Mathematical aspects of design of beam shaping surfaces in geometrical optics. (English) Zbl 1062.78002

Oliker, Vladimir

Kirkilionis, Markus (ed.) et al., Trends in nonlinear analysis. On the occasion of the 60th birthday of Willi Jäger. Berlin: Springer (ISBN 3-540-44198-0/hbk). 193-224 (2003).

Summary: Numerous optical and electromagnetic applications require synthesis of reflecting and refracting surfaces capable of reshaping the energy radiation intensity of a given source into a prescribed output irradiance distribution. Determination of such surfaces requires investigation of nonlinear, second order partial differential equations of Monge-Ampère type and development of computational algorithms for constructing their numerical solutions. In this paper we survey some of these problems and describe the current progress in their study.
For the entire collection see [Zbl 1001.00073].

MSC:

78A05	Geometric optics
78A60	Lasers, masers, optical bistability, nonlinear optics
35Q60	PDEs in connection with optics and electromagnetic theory

Keywords:

survey paper; far-field; near-field; laser optics; shaped reflectors; nonlinear second order partial differential equations of Monge-Ampère type; algorithms