Analytical Approach to Assess the Impact of Pulse-to-Pulse Phase Coherence of Optical Frequency Combs

We derive analytical expressions to show that the pulse-to-pulse phase coherence is critical to generate an optical frequency comb with clearly defined comb lines. Our results are verified by supporting numerical simulations. We build upon previous works that only considered the pulse timing jitter; here, we consider the effect of the pulse-to-pulse phase coherence on the spectrum of optical frequency combs. We evaluate the spectrum of the comb when the pulse-to-pulse phase varies as a Weiner-Levy (Brownian motion) process where the phase of the pulses maintains memory of the phase of the preceding pulses or when the phases of the pulses have no memory of the phases of preceding pulses. We prove that if the phase of the optical pulses in a pulse train varies without memory of the phase of preceding pulses, then the spectrum is a continuum and does not present any discernible comb lines. The results are important to analyze the spectral content of the optical frequency combs from gain-switched lasers, where both types of pulse-to-pulse phase coherence, Weiner-Levy or random, can arise depending on the operating conditions.