Deterministic access of broadband frequency combs in microresonators using cnoidal waves in the soliton crystal limit

Abstract

We present a method to deterministically obtain broad bandwidth frequency combs in microresonators. These broadband frequency combs correspond to cnoidal waves in the limit when they can be considered soliton crystals or single solitons. The method relies on moving adiabatically through the (frequency detuning)×(pump amplitude) parameter space, while avoiding the chaotic regime. We consider in detail Si 3 N 4 microresonators with small or intermediate dimensions and an SiO 2 microresonator with large dimensions, corresponding to prior experimental work. We also discuss the impact of thermal effects on the stable regions for the cnoidal waves. Their principal effect is to increase the detuning for all the stable regions, but they also skew the stable regions, since higher pump power corresponds to higher power and hence increased temperature and detuning. The change in the detuning is smaller for single solitons than it is for soliton crystals. Without temperature effects, the stable regions for single solitons and soliton crystals almost completely overlap. When thermal effects are included, the stable region for single solitons separates from the stable regions for the soliton crystals, explaining in part the effectiveness of backwards-detuning to obtaining single solitons.

Study of microcomb threshold power with coupling scaling

“…In addition, although we do not take into account the thermally induced resonance shift which could be more significant than SPM, this red-shift effect could be approximated to be proportional to the intracavity power 33 . Therefore, the frequency shift is expressed as: where is the coefficient for the thermally induced shift which could be typically 5 to 10 times higher than 33 , 34 . We can use this approximation, at least qualitatively, to explain the thermally resulted resonance shift.…”

Soliton crystals in optical Kerr microresonators in the presence of thermo-optic effects

“…Although experiments suggest that solitoncomb structures are more likely to form on the red-detuned side of microresonator's pump resonance mode [22][23][24], it has been observed that in this spectral region thermo-optical effects can be so sizable that the soliton crystal stability is hampered [22][23][24]. To understand the influence of thermooptic effects on the dynamics of soliton-comb structures in Kerr optical microresonators, recently a theoretical model was proposed [25,26]. The model consists of the Lugiato-Lefever equation for the optical field propagation, with a term accounting for thermal detuning associated with the temperature variation in the microresonator cavity.…”

“…The temperature variation in this model is governed by the one-dimensional heat equation, in which the heat source term is proportional to the average power of the optical field within the microresonator cavity. In [25] the authors examined the influence of thermooptic effects on the stability of single-soliton and solitoncrystal structures in the ring-shaped optical Kerr microresonator, thus they established that in the absence of thermo-optic effects the stable regions for single solitons and soliton crystals partially overlap. However, when thermal effects are included via the thermal detuning term in the Lugiato-Lefever equation, the stability region of single solitons separates completely from the one of soliton crystal.…”

“…They inferred that the differences in stability features were an evidence of the effectiveness of backwards-detuning in obtaining single-soliton structures in optical Kerr microresonators. But to gain a more detailed picture of the influence of thermo-optic effects on solitoncomb structures in the ring microresonator, it is more interesting to examine profiles of the soliton combs by solving the Lugiato-Lefever equation and the heat equation coupled to it [25,26].…”

Kerr Frequency Comb Interaction with Raman, Brillouin, and Second Order Nonlinear Effects

“…[ 96 ] Versatile frequency detuning regimes for different Kerr comb behaviors have been experimentally and theoretically investigated through wavelength scanning involving thermal effects. [ 18–20,23,97–105 ] In particular, step‐like transitions are found to be associated with solitons and soliton crystals in Kerr microcavities. [ 18–20,23,106–108 ] For a fixed‐frequency pump laser, the detuning scanning to access soliton regimes can be realized by externally tuning the cavity temperature thus the relative wavelength detuning between the fixed‐wavelength laser and the resonance position.…”