# Marc Sciamanna

## How fast is the self-pulsation in a laser diode with optical feedback?

When subject to optical feedback, a laser diode exhibits a large variety of nonlinear dynamics including self-pulsation, period-doubling bifurcations, intermittent pulsating dynamics and chaos. In the past forty years these dynamics have been scrutinized both theoretically and experimentally, paving the way towards innovative applications such as in chaos-based cryptography, physical sources of entropy, or, recently, neuromorphic computing [1].

A crucial question is how fast can self-pulsation occur. As in any system with time-delayed feedback, competition may occur between the natural time-scale of the damped nonlinear oscillator and the time-delay. Within the framework of a rate equation model one can easily demonstrate that when increasing the amount of optical feedback, a laser diode bifurcates from a steady-state to self-pulsation (Hopf bifurcation) with a frequency either close to the relaxation oscillation frequency of the free-running laser diode (internal, natural frequency of the nonlinear damped oscillator), or, close to the inverse of the time-delay [2]. Integrating a passive feedback section into an active laser medium therefore leads to a short time-delay enabling several tens of GHz self-pulsation from a laser diode [3].

A slightly different situation was analyzed in the early 1980s, in which the optical feedback does not occur from a conventional mirror but from a phase-conjugate mirror. In that situation, summarized as "phase-conjugate feedback (PCF)", self-pulsation at frequencies being harmonic of the inverse of time-delay have been theoretically predicted [4]. Recently we have found these dynamics experimentally [5] and analyzed how they get stabilized and bifurcate when varying the feedback strength and/or time-delay [6]. We will summarize our latest conclusions on the PCF configuration and shall highlight the important role played by the filtering effect in the phase-conjugate mirror on the high-speed self-pulsating dynamics [7]. For a relatively long nonlinear mirror, the dynamics get close to those observed in a laser diode with optical injection [8].

[1] M. Sciamanna, K.A. Shore, Nat. Photonics 9, 151-162 (2015)

[2] Th. Erneux, A. Gavrielides, M. Sciamanna, Phys. Rev. A 66, 033809 (2002)

[3] O. Ushakov, S. Bauer, O. Brox, H.J. Wünsche, F. Henneberger, Phys. Rev. Lett. 92, 043902 (2004)

[4] G.P. Agrawal, J.T. Klaus, Opt. Lett. 16, 1325-1327 (1991)

[5] A. Karsaklian Dal Bosco, D. Wolfersberger, M. Sciamanna, Appl. Phys. Lett. 105, 081101 (2014)

[6] E. Mercier, C.H. Uy, L. Weicker, M. Virte, D. Wolfersberger, M. Sciamanna, Phys. Rev. A 94, 061803 (2016)

[7] E. Mercier, L. Weicker, D. Wolfersberger, D.M. Kane, M. Sciamanna, Opt. Lett. 42, 306-309 (2017)

[8] L. Weicker, T. Erneux, D. Wolfersberger, M. Sciamanna, Phys. Rev. E 92, 022906 (2015)