Metasurfaces and Optimal Transport

In this talk, I will report recent results motivated from an active area of research in engineering of meta materials concerning the design of metalenses and metamirrors. These are ultra thin optical components composed of nanomaterials that potentially can replace traditional lenses. By carefully arranging nanomaterials on a given substrate surface, through a function known as phase discontinuity, light can be refracted or reflected according to predetermined specifications. The existence of phase discontinuity functions is closely related with both the curvature of the given surface and the given set of directions where the radiation is desired to be steered. This necessitates the formulation of a generalized vector Snell’s law that incorporates phase discontinuities. Furthermore, problems associated with incident and transmitted light distributions will be addressed using methods from optimal transport, and numerical examples will be shown.

References

[1] C. E. Guti´errez and L. Pallucchini. Reflection and refraction problems for metasurfaces related to Monge-Amp`ere equations. Journal Optical Society of America A, 35(9):1523–1531, 2018.

[2] C. E. Guti´errez, L. Pallucchini, and E. Stachura. General refraction problems with phase discontinuities on nonflat metasurfaces. Journal Optical Society of America A, 34(7):1160–1172, 2017.

[3] C. E. Guti´errez and A. Sabra. Chromatic aberration in metalenses. Advances in Applied Mathematics, Vol. 124, March 2021

[4] C. E. Guti´errez, Q. Huang, Q. M´erigot, and B. Thibert. Metasurfaces and Optimal Transport. Journal of Computational Mathematics 22(8), 2022