Generation of an astronomical optical frequency comb in three fibre-based nonlinear stages

The generation of a broadband optical frequency comb with 80 GHz spacing by propagation of a sinusoidal wave through three dispersion-optimized nonlinear stages is numerically investigated. The input power, the dispersion, the nonlinear coefficient, and lengths are optimized for the first two stages for the generation of low-noise ultra-short pulses. The final stage is a low-dispersion highly-nonlinear fibre where the ultra-short pulses undergo self-phase modulation for strong spectral broadening. The modeling is performed using a Generalized Nonlinear Schrodinger Equation incorporating Kerr and Raman nonlinearities, self-steepening, high-order dispersion and gain. In the proposed approach the sinusoidal input field is pre-compressed in the first fibre section. This is shown to be necessary to keep the soliton order below ten to minimize the noise build-up during adiabatic pulse compression, when the pulses are subsequently amplified in the next fibre section (rare-earth-doped-fibre with anomalous dispersion). We demonstrate that there is an optimum balance between dispersion, input power and nonlinearities, in order to have adiabatic pulse compression. It is shown that the intensity noise grows exponentially as the pulses start to be compressed in the amplifying fibre. Eventually, the noise decreases and reaches a minimum when the pulses are maximally compressed. A train of 70 fs pulses with up to 3.45 kW peak power and negligible noise is generated in our simulations, which can be spectrally broadened in a highly-nonlinear fibre. The main drawback of this compression technique is the small fibre length tolerance where noise is negligible (smaller than 10 cm for erbium-doped fibre length of 15 m). We finally investigate how the frequency comb characteristics are modified by incorporating an optical feedback. We show that frequency combs appropriate for calibration of astronomical spectrographs can be improved by using this technique.