Matthias Maier
Texas A&M University-College Station, TX·Mathematics & Statistics·Early-career
Metamaterials are engineered structures, often patterned at the nanoscale, that steer light in ways ordinary materials cannot. Designing optical devices from them requires computer simulations that predict how light interacts with these tiny, complex geometries.
- Fields
Mathematics & Statistics
Physics
Engineering
- Topics
metamaterials
computational electromagnetics
Maxwell's equations
- Grants
- 1 known grant, through Aug 2027
What they work on
- Develop and analyze numerical methods for time-harmonic (single-frequency) simulations of non-local conductivity, where a material's electrical response depends on nearby conditions, in nanoscale optical geometries.
- Build scalable, distributed time-stepping algorithms that couple time-dependent Maxwell's equations for light with 2D evolution equations describing the conductivity response of a thin layer.
- Apply these methods in collaborations designing nanoscale optical devices that modulate and control the path of light.
- Test fluid-mechanical models of electron response, which treat electrons like a flowing fluid, against recent experimental results using direct numerical simulation.
More about the research
Those simulations are hard. At the nanoscale, a device's response depends on how incoming electromagnetic waves interact with the device's electrons. Existing numerical methods are often not reliable or controllable enough to capture this, and the needed tools are not available commercially. This work develops and mathematically analyzes robust, high-performance computational methods to close the gap between physical theory and optical device engineering.
Why it matters
Engineers designing nanoscale optical devices, such as components that modulate or redirect light, need simulations they can trust. This work could provide reliable numerical tools for predicting the optical behavior of metamaterials and thin conducting layers. Such tools could let device designers test ideas computationally before building them. They could also help physicists check models of electron behavior against experimental data.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Ignacio Tomas
Texas Tech University, TX·Mathematics & Statistics
Develop semi-implicit time-stepping schemes for the Euler-Maxwell and Euler-Poisson fluid models of charge transport that keep density positive and energy stable, even when fast plasma oscillations are present.
Mingchao Cai
Morgan State University, MD·Mathematics & Statistics
Develop monolithic parameter-robust preconditioners, which speed up solvers for the whole coupled system, for quasi-static and fully dynamic thermo-poroelastic models, with mathematical proofs of stability and convergence.
Qingguo Hong
Missouri University of Science and Technology, MO·Mathematics & Statistics
Develop discretizations of multiple-network poroelastic (MPET) models that remain robust across parameter ranges, strongly conserve mass, and keep the stress tensor exactly symmetric.
The school
Texas A&M University-College Station: 23 labs on PI Pages, $1.4B a year on research, 768 research doctorates a year.
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