Localized solutions of Lugiato Lefever equations with focused pump
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2017
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Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the
dynamics of optical felds 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 confned modes supported by the localized pump. In the 1D setting, we
frst 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 confned 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 fndings 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 specifc condition, necessary for the existence of the analytical solution, does not hold). In 2D,
vast families of stable confned modes are produced by means of a variational approximation and full
numerical simulations.
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CARDOSO, Wesley B.; SALASNICH, Luca; MALOMED, Boris A. Localized solutions of Lugiato-Lefever equations with focused pump. Scientific Reports, Berlim, v. 7, e16876, 2017. DOI: 10.1038/s41598-017-16981-3 . Disponível em: https://www.nature.com/articles/s41598-017-16981-3#citeas. Acesso em: 1 jun. 2023.