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Proceedings Paper

Faster learning algorithm convergence utilizing a combined time-frequency representation as basis
Author(s): A. J. Hendriks; Hermann Uys; Anton du Plessis; Christine Steenkamp
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Paper Abstract

Light is capable of directly manipulating and probing molecular dynamics at its most fundamental level. One versatile approach to influencing such dynamics exploits temporally shaped femtosecond laser pulses. Oftentimes the control mechanisms necessary to induce a desired reaction cannot be determined theoretically a priori. However under certain circumstances these mechanisms can be extracted experimentally through trial and error. This can be implemented systematically by using an evolutionary learning algorithm (LA) with closed loop feedback. Most frequently, pulse shaping algorithms operate within either the time or frequency domain, however seldom both. This may influence the physical insight gained due to dependence on the search basis, as well as influence the speed the algorithm takes to converge. As an alternative to the Fourier domain basis, we make use of a combined time-frequency representation known as the von Neumann basis where we observe temporal and spectral effects at the same time. We report on the numerical and experimental results obtained using the Fourier, as well as the von Neumann basis to maximize the second harmonic generation (SHG) output in a non-linear crystal. We show that the von Neumann representation converges faster than the Fourier domain when compared to searches in the Fourier domain. We also show a reduced parameter space is required for the Fourier domain to converge efficiently, but not for von Neumann domain. Finally we show the highest SHG signal is not only a consequence of the shortest pulse, but that the pulse central frequency also plays a key role. Taken together these results suggest that the von Neumann basis can be used as a viable alternative to the Fourier domain with improved convergence time and potentially deeper physical insight.

Paper Details

Date Published: 7 October 2013
PDF: 11 pages
Proc. SPIE 8843, Laser Beam Shaping XIV, 88430S (7 October 2013); doi: 10.1117/12.2029492
Show Author Affiliations
A. J. Hendriks, CSIR National Laser Ctr. (South Africa)
Hermann Uys, CSIR National Laser Ctr. (South Africa)
Anton du Plessis, Stellenbosch Univ. (South Africa)
Christine Steenkamp, Stellenbosch Univ. (South Africa)

Published in SPIE Proceedings Vol. 8843:
Laser Beam Shaping XIV
Andrew Forbes; Todd E. Lizotte, Editor(s)

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