6 papers
Refraction laws in spatio-temporal media
Cristian E. Gutiérrez, Eric Stachura
We study the time-dependent Maxwell system, formulated in the sense of distributions, for electromagnetic waves propagating through media with temporal and spatial material interfa…
Refraction laws in temporal media
Cristian E. Gutiérrez, Eric Stachura
We consider the time dependent Maxwell system in the sense of distributions in the context of temporal interfaces. Just as with spatial interfaces, electromagnetic waves at tempora…
The Multi-marginal Monge Problem and an Application to Metasurfaces
Irem Altiner, Cristian E. Gutiérrez
This paper studies the multi-marginal Monge problem in the setting of compact metric spaces proving existence and uniqueness of solutions when the cost function is Lipschitz. We ap…
Double metasurfaces and Optimal transport
Irem Altiner, Cristian E. Gutiérrez
This paper constructs metalenses that separate homogeneous media with different refractive indices, refracting one domain into another while conserving a prescribed energy distribu…
Differentiability of monotone maps related to non-quadratic costs
Cristian E. Gutiérrez, Annamaria Montanari
The cost functions considered are , with , homogeneous of degree , with positive definite Hessian in the unit sphere. We consider monotone ma…
Generalized Snell's law and Maxwell equations
Cristian E. Gutiérrez, Ahmad Sabra
This paper examines the Maxwell system of electrodynamics within the framework of distributions. A primary objective is to establish boundary conditions for fields at interfaces wh…