Localized solutions of Lugiato-Lefever equations with focused pump
arXiv:1711.07939 · doi:10.1038/s41598-017-16981-3
Abstract
Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too -- in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.
arXiv comment26 pages, 9 figures, accepted for publication in Scientific Reports
References in corpus (23)
- Formation and Propagation of Matter Wave Soliton Trains
- Formation of a Matter-Wave Bright Soliton
- Dark Solitons in Bose-Einstein Condensates
- Bright gap solitons of atoms with repulsive interaction
- Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model
- Optical frequency comb technology for ultra-broadband radio-frequency photonics
- Spatiotemporal Model for Kerr Comb Generation in Whispering Gallery Mode Resonators
- Formation of bright matter-wave solitons during the collapse of Bose-Einstein condensates
- Direct Frequency Comb Spectroscopy in the Extreme Ultraviolet
- Observation of bright polariton solitons in a semiconductor microcavity
- Controlled formation and reflection of a bright solitary matter-wave
- Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs
- Radially symmetric and azimuthally modulated vortex solitons supported by localized gain
- Solitons in a medium with linear dissipation and localized gain
- Origin of Rigidity in Dry Granular Solids
- Two-dimensional dissipative solitons supported by localized gain
- Effects of inhomogeneities and drift on the dynamics of temporal solitons in fiber cavities and microresonators
- Rotating vortex solitons supported by localized gain
- Solitary vortices supported by localized parametric gain
- Solitons supported by localized parametric gain
- Extended temporal Lugiato-Lefever equation and the effect of conjugate fields in optical resonator frequency combs
- Dissipative quadratic solitons supported by a localized gain
- Zero-dimensional limit of the two-dimensional Lugiato-Lefever equation
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- Stability and variational analysis of cavity solitons under various perturbations
- Bistability and nonequilibrium condensation in a driven-dissipative Josephson array: a c-field model