Irem Altiner, Temple University
2023 AWM Research Symposium
Advances in Partial Differential Equations and Applications [Organized by Maya Chhetri, Nsoki Mavinga and Irina Mitrea]

Metalenses are ultra thin surfaces that are composed of nano structures to focus light. These nano structures manipulate light waves by abrupt phase shifts over the scale of the wavelength to bend them in unusual ways. Compared to the bulky, thick shapes of the conventional lenses, metalenses offer many advantages in optical applications due to their reduced thicknesses and multifunctionalities. Mathematically, a metalens can be represented by a pair (Gamma, phi) where Gamma is a surface in mathbb{R}^3, and phi is a C^1 function defined in a neighborhood of Gamma, called phase discontinuity. The knowledge of phi yields the type of arrangements of the nano structures on the surface that are needed for a specific refraction job. In this talk we are going to discuss problems associated with incident and transmitted light distributions using methods from optimal transport.

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