High-order external cavity modes and restabilization of a laser diode subject to a phase-conjugate feedback

Abstract

We experimentally report the sequence of bifurcations destabilizing and restabilizing a laser diode with phase-conjugate feedback when the feedback rate is increased. Specifically, we successively observe the initial steady state, undamped relaxation oscillations, quasi-periodicity, chaos, and oscillating solutions at harmonics up to 13 times the external cavity frequency but also the restabilization to a steady state. The experimental results are qualitatively well reproduced by a model that accounts for the time the light takes to penetrate the phase-conjugate mirror. The theory points out that the system restabilizes through a Hopf bifurcation whose frequency is a harmonic of the external cavity frequency.

Wideband chaos from a laser diode with phase-conjugate feedback

“…Furthermore the re-stabilization to the steady-state is only found theoretically in the filtered PCF case and not in the instantaneous PCF case, as already reported in Ref. [20]. The theory therefore matches qualitatively very well with the experimental findings and confirms the importance of accounting for the filtering properties of the PCM.…”

“…close to the measurement limit -is measured at a feedback ratio of about 10 %. In that range of feedback ratios, the dynamics shows several stable ECMs at very high harmonic frequencies of the external cavity frequency, as also suggested by previous theoretical analyses [20]. For still larger feedback ratios, the laser diode re-stabilizes to a steady-state.…”

“…Two parameters are introduced to describe the geometry of the beam entering the PCM: θ, the angle between the c-axis of the non-linear crystal and the input beam and x the distance between the edge and the point of incidence in the crystal. A laser diode with PCF is known to exhibit successive bifurcations of dynamic states, depending on the feedback ratio γ: steady-state for zero or very weak optical feedback, self-pulsing dynamics at frequency near the relaxation oscillation frequency for low levels of feedback [17][18][19][20], chaos for higher values of feedback (> 0.03 %) [18][19][20]. A further increase of the feedback strength results in a chaos crisis leading to self-pulsing [19,20] and finally restabilization for very high values of the feedback strength [17,18,20].…”

“…A further increase of the feedback strength results in a chaos crisis leading to self-pulsing [19,20] and finally restabilization for very high values of the feedback strength [17,18,20]. Self-pulsing states are oscillating at multiples of the frequency of the external cavity and hence have been named ECMs or external-cavity modes [20]. The power spectrum of this external cavity laser output shows components at multiples of the external-cavity frequency.…”

“…In Refs. [20,25,26] the PCF laser model has been extended to account for the finite penetration time τ r of light inside the PCM.…”