Xian Hadia

I am a Ph.D. candidate in Computational Science and Engineering at Georgia Tech, advised by Prof. Raphaël Pestourie, specializing in large-scale inverse design for nanophotonics. My research focuses on developing high-performance computational frameworks to solve complex electromagnetic inverse problems, bridging adjoint-based optimization, data-driven surrogate modeling, and scalable numerical solvers.

I build custom physics solvers utilizing finite-difference methods (FDTD, FDFD), finite element methods (FEM), and rigorous coupled-wave analysis (RCWA), alongside tools like Tidy3D, MEEP, COMSOL, and Ansys Lumerical. To make large-area nanophotonic device optimization computationally tractable, I architect high-performance computing (HPC) workflows that leverage multi-GPU parallelization, domain decomposition, and tensor-based linear algebra formulations. Beyond theoretical and algorithmic development, I bridge simulation with hardware by designing fabrication-constrained metasurfaces—for beamforming, focusing, and arbitrary wavefront engineering—and validating them via hands-on cleanroom lithography, optical metrology, and experimental bench characterization.

Keywords: Nanophotonics · Inverse Design · Adjoint Optimization · Computational Electromagnetics · Surrogate Models · Scientific Computing

Here is a glimpse into what I do. Much of my work involves modeling and solving partial differential equations (PDEs) under various boundary conditions and across complex geometries - most notably, Maxwell’s equations, which govern electromagnetic phenomena.

My research lies at the intersection of numerical methods, physics, and scientific computing. Classical electromagnetism is one of the most thoroughly understood areas of physics, yet efficiently solving Maxwell’s equations across complex geometries, material configurations, and operating conditions remains a significant computational challenge. While the underlying physics is well established, translating these equations into practical engineering design tools requires increasingly sophisticated computational methods.

One of my primary research goals is to develop efficient numerical methods and physics-based surrogate models that balance computational cost with the appropriate level of physical fidelity, enabling faster simulation, optimization, and inverse design of complex engineering systems.

One of the primary motivations for developing fast, approximate, yet physically grounded solvers of Maxwell’s equations is not only to simulate electromagnetic phenomena, but also to design devices that exhibit a desired electromagnetic response.

Consider a metasurface: an optical device composed of subwavelength structures that manipulate the amplitude, phase, or polarization of light. Despite their relatively small physical dimensions, these devices can possess extraordinarily large design spaces. For example, a circular metasurface just 1 mm in diameter, consisting of individually tunable nanostructures arranged on a 400 nm lattice, could have nearly five million independent design parameters.

This raises a fundamental computational question: How can we efficiently search a design space containing millions of degrees of freedom?

One approach is to formulate the engineering task as a mathematical optimization problem. We begin by defining an objective function that quantifies how closely a device’s electromagnetic response matches its intended behavior. The geometry and material properties of the device become the design variables, and the goal is to iteratively update these parameters to improve the objective.

Mathematically, this can be expressed as

\[\min_{\boldsymbol{\theta}}\; \mathcal{L}\left(\mathbf{E}(\boldsymbol{\theta}), \boldsymbol{\theta}\right)\]

subject to Maxwell’s equations, where \(\boldsymbol{\theta}\) represents the device’s design parameters, \(\mathbf{E}\) is the resulting electromagnetic field, and \(\mathcal{L}\) measures the discrepancy between the simulated and desired performance.

However, directly computing the sensitivity of the objective to millions of parameters through finite differences would be prohibitively expensive, potentially requiring millions of additional electromagnetic simulations per optimization iteration.

This is where adjoint optimization becomes particularly powerful.

Rather than perturbing each design parameter individually, the adjoint method exploits the mathematical structure of the governing equations to compute the gradient of a scalar objective with respect to all design parameters using just two electromagnetic solves: one forward simulation and one adjoint simulation.

Remarkably, the number of required solves does not grow with the number of design parameters. Whether a metasurface has hundreds or millions of geometric variables, the entire gradient can be obtained from these two solves, under the appropriate assumptions.

This connection between electromagnetic physics, numerical simulation, and gradient-based optimization is what makes inverse design such an interesting problem at the intersection of applied mathematics, physics, and scientific computing.

The animation below illustrates this process for a metasurface hologram, where the device’s geometry is iteratively optimized to produce a desired optical field distribution. Use the slider to see how the design converges at a set iteration.

Replay animation

The scalar model assigns each pillar a phase delay from an idealized, linear diameter-to-phase map. Relaxed Gerchberg–Saxton iterations alternate between the prescribed Gaussian input amplitude and the target far-field amplitude using forward and inverse FFTs. The optimizer allows some light to spill outside the displayed window so it can better match the target inside it. The model assumes unit transmission and independent pillars. Georgia Tech logo reference

Here are some of my projects. The individual project pages are under construction.