# Harmonic Frequency Locking and Tuning of Comb Frequency Spacing through Optical Injection

## TL;DR

This paper investigates how optical injection can induce harmonic locking and tuning of comb frequency spacing in lasers, revealing mechanisms to control and generate optical combs through experimental and theoretical analysis.

## Contribution

It introduces two distinct locking mechanisms in injected lasers that reduce comb spacing, with detailed analysis of their stability and dynamics, advancing optical comb control techniques.

## Key findings

- Locking mechanisms reduce comb frequency spacing
- Relaxation oscillations can become undamped and lock to rational frequencies
- Locking can occur between the slave laser and injected comb lines

## Abstract

We show, both experimentally and theoretically, that a slave laser injected with an optical frequency comb can undergo two distinct locking mechanisms, both of which decrease the output optical comb's frequency spacing. We report that, for certain detuning and relative injection strengths, slave laser relaxation oscillations can become undamped and lock to rational frequencies of the optical comb spacing, creating extra comb tones by nonlinear dynamics of the injected laser. We also study the frequency locking of the slave laser in between the injected comb lines, which add the slave laser's frequency to the comb. Our results demonstrate the effect of the alpha parameter, stability of the locked states, and indicate how the frequency of the relaxation oscillations affect both of these locking mechanisms. These optical locking mechanisms can be applied to regenerate or multiply optical combs.