Nonlinear optics represents a significant area of research and technology concerned with the modification of material optical properties using light. The interaction between light and such materials gives rise to a multitude of nonlinear optical effects, including second har-monic generation, third harmonic generation, high harmonic generation, and sum frequency generation. This thesis focuses on a specific and relevant nonlinear phenomenon within this field, namely the nonlinear Kerr effect, which involves the modification of a material’s re-fractive index through the exposure to an intense beam of light. The nonlinear Kerr effect holds promise for various applications, such as self-phase modulation in laser technology and the utilization of optical solitons in telecommunications. However, the limited availability of materials with sufficiently strong Kerr effects often restricts the practical application of this effect across different industries. Concurrently, optical time-varying systems play crucial roles in modern technologies, in-cluding optical modulators, LiDAR systems, and adaptive cameras. These systems involve the dynamic modification of optical properties. To achieve ultra-fast modulation of light properties, it is beneficial to explore materials with ultra-fast modulation speeds of the op-tical refractive index for integration into time-varying systems. While electro-optical effects represent the most common methods for achieving high-speed modulation of the effective refractive index, the utilization of all-optical methods, such as the nonlinear Kerr effect, presents an alternative approach. Nevertheless, the absence of simultaneous high speed and large nonlinear Kerr response in the majority of well-established materials restricts the utilization of the Kerr effect in time-varying systems.This thesis focuses on the study of a group of materials known as epsilon-near-zero (ENZ) materials, where the real part of the permittivity vanishes at a specific wavelength referred to as the ENZ wavelength. Specifically, indium-tin-oxide (ITO), a transparent conducting oxide, is investigated, with its ENZ wavelength falling within the infrared region of the elec-tromagnetic spectrum. ITO has been shown to possess a record-breaking large nonlinear Kerr effect with sub-picosecond response times, making it an excellent candidate for all-optical time-varying systems. The primary objective of this research is to investigate the applications of this large, fast nonlinear response and, where possible, enhance its effective-ness. One notable application of rapid and substantial modifications in the refractive index of a material is adiabatic wavelength conversion of light. In one project, a thin layer of ITO is subjected to a pump-probe setup, where an intense pump beam of light triggers the nonlinear response of ITO, causing the refractive index to rapidly change while a probe beam passes through the modulated system. Consequently, the wavelength of the probe beam undergoes conversion. Furthermore, it has been demonstrated that the nonlinear response of ITO can be sig-nificantly enhanced in the presence of a plasmonic metasurface. Metasurfaces consist of two-dimensional arrays of sub-wavelength scattering objects capable of manipulating the vectorial properties of light. In another project, we design a gradient metasurface composed of gold placed over ITO, enabling the diffraction of incident light into various diffraction orders depending on the ratio between the wavelength of light and the periodicity of the metasurface. This unique property is utilized to dynamically steer the diffraction orders of the probe beam, achieving wavelength conversion by exciting the nonlinear response of the ITO substrate with a second pump beam. Additionally, we investigate the interaction of resonance modes in an amorphous silicon metasurface, known as Mie modes, with an inherently dark mode in a thin layer of ITO known as the ENZ mode. Through experimental and analytical approaches, we demonstrate that two fundamental Mie modes, electric dipole resonance and magnetic dipole resonance, can strongly couple with the ENZ mode. This strong coupling creates a highly complex system with a large and rapid nonlinear response, enabling the manipulation of light on sub-picosecond timescales. In our final main project, we delve into investigating the nonlinear response of ITO nanoparticles. To accomplish this, we put forth a numerical recursive approach that allows us to incorporate the significant nonlinear Kerr effect of ITO into inherently linear simulation environments. Subsequently, we employ this proposed method to extract the scattering pattern of sub-wavelength antennas fabricated from ITO in both linear and nonlinear optical regimes. Our objective is to explore the potential applications of ITO nanoantennas in various fields. Moreover, this thesis encompasses other projects related to ENZ materials. We investi-gate the nonlinear response of an artificially created ENZ medium by stacking subsequent layers of materials with negative and positive permittivities within the visible range of the electromagnetic spectrum. Additionally, we explore the nonlinear response of nanoparticles made of ITO. Lastly, we present our investigations into the strong coupling of the ENZ mode in a thin layer of ITO with surface plasmon polaritons in a layer of gold in contact with ITO.

In this dissertation we have studied nearield phenomena in dipole radiation. We have studied first the energy flow patterns of the radiation emitted by an electric dipole located in between parallel mirrors. The field lines of the Poynting vector have intricate structures, including many singularities and vortices. For a dipole parallel to the mirror surfaces, vortices appear close to the dipole. Vortices are located where the magnetic field vanishes. Also, a radiating electric dipole near the joint of two orthogonal mirrors is considered, and also here we find numerous singularities and vortices in the energy flow patterns. We have also studied the current density in the mirrors. Next we have studied the reflection of radiation by and the transmission of radiation through an interface with an  -near-zero (ENZ) material. For p polarization, we find that the reflection coefficient is -1, and the transmission coefficient is zero for all angles of incidence. The transmitted electric field is evanescent and circularly polarized. The transmitted magnetic field is identically zero. For s polarization, the transmitted electric field is s polarized and the transmitted magnetic field is circularly polarized. The next topic was the study of the force exerted on the dipole by its own reflected field near an ENZ interface. We found that, under certain circumstances, it could be possible that the dipole would levitate in its reflected field. This levitation is brought about by evanescent reflected waves. Finally, power emission by an electric dipole near an interface was considered. We have derived expressions for the emitted power crossing an interface. The power splits in contributions from traveling and evanescent incident waves. We found that for an ENZ interface, only evanescent dipole waves penetrate the material, but there is no net power flow into the material.

Cette thèse porte sur l’étude numérique et expérimentale de l’utilisation de métamatériaux pour le contrôle des ondes à la surface de l’eau. Dans la première partie, nous avons montré comment focaliser les ondes à la surface de l’eau en utilisant une analogie existant avec des métamatériaux électromagnétiques de permittivité diélectrique quasi nulle qualifiés de ”epsilon-near-zero”. Cela a permis d’adapter le motif de phase à l’interface circulaire entre deux domaines présentant un contraste élevé de profondeur d’eau. L’analogie a donné lieu a un comportement fortement non linéaire des ondes, qui se manifeste par la génération d’une cascade de points focaux associés à des sous-multiples de longueurs d’onde par rapport à l’onde incidente. La deuxième application envisagée des métamatériaux pour les ondes à la surface est de rendre invisible les défauts géométriques d’un guide pour un observateur situé en champ lointain. Dans le premier projet lié au cloaking, des guides d’onde possédant différentes sections transverses ont été analysés. L’efficacité de la bathymétrie, donnée par la cartographie conformationnelle, a été evaluée numériquement en termes de propriétés de diffusion. Dans le second projet, nous avons montré numériquement comment rendre invisible un cylindre qui est décalé de l’axe d’un guide d’onde. Utiliser une bathymétrie de cloaking lisse autour du cylindre permet de reduire de manière significative la dispersion dans une large gamme de frequences. Des experiences réalisées avec des bathymétries conformes aux simulations ont confirmé une augmentation de la transmission par rapport à un scenario de référence avec fond plat. / This thesis presents numerical and experimental results concerning usage of metamaterials for water waves control. Two applications were considered. Firstly, we showed how to focus water waves using analogy to a group of metamaterials called epsilon-near-zero. This allowed to tailor phase pattern at the circular interface between two domains with high contrast in water depth. The analogy resulted in highly nonlinear behaviour of waves, manifested by sub-wavelength cascade of focal spots with respect to the incident wave. The second considered application of metamaterials for water waves was hiding (cloaking) defects in a waveguide from the far-field observer. In the first project, related to cloaking, waveguide with varying cross-sections was analyzed. The efficiency of bathymetry, rendered by conformal mapping, was evaluated in terms of scattering properties. The influence of water waves dispersivity on the cancellation of scattering was also determined. Cloaking properties of the obtained bathymetry were experimentally confirmed using a wave packet characterized by broadband spectrum. In the second project, we showed how to cloak a cylinder that is shifted from the centreline of a waveguide. Smooth cloaking bathymetry surrounding a cylinder was able to significantly reduce the scattering in broad range of frequencies. The experimental counterparts confirmed increase in transmission with respect to a reference case with flat bathymetry. The remainder of the thesis presents novel method for the analysis of fringe profilometry images. Performance of the new method was compared to the Fourier Transform Profilometry. We obtained significant enhancement in spectral capabilities.

<p>One of the longstanding goals of photonics research has been to obtain strong optical nonlinearities. A promising method to achieve this goal is to operate in the so-called epsilon near zero (ENZ) spectral regime, where the real part of the dielectric permittivity changes sign. If accompanied by low losses, this region enables a platform to achieve extraordinarily high nonlinear response, along with many other interesting optical phenomena. In this work, some of the common all-optical switching structures employing homogeneous ENZ materials are investigated under varying conditions of frequency, incidence angle, and polarization. The optimum switching conditions have been highlighted to pave the way forward to the best experimental configurations in future studies. Moreover, the properties of some of the emerging novel plasmonic materials such as aluminum-doped zinc oxide (AZO) and titanium nitride (TiN) are investigated, specifically for ENZ applications. Their thickness-dependent crystalline structure and carrier densities are employed as a method to control their optical properties. A near-perfect absorption scheme is demonstrated utilizing the Ferrell-Berreman mode occurring at the ENZ region of ultrathin AZO and TiN film. The ENZ frequency and the associated absorption peak of AZO are engineered through thickness-dependence to cover most of the telecom range. This work covers the theoretical background for ENZ nonlinearities and looks into the materials aspect for better control of nonlinearities in experimental realizations.</p>

Various anomalous effects that emerge when the interfaces between media are involved in sound-matter or light-matter interactions are studied. The three specific systems examined are a fluid channel between elastic metal plates, a linear chain of metallic perforated cylindrical shells in air, and a metal-dielectric slab with the interfaces treated as finite regions of smoothly changing material properties. The scattering of acoustic signals on the first two is predicted to be accompanied by the effects of redirection and splitting of sound. In the third system, which supports the propagation of surface plasmons, it is discovered that the transition region introduces a nonradiative decay mechanism which adds to the plasmon dissipation. The analytical results are supported with numerical simulations. The outlined phenomena provide the ideas and implications for applications involving manipulation of sound or excitation of surface plasmons.

<p>Dipole-dipole interactions are ubiquitous fundamental physical phenomena that govern physical effects such as Casimir Forces, van der Waals forces, collective Lamb shifts, cooperative decay, and resonance energy transfer. These interactions are associated with real and virtual photon exchange between the interacting emitters. Such interactions are crucial in realizing quantum memories, novel super-radiant light sources, and light-harvesting devices. Owing to this, the control and modification of dipole-dipole interactions have been a longstanding theme. The electromagnetic environment plays a crucial role in enhancing the range and strength of the interactions. This work focuses on modifying the nanophotonic environment near interacting emitters to enhance dipole-dipole interactions instead of spontaneous emission. To this end, we focus on engineering the nanophotonic environment to enhance the strength and range of dipole-dipole interactions between an ensemble of emitters. We explore ordered and disordered nanophotonic structures. We experimentally demonstrate long-range dipole-dipole interactions mediated by surface lattice resonances in a periodic plasmonic nanoparticle lattice. Further, the modified electromagnetic environment reduces the apparent dimensionality of the interacting system compared to non-resonant in-homogeneous and homogeneous environments. We also develop a spectral domain inverse design technique for the accelerated discovery of disordered metamaterials with unique spectral features. </p> <p>Further, we explore the novel regimes of light localization at near-zero-index in such disordered media. The disordered near-zero-index medium reveals enhanced localization and near-field chirality. This work paves the way to engineer the electromagnetic nanophotonic environment to realize enhanced long-range dipole-dipole interactions.</p>