Fig. 5: Temporal dynamics, threshold, and linewidth of the forward Brillouin fibre laser.

a Relative magnitude (dB scale) of the short-time Fourier transform (STFT) of the detected beating between the lasing signal and the local oscillator over 200 milliseconds. The pump power was 29 dBm. Multiple lasing signals through acoustic modes of different frequencies switch on and off on a time scale of milliseconds, due to environmental drifting of the longitudinal cavity modes across the narrow gain bandwidths of forward SBS. b Magnified view of an STFT map similar to that of panel a, with the same pump power. The instantaneous lasing frequency through the 169 MHz acoustic mode is drifting by tens of kHz over milliseconds. c Measured optical power of the laser output signal as a function of the optical pump power. Results are shown for forward SBS lasing through the 68 MHz acoustic mode. Blue markers denote data points, the red trace represents a trend line. A lasing threshold is observed at a pump power level of 26.5 dBm. d Measured half-width linewidth as a function of the laser output power, for the same mode shown in panel c. Linewidth were calculated through short-time Fourier transform of detected waveforms, with temporal duration of 250 μs. The linewidths decrease from 6–8 kHz well below threshold to 2.5–3.5 kHz well above threshold. The latter values are transform-limited. Environmental drifting restricts further narrowing of the lasing linewidth when observed over milliseconds or longer. e Power spectral density of the beating between spontaneous emission from the fibre cavity through the 169 MHz acoustic mode and the local oscillator (blue, see Fig. 3a). The half-width linewidth of spontaneous inter-modal forward Brillouin scattering is 250 kHz. The green trace shows the spectrum of forward SBS amplification through the same acoustic mode (Fig. 3a). The linewidth of the gain curve is 175 kHz. The magenta trace shows the spectrum of the beating between the lasing signal above threshold and the local oscillator, over a 2 ms-long trace. The pump power was 28 dBm. The beating linewidth is reduced to 5 kHz.