Presentation + Paper
16 February 2018 Solving the logarithmic Monge-Ampère equation with a RK4-algorithm for beam shaping purposes of femtosecond laser beams with spatial light modulators
Alexander Kratsch, Markus Olbrich, Steffen Weißmantel, Alexander Horn
Author Affiliations +
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).
Conference Presentation
© (2018) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Alexander Kratsch, Markus Olbrich, Steffen Weißmantel, and Alexander Horn "Solving the logarithmic Monge-Ampère equation with a RK4-algorithm for beam shaping purposes of femtosecond laser beams with spatial light modulators", Proc. SPIE 10518, Laser Resonators, Microresonators, and Beam Control XX, 105181L (16 February 2018); https://doi.org/10.1117/12.2287454
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KEYWORDS
Beam shaping

Diffraction

Spatial light modulators

Convolution

Computer generated holography

Freeform optics

Near field

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