Due to the increased demand for high-operating-speed systems and ultra-compact optical devices, nanophotonic waveguides such as plasmonic waveguides have been a subject of intense interest over the past few years. The ability of plasmonic waveguides to guide light within nano-scale structures beyond the diffraction limit has driven researchers in different fields to exploit their unique features. Even though plasmonic waveguides have shown a strong mode confinement at nano-scale dimensions, they have high propagation loss. Consequently, many geometries and structures have been proposed to investigate ways to reduce this loss. The most recent type of plasmonic waveguide that shows high mode confinement and low propagation loss compared with the other types is the hybrid plasmonic waveguide (HPW). An HPW consists of a low-index dielectric layer sandwiched between a high-index dielectric material and a metal layer; the mode is predominantly confined within the low-index layer. This thesis addresses the use of HPWs for nonlinear applications such as optical switching devices based on the nonlinear phenomenon known as the Kerr effect, where the sub-wavelength dielectric layer has a pronounced nonlinear response. Using Finite Element Method analysis, the nonlinear hybrid plasmonic waveguide (NLHPW) is modeled, and the performance of the NLHPW has been investigated by using appropriate figures of merit to measure the Kerr nonlinearity of the NLHPW with and without the linear loss of the waveguide. These are shown to compare favourably with those of alternate waveguiding geometries. Moreover, the NLHPW has been shown a good balance between mode confinement and loss; small effective mode areas of 0.04 – 0.15 µm2 at a wavelength of λ=1.55 µm and relatively long propagation lengths of 30 to 160 µm can be realized, which make NLHPWs promising candidates for nonlinear applications. As a result, a nonlinear ring resonator with a radius of 1 µm based on the NLHPW is designed and investigated numerically by using frequency domain simulations. It is found that the field intensity in the ring is enhanced four times higher than the field intensity in the input waveguide, and that a nonlinear resonance shift is realized when changing the intensity of the data signal.

Due to the increased demand for high-operating-speed systems and ultra-compact optical devices, nanophotonic waveguides such as plasmonic waveguides have been a subject of intense interest over the past few years. The ability of plasmonic waveguides to guide light within nano-scale structures beyond the diffraction limit has driven researchers in different fields to exploit their unique features. Even though plasmonic waveguides have shown a strong mode confinement at nano-scale dimensions, they have high propagation loss. Consequently, many geometries and structures have been proposed to investigate ways to reduce this loss. The most recent type of plasmonic waveguide that shows high mode confinement and low propagation loss compared with the other types is the hybrid plasmonic waveguide (HPW). An HPW consists of a low-index dielectric layer sandwiched between a high-index dielectric material and a metal layer; the mode is predominantly confined within the low-index layer. This thesis addresses the use of HPWs for nonlinear applications such as optical switching devices based on the nonlinear phenomenon known as the Kerr effect, where the sub-wavelength dielectric layer has a pronounced nonlinear response. Using Finite Element Method analysis, the nonlinear hybrid plasmonic waveguide (NLHPW) is modeled, and the performance of the NLHPW has been investigated by using appropriate figures of merit to measure the Kerr nonlinearity of the NLHPW with and without the linear loss of the waveguide. These are shown to compare favourably with those of alternate waveguiding geometries. Moreover, the NLHPW has been shown a good balance between mode confinement and loss; small effective mode areas of 0.04 – 0.15 µm2 at a wavelength of λ=1.55 µm and relatively long propagation lengths of 30 to 160 µm can be realized, which make NLHPWs promising candidates for nonlinear applications. As a result, a nonlinear ring resonator with a radius of 1 µm based on the NLHPW is designed and investigated numerically by using frequency domain simulations. It is found that the field intensity in the ring is enhanced four times higher than the field intensity in the input waveguide, and that a nonlinear resonance shift is realized when changing the intensity of the data signal.

Le but de cette thèse est de développer les outils numériques et semi-analytiques qui nous permettent d’étudier des guides non-linéaires complexes et réalistes qui pourraient être fabriqués et caractérisés expérimentalement.Nous présentons une étude complète d’une version améliorée du guide d’onde plasmonique non-linéaire à une dimension, en ajoutant deux couches tampons de diélectrique linéaire entre le cœur non-linéaire isotrope et les deux gaines métalliques. Ses couches réduisent les pertes et permettent leur diminution avec la puissance contrairement aux guides simples. De plus, les principaux modes plasmoniques non-linéaires peuvent présenter une transition spatiale vers des modes de types différents, qui peut être contrôlée par la puissance.Par la suite, nous étudions un nouveau guide plasmonique non-linéaire à fente utilisant un métamatériau, soit dans le cœur non-linéaire soit dans les gaines linéaires. Nous avons mis au point une méthode semi-analytique et une méthode numérique afin d’étudier les solutions stationnaires non-linéaires dans ce nouveau guide non-linéaire anisotrope. Nous avons montré analytiquement et numériquement que le cœur non-linéaire anisotrope peut être conçu afin d’atteindre de forts effets non-linéaires à faible puissance. Pour certains métamatériaux dans les gaines linéaires, la figure de mérite de ce guide d’onde augmente de plus de 50 fois par rapport aux guides isotropes.Pour conclure, nous présentons une nouvelle méthode basée sur la méthode des éléments finis de type vectoriel couplée à l’algorithme à puissance fixée pouvant calculer rigoureusement les effets non-linéaires dans des guides d’onde plasmoniques 2D. / The main goal of this PhD is to develop the semi-analytical and the numerical tools that allow us to study complicated and realistic nonlinear plasmonic waveguides which can be fabricated and characterized experimentally.First, we present a full study of an improved version of the one-dimensional nonlinear plasmonic slot waveguide, by adding two linear dielectric buffer layers between the isotropic nonlinear core and the two metal claddings. These additional layers reduce the overall losses and allow the losses to decrease with the power for some configurations unlike the usual slot. Furthermore, the main plasmonic modes can exhibit nonlinear spatial modal transitions towards new families of modes that can be controlled with the power.Second, we propose and study new one-dimensional nonlinear plasmonic slot waveguides with metamaterial regions either in the nonlinear core or in the linear claddings. For the metamaterial nonlinear core, we developed semi-analytical and fully numerical methods in order to study the nonlinear stationary solutions propagating in this anisotropic nonlinear waveguide. We have demonstrated both analytically and numerically that the anisotropic nonlinear core can be designed in order to achieve strong nonlinear effects at low power.For the structures with metamaterial linear claddings, the figure of merit can be extremely enhanced by more than 50 times compared with the simple one. Finally, we present the full derivation of a new nonlinear full vectorial finite element method based on the fixed power algorithm in order to quantify rigorously the nonlinear characteristics of realistic two-dimensional nonlinear plasmonic structures.