Elliptic-type soliton combs in optical ring microresonators

Abstract

Soliton crystals are periodic patterns of multi-spot optical fields formed from either time or space entanglements of equally separated identical high-intensity pulses. These specific nonlinear optical structures have gained interest in recent years with the advent and progress in nonlinear optical fibers and fiber lasers, photonic crystals, wave-guided wave systems and most recently optical ring microresonator devices. In this work an extensive analysis of characteristic features of soliton crystals is carried out, with emphasis on their one-to-one correspondance with Elliptic solitons. In this purpose we examine their formation, their stability and their dynamics in ring-shaped nonlinear optical media within the framework of the Lugiato-Lefever equation. The stability analysis deals with internal modes of the system via a $2\times 2$-matrix Lamé type eigenvalue problem, the spectrum of which is shown to possess a rich set of boundstates consisting of stable zero-fequency modes and unstable decaying as well as growing modes. Turning towards the dynamics of Elliptic solitons in ring-shaped fiber resonators with Kerr nonlinearity, first of all we propose a collective-coordinate approach, based on a Lagrangian formalism suitable for Elliptic-soliton solutions to the nonlinear Schródinger equation with an arbitrary perturbation. Next we derive time evolutions of Elliptic-soliton parameters in the specific context of ring-shaped optical fiber resonators, where the optical field evolution is tought to be governed by the Lugiato-Lefever equation. By solving numerically the collective-coordinate equations an analysis of the amplitude, the position, the phase of internal oscillations, the phase velocity and the energy is carried out and reveals a complex dynamics of the Elliptic soliton in ring-shaped optical microresonators.

10 pages, 29 figures

References in corpus (9)

• Soliton crystals in Kerr resonators
• High-precision wavelength calibration of astronomical spectrographs with laser frequency combs
• Octave-spanning dissipative Kerr soliton frequency combs in $S{i}_3{N}_4$ microresonators
• Soliton dual comb in crystalline microresonators
• Elliptic solitons in optical fiber media
• Fundamental modes of a trapped probe photon in optical fibers conveying periodic pulse trains
• Multistability and coexisting soliton combs in ring resonators: the Lugiato-Lefever approach
• Characteristics and stability of soliton crystals in optical fibres for the purpose of optical frequency comb generation
• Induced soliton ejection from a continuous-wave source waveguided by an optical pulse-soliton train

Cited by in corpus (9)

• Soliton-comb structures in ring-shaped optical microresonators: generation, reconstruction and stability
• Continuous-wave stability and multi-pulse structures in a universal Complex Ginzburg-Landau model for passively mode-locked lasers with saturable absorber
• Laser dynamics in nonlinear transparent media with electron plasma generation: effects of electron-hole radiative recombinations
• Soliton metacrystals: topology and chirality
• Soliton crystals in optical Kerr microresonators in the presence of thermo-optic effects
• Soliton-mode proliferation induced by cross-phase modulation of harmonic waves by a dark-soliton crystal in optical media
• Exciton-polariton soliton wavetrains in molecular crystals with dispersive long-range intermolecular interactions
• Exciton-polariton solitons in a semiconductor microwire of finite size
• Solitons in a discrete model of chiral liquid crystals with competing interactions