Origins of clustered frequency combs in Kerr microresonators

Abstract

Recent experiments have demonstrated the generation of widely spaced parametric sidebands that can evolve into "clustered" optical frequency combs in Kerr microresonators. Here we describe the physics that underpins the formation of such clustered comb states. In particular, we show that the phase matching required for the initial sideband generation is such that (at least) one of the sidebands experiences anomalous dispersion, enabling the sideband to drive frequency comb formation via degenerate and non-degenerate four-wave mixing. We validate our proposal through a combination of experimental observations made in a magnesium-fluoride microresonator and corresponding numerical simulations. We also investigate the coherence properties of the resulting clustered frequency combs. Our findings provide valuable insights on the generation and dynamics of widely spaced parametric sidebands and clustered frequency combs in Kerr microresonators.

Optical Frequency Combs Generated in Silica Microspheres in the Telecommunication C-, U-, and E-Bands

“…The qualitative explanation of OFC generation in the sidebands is based on degenerate four-wave mixing (FWM) processes under the strong intracavity CW field approximation. Note that similar spectra were previously demonstrated in different microresonators (for example, in [40,42,47]). We have also investigated the pump frequency varying in the 190-198 THz range.…”

“…To estimate the possibility of generating sidebands via degenerate FWM under the strong intracavity field approximation, we followed the approach developed in [35,42] (which can be extended taking into account the dispersion of finesse [43]). We assumed that the total intracavity field can be approximated as the sum of a strong CW field E 0 found from Equation ( 7) and two small-amplitude sidebands (|a ± | << |E 0 |) symmetrically shifted by ±Ω from the pump frequency…”

Octave-wide phase-matched four-wave mixing in dispersion-engineered crystalline microresonators

“…Since a normal dispersion usually does not allow modulation instability (MI) near the pump, phase-matched FWM may be considered to occur only in an anomalous dispersion resonator. However, higher-order dispersion, particularly even orders of dispersion, enables a resonant MI process, called clustered frequency combs, to occur far from the pump mode [7][8][9]. Clustered combs, characterized by FWM generation with parametric sidebands that have a * takasumi@elec.keio.ac.jp large-frequency shift, have been reported using an MgF 2 microresonator [7,9] and silica microtoroids [8].…”

“…However, higher-order dispersion, particularly even orders of dispersion, enables a resonant MI process, called clustered frequency combs, to occur far from the pump mode [7][8][9]. Clustered combs, characterized by FWM generation with parametric sidebands that have a * takasumi@elec.keio.ac.jp large-frequency shift, have been reported using an MgF 2 microresonator [7,9] and silica microtoroids [8]. The fact that clustered combs have the potential to utilize microcomb source emitting in the 1.0 to 3.5 µm wavelength region with just a near-infrared pump indicates interesting potential applications, for example laser processing and optical communication.…”

“…Here, D int shows the cubic function affected by D 3 , however only even orders of dispersion play a role as regards the phase-matching condition for the initiation of sidebands. The formation scheme for a clustered comb is introduced in [9] as follows; after primary sideband (signal and idler pair) generation, secondary sidebands are generated via degenerate FWM from one primary sideband experiencing anomalous dispersion, which is ordinarily low frequency (longer wavelength) signal light. Once the secondary sidebands have been generated, nondegenerate FWM will occur and form other comb lines in the vicinity of the idler and pump lights.…”