Spectral dynamics in broadband frequency combs with overlapping harmonics

Abstract

Optical frequency combs and their spectra of evenly spaced discrete laser lines are essential to modern time and frequency metrology. Recent advances in integrated photonic waveguides enable efficient nonlinear broadening of an initially narrowband frequency comb to multi-octave bandwidth. Here, we study the nonlinear dynamics in the generation of such ultra-broadband spectra where different harmonics of the comb can overlap. We show that a set of interleaved combs with different offset frequencies extending across the entire spectrum can emerge, which transform into a single evenly spaced ultra-broadband frequency comb when the initial comb is offset-free.

Figures (5)

• Figure 1: Offset dynamics in broadband frequency combs with overlapping harmonics. (a) Self-phase modulation (SPM), as well as sum- and difference frequency generation (SFG/DFG) result in spectral broadening and harmonic generation. (b) As the spectrum evolves, harmonics may overlap. (c) Harmonics with different offsets enter into additional nonlinear mixing processes, resulting in nonlinear gain for combs at new offset frequencies throughout the spectrum.
• Figure 2: Numerical simulation results.(a) Spectral envelope evolution of comb spectra with different harmonic index $n$ along propagation z. Dashed black line indicates the output spectrum. PSD: power spectral density. (b) Magnified view of the output spectrum around 75 THz and 200 THz in the condition of: upper panels: $f_\mathrm{ceo}=f_\mathrm{rep}/4$, and lower panels: $f_\mathrm{ceo}=0$. Dashed grey lines mark the offset-free frequency position.
• Figure 3: Experiments with non-zero offset. (a) Schematic setup and a photograph of the chip during operation. PPLN: periodically poled lithium niobate; OSA: optical spectrum analyzer; ESA: electrical spectrum analyzer; Col.: collimator; DM: dichroic mirror; BPF: bandpass filter; ND: neutral density filter; PD: photodetector. (b) Optical spectra with increasing pump energy (faded to dark: 139 pJ, 166 pJ, 191 pJ, 214 pJ, 238 pJ, 284 pJ, and 347 pJ). The spectra are shifted by 25 dB for visibility. Colored vertical bars mark frequency positions used to measure the RF beatnote, with (i) 1610$\pm$6 nm, (ii) 1300$\pm$15 nm, (iii) 780$\pm$5 nm, and (iv) 520$\pm$18 nm. (c) The RF beatnote at around 1300 nm with increasing pump energy with resolution bandwidth (RBW) of 10 kHz. (d) Scaling of the sideband suppression ratio (SSR) with the pulse energy. Data points represent the ratio between $P_\mathrm{rep}$ and $P_\mathrm{ceo}$ at different frequencies marked in (b).
• Figure 4: Experimental results with offset-free pump source. (a) Generated optical spectrum. (b) RF beatnote measured at optical frequencies same as in the non-offset-free pump experiments. Grey backgrounds mark the noise floor of PDs. RBW=1 kHz.
• Figure S1: Evolution of all RF spectra obtained after photodetection of the bandpass filtered spectra around fundamental, second harmonic, and third harmonic with increasing pump energy. Resolution bandwidth 10 kHz. Video bandwidth 30 Hz.