Radically tunable ultrafast photonic oscillators via differential pumping

Abstract

We present the controllability capabilities for the limit cycles of an extremely tunable photonic oscillator, consisting of two coupled semiconductor lasers. We show that this system supports stable limit cycles with frequencies ranging from a few to more than a hundred GHz that are characterized by a widely varying degree of asymmetry between the oscillations of the two lasers. These dyamical features are directly controllable via differential pumping as well as optical frequency detuning of the two lasers, suggesting a multi-functional oscillator for chip-scale radio-frequency photonics applications.Limit cycles are the fundamental ingredients of a wide variety of physical as well as man-made systems exhibiting characteristic self-sustained oscillations. Their existence is directly related to the interplay of two characteristic features that can be met in almost all realistic models, namely nonlinearity and dissipation. In contrast to oscillations of conservative nonlinear systems whose frequency is determined by the initial energy of the system, limit cycles have frequencies that are determined solely by the parameters of the system and often constitute global attractors to which the system evolves for any initial condition [1]. The existence of such robust limit cycles renders them crucial for the life itself, since they often occur in chemical and biological rhymes such as circadian oscillations [2-5], whose frequencies are determined by enviromental physical parameters. On the other hand, the existence of such limit cycles in manmade systems is crucially important for key technological applications such as time or frequency references [6,7] with their range of frequencies being controllable by the system parameters with significantly greater freedom in comparison to biological oscillators.Currently, there is intense interest in various implementations of ultrafast reconfigurable oscillators in systems and functional devices for next generation Photonic Integrated Circuits (PIC) [8,9] and RF photonics applications [10]. Due to the fact that single semiconductor lasers are not capable of supporting limit cycles, configurations based on optically coupled lasers have been proposed and intensively studied for more than four decades [11]. In this context, Optically Injected Lasers (OIL) corresponding to a one-way coupling in a master-slave configuration [ Fig. 1(a)] have been shown to support relatively tunable limit cycles [12][13][14][15]; however, the need for a bulky optical isolator prevents their on-chip integration [9] and significantly restricts their applications. The utilization of strong mutual coupling, corresponding to complicated configurations where a single electric field mode is amplified by two gain blocks, has been shown to result to a gain-lever mechanism [ Fig. 1(b)] allowing for significant bandwidth-enhancing [16,17]. The case of evanecently coupled diode lasers is shown to be the most promising for photonic integration [9] and also capable of supporting stable limit cycles [18][19][20]. Ho...

Dynamics of Evanescently-Coupled Laser Pairs With Unequal Pumping: Analysis Using a Three-Variable Reduction of the Coupled Rate Equations

“…Encouraging agreement is also found for the limits of stability using the SN bifurcation approximation from (14). In addition we calculated the Hopf bifurcation using (15) and (11). For this we needed the value of τ N which is not given in [12]; since in other publications, e.g.…”

“…By performing a small-signal analysis of ( 5) -( 7) (see Appendix B), approximate expressions for the stability boundaries of the system can be found as: Equation ( 15), in combination with (11), corresponds to the Hopf bifurcation. Equation ( 14) describes the saddle-node (SN) bifurcation.…”

“…HE study of small arrays of coupled semiconductor lasers, especially those with independent control of pumping for each element [1][2][3][4], is an area which is receiving increasing interest and attention. For the case of VCSEL arrays this has been driven by attractive properties including phase front engineering and beam-steering [5,6], extended bandwidth [7,8] and enhanced digital modulation [9,4], with one exemplar application being the prospect of tunable ultrafast photonic oscillators [10,11]. At the fundamental level, such arrays have been shown to exhibit non-Hermiticity [12,13], exceptional points [13][14][15] and parity-time symmetry breaking [1].…”

“…At the fundamental level, such arrays have been shown to exhibit non-Hermiticity [12,13], exceptional points [13][14][15] and parity-time symmetry breaking [1]. Theoretical understanding and modelling of these effects has been largely based on coupled rate equations [1,2,[10][11][12][14][15][16]. These apply in the general case of unequal pumping and have also been extended to include asymmetry in coupling coefficient and photon and carrier lifetimes [17].…”

Parametric control of self-sustained and self-modulated optomechanical oscillations

“…Moreover, complex collective dynamics and synchronization effects have been studied in large optomechanical arrays [36][37][38][39][40] and dimer systems [41][42][43][44][45]. It is worth mentioning that such dynamical features are also common to configurations where a cavity field is coupled to another optical field either in a master-slave [46][47][48] or in a mutual [49,50] fashion.…”