K. Hayata

Vectorial Finite-Element Method Without Any Spurious Solutions for Dielectric Waveguiding Problems Using Transverse Magnetic-Field Component

An improved finite-element method for the analysis of dielectric waveguiding problems is formulated rising the transverse magnetic-field component. In this approach, the divergence relation /spl nabla/ · H = 0 is satisfied and the spurious, nonphysical solutions which have been necessarily included in the solutions of earlier vectorial finite-element methods are completely eliminated in the whole region of a propagation diagram. To verify the accuracy of the present method, numerical results for a rectangular metallic waveguide half filled with dielectric are presented and compared with exact and earlier finite-element solutions. Dielectric rectangular waveguides are also analyzed for both isotropic and anisotropic cases.

Finite-element analysis of quantum wells of arbitrary semiconductors with arbitrary potential profiles

A finite-element method for the analysis of eigenstates in a quantum well, which is based on the Galerkin procedure, is discussed. A general boundary condition of the envelope function at the heterointerface is introduced by using the transfer matrix. The validity of the method is confirmed by calculating the eigenstates of GaAs/AlGaAs and InAs/GaSb rectangular quantum wells. Numerical examples of voltage-applied quantum wells are presented. >

Finite-element formalism for nonlinear slab-guided waves

A unified computer-aided numerical approach, based on the finite-element method, is developed for analyzing optical waves guided by dielectric slab waveguiding structures with arbitrary nonlinear media. In the formulations, both TE and TM polarizations are considered. For the TM case, the biaxial nature of nonlinear refractive index is considered without any approximation. Numerical results are presented for nonlinear TE and TM waves propagating in symmetric slab waveguides. The dependence of dispersion relations on the refractive-index profile of the film is examined. >

Split-step finite-element method applied to nonlinear integrated optics

A useful numerical simulation technique is presented to solve nonlinear guided-wave problems in a planar or coaxial optical waveguide. This technique is a combination of the finite-element method and the finite-difference method. The former is applied to the waveguide cross section (xy or rθ plane), whereas the latter is applied to the propagation direction (z axis). With the split-step procedure a significant enhancement of computational efficiency is achievable. The usefulness of the present approach is demonstrated through a number of numerical examples, some of which are displayed here.

Finite element formulation for lossy waveguides

An efficient computer-aided solution procedure based on the finite-element method is developed for solving general waveguiding structures composed of lossy materials. In this procedure, a formulation in terms of the transverse magnetic-field components is adopted and the eigenvalue of the final matrix equation corresponds to the propagation constant itself. Thus, it is possible to avoid the unnecessary iteration using complex frequencies. To demonstrate the strength of the presented method, numerical results for a rectangular waveguide filled with lossy dielectric are presented and compared with exact solutions. As more advanced applications of the presented method, a shielded image line composed of a lossy anisotropic material and a lossy dielectric-loaded waveguide with impedance walls are analyzed and evaluated. >

Approximate Scalar Finite-Element Analysis of Anisotropic Optical Waveguides with Off-Diagonal Elements in a Permittivity Tensor

An approximate scalar finite-element program for the analysis of anisotropic optical waveguides having a permittivity tensor with nonzero off-diagonal elements is described. In this approach, the nonphysical spurious solutions which are included in the solutions of the earlier vectorial finite-element method in an axial-components formulation do not appear. Numericaf examples On an anisotropic dielectric rectangular wave-guide composed of a uniaxial medium are given. Our results for the waveguide whose optic axis lies in the plane ( xy-plane) normal to the direction (z-axis) of propagation agree well with the results of the vectorial wave analysis using the variational method. We also demonstrate the application of this approach by analyzing the anisotropic dielectric rectangular waveguide whose optic axis lies in the xz - or yz -plane.

Numerical analysis of the absorption and the refractive index change in arbitrary semiconductor quantum-well structures

A numerical method for the analysis of the absorption spectrum and the refractive index change due to an external electric field in quantum-well structures is presented. The finite-element method and the variational method are used to obtain the subband and the exciton energies in a quantum-well structure, respectively. The absorption spectrum due to the band-to-band and the excitonic transitions is then calculated, and the refractive index change is obtained using the Kramers-Kronig relations. This method is applicable to quantum-well structures with arbitrary potential profiles made of arbitrary semiconductors, because it is based on the finite-element method in which the general boundary condition for the heterointerface is employed. The validity of the method is confirmed by comparing the computed results with the measured ones. >

Full vectorial analysis of nonlinear-optical waveguides

Intensity-dependent properties of nonlinear-optical waves guided by dielectric waveguiding structures with two-dimensional power confinement are analyzed by the vectorial finite-element method. In this approach self-consistent solutions are obtainable through an iterative procedure, and no spurious solutions are involved in the region under consideration.

Enhancement of the guided‐wave second‐harmonic generation in the form of Cerenkov radiation

A method for enhancing guided‐wave second‐harmonic generation (SHG) phase matched by a Cerenkov radiation scheme by means of tailoring the transverse (y direction) nonlinear susceptibility profile in the waveguide channel is proposed. Specifically, linear and domain‐inverted (poled) channels embedded in a nonlinear substrate are considered, and the SHG efficiency for each structure is compared with that for the conventional nonlinear channel without domain inversion. Through electromagnetic field analysis, a significant enhancement of SHG is demonstrated, particularly with the domain inverted channel.

Lateral mode analysis of buried heterostructure diode lasers by the finite-element method

Lateral mode analysis of buried heterostructure-type index guided diode lasers is presented using the finite-element method. The vectorial and the approximate scalar finite-element methods based on a Galerkins procedure are formulated for the analysis of the waveguides composed of active or lossy media. By using these methods, the accuracy of the effective refractive index method, which has been widely used, is investigated in detail and the limit of this approximate method is indicated. Furthermore, the modal gain and its difference between the fundamental and the higher order modes, which may be important for the design of diode lasers, are evaluated for GaInAsP/ InP buried heterostructure diode lasers. As a result, the finite-element method, especially the approximate scalar finite-element method, is found to be useful for the lateral mode analysis of diode lasers, and suggested the possibility as a means for device simulation techniques.