Research Portfolio
My scientific work sits at the intersection of Metaoptics, Computational Photonics, and Machine Learning. I am particularly interested in how subwavelength structures (metasurfaces) can be engineered to control light at the nanoscale, and how data-driven inverse design can accelerate this process.
Core Research Focus Areas
Metaoptics & Metasurfaces
Designing engineered subwavelength optical antennas to control phase, amplitude, and wavefronts.
Metalenses
Flat optics replacing bulky lenses through precise phase mapping and geometric phase engineering.
Computational Electromagnetics
FDTD simulations, near-field/far-field optics, and numerical modeling of Maxwell's equations.
Nonlinear Optics
Modeling light-matter interactions, harmonic generation, and predicting nonlinear refractive indices.
Machine Learning for Physics
Inverse design of photonic structures, Physics-Informed Neural Networks (PINNs), and optimization.
Electrodynamics & Optics
Classical wave theories, diffraction, scattering, optical path length, and analytical formulations.
Primary Research Narrative
Physics-Informed Neural Networks for Nonlinear Optics
The Nonlinear Schrödinger Equation (NLSE) governs pulse propagation in optical fibers and is notoriously expensive to solve numerically at scale. I am developing PINN architectures that embed physical symmetries directly into the network topology, dramatically reducing training data requirements while maintaining physical consistency.
\[i\frac{\partial A}{\partial z} + \frac{\beta_2}{2}\frac{\partial^2 A}{\partial t^2} - \gamma|A|^2 A = 0\]Soliton Dynamics & Stability
Optical solitons are self-sustaining wave packets that arise from a precise balance of dispersion and nonlinearity. I investigate their stability under perturbation and interactions in multi-mode fibers using high-performance numerical simulation in Julia.
Electrodynamics & Computational Methods
Numerical integration of Maxwell’s equations (FDTD methods), the Runge-Kutta family of solvers for ODEs, and Monte Carlo methods for stochastic physical systems.
Machine Learning Theory
Optimization landscapes, gradient flow, and the theoretical foundations of deep learning — particularly in the context of physics applications.
Tools & Methods
| Domain | Methods | Software |
|---|---|---|
| Nonlinear Optics | Split-step Fourier, NLSE | Python, Julia |
| Machine Learning | PINNs, CNNs, gradient descent | PyTorch, NumPy |
| Computational Physics | RK4, FDTD, Monte Carlo | C++, SciPy |
| Scientific Writing | LaTeX, BibTeX | Overleaf |