Semiconductor Rib Waveguides Research Articles

Modelling of semiconductor rib wave guides by a finite difference method

The method of finite differences is used to solve the scalar wave equation for semiconductor rib wave guides. Boundary conditions derived from continuity relations are applied between regions of different refractive index, allowing more accurate evaluation of the propagation constants for ideal cases of abrupt change in the index. Also appropriate external boundary conditions alleviate the inaccuracy generally introduced by setting the field equal to zero on the external limit of the mesh. Our results agree with various other techniques when applied to typical guiding structures. As an example, we model a multiple-quantum-well structure by using an equivalent layered structure. Mode characteristics and confinement factors obtained by the method are of interest in understanding the behaviour of the lasers and modulators fabricated in our laboratory.

Analysis of Z-invariant and Z-variant semiconductor rib waveguides by explicit finite difference beam propagation method with nonuniform mesh configuration

An efficient and simple explicit finite difference beam propagation method (EFD-BPM) incorporating nonuniform mesh is described. The criteria for stability are developed, and it is shown that this algorithm is power conserving when the stability criteria are met. EFD-BPM is applied to the analysis of single and coupled semiconductor rib waveguides and its accuracy is confirmed by comparing the results with the reported results. Nonuniform mesh is found to improve the efficiency of the method significantly for the analysis of weakly guiding waveguide structures. Several coupled rib waveguide structures with curved input and output branching sections are analyzed using both three-dimensional EFD-BPM and two-dimensional finite difference BPM combined with effective index approximation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Large single-mode rib waveguides in GeSi-Si and Si-on-SiO/sub 2/

Mode-matching and beam-propagation methods are used to analyze single-mode operation of optical GeSi-Si and Si-SiO/sub 2/ semiconductor rib waveguides. The waveguide dimensions that allow only the fundamental HE/sub 00/ or EH/sub 00/ mode to propagate have been determined. For both material systems, it is found that the rib can be several microns wide and several microns high, thus allowing efficient coupling to single-mode fibers. Numerical examples are given for monomode guiding group-IV materials, but the results apply to III-V rib waveguides. It is shown that single-mode rib guides with large cross sections are feasible as long as the waveguide is at least several millimeters long. >

Polarised modes of semiconductor rib waveguides

A simple vector correction is applied to the polarised solution obtained from a single component wave equation. The resulting propagation constants are shown to be indistinguishable from six-component vector finite element results used as a benchmark. This considerably strengthens the validity of the polarised solution for the accurate modelling of rib and stripe waveguides, and shows that emphasis should be placed on finding quick and reliably accurate methods for the polarised approximation. Only then does the vector correction itself become accurate.

Generalized propagation techniques-application to semiconductor rib waveguide Y-junctions

The simulation of electric fields in strongly guiding semiconductor rib waveguide Y-junctions with a new, general operator identity which yields a series of practical and easily programmed fourth-order accurate propagation algorithms is described. While the methods require 3-6 times the computation time of standard procedures for a given propagation step, they are typically more precise by several orders of magnitude for reasonably small propagation step lengths. The exact ratio of CPU times required to achieve a given accuracy, however, is somewhat problem dependent. It is noted that the procedure has been generalized to all orders.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimization of strongly guiding semiconductor rib waveguide Y-junctions

The three-dimensional split-step fast Fourier transform beam propagation method is used to demonstrate that losses associated with a strongly guiding semiconductor rib waveguide Y-junction can be substantially reduced by adding an optimized length of an initial straight broad waveguide segment. It is shown that the resulting transmission is relatively insensitive to the exact waveguide dimensions and in particular to the geometry of the Y-junction vertex.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Explicit finite difference beam propagation method: application to semiconductor rib waveguide Y-junction analysis

A novel explicit finite difference beam propagation method is developed and applied to the analysis of a strongly guiding semiconductor rib waveguide Y-junction. Its accuracy is confirmed by comparison with reported results. This method is much more efficient than the standard beam propagation method for the rib waveguide analysis.

Forward wide-angle light propagation in semiconductor rib waveguides

We derive and examine a new nonparaxial wide-angle equation for unidirectional light propagation. We then develop a rapid unitary solution procedure utilizing both the split-step fast-Fourier-transform and finite-difference techniques. Our calculated losses for the test case of a strongly guiding semiconductor rib-waveguide Y junction are in good agreement with the results of Fresnel equation methods.

