Share Email Print

Proceedings Paper

Polarization properties of state-of-art lithography optics represented by first canonical coordinate of Lie group
Author(s): Toru Fujii; Yuji Kudo; Yasuhiro Ohmura; Kosuke Suzuki; Jun Kogo; Yasushi Mizuno; Naonori Kita; Masayasu Sawada
Format Member Price Non-Member Price
PDF $17.00 $21.00

Paper Abstract

The polarization characteristics of the state-of-art of optical lithography equipment are approximately ideal, i.e., in general only small polarization changes are induced by optical elements. Because of that, the polarization matrices of the optics are close to the unit element, which can be represented using the first canonical coordinate of a Lie group. The four-matrix basis of real general linear group of degree two is classified from a geometrical point of view. The complex versions of the four matrices are added to the four real matrices to obtain the basis of Lie ring of two-dimensional complex linear group, which is sufficient for physically possible polarization transformations. Each geometrical basis matrix generates non-Jones space of easy to understand individual optical phenomena. We propose a new physical polarization representation of projection optics for microlithography, which has eight real parameters, suitable for conventional pupil representation, with individual real optical characteristics applicable to optical elements. Pupil maps of a simulated projection lens whose polarization aberration and diattenuation induced by compensated intrinsic birefringence of CaF2 lens elements, are shown using the representation.

Paper Details

Date Published: 27 March 2007
PDF: 8 pages
Proc. SPIE 6520, Optical Microlithography XX, 65204W (27 March 2007); doi: 10.1117/12.710784
Show Author Affiliations
Toru Fujii, Nikon Corp. (Japan)
Yuji Kudo, Nikon Corp. (Japan)
Yasuhiro Ohmura, Nikon Corp. (Japan)
Kosuke Suzuki, Nikon Corp. (Japan)
Jun Kogo, Nikon Corp. (Japan)
Yasushi Mizuno, Nikon Corp. (Japan)
Naonori Kita, Nikon Corp. (Japan)
Masayasu Sawada, Nikon System (Japan)

Published in SPIE Proceedings Vol. 6520:
Optical Microlithography XX
Donis G. Flagello, Editor(s)

© SPIE. Terms of Use
Back to Top
Sign in to read the full article
Create a free SPIE account to get access to
premium articles and original research
Forgot your username?