Abstract

We theoretically investigate the dynamics of an optical dissipative soliton (DS) inside a silver-nanoparticle-doped Si-based waveguide immersed in an externally pumped ${\mathrm{Al}}_2{\mathrm{O}}_3\text{:}{\mathrm{Er}}^{3+}$ that exhibits a strong frequency-dependent Kerr nonlinear coefficient. Depending on the input frequency, the Kerr coefficient can be positive or negative. At some specific frequency, the Kerr coefficient can be zero, and we called this specific frequency the zero-nonlinearity frequency (ZNF). The dynamics of the DS is found to be very interesting near the ZNF when higher order effects are present. We model the pulse dynamics by a complex Ginzburg–Landau equation (GLE) that includes Raman scattering and third-order dispersion (TOD) terms as higher order perturbations. We adopt a variational technique to theoretically investigate the overall dynamics of DSs near the ZNF by choosing a Pereira–Stenflo type soliton as our ansatz. The study based on the numerical solution of GLE reveals that the ZNF plays a dominant role on the pulse dynamics and, depending on its relative location with respect to input frequency, Raman-induced frequency down-shifting can be either suppressed or enhanced. We provide a theoretical description of this phenomenon by using a variational method that quantitatively determines the location of the Raman frequency as a function of the ZNF. The dispersive radiation generated due to TOD is also affected by the location of the ZNF. We analytically derive a phase-matching equation that predicts the location of radiation frequency in the presence of the ZNF. The results obtained from the analytical treatment agree well with full numerical simulations.

© 2019 Optical Society of America

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