Spectral index method for polarized modes in semiconductor rib waveguides

A fast way of modeling polarized modes in semiconductor rib waveguides is presented and shown to be in excellent agreement with a semivectorial finite-difference computer program. The method uses little storage and has been implemented on a personal computer.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The unitarity of split-operator finite difference and finite-element methods: Applications to longitudinally varying semiconductor rib waveguides

Split-operator finite-difference and finite-element techniques are applied to the calculation of losses in semiconductor rib waveguide Y junctions. It is shown that, unlike the finite-difference procedure, which is unitary for both uniform and nonuniform grid-point spacings, considerable care must be exercised in formulating the split-operator finite-element method in order to preserve the power in the propagating electric field. The calculations are performed in the context of the Fresnel approximation to the scalar Helmholtz equation, which yields accurate solutions for transverse electric (TE)-polarized electric fields in rib waveguides far from cutoff.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analysis of the spectral index method for vector modes of rib waveguides

The spectral index method is a new and simple way of finding quickly and easily the guided modes and propagation constants of semiconductor rib waveguides. Here, the method itself is analysed, and its accuracy as compared with finite-difference results is confirmed. Even in its simplest form, the method produces accurate propagation constants and E or H field profiles using little CPU time and negligible storage.

Efficient beam propagation techniques

It is shown that suitable modifications of the free-space-propagation operator in the standard fast-Fourier-transform beam propagation procedure yield a far more rapid code in the context of semiconductor rib waveguide calculations. The procedure curtails the diffraction experienced by the high-order Fourier components of the electric field and mirrors the structure of the recently introduced finite-difference beam propagation algorithm. It is used to investigate the propagation losses of a Y-junction composed of single-mode rib waveguides and illuminated by its normalized guided mode.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Spectral analysis with various beam propagation techniques

We compare the modal electric field distributions and propagation constants of strongly guiding semiconductor rib waveguides obtained with several newly proposed beam propagation techniques to those of the standard beam propagation method.

Analysis of forward wide-angle light propagation in semiconductor rib waveguides and integrated-optic structures

We analyse longitudinally varying semiconductor rib waveguides with a new nonparaxial wide-angle equation for unidirectional light propagation. We further develop a solution method involving multiplication of the incoming electric field by a series of unitary operators which are evaluated by splitstep fast Fourier transform and finite difference techniques. In the test case of a strongly guiding rib waveguide Yjunction, the estimated losses nearly coincide with those of standard Fresnel equation procedures. We also present a numerical analysis of an integrated-optic lens, demonstrating significant errors in previous results. Finally, we explicitly illustrate the increased accuracy of our new method in comparison to the Fresnel equation for a highly nonparaxial Gaussian beam.

Scattering loss from rough sidewalls in semiconductor rib waveguides

A new scattering formula is applied to the slab loaded rib waveguide. Rib corrugations of up to 50 nm in amplitude lead to losses of the order of a few dB/cm, with trends which agree with experiment

Erratum: Analysis of forward wide-angle light propagation in semiconductor rib waveguides and integrated-optic structures

Erratum: Analysis of forward wide-angle light propagation in semiconductor rib waveguides and integrated-optic structures

Fast and accurate method for calculation of polarised modes in semiconductor rib waveguides

A new semivectorial ‘spectral index’ (SI) method for finding the guided modes of semiconductor rib waveguides is described. The results are shown by comparison to be of the same accuracy as well established finite difference calculations. A useful by-product is a contour map of the principal field component. The propagation constants are found using novel transcendental equations which are easy to set up and are given here explicitly. These discriminate clearly between the TE and TM modes and are variational in nature.

Spectral index method for rib waveguide analysis

A new model for semiconductor rib waveguides is presented which provides fast and accurate solutions of the wave equation. The model has been implemented on a personal computer and produces values for the modal index (neff) differing by less than 0.006% from those calculated using a sophisticated finite difference program.

Fresnel equation studies of longitudinally varying semiconductor rib waveguides: reference wavevector dependence

We demonstrate that the accuracy of paraxial loss calculations for longitudinally varying semiconductor rib waveguides is significantly affected by the value assumed for the reference refractive index, n0. We then perform a full threedimensional simulation of a weakly guiding single-mode rib waveguide Y-junction, and compare our results to those of the effective index method, obtaining excellent agreement when n0 nearly coincides with the refractive index of the guided mode.

Split-step finite difference analysis of rib waveguides

We present a new rapid approach to the analysis of strongly guiding and longitudinally varying semiconductor rib waveguide structures. Our technique, which is a synthesis of the beam propagation and finite difference methods is Hermitian, second-order accurate and intrinsically stable.