Nonlinear Dynamics in Semiconductor Lasers 2023 - Abstract
Javaloyes, Julien
In this contribution we want to answer a seemingly obvious question: Are the pulses in a harmonic mode-locked state coherent with each other? Similarly, one may ask if the HML solution is unique. The answer to these questions is actually far from trivial if one considers a unidirectional ring laser or a Vertical External-Cavity Surface-Emitting Laser. In these configurations, the pulses never cross each other within the active material: How could they then exchange information regarding their relative phase?
We base our analysis upon the well accepted Haus master equation [1,2,3] as well as the Vladimirov and Turaev model [4] and we demonstrate that, due to residual interaction between the pulses$'$tails, a phase information may be transferred between the nearest neighbor. However, this extremely weak interaction must be sufficiently large to compensate for the spontaneous emission noise that randomizes the phases. We introduce an order parameter as a measure of the degree of coherence in the HML configuration and we predict the existence of a continuous transition from perfect coherence to total incoherence. In addition, we demonstrate that a HML solution may exist in N different states which, in the frequency spectrum, correspond to shifted frequency combs. We predict multistability between N/2 of these states and that the system may randomly explore. This has a profound implication on the notion of coherence that is a time averaged quantity.
[1] H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[2] A. M. Perego, B. Garbin, F. Gustave, Nat Commun 11, 311 (2020).
[3] J. Hausen, K. Lüdge, S. V. Gurevich, and J. Javaloyes, Opt. Lett. 45, 6210-6213 (2020).
[4] A. Vladimirov and D. Turaev, Phys. Rev. A 72, 033808 (2005).