Previous research

David Yevick

Our initial work in optics centered on the relationship between the observed pulse delay and the input single mode fiber position for selectively excited multimode fibers in the presence of mode coupling. This led to a model that was subsequently employed industrially at Ericsson. We extended fast-Fourier based optical beam propagation methods to anisotropic, periodically perturbed and nonlinear media, leading to programs that were applied at Ericsson, and subsequently adapted at Xerox PARC to electro-optic spatial light modulator based printheads. We also extended the beam propagation method to mode coupling in perturbed and tapered waveguides, fiber bending losses and soliton propagation and interaction.

At the Heinrich-Hertz Institute and Xerox PARC we constructed self-consistent stripe-geometry semiconductor diode laser models based on beam propagation methods, analytic descriptions of cleaved-coupled-cavity lasers and formulas for DBR semiconductor laser linewidths. Subsequently, we demonstrated the applicability of fast Fourier-transform and finite-element techniques to the band structure of semiconductor crystals and to multiple stripe geometry lasers. We further extended imaginary distance beam propagation and matrix methods to optical modal field analysis and in particular to supermodes of periodic waveguide and laser arrays. 

Optical properties of III-V semiconductors

Next, we investigated the optical properties of III-V semiconductors. Beginning with Auger processes, which provide a nonradiative loss channel for recombining carriers in semiconductor lasers, we developed a precise model for the Coloumb interaction between the colliding electrons that can strongly affect the recombination rate. We further incorporated for the first time the full valence band structure into calculations of hot-carrier transport in transistors, band gap renormalization and gain in lasers and transistors and electroabsorption and electrorefraction in quantum-well modulators. Their programs were later extensively employed in high-speed modulator design at Nortel.

Numerical algorithms

Regarding numerical algorithms, major advances included generalized propagation techniques. Discovered concurrently in several fields, these recast the exponential propagation operator as a high-order accurate product of a sequence of individual exponential operators. This work was followed by the analysis of different wide-angle, fast-fourier transform, finite difference and Lanczos algorithms for three-dimensional wide-angle electric field propagation. Numerous applications have since emerged for these methods, for example in underwater acoustics which we examined for several years in collaboration with the Defense Research Establishment Pacific and Atlantic. We also worked on semiconductor rib waveguides without cladding layers where we demonstrated that for properly chosen grid point positions and boundary conditions, a simple scalar finite-difference analysis could accurately model field evolution. These programs were employed at Nortel to optimize numerous waveguide components.

Programmed numerical boundary condition for parabolic wave equation

Another technique to emerge from our studies was an exact and easily programmed numerical boundary condition for the two-dimensional parabolic wave equation. We also examined finite difference and finite element one-way propagation methods for polarized electric fields and demonstrated the existence of intrinsic divergences, the effect of which, however, can be effectively circumvented by replacing the propagation operator by a suitably chosen Pade approximant with complex coefficients. A similar procedure that has again been widely applied industrially was found to accurately describe anti-reflection coated waveguide facets.


 Beam Propagation (Wave Propagation)

An overview presentation (PDF) of some older work on beam propagation by David Yevick and his coworkers and students. Detailed discussions of these results can be found by consulting the publication list.

Multicanonical and Transition Method Presentation

A overview presentation (PDF) on a sample of our work on of the multicanonical and transition matrix procedures. Again, details are available from the above publication list. An introduction to our implementation of multicanonical methods can also be found in our science and engineering textbook (Textbook and CD version avaliable through the US catalogue).

Muller Matrix Formalism of Polarization Mode Dispersion

Several contributions to the application of modern operator techniques to polarization mode dispersion and polarization dependent loss are summarized in our graduate student Michael Reimer's thesis.