Noniterative calculation of complex propagation constants in planar waveguides.

We adapt an efficient finite-difference procedure for determining complex propagation constants to the analysis of modes in planar waveguides. The method requires solving a single rather than multiple eigenvalue equations and does not require prior knowledge of either the nature of the solutions or the position of the modal eigenvalues in the complex plane.

Impedance-matched absorbers for finite-difference parabolic equation algorithms

In this paper, a perfectly matched layer (PML) absorber, recently introduced into the electromagnetic propagation literature by Berenger [J. Comput. Phys. 114, 185-200 (1994)], is adapted for use with both paraxial and wide-angle acoustic parabolic equations (PEs). Our procedure incorporates an imaginary component into the transverse coordinate that mimics the introduction of a fictitious absorber on the edge of the computational grid. Use of such an impedance-matched layer can significantly reduce spurious reflections compared to physical absorbing layer methods and thus allows a smaller number of boundary points to be employed in PE calculations. Numerical results obtained with several higher-order propagator approximations confirm that such impedance-matched absorbers efficiently eliminate reflections.

Numerical studies of split-operator finite-difference alternating-direction implicit propagation techniques based on generalized Padé approximants.

We study numerically high-order propagation methods that incorporate representations of the exponential of two noncommuting operators as alternating products of Padé approximants of the individual operators. We demonstrate that these generalized Padé approximants are easily assembled through simple recursions and verify the central fact that their order need be far less than that of the overall method. We then analyze light propagation through an integrated-optic microlens using a sixth-order generalized Padé technique and compare its rate of convergence to that of standard propagation algorithms.

Generalized propagation techniques.

We introduce a new identity that relates the exponential of the sum of two noncommuting operators to the exponentials of the individual operators. This formula generates rapid fourth-order split-step fast-Fourier-transform, split-operator finite-difference, split-operator finite-element, and real-space propagation algorithms. To illustrate the procedure, we model the focusing of a light beam by a spherical integrated-optic microlens.

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.

Analysis of Y-junction and coupled laser arrays.

We demonstrate that a recently developed reformulation of the beam propagation method can be employed to give the exact modal structure of infinite Y-junction laser arrays. Our results for realistically short ( asymptotically equal to50-microm) Y-junction lengths are similar to those of previous approaches based on perfect Y-junction arrays. However, we find a previously unreported anomalous behavior for the gain of some higher-order supermodes. We also study short and weakly guiding nonideal Y-junction laser arrays. We then describe the behavior of coupled laser arrays in terms of band structure and subsequently propose a new high power strongly coupled laser array configuration.

Influence of mode coupling on differential mode delay.

The manner in which the differential mode delay (DMD) pulse response is affected by ellipticity- and microbending-induced mode coupling has been analyzed numerically. We have considered both a fiber profile containing a central index dip and fiber profiles with sinusoidal ripples. We find that slowly varying profile components can be correctly estimated from DMD results even in the presence of substantial mode coupling.

Effect of mode coupling on the total pulse response of perturbed optical fibers.

A computer program has been developed to study the total pulse response of optical fibers with profile ripple and central index depressions in the presence of arbitrary mode coupling. We have found that the magnitude of the compression of the total pulse response generated by mode coupling depends significantly on the details of the refractive-index profile of the test fiber.

Optical phase conjugation for time-domain undoing of dispersive self-phase-modulation effects.

We show that the temporal distortion and spectral broadening of a pulse generated by the combined effects of group-velocity dispersion and self-phase modulation is removed by reflection of a cw-pumped, broadband, unityreflecting Kerr-like optical phase conjugator followed by retraversal of the nonlinear medium. We also examinenumerically the effects of finite linear loss in the material, of nonunity conjugate reflectivity, and of finite conjugator thickness.

Numerical investigation of mode coupling in sinusoidally modulated GRIN planar waveguides.

We study mode coupling in planar 2-D graded-index optical waveguides with the beam propagation method. In particular we examine the effect of periodic radial deformations along the axis of a parabolic refractiveindex waveguide and compare our results to the results of perturbation theory.