refractive indices of LiNbO 3 Δn e( Mg) =−0.002 and Δ n o(Mg)=−0.001, decreases the linear coupling length from L c=73 to 44 mm.

A FDTD scheme for the computation of VLF-LF propagation in the anisotropic earth-ionosphere waveguide

De part la presence du champ magnetique naturel, l’ionosphere terrestre est un milieu anisotrope de type gyrotropique. Cet article presente un schema numerique aux differences finies adapte a ce milieu, developpe pour calculer la propagation des ondes VLF-LF dans le guide d’onde constitue de la terre et de l’ionosphere. Le schema est decrit en detail, avec une attention particuliere portee a la question de la stabilite numerique.

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.

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 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.

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.

Modes of open layered anisotropic waveguides : a numerical method with exponential convergence

A spectral-element type approach to determine the propagation characteristics of the bound modes of an open planar layered anisotropic waveguide is proposed. The main feature is the expansion of the electromagnetic field in each internal layer on different sets of Legendre polynomials. In the two embedding halfspaces, sets of weighted Laguerre polynomials are used. In this way, the method converges with exponential rate with increasing number of basis functions. No transcendental equation has to be solved and even modes that may exhibit coinciding or very close propagation constants are computed with great accuracy. A detailed analysis of the convergence properties of the algorithm is carried out and a way to estimate and control the error on the propagation constants is discussed.

Thin-film chemical sensors with waveguide Zeeman interferometry

We describe a highly sensitive chemical sensor scheme using a channel waveguide with a selective surface coating based on polarimetric Zeeman interferometry. The sensing is based on measurement of the phase difference between TE and TM modes propagating in the anisotropic waveguide structure under exposure to toluene vapour. A real-time and reversible response at low ppm level is observed. Modelling results of the sensor structure to further increase its sensitivity are presented.

Light propagation in nonlinear waveguide and classical two-dimensional oscillator

The quantum optical problem of the propagation of electromagnetic waves in a nonlinear waveguide is related to the solutions of the classical nonstationary harmonic oscillator using the method of linear integrals of motion [Malkin et al., Phys. Rev. D 2 (1970) 1371]. An explicit solution of the classical oscillator with a varying frequency, corresponding to the light propagation in an anisotropic waveguide is obtained using the expressions for the quantum field fluctuations. Substitutions have been found which allow to establish connections of the linear and quadratic invariants of Malkin et al. to several types of invariants of quadratic systems, considered in later papers. These substitutions give the opportunity to relate the corresponding quantum problem to that of the classical two-dimensional nonstationary oscillator, which is physically more informative.

Origin of optical anisotropy in planar polymer waveguides

Many optical gas-sensor-devices utilise the optical anisotropy Δ N eff (difference of effective mode indices) in a planar waveguide that may be induced by molecule diffusion into the guiding film. The time dependence of Δ N eff can be obtained in a dynamic waveguide experiment from the phase shift between two guided modes of different polarization. Different effects of diffusing molecules on the guiding polymer film are discussed for isotropic and anisotropic waveguide films. All effects on refractive indices and film thickness have been studied additionally by the m-line spectroscopy in transmission. For the sensitive polyimide Ultradel® 9020D the origin of the complicated anisotropy change is investigated.