Theoretical Study on Dual-Comb Generation and Soliton Trapping in a Single Microresonator with Orthogonally Polarized Dual Pumping

Abstract

Microresonator-based optical frequency combs (known as microcombs or Kerr combs) have a large repetition frequency ranging typically from 10 to 1000 GHz, which is compatible with fast-scanning applications, including dual-comb spectroscopy and LiDAR. In this research, we numerically study dual-comb generation and soliton trapping in a single microresonator, whose two transverse modes are excited with orthogonally polarized dual pumping. The simulation model is described by using coupled Lugiato-Lefever equations (LLEs), which take account of cross-phase modulation and the difference in repetition frequencies. The numerical simulation calculates the dual-comb formation in a microresonator, whose microcombs propagate as soliton pulses and cause soliton trapping depending on the parameters. In the simulation, a trapped soliton is seeded by one of the original solitons in two transverse modes. In addition, we introduce an analytical solution for trapped solitons in coupled LLEs using a Lagrangian perturbation approach and clarify the relation between the parameters. Revealing the conditions of dual-comb soliton generation and soliton trapping is helpful in terms of optimizing the conditions for causing or avoiding these phenomena.

Coexistence and Interactions between Nonlinear States with Different Polarizations in a Monochromatically Driven Passive Kerr Resonator

“…In conclusion, we have reported on experimental observations of coexistence and interactions between nonlinear states with different polarizations in a monochromatically driven passive Kerr resonator. In addition to experimentally confirming earlier theoretical predictions [39,41], our work shows that the simultaneous excitation of several cavity modes with a single carrier frequency can engender very rich dissipative dynamics. The ability to control the frequency separation between two modes (as demonstrated in our work) paves the way for further studies of such dynamics, and will allow for the systematic exploration of questions such as: what are the exact parameter conditions required for coexistence of nonlinear states; how does linear mode coupling affect the cavity dynamics; can the coexistence of nonlinear states be linked to the well-known symmetry breaking behaviour of driven Kerr resonators [52,53]?…”

“…During transients, where the CSs are not yet pinned to amplitude inhomogeneities, the group-velocity mismatch can lead to collisions and other forms of interactions between coexisting CSs. Our experiments show a rich diversity of possible interaction scenarios, ranging from the formation of bound states (as predicted in [41]) to soliton annihilation. Figure 4 shows an example of a temporally resolved experimental measurement of CS evolution dynamics.…”

Spectral extension and synchronization of microcombs in a single microresonator

“…The negative sign of γ causes the P2 DW to appear on the red side of the auxiliary mode (see also next section for a discussion of the phase-matching conditions of the DWs). For the case, in which the auxiliary laser is coupled into a mode that does not belong to the soliton mode family, we solve a system of two simultaneous generalized LLEs, which are expanded with XPM and a group velocity mismatch γ between the primary and auxiliary pump modes 25,26 :…”

“…For the case, in which the auxiliary laser is coupled into a mode that does not belong to the soliton mode family, we solve a system of two simultaneous generalized LLEs, which are expanded with XPM and a group velocity mismatch γ between the primary and auxiliary pump modes 25 , 26 : where ψ p ( θ,τ ) and ψ a ( θ,τ ) are the intracavity primary and auxiliary field envelopes, respectively. σ is the XPM coefficient (2/3 for orthogonal polarization and 2 for the same polarization assuming perfect spatial mode overlap, otherwise less).…”

“…Bichromatic pumping of microresonators at similar wavelengths has been studied for microcomb generation with the benefits of a thresholdless pump intensity and stabilization of the frequency comb repetition rate [20][21][22][23][24] . More recently, bichromatic pumping has been demonstrated for the generation of dual orthogonally polarized microcombs both theoretically and experimentally 25,26 . Similar to bichromatic pumping, it has also been shown that a second frequency comb can be generated through Raman gain within a microresonator 27 .…”