Spectral signatures of coexisting isolas and four-wave mixing under the effect of noise in photonic oscillators

Abstract

The optical power spectrum is the prime observable to dissect, understand, and design the long- time behavior of small and large arrays of optically coupled semiconductor lasers. A long-standing issue has been identified within the literature of injection locking in photonic oscillators: first how the thickness of linewidth and the lineshape spectral envelope correlates with the deterministic evolution of the monochromatic injected laser oscillator and second how the presence of noise and the typically dense proximity in phase space of coexisting limit cycles of the coupled system are shaping and influencing the overall spectral behavior. In addition, we are critically interested in the regions where the basin of attraction has a fractal-like structure, still, the long-time orbits are P1 (period 1) and/or P3 (period 3) limit cycles. Numerically computed evidence shows that, when the coupled system lives in the regions of coexisting isolas and four-wave mixing (FWM) limit cycles, the overall optical power spectrum is deeply imprinted by a strong influence from the underlying noise sources. A particularly intriguing observation in this region of parameter space that we examine is that the isolas draw most of the trajectories on its phase space path.