Fig. 5: Numerical simulation of the Fourier domain mode-locked (FDML) output.

a The all-mode phase evolution plot presents the relative phase accumulation per roundtrip of the FDML laser and is plotted for various values of residual dispersion in the fibre cavity (see legend). The curves show good agreement with the experimental data in Fig. 4 since the ultra-stable regime and the connected small dispersion exhibit a constant carrier-envelope phase slip (CEPS). Higher dispersion induces a non-constant CEPS. By simulating up to 1000 consecutive sweeps it is possible to investigate the frequency spectrum at optimal spectral resolution and reveal a comb-like structure of the FDML laser output (b). In the ultra-stable regime^28,29 (i.e. negligible dispersion effects, here residual dispersion of 150 fs) the FDML laser presents a stable frequency comb with fixed carrier-envelope offset, i.e. without CEPS from sweep-to-sweep. Thus, a frequency comb is present with mode spacing corresponding to the sweep repetition rate (i.e. 411 kHz). Zoom into a comb-line (inset in (b)) reveals a linewidth of 5.75 kHz. This is in good agreement with the experimentally determined, resolution-limited linewidth of 12 kHz (Fig. 3d), which however stems from a simultaneous beating of ~100 spectral modes within the sampling gate window width (see methods). c For a non-dispersion compensated FDML laser cavity (residual dispersion of 192 ps) the comb lines are broadened as a result of high-frequency fluctuations (Nozaki-Bekki holes) in the intensity trace and the loss of coherence^24,26,29,32. The good agreement between theory and experiment confirms the observed comb-like structure of the FDML and paves the way towards an FDML frequency comb with a stabilized carrier-envelope offset.