# Nonlinear synchronization through vector subharmonic entrainment

## TL;DR

The paper introduces vector subharmonic entrainment, a new synchronization mechanism in fiber lasers that allows control over mode-locking and polarization using weak external signals.

## Contribution

The paper introduces vector subharmonic entrainment (VSHE), a novel synchronization mechanism in fiber lasers using vector coupling.

## Key findings

- Vector subharmonic entrainment (VSHE) synchronizes laser dynamics through polarization states of weak external signals.
- VSHE results in a partially mode-locked regime with frequency ratios of ten multiples.
- VSHE offers new control techniques for mode-locking and polarization states in fiber lasers.

## Abstract

Synchronization is a universal phenomenon underpinning various natural processes and finds direct application in control engineering and photonics. Among several synchronization mechanisms, subharmonic entrainment (SHE) is a nonlinear synchronization phenomenon where an oscillator locks to an external drive with a fraction of the oscillator’s frequency. While its mechanism is well understood for scalar couplings and finds application in the stabilization of ultrafast laser pulses, the potential of SHE with vectorial coupling is still unexplored. In this work, we demonstrate vector SHE (VSHE) using a passively mode-locked fiber laser as a testbed. We unveil the mechanism of vector SHE, in which weak external signals can entrain internal laser dynamics through vector coupling. Vector SHE presents in the form of synchronization between the subharmonic of mode-locking-driven oscillations and continuous wave (CW) signal with an evolving state of polarization. This CW signal, driven by the internal dynamics of the injected signal, causes VSHE with the frequencies’ ratios of multiples of ten, resulting in a partially mode locking regime operation. Our findings offer new control techniques over mode-locking and additional dimension such as polarization states.

Subharmonic entrainment (SHE) is a nonlinear synchronization phenomenon where an oscillation locks to an external periodic driving with a fraction of the oscillator frequency. This work introduces Vector Subharmonic Entrainment, demonstrating how the polarization of weak external signals can entrain internal fiber laser dynamics, offering control over mode-locking and polarization states.