Modular Arithmetic of Microwave Frequency Combs Generated by a Modulated Photonic Oscillator

This study explores the dynamics of optically injected semiconductor lasers under current modulation by periodic pulse sequences of various characteristics, focusing on the generation and control of microwave frequency combs (MFCs). Using simplified one-dimensional models –Poincaré circle maps–, the system's response to Dirac-delta, rectangular, and Gaussian pulse trains is analyzed. Modulation parameters such as amplitude, pulse width, and frequency detuning govern the emergence of frequency-locked states and chaotic oscillations, leading to distinct spectral outputs. A modular arithmetic relation between the frequencies of the modulation and the internal oscillation is shown to result in integer and fractional frequency division. The findings offer insights into tuning MFCs for applications in high-resolution measurement, microwave photonics, and data transmission.