# David Yevick

## Biography

Professor Yevick' s research group delivers practical, innovative and leading-edge solutions to industry while developing general physical and mathematical results and techniques that can be employed in wide areas of applied physics.

Professor Yevick's current research, performed in collaboration with CIENA, concentrates on efficient procedures for analyzing statistically unlikely quantities such as random bit errors, measurement techniques for communication systems with emphasis on very high-speed measurements of polarization activity and polarization mode delay in optical communication components and theoretical and numerical models of polarization evolution.

Professor Yevick's current research, performed in collaboration with CIENA, concentrates on efficient procedures for analyzing statistically unlikely quantities such as random bit errors, measurement techniques for communication systems with emphasis on very high-speed measurements of polarization activity and polarization mode delay in optical communication components and theoretical and numerical models of polarization evolution.

## Research Interests

- Beam Propagation (Wave Propagation)
- Multicanonical and Transition Method
- Muller Matrix Formalism of Polarization Mode Dispersion
- Technology and Optics
- Photonics
- Optical Systems

## Scholarly Research

Professor Yevick's 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. They 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 they 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, they demonstrated the applicability of fast Fourier-transform and finite-element techniques to the band structure of semiconductor crystals and to multiple stripe geometry lasers. They 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.
Next, they 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. The full valence band structure was incorporated for the first time 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.
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. They 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.
Another technique to emerge from their studies was an exact and easily programmed numerical boundary condition for the two-dimensional parabolic wave equation. They 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.
Our present research adresses polarization effects in optical communications and in particular the time varying polarization-dependent component of the transit times of electric fields in optical fibers (polarization mode dispersion). To model the resulting system impact we advanced an analogy between the probability density function in a communication system and the statistical mechanical density of states. This enabled the application of multicanonical approach to generate the probability distribution function of the relative delay times in the presence of polarization mode dispersion or to determime the bit-error-rate in an optical fiber systems. The procedure samples all regions of the distribution function equally through an automated, iterative technique and can be widely applied in communication and systems theory. (see here and here for a short review of the method). They then implemented the multicanonical method experimentally, achieving significant improvements in speed and accuracy compared to standard measurements of quantities such as bit-error-rates. They further advanced a transition matrix based approach that incorporates the multicanonical methods and its variants but can additionally be extended to the analysis of the statistical time evolution of arbitrary stochastically varying memoryless time-varying channels. Finally, highly accurate and versatile procedures for describing the frequency variation of polarization fluctuations both in the absence and presence of polarization dependent losses were developed. These procedures originate in but greatly extend our original work on the Magnus expansion and generalized propagation methods by incorporating the four-dimensional Stokes matrices.

## Education

- 1985, Docent Physics, University of Lund, Lund, Sweden
- 1977, Doctorate Physics, Princeton University, Princeton, New Jersey, U.S.A
- 1975, Master of Arts Physics, Princeton University, Princeton, New Jersey, U.S.A
- 1973, Bachelor of Arts Physics, Harvard University, Cambridge, Massachusetts, U.S.A.

## Teaching*

- NE 217 - Advanced Calculus and Numerical Methods 2
- Taught in 2022, 2023

- NE 451 - Simulation Methods
- Taught in 2020, 2021, 2022

- PHYS 239 - Computational Physics 2
- Taught in 2019

- PHYS 342 - Electricity and Magnetism 2
- Taught in 2020, 2023

- PHYS 363 - Intermediate Classical Mechanics
- Taught in 2019, 2021, 2023

- PHYS 364 - Mathematical Physics 1
- Taught in 2019, 2020, 2022

* Only courses taught in the past 5 years are displayed.

## Selected/Recent Publications

- Efficient beam propagation techniques D Yevick, B Hermansson IEEE Journal of quantum electronics 26 (1), 109-112
- New formulations of the matrix beam propagation method: application to rib waveguides D Yevick, B Hermansson IEEE Journal of Quantum Electronics 25 (2), 221-229
- Correspondence of variational finite-difference (relaxation) and imaginary-distance propagation methods for modal analysis D Yevick, W Bardyszewski Optics letters 17 (5), 329-330
- A guide to electric field propagation techniques for guided-wave optics D Yevick Optical and Quantum Electronics 26 (3), S185-S197
- Design rules for slanted-angle polarization rotators H Deng, DO Yevick, C Brooks, PE Jessop Journal of lightwave technology 23 (1), 432
- Efficient beam propagation techniques D Yevick, B Hermansson IEEE Journal of quantum electronics 26 (1), 109-112
- New formulations of the matrix beam propagation method: application to rib waveguides D Yevick, B Hermansson IEEE Journal of Quantum Electronics 25 (2), 221-229
- Correspondence of variational finite-difference (relaxation) and imaginary-distance propagation methods for modal analysis D Yevick, W Bardyszewski Optics letters 17 (5), 329-330
- A guide to electric field propagation techniques for guided-wave optics D Yevick Optical and Quantum Electronics 26 (3), S185-S197
- Design rules for slanted-angle polarization rotators H Deng, DO Yevick, C Brooks, PE Jessop Journal of lightwave technology 23 (1), 432