Lorentz geometry technique in nonimaging optics

Pages: 386 - 392, Issue Special, July 2003

 Abstract        Full Text (175.8K)              

Manuel Gutiérrez - Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, 29071- Málaga, Spain (email)

Abstract: Nonimaging optics is a field that studies optimal concentration of light from a source distribution to a receiver. The relevant information is codified by a field of cones at each point of the concentrator, formed by those rays that we want to reach the receiver (perhaps after some reflections on the wall of the concentrator). This suggests that we can use Lorentz geometry to analyze the problem. We will establish a technique to design three dimensional ideal concentrators with arbitrary media which generalizes a previous one for the homogeneous case.

Keywords:  Nonimaging optics, Lorentz geometry, Christoffel symbols, Frobenius theorem.
Mathematics Subject Classification:  Primary: 78A05; Secondary: 53C50.

Received: July 2002;      Revised: April 2003;      Published: April 2003.