Lasers and more

Research Interests

I am a mathematical modeler interested in the broad fields of nonlinear optics, computational physics, PDEs, and semiconductor quantum theory. CUrrently a fifth year doctoral student in Applied Mathematics at the University of Arizona. My dissertation work involes investigating semiconductor disc lasers through a quantum many body model. Working to advance a system of numerical tools for coupling semiconductor physics to beam propagation in multiple dimensions.

Here is a CV link with my full experience. Here is a Resume link (Last updated 2021). Following are a short list of selected publications:

Microscopic modeling of non-normal incidence vertical external cavity surface-emitting laser cavities, Appl. Phys. Lett. 118, 121103 (2021)

Microscopic charge carrier dynamics within non-normal incidence VECSEL cavities

Microscopic modeling of transverse mode instabilities in mode-locked vertical external-cavity surface-emitting lasers

Microscopic modeling of transverse non-equilibrium dynamics in mode-locked VECSELs

The Transverse Maxwell Semiconductor Bloch Equations

The transverse Maxwell Semiconductor Bloch Equations (tMSBE) couple together Maxwell's wave equation the the Semiconductor Bloch Equations to model realisitic semicodunctor laser cavities from a quantum mechanical many body perspective rather than the traditional purely phenomenological methods.

The Semiconductor Bloch Equations model are the state of the art when modeling the response of a semiconductor quantum well system to an applied electric field. Below we see the polarization and carrier responses to an incoming pulse. Notice how the pulse burns a kinetic hole in the carriers.

The added flexibility of the transverse dimensions allows us to visualize higher order modes in novel ways.

We extended this to model a variety of interesting cavity types. Colliding pulses within a ring cavity VECSEL exhibit an interference pattern which affects the charge carrier population inversions in a truly inhomogenous manner. The competition in carriers between the two directions leads to unequal pulse intensities.

Gratuitous KdV simulation

A compact FDTD two soliton numerical solution to the Korteweg deVries equation showing the time delay between impacting solitons.