Polarization properties of state-of-art lithography optics represented by first canonical coordinate of Lie group

Toru Fujii; Yuji Kudo; Yasuhiro Ohmura; Kosuke Suzuki; Jun Kogo; Yasushi Mizuno; Naonori Kita; Masayasu Sawada

doi:10.1117/12.710784

27 March 2007 Polarization properties of state-of-art lithography optics represented by first canonical coordinate of Lie group

Toru Fujii, Yuji Kudo, Yasuhiro Ohmura, Kosuke Suzuki, Jun Kogo, Yasushi Mizuno, Naonori Kita, Masayasu Sawada

Author Affiliations +

Proceedings Volume 6520, Optical Microlithography XX; 65204W (2007) https://doi.org/10.1117/12.710784
Event: SPIE Advanced Lithography, 2007, San Jose, California, United States

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.

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Toru Fujii, Yuji Kudo, Yasuhiro Ohmura, Kosuke Suzuki, Jun Kogo, Yasushi Mizuno, Naonori Kita, and Masayasu Sawada "Polarization properties of state-of-art lithography optics represented by first canonical coordinate of Lie group", Proc. SPIE 6520, Optical Microlithography XX, 65204W (27 March 2007); https://doi.org/10.1117/12.710784

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