| Summary: | This thesis discusses nonlinear effects, such as modulation instability and solitons in nano-structured waveguides. The nanoscale optical waveguides have extremely small transverse dimensions, which can provide tight confinement of light. Therefore, by changing the waveguide geometry, the waveguide dispersion can be strongly altered. On the other hand, the confinement also enhances the nonlinear dispersion, allowing for nonlinear optical phenomena supported by dispersion of nonlinearity. The new models governing evolution of the amplitudes of components of the optical waves interacting in the waveguides are derived for continuous wave and pulse wave using perturbation expansion method. The new modulation instability condition is found, as we take into account the dispersion of nonlinearity which is enhanced through a strong variation of the modal profile with the wavelength of light in sub-wavelength waveguides. We demonstrate that this dispersion of nonlinearity can lead to the modulation instability in the regime of normal group velocity dispersion through the mechanism independent from higher order dispersions of linear waves for continuous wave. We address that the new mechanism highly associated with dispersion of nonlinearity in sub-wavelength semiconductor waveguide induces the modulation instability in picsecond regime together with the cascaded generation of higher-order sidebands. The impact of the dispersion of nonlinearity on spectral broadening of short pulses in a silicon waveguide also is considered. We study the temporal evolutions of fundamental and one-ring solitary waves with phase dislocation in dielectric-metal-dielectric waveguides with PT-symmetry and numerically analyze the properties of these nonlinear localized modes and, In particular, reveal different scenarios of their instability.
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