Inverse design methods for optical applications

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

This project concerns analytical studies and the development of computational approaches to two problems arising in optics. The first problem arises in the design of progressive lenses which must have desired corrective powers and minimal aberrations. The optical phenomenon in this case is well described by geometrical optics. The second problem arises in the design of optical devices that exploit photonic bandgap phenomena. In this problem, the wavelength of light is about the same size as the structure, and calls for modeling of the light's propagation using Maxwell's equation. In both cases, the design problem may be posed as an inverse problem where the desired performance can be viewed as data and the design parameters as unknowns. The aim of this research is to use analytical tools to guide in the development of effective computational methods to solve these inverse problems. Many people over 45 years old suffer a condition called presbyopia, which is the loss of the ability of the eye to focus on near objects. Progressive lenses, which correct for seeing both far and near objects, are often prescribed to presbyopia patients. The design of such lenses, taking into account the patient's need and the comfort, is a mathematical problem that involves optics, differential geometry, and optimization. The dream of creating optical computers that have the capability of high processing speeds requires the development of optical devices that are counterparts of electronic devices. The design of optical devices requires modeling of light propagation in complex nanostructures, which can be described by partial differential equations. In order to create devices that perform certain functions, it is necessary to solve a mathematical problem of optimal design. The unifying theme in the design of these two optical devices is the mathematics of inverse problems. The research to be carried out will help create lenses of unprecedented performance and optical computing subsystems for future optical computers.