Dispersion of nonlinearity and modulation instability in subwavelength semiconductor waveguides

Abstract

Tight confinement of light in subwavelength waveguides induces substantial dispersion of their nonlinear response. We demonstrate that this dispersion of nonlinearity can lead to the modulational instability in the regime of normal group velocity dispersion through the mechanism independent from higher order dispersions of linear waves. A simple phenomenological model describing this effect is the nonlinear Schrödinger equation with the intensity dependent group velocity dispersion.

Dispersion of nonlinearity in subwavelength waveguides: derivation of pulse propagation equation and frequency conversion effects

“…The onset of MI can be analyzed and numerically modeled with the help of the reduced HP model, which includes only three interacting harmonics [13]. However, its evolution generally leads to generation of multiple higher-order harmonics, see Fig.…”

“…From Eqs. (22)-(24) it is straightforward to derive the corresponding condition of existence of MI [13]:…”

“…Most important, the geometry-induced dispersion of nonlinearity can lead to a range of new effects. Recently we identified the novel mechanism of modulational instability (MI) of a constant-amplitude wave, mediated by the dispersion of nonlinearity in subwavelength waveguides [13]. We also introduced a simple phenomenological model describing this effect, which is based on the generalized version of the NLS equation where the second-order dispersion of nonlinearity term was added (γ 2 d 2 γ∕dω 2 ).…”

“…It is therefore the dependence on four frequencies of all the interacting waves, rather than single frequency dependence γω as in the above NLS models, which needs to be taken into consideration [1,7,8,13]. This can be done most naturally by considering pulse propagation in the frequency domain.…”

“…This can be done most naturally by considering pulse propagation in the frequency domain. However, the resulting model that describes evolution of individual harmonics with the propagation distance, the harmonic propagation (HP) model, contains a network of nonlocal nonlinear interactions [8,13], and appears to be complicated for analysis and resource demanding for numerical integration.…”