P.C. Kendall

The weighted index method: a new technique for analyzing planar optical waveguides

A method of analyzing optical waveguides called the weighted-index technique is presented. It is particularly appropriate for planar geometries with abrupt refractive index profiles, such as semiconductor waveguides. The method is an extension of the simple effective-index and transverse-resonance methods and has a strong physical foundation. The weighted-index method is shown to give more accurate results and be valid for a wider range of structures. Although it is more complicated than the effective-index method, it can be implemented on the smallest of personal computers. >

Rib waveguide spot-size transformers: modal properties

Efficient spot-size convertors are an essential component of modern integrated optoelectronics, providing a simple and reliable interface with fibers. One recently proposed design functions by forcing the field from a small spot rib waveguide into a large spot one by using a taper. Accurate models of these structures, and a clear understanding of the coupling mechanisms they rely upon, are essential if optimized designs are to be produced. Furthermore, it is necessary to develop analysis techniques which are accurate yet not computationally intensive, suitable for use within an iterative design environment. Here, the well known and proven spectral index method is extended to efficiently analyze this class of vertically coupled rib waveguide spot-size transformer, providing both the guided modes and for the first time, the substrate radiation modes of the structure. These modes can then subsequently be used to design and determine the performance of the full tapered structure.

New formula for semiconductor laser facet reflectivity

An analytic expression for the main mode reflectivity of a multicoated laser facet at normal incidence is derived using the free space radiation mode technique. This uses exact guided modes, and accurately models the radiation modes near the facet. The results compare favorably with exact TE and TM benchmarks while retaining the simplicity and speed of the Fresnel approximations.<<ETX>>

Full vector analysis of two-dimensional angled and coated optical waveguide facets

We analyze the important problem of scattering from two-dimensional (2-D) optical waveguide facets, including the effects of both antireflection coatings and facet angle. The facet is allowed to be angled in both vertical and horizontal planes, necessitating a fully vectorial approach to model correctly the polarization coupling that occurs. To achieve this, the highly efficient Free Space Radiation Mode method has been extended to the general vector case, yielding novel expressions for both the reflectivity and the coupling coefficients which can be rapidly evaluated on a desktop PC for a wide variety of practical structures. Results are presented for both angled, coated and coated angled facets. Full field profiles, also available from the approach, are presented and provide useful design information and aids to understanding.

Novel vectorial analysis of optical waveguides

A nonlinear iterative (NLI) method, originally developed by Hewson-Browne in geomagnetism, is applied to the vectorial analysis of optical waveguides. The method explicitly shows the interrelations between the scalar, polarized and vectorial operators and can be conveniently implemented using finite difference methods. Excellent accuracy in the normalized propagation constant is claimed along with agreement with earlier work and field distributions. The method presented enables vector results to be obtained simply by using computer programs, often available, for either polarized or scalar modes. This procedure proves more efficient than a standard vectorial finite difference technique.

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. >

Bi-oblique propagation analysis of symmetric and asymmetric Y-junctions

A novel finite difference beam propagation method (BPM) analysis based upon a bi-oblique coordinate representation is presented. The analysis yields a computationally efficient algorithm that permits accurate simulation of a wide variety of structures to be made without staircase approximations. Further, the independent paraxial and wide angle approximations, centered upon the direction of optical field propagation in each branching waveguide, may be incorporated into the algorithm. This feature allows a low-order approximation to be used in the algorithm even if one or both of the branching angles is large. The approach has been applied to both symmetric and asymmetric optical waveguide Y-junctions and produces results in excellent agreement with those in the literature.

Novel beam propagation algorithms for tapered optical structures

Novel beam propagation algorithms for tapers have been developed that eliminate errors caused by staircase approximations. Nonorthogonal coordinate systems are introduced that model the effects of beam spreading and obliqueness while retaining the standard coordinate z to advance the solution forward uniformly. Both two- and three-dimensional (2-D) and (3-D) examples are considered to illustrate both the accuracy and utility of the scheme. The new method maintains its accuracy with fewer sample points allowing significant reduction in calculation time.

The dispersion characteristics of oblique coordinate beam propagation algorithms

The use of an oblique coordinate system with the finite difference beam propagation method has previously been demonstrated to offer significant computational advantages over using rectangular coordinates for a wide range of practical optical structures. The effects of finite mesh resolution, step size, and order of the algorithm in terms of numerical dispersion and dissipation are here investigated and quantified for the first time.

Nonstandard beam propagation

A nonorthogonal coordinate system that extends the present range of angled configurations for which the beam propagation method (BPM) is accurate is introduced. This offers an extra degree of freedom within configuration and method when the BPM is applied in the design of general photonic integrated circuits incorporating angled waveguide sections.