Frequency-comb formation in doubly resonant second-harmonic generation

Abstract

We theoretically study the generation of optical frequency combs and corresponding pulse trains in doubly resonant intracavity second-harmonic generation (SHG). We find that, despite the large temporal walk-off characteristic of realistic cavity systems, the nonlinear dynamics can be accurately and efficiently modeled using a pair of coupled mean-field equations. Through rigorous stability analysis of the system's steady-state continuous-wave solutions, we demonstrate that walk-off can give rise to an unexplored regime of temporal modulation instability. Numerical simulations performed in this regime reveal rich dynamical behaviors, including the emergence of temporal patterns that correspond to coherent optical frequency combs. We also demonstrate that the two coupled equations that govern the doubly resonant cavity behavior can, under typical conditions, be reduced to a single mean-field equation akin to that describing the dynamics of singly-resonant-cavity SHG [F. Leo et al., Phys. Rev. Lett. 116, 033901 (2016)]. This reduced approach allows us to derive a simple expression for the modulation instability gain, thus permitting us to acquire significant insight into the underlying physics. We anticipate that our work will have a wide impact on the study of frequency combs in emerging doubly resonant cavity SHG platforms, including quadratically nonlinear microresonators.

Numerical modelling of frequency comb generation in nonlinear resonators

“…When neglecting 978-1-4673-8603-6/16/$31.00 ©2016 IEEE Numerically simulated frequency comb in a singlyresonant, macroscopic SHG system. For details and parameters, see [18] and [15], respectively.…”

“…Notably, the functional form of ( ) is different for singly-and doubly-resonant cavity constructions (see [15] and [16] for details).…”

“…However, if a particular second-order process dominates the dynamics, the problem can be greatly simplified by introducing a set of distinct field envelopes with widelyspaced carrier frequencies. For the particular case of secondharmonic generation (SHG) in high-finesse cavities, where frequency combs have been experimentally observed [14], the second-harmonic field is found to be dynamically slaved to the fundamental field, with the latter evolving according to the following mean-field equation [15], [16]:…”

“…In particular, experiments have shown that, similarly as for Kerr cavities, a cw laser coupled into a quadratically nonlinear cavity can transform into a frequency comb [14]. The ability to leverage second-order effects for frequency comb generation holds great promise to enable sources at spectral regions that are difficult to access with alternative comb technologies, such as the visible and mid-infrared spectral ranges [15], [16].…”

Weak Langmuir optical turbulence in a fiber cavity

“…As discussed in previous works [52,53], the passive cavity does not operate as a resonant 'phase-sensitive interferometer' [54,55,[83][84][85][86][87][88], and the temporal modes of the cavity do not play any key role in the dynamics of the incoherent wave. The wave circulating in the cavity and the pump wave are thus mutually incoherent with each others, and the boundary conditions are not sensitive to the random relative phase among them:…”