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Proceedings Paper

Solving the logarithmic Monge-Ampère equation with a RK4-algorithm for beam shaping purposes of femtosecond laser beams with spatial light modulators
Author(s): Alexander Kratsch; Markus Olbrich; Steffen Weißmantel; Alexander Horn
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Paper Abstract

We will demonstrate a Runge Kutta based algorithm for solving the Mone-Ampère-Problem. The method is utilizing its parabolic type. We will show the exact numerical solving method down to each step. The derived solution is used in the context of laser beam shaping to reshape any given input distribution to arbitrary output distributions free of any constraints other than diffraction, which includes a true black in said distribution. The presented algorithm will give the required phase which will be used to verify the solution theoretically via diffraction integral and practically via Spatial Light Modulator (SLM).

Paper Details

Date Published: 16 February 2018
PDF: 12 pages
Proc. SPIE 10518, Laser Resonators, Microresonators, and Beam Control XX, 105181L (16 February 2018);
Show Author Affiliations
Alexander Kratsch, Laser Institute of Univ. Mittweida (Germany)
Markus Olbrich, Laser Institute of Univ. Mittweida (Germany)
Steffen Weißmantel, Laser Institute of Univ. Mittweida (Germany)
Alexander Horn, Laser Institute of Univ. Mittweida (Germany)

Published in SPIE Proceedings Vol. 10518:
Laser Resonators, Microresonators, and Beam Control XX
Alexis V. Kudryashov; Alan H. Paxton; Vladimir S. Ilchenko, Editor(s)

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