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.
Highlights
One of the unexpected features of early laser systems was the emergence of output pulsations.Even before the first laser has been built, researchers had undertaken studies of instabilities in masers
The laser works by the same principle as the maser but produces higher frequency coherent radiation at visible wavelengths) and pulsations were observed in ruby masers in 1958 [1,2]
The first working laser was a ruby laser made by Maiman in 1960
Summary
One of the unexpected features of early laser systems was the emergence of output pulsations. Computer simulations predicted a train of regular and damped spikes at the output of the laser [7,8,9] In 1965, Statz et al [8] investigated theoretically and experimentally the conditions under which spiking in the laser output can be completely suppressed using a delayed optical feedback. They consider the laser rate equations supplemented by a delayed feedback term. The same stabilization problem due to a delayed feedback has been later considered by Krivoshchekov et al [15] Their rate equations are documented in Appendix B. We discuss the role of the damping rate on the stability conditions
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