Non-Spiking Laser Controlled by a Delayed Feedback

Anton V. Kovalev, Evgeny A. Viktorov and Thomas Erneux
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Anton V. Kovalev: Birzhevaya Liniya 14, ITMO University, 199034 Saint Petersburg, Russia
Evgeny A. Viktorov: Birzhevaya Liniya 14, ITMO University, 199034 Saint Petersburg, Russia
Thomas Erneux: Optique Nonlinéaire Théorique, Université Libre de Bruxelles, Campus Plaine C.P. 231, 1050 Bruxelles, Belgium

Mathematics, 2020, vol. 8, issue 11, 1-12

Abstract: In 1965, Statz et al. (J. Appl. Phys. 30, 1510 (1965)) investigated theoretically and experimentally the conditions under which spiking in the laser output can be completely suppressed by using a delayed optical feedback. In order to explore its effects, they formulate a delay differential equation model within the framework of laser rate equations. From their numerical simulations, they concluded that the feedback is effective in controlling the intensity laser pulses provided the delay is short enough. Ten years later, Krivoshchekov et al. (Sov. J. Quant. Electron. 5394 (1975)) reconsidered the Statz et al. delay differential equation and analyzed the limit of small delays. The stability conditions for arbitrary delays, however, were not determined. In this paper, we revisit Statz et al.’s delay differential equation model by using modern mathematical tools. We determine an asymptotic approximation of both the domains of stable steady states as well as a sub-domain of purely exponential transients.

Keywords: first delay differential equation in laser physics; stabilization by optical feedback; suppression of damped relaxation oscillations; purely exponential transients (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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