Disorder-mediated synchronization resonance in coupled semiconductor lasers

Disorder can profoundly influence synchronization in networks of nonlinear oscillators, sometimes enhancing coherence through external tuning. In semiconductor lasers, however, achieving high-quality steady-state synchronization is desired, while intrinsic and typically uncontrollable disorder poses a major challenge. Under fixed frequency disorder, we investigate homogeneous fully coupled external-cavity semiconductor lasers governed by the complex, time-delayed Lang-Kobayashi equations with experimentally relevant parameters and identify an optimal coupling strength that maximizes steady-state synchronization in the weak-coupling regime, which we term disorder-mediated synchronization resonance. This optimum appears for any fixed configuration of intrinsic frequency detuning and scales inversely with the number of lasers, leading to a linear scaling of the total coupling cost with the number of lasers. A theory based on an effective thermodynamic potential explains this disorder-mediated optimization, revealing a general mechanism by which moderate coupling can overcome static heterogeneity in nonlinear physical systems.

💡 Research Summary

In this paper the authors investigate synchronization in a network of external‑cavity semiconductor lasers that are all‑to‑all coupled and possess fixed intrinsic frequency disorder. The dynamics of each laser are modeled by the delayed Lang‑Kobayashi equations, which include carrier‑photon interactions, amplitude‑phase coupling (α‑factor), and a common external feedback delay τ≈3 ns. The lasers are assigned random frequency detunings Δi drawn from a Gaussian distribution with standard deviation σΔ≈14 rad/ns, reflecting realistic fabrication‑induced heterogeneity.

The central question is whether, for a given realization of disorder and within the weak‑coupling regime (global coupling strength κ much smaller than σΔ), one can identify an optimal κ that maximizes steady‑state synchronization. Synchronization is quantified by ⟨S⟩, the normalized squared magnitude of the sum of complex electric fields, which equals 1 for perfect amplitude, phase, and frequency locking.

Numerical simulations with M=24 lasers reveal a non‑monotonic dependence of ⟨S⟩ on κ. At κ=0 the lasers remain at their individual frequencies and ⟨S⟩≈0. As κ is increased, ⟨S⟩ rises slowly at first, then sharply reaches a maximum ⟨S⟩≈0.84 around κ*≈0.4 ns⁻¹. Beyond this point the system crosses a boundary into chaotic dynamics induced by the time delay, and ⟨S⟩ collapses. This peak is termed “disorder‑mediated synchronization resonance” because the optimal coupling compensates the static frequency spread without eliminating it.

A striking scaling law emerges: the optimal coupling strength κ* scales inversely with the number of lasers, κ*∝1/M. Consequently the total coupling cost C_total=κ*·M grows linearly with M, rather than quadratically as would be expected for a coupling strength independent of system size. This linear scaling makes it feasible to synchronize large arrays while keeping the required optical power and hardware resources modest.

To rationalize these findings, the authors recast the delayed phase dynamics into a gradient flow on an effective thermodynamic potential Φ(θ). In this picture, each laser’s phase experiences a landscape shaped by its intrinsic detuning; the all‑to‑all coupling adds a global term that tends to flatten the landscape. For weak κ the potential contains many shallow minima corresponding to the disordered frequencies. As κ increases, these minima merge into a single deep well, producing strong synchronization. If κ becomes too large, the shape of Φ changes dramatically, creating new minima and saddle points that correspond to chaotic trajectories. Thus the “sweet spot” κ* is precisely the coupling strength at which the potential has a single, robust minimum without yet developing the complex structure that leads to chaos.

The paper also discusses why traditional master‑stability‑function analysis, which works for identical oscillators, fails in the presence of strong heterogeneity. Instead, the authors rely on the ratio κ/σΔ as the key control parameter and demonstrate that the resonance phenomenon persists across a wide range of σΔ (1–14 rad/ns) and for different network sizes.

Experimentally, the authors propose implementing the all‑to‑all coupling with a spatial light modulator (SLM) placed in the Fourier plane of the laser array. The SLM can impose the required phase‑shifted feedback and the common delay τ, while the global coupling strength κ can be tuned by adjusting the SLM reflectivity or the external feedback gain. This architecture is compatible with existing photonic integration platforms and allows rapid reconfiguration of κ to locate the resonance point.

In summary, the study establishes that even in the presence of unavoidable, fixed frequency disorder, a semiconductor‑laser array can achieve high‑quality steady‑state synchronization by operating in a weak‑coupling regime and selecting an optimal coupling strength that scales as 1/M. The underlying mechanism is captured by an effective potential framework, revealing a general principle: moderate coupling can overcome static heterogeneity in nonlinear delayed systems, leading to a disorder‑mediated synchronization resonance. The results have immediate relevance for designing high‑power, low‑noise laser arrays for coherent communications, lidar, and other photonic applications where both scalability and stability are essential.