Localized solutions of Lugiato-Lefever equations with focused pump

Year: 2017

Authors: Cardoso WB., Salasnich L., Malomed BA.

Autors Affiliation: Univ Fed Goias, Inst Fis, BR-74690900 Goiania, Go, Brazil; Univ Padua, Dipartimento Fis & Astron Galileo Galilei, Via Marzolo 8, I-35131 Padua, Italy; Univ Padua, CNISM, Via Marzolo 8, I-35131 Padua, Italy; CNR, Ist Nazl Ott, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy; Tel Aviv Univ, Sch Elect Engn, Dept Phys Elect, Fac Engn, IL-69978 Tel Aviv, Israel; ITMO Univ, St Petersburg 197101, Russia.

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.

Journal/Review: SCIENTIFIC REPORTS

Volume: 7      Pages from: 16876-1  to: 16876-11

More Information: W.B.C. acknowledges financial support from the Brazilian agencies CNPq (grant # 458889/2014-8) and the National Institute of Science and Technology (INCT) for Quantum Information. The work of B.A.M. is supported, in part, by grant No. 2015616 from the joint program in physics between NSF (US) and Binational (US-Israel) Science Foundation, and by grant No. 1287/17 from the Israel Science Foundation. The work of L.S. is supported, in part, by BIRD project No. 164754 of University of Padova.
KeyWords: Spatial Solitons; Dissipative Solitons; Optical Solitons; Propagation; Vortices; Light; Gain
DOI: 10.1038/s41598-017-16981-3

Citations: 17
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