Michael Munowitz

Analysis of finite rib waveguides by matrix methods

The modal structure of finite lateral extent waveguides differs from that of the associated infinite structures by the presence of additional guided modes arising from the boundary conditions and by the discrete representation of the continuum modes. These differences are analyzed for a rib waveguide using matrix methods. The origin of the additional modes and their evolution with changing system parameters are discussed. The development of localized modes from delocalized modes is of particular interest, as is the evolution of radiation modes into discrete, localized modes of higher order as the rib increases in height. These developments are followed in detail and the changes in modal character are related to the properties of the finite systems dispersion curves. Illustrations of the effect of increasing system size on the localized and delocalized modes are given. >

Numerical modeling of coherent coupling and radiation fields in planar Y-branch interferometers

The beam-propagation method is used to study intermodal power transfer and radiation losses in slab waveguide splitters and combiners. Numerical computations demonstrate how modal power at an interferometers recombination point exhibits an oscillatory dependence on the length of each distinct section of the structure. Recoupling of guided and unguided modes can be anticipated and adjusted so as to maximize output modal power and minimize sensitivity to transition lengths. Examples are given for systems formed from both angle bends and S bends. >

Design of strip-loaded optical waveguides for low-loss coupling to optical fibers

Mismatch between the fundamental mode of a waveguide and that of an attached optical fiber may cause a significant loss of power in a guided-wave structure. These losses can be minimized, however, by proper shaping of the waveguide mode through judicious choice of dimensions and refractive indexes. It is shown by computer modeling and qualitative arguments that coupling losses between standard optical fibers (5-10- mu m modal diameter) and strip-loaded waveguides constructed of GaAs/AlGaAs may be reduced to less than 10% at each facet. A wavelength of 0.85 mu m is used as a specific example, with modal shapes explored systematically for a series of different waveguide structures. >

Application of the Fourier-grid method to guided-wave problems

A method recently developed for solving the Schrodinger equation is applied to dielectric waveguides. The technique, which is extremely simple to implement, involves representing the differential operator in the scalar Helmholtz equation on a grid of discrete points in coordinate space, and then diagonalizing the resulting matrix to reveal the propagation constants and field patterns of the guided modes. The square of the transverse index profile is specified directly as a diagonal matrix in coordinate space, while the matrix for the transverse Laplacian is obtained through the Fourier relationship between its diagonal form in momentum space and the equivalent representation in coordinate space. The accuracy and computational performance of this procedure is assessed for one- and two-dimensional transverse profiles. Modal refractive indices and fields computed by the grid method are found to agree well with those derived by means of other techniques. >

An investigation of the modal coupling of simple branching semiconductor ring lasers

We have investigated, by simulation, the coupling efficiencies of a ring laser into a straight guide in terms of the power splitting ratio between the fundamental modes of the ring and straight output guide, as well as the proportion of power lost to higher-order excitations of the straight guide. The results show that the typical design for a branching ring laser can be optimized by offsetting the output guide position and choosing the proper guide width. This analysis also shows that the symmetrical dual output port design (i.e. tangential straight guide) can result in very poor output coupling efficiencies as compared to the single output port design. >

Numerical procedures for constructing equivalent slab waveguides-an alternative approach to effective-index theory

Standard effective-index methods may fail when properties of a waveguide are cut off. As an alternative, a simple numerical procedure is presented by which an equivalent slab waveguide is similarly substituted for the original two-dimensional refractive-index profile. The technique is demonstrated for a rib waveguide and shown to be in agreement with exact results obtained by other means. It provides an efficient way to replace a two-dimensional transverse distribution of refractive indexes with an equivalent one-dimensional profile. Consistent with the rationale of effective-index theory, it seeks to produce the most reasonable one-dimensional representation of an intrinsically two-dimensional distribution. An equivalent slab formulated in this way should provide a good starting point for subsequent beam propagation calculations involving longitudinally varying structures. >

Lateral confinement in generalized strip‐loaded optical waveguides

Mode structure in strip‐loaded waveguides is studied using an eigenvalue method based on a two‐dimensional Fourier analysis. Modified guides where the loading strip is displaced above the core by an additional layer of cladding are considered as a general case. Lateral confinement is found to depend largely on the extent to which the field decays over the strip, and generally worsens as vertical confinement (in the direction perpendicular to the layers of the guide) improves. Conditions that degrade lateral confinement include a large difference in refractive index between core and cladding, a core wide relative to operating wavelength, and large separation between strip and core. Lateral confinement does not vary monotonically with vertical confinement, moreover, but instead may be maximized over a specific range of the guide’s refractive indices.

Mode structure and lateral confinement in strip-loaded optical waveguides: Effects of asymmetric cladding

Strip-loaded waveguides formed from three dielectric layers are used in integrated optics to confine and channel light in two dimensions. The numerical analysis reported shows that modal characteristics of such systems can be strongly affected by any differences between the refractive indexes of the upper and lower cladding. Asymmetries that tend to shift intensity toward the upper cladding generally act to tighten lateral confinement, introduce additional lateral modes, and displace the modes up into the strip. These effects are explained by noting the interplay of vertical and lateral confinement in a strip-loaded waveguide, and by analogy to one-dimensional slab waveguides. >

Beam propagation computations in one and two transverse dimensions

Abstract Substitution of slab geometries for two-dimensional index profiles is commonly employed in calculations involving the beam propagation method, and is based on using effective-index theory to replace the full system by a one-dimensional representation with the same propagation constants. Results obtained for sample one-dimensional model systems are compared critically herein with those determined for complete structures described by two transverse coordinates. We show that in most respects the effective-index approach remains qualitatively useful for waveguide design, notwithstanding some clear discrepancies between the one- and two-dimensional results.

Two-dimensional model for waveguide junctions

Losses in branched waveguides are often estimated from the overlap between incident and transmitted electric fields, with the effective-index method typically used to reduce the problem to one dimension. We extend this technique to two dimensions by combining the analytical formalism with numerically computed series expansions for the modal fields. The hybrid procedure is simple to use and widely applicable, in particular to those structures for which effective-index theory may fail.