A new version of the scalar TE wave equation is introduced, one that is particularly useful in bent waveguide analysis. The slowly varying envelope equation in cylindrical coordinates for the field amplitude E is finite-differenced, with no other approximations made to it. It will be shown that this version of the equation has several advantages over other forms and gives good results for the power loss rates even at radii /spl les/100 /spl mu/m, as well as being useful for the study of curved structures with varying radii of curvature. Evidence is provided to show that the loss rates calculated from this equation using the two dimensional finite difference beam propagation method compare favorably with other numerical and analytical results found in the literature. Special care must be taken when applying transparent boundary conditions as the curvature increases. >

A finite difference BPM analysis of bent dielectric waveguides

We propose a drastically new method for generating single photons in a deterministic way by interaction of electron beams with optical waveguides. We find a single swift electron to produce a guided photon with large probability. The change in energy and propagation direction of the electron reveals the creation of a photon, with the photon energy directly read from the energy-loss spectrum or the beam displacement. Our study demonstrates the viability of deterministically creating single guided photons using electron beams with better than picosecond time uncertainty, thus opening a new avenue for making room temperature, heralded frequency-tunable sources affordable for scientific and commercial developments.

Single-photon generation by electron beams.

A simple and effective method is introduced to calculate the bending loss and phase enhancement of a bent planar waveguide. The wave field is represented in terms of Airy functions and an eigenvalue equation is derived by matching the boundary conditions and the radiation condition in the outer cladding layer. The complex propagation constant is obtained by solving the eigenvalue equation with the Newton-Raphson method, and the imaginary part of the propagation constant gives directly the bending loss of the bent waveguide. The results are compared with the previous experimental and numerical results and are shown to be highly accurate and effective. The phase enhancement due to the bending is also studied.

A Simple and Effective Method for Calculating the Bending Loss and Phase Enhancement of a Bent Planar Waveguide

We discuss the effects of waveguide geometry on the radiation loss of tightly curved multimode dielectric waveguides. Three waveguide geometries are investigated: a ridge waveguide, a buried waveguide, and an interdiffused waveguide. We compare the effective index method with both semi- and full-vectorial method-of-lines analyses for these waveguide geometries. This comparison shows that the effective index method is accurate for curved waveguides except where the outer confinement region is in cut-off or, in the case of TM-polarization, for the ridge waveguide. In the latter case, the full-vectorial method-of-lines predicts a resonant feature of the TM-mode radiation loss of curved ridge waveguides; this is not predicted by either the semivectorial method-of-lines or the effective index method.

Comparative analysis of the method-of-lines for three-dimensional curved dielectric waveguides

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. >

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

A semiempirical relation has been developed for determining the minimum allowable radius of curvature of a circular waveguide with an edge-guided fundamental mode. The specified parameters are the wavelength, the effective refractive index of the waveguide, the lateral index step, and the allowable radiation loss coefficient. This relation was fitted and verified against numerically evaluated solutions of Maxwell's equations in two dimensions for lateral index steps 0.01 >

R.S. Burton

Papers

Semiempirical relation for curved optical waveguide design in the edge-guided mode regime