Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30 degrees rotation, was measured in the experiments performed. The parameters relevant for characterizing soliton collision processes were also studied in detail. Measurements were performed for various collision angles (from 0.2 to 4 degrees), phase mismatch, relative phase between the solitons and the distance to the collision point within the sample (which affects soliton formation). Both the individual and combined effects of these collision variables were investigated. Based on the research conducted, several all-optical switching scenarios were proposed.

Discrete optical systems are a subgroup of periodic structures in which the evolution of a continuous electromagnetic field can be described by a discrete model. In this model, the total field is the sum of localized, discrete modes. Weakly coupled arrays of single mode channel waveguides have been known to fall into this class of systems since the late 1960's. Nonlinear discrete optics has received a considerable amount of interest in the last few years, triggered by the experimental realization of discrete solitons in a Kerr nonlinear AlGaAs waveguide array by H. Eisenberg and coworkers in 1998. In this work a detailed experimental investigation of discrete nonlinear wave propagation and the interactions between beams, including discrete solitons, in discrete systems is reported for the case of a strong Kerr nonlinearity. The possibility to completely overcome "discrete" diffraction and create highly localized solitons, in a scalar or vector geometry, as well as the limiting factors in the formation of such nonlinear waves is discussed. The reversal of the sign of diffraction over a range of propagation angles leads to the stability of plane waves in a material with positive nonlinearity. This behavior can not be found in continuous self-focusing materials where plane waves are unstable against perturbations. The stability of plane waves in the anomalous diffraction region, even at highest powers, has been experimentally verified. The interaction of high power beams and discrete solitons in arrays has been studied in detail. Of particular interest is the experimental verification of a theoretically predicted unique, all optical switching scheme, based on the interaction of a so called "blocker" soliton with a second beam. This switching method has been experimentally realized for both the coherent and incoherent case. Limitations of such schemes due to nonlinear losses at the required high powers are shown.

Since the first demonstration of femtosecond laser written waveguides in 1996, femtosecond laser direct writing (FLDW) has been providing a versatile means to fabricate embedded 3-D microstructures in transparent materials. The key mechanisms are nonlinear absorption processes that occur when a laser beam is tightly focused into a material and the intensity of the focused beam reaches the range creating enough free electrons to induce structural modification. One of the most useful features that can be exploited in fabricating photonic structures is the refractive index change which results from the localized energy deposition. The laser processing system for FLDW can be realized as a compact, desktop station, implemented by a laser source, a 3-D stage and focusing optics. Thus, FLDW can be readily adopted for the fabrication of the photonic devices. For instance, it has been widely employed in various areas of photonic device fabrication such as active and passive waveguides, couplers, gratings, opto-fluidics and similar applications. This dissertation describes the use of FLDW towards the fabrication of custom designed diffractive optical elements (DOE’s). These are important micro-optical elements that are building blocks in integrated optical devices including on-chip sensors and systems. The fabrication and characterization of laser direct written DOEs in different glass materials is investigated. The design and performance of a range of DOE’s is described, especially, laser-written embedded Fresnel zone plates and linear gratings. Their diffractive efficiency as a function of the fabrication parameters is discussed and an optimized fabrication process is realized. The potential of the micro-DOEs and their integration shown in this dissertation will impact on the fabrication of future on-chip devices involving customized iv DOEs that will serve great flexibility and multi-functional capability on sensing, imaging and beam shaping.

This dissertation describes the development of novel techniques for characterization of nonlinear properties of materials. The dissertation is divided into two parts, a background and theory section and a technique development section. In the background and theory section we explain the origins of the nonlinear optical response of materials across many different spatial and temporal scales. The mechanisms that we are most interested in are the electronic nuclear and reorientational responses, which occur on the range of sub-femtosecond to several picoseconds