2018/01/22 by Gutierrez, Cristian E., Sabra, Ahmad
#34K10 #78A05 #78A46 #93C23 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Optics (physics.optics)
paper · doi:10.48550/arxiv.1801.07223
Due to dispersion, light with different wavelengths, or colors, is refracted at different angles. Our purpose is to determine when is it possible to design a lens made of a single homogeneous material so that it refracts light superposition of two colors into a desired fixed final direction. Two problems are considered: one is when light emanates in a parallel beam and the other is when light emanates from a point source. For the first problem, and when the direction of the parallel beam is different from the final desired direction, we show that such a lens does not exist; otherwise we prove the solution is trivial, i.e., the lens is confined between two parallel planes. For the second problem we prove that is impossible to design such a lens when the desired final direction is not among the set of incident directions. Otherwise, solving an appropriate system of functional equations we show that a local solution exists.