This project involves using mathematical models to optimize the performance of a diffractive optical element. Unlike the usual optimization problem, we will seek methods for finding an optimal design in the presence of environmental variability. Sources of variability can include changes in manufacturing or operating conditions. The methods will be applied to designing a diffractive optical ele...

The notion of a spherical angular spectrum leads to the decomposition of the field amplitude on a spherical emitter into a sum of spherical waves that converge onto the Fourier sphere of the emitter. Unlike the usual angular spectrum, the spherical angular spectrum is propagated as the field amplitude, in a way that can be expressed by a fractional order Fourier transform.

Unlike the usual turbo codes, “unifilar turbo codes” are based on only one underlying trellis code. If terminated (i.e., as block codes), they perform as well as (ordinary) turbo codes; if not termina ted (i.e., as convolutional codes), they are attractive for continuous transmission under tight delay

In a two flavour world, the usual equal p, equal E, or equal v assumptions used to derive the neutrino oscillation length can be replaced by a specific definition of the velocity of the oscillating state which, unlike those assumptions, is compatible with exact production kinematics. This definition is further vindicated by the analysis of π µ2 decay at rest.

In this paper we prove another pairing theorem for bordered Floer homology. Unlike the original pairing theorem, this one is stated in terms of homomorphisms, not tensor products. The present formulation is closer in spirit to the usual TQFT framework, and allows a more direct comparison with Fukaya-categorical constructions. The result also leads to various dualities in bordered Floer homology.