Computing Laser Beam Paths in Optical Cavities: An Approach Based on Geometric Newton Method

Davide Cuccato (), Alessandro Saccon (), Antonello Ortolan () and Alessandro Beghi ()
Additional contact information
Davide Cuccato: University of Padova
Alessandro Saccon: Eindhoven University of Technology
Antonello Ortolan: INFN - National Laboratories of Legnaro
Alessandro Beghi: University of Padova

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 1, No 15, 297-315

Abstract: Abstract In the last decade, increasing attention has been drawn to high-precision optical experiments, which push resolution and accuracy of the measured quantities beyond their current limits. This challenge requires to place optical elements (e.g., mirrors, lenses) and to steer light beams with subnanometer precision. Existing methods for beam direction computing in resonators, e.g., iterative ray tracing or generalized ray transfer matrices, are either computationally expensive or rely on overparameterized models of optical elements. By exploiting Fermat’s principle, we develop a novel method to compute the steady-state beam configurations in resonant optical cavities formed by spherical mirrors, as a function of mirror positions and curvature radii. The proposed procedure is based on the geometric Newton method on matrix manifold, a tool with second-order convergence rate, that relies on a second-order model of the cavity optical length. As we avoid coordinates to parametrize the beam position on mirror surfaces, the computation of the second-order model does not involve the second derivatives of the parametrization. With the help of numerical tests, we show that the convergence properties of our procedure hold for non-planar polygonal cavities, and we assess the effectiveness of the geometric Newton method in determining their configurations with high degree of accuracy and negligible computational effort.

Keywords: Geometric Newton method; Oblique manifold; Ring laser; Optical cavity; 58E50; 49Q99 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-016-0981-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:171:y:2016:i:1:d:10.1007_s10957-016-0981-3

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-016-0981-3

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().