All optical chaos synchronization between nonidentical optomechanical cavities

TL;DR

This work tackles the problem of achieving complete chaos synchronization between nonidentical optomechanical cavities connected via an optical fiber in a master-slave configuration. The authors formulate a semiclassical model with normalized variables $\alpha_{1,2}$ and $\beta_{1,2}$, and show that complete synchronization requires matching decay rates and mechanical damping, equal dimensionless power, and a detuning offset satisfying $\Delta_1-\Delta_2=\sqrt{\kappa_{e1}\kappa_{e2}}$, with a phase lock $e^{i\phi_{lock}}=-i$. Numerical results reveal a route to synchronization as coupling $\kappa_e$ is increased: a desynchronized chaotic regime at weak coupling, a low-dimensional intermediate state, and finally a stable synchronized chaotic manifold characterized by negative transverse Lyapunov exponents and $I_C=H_{KS}$. The findings indicate robust all-optical synchronization under parameter heterogeneity and provide a foundation for long-distance, phase-controlled chaotic optical communications with optomechanical platforms.

Abstract

Optomechanical cavities, with nonlinear photon-phonon interactions, offer a more compact approach to chaos generation than conventional feedback-based optical systems. However, proper study on chaos synchronization of two optomechanical cavities connected by optical means is still unexplored. In this work, we theoretically investigate all-optical complete synchronization between unidirectionally coupled optomechanical cavities in the master-slave configuration. Traditionally, achieving complete synchronization in nonlinear coupled oscillators and in optical systems necessitates identical systems. Our findings, which arise naturally from the fundamental mathematical properties of optomechanical cavities, demonstrate that parameter heterogeneity can, in fact, not only enable complete synchronization but make it stable.

Figures (11)

• Figure 1: Schematic of a master and a slave OMC coupled unidirectionally by optical fiber with the excitation laser being provided separately with amplitude $s^{\text{in}}_{1,2}$ and detuning $\Delta_{1,2}$. The phase controller block "$\Phi_c$" adjusts the phase of the optical field coming from master cavity to realize chaos synchronization
• Figure 2: (a) The parameter space of $P_1$ and $\Delta_1$ of master cavity (cavity 1) illustrating regions of fixed point, limit cycle and chaotic attractor. The same is valid for cavity 2 as well, if uncoupled. (b) The bifurcation diagram of the mechanical oscillation amplitude under varying $\Delta_1$ at $P_1=1.3$. (c) The corresponding Lyapunov spectrum, consisting of two largest exponents ($\lambda_1$ and $\lambda_2$). (d)-(e) The magnified bifurcation diagram of the boxed part and it corresponding Lyapunov spectrum. The different dots labeled $1$, $2$, $3$ and $4$ are the considered operational points in the subsequent sections.
• Figure 3: The variation of the largest transverse Lyapunov exponent under varying external coupling rate $\kappa_e$,in which the stable region appears at $\kappa_e\gtrsim0.69\kappa$. The inset shows the chaotic attractor at the master cavity in the mechanical phase plane.
• Figure 4: (a) The identical chaotic time series of mechanical oscillations of master and slave cavity. (b) The corresponding intracavity dynamics that are completely synchronized as well. The inset shows a projection of the chaotic attractor in the $I_1$-$I_2$ plane with perfect correlation of $C=1$ between the two time series. Note that, $\Delta_1=-0.44\omega_m$ and $\kappa_e=0.9\kappa$; and thereby $\Delta_2=\Delta_1-\kappa_e=-1.097\omega_m$
• Figure 5: $H_{\text{KS}}$ and $I_C$ under varying external coupling rate $\kappa_e$. The parameters are same as in Fig. \ref{['fig4']} expect for $\Delta_2$ and $\kappa_e$. The units of these metrics are in bits per time unit.