Fig. 2

Principles of phase multiplication via laser feedback. a Schematic of the frequency-swept modulation and frequency-shifted modulation systems. In both configurations, a stable frequency difference exists between the feedback light and the intracavity field. Consequently, their cavity dynamics with laser feedback are similar. b Simulation results based on the L‒K equations and experimental measurements at the fixed frequency shift \(\varOmega /2{\rm{\pi }}=500\) kHz. The number of harmonics progressively increases with increasing feedback strength \(\kappa\). c Top: simulated laser output spectrum. The frequency interval between sidebands corresponds to the set modulation frequency \(\varOmega /2{\rm{\pi }}=1\) MHz. Bottom: experimentally measured laser output spectrum. Modulation sidebands emerge under optical feedback, aligning with the simulation results. d Number of harmonics in interference signals excited at a fixed \(\kappa\) for different modulation frequencies. e SNR of interference signal harmonics versus feedback power attenuation (\({\kappa }^{2}\)). Linear relationships are observed for the harmonics