Time-Scale Independent Permutation Entropy of a Photonic Integrated Device

A new measure of complexity, time-scale independent permutation entropy, has been developed and applied to fully characterize the relative complexity of the emission of a four-section photonic integration chip (PIC) laser. The new technique allows the relative complexity of dynamics with different characteristic time scales to be compared. The analysis reveals the range of possible outputs the PIC device can produce over a three-dimensional operating parameter space. From the perspective of using such devices as synchronized transmitter and receiver pairs in chaos-based secure communication applications, a region of uninterrupted, highly complex, unpredictable dynamics has been identified for the device. Regions surrounding this desired complex state show intermittency, pulse packages, and limit-cycle oscillations. The effect of varying the laser's biasing current, feedback strength, and feedback phase reveals the extent of the short-cavity regime and provides insight to the fundamental physics driving the integrated device dynamics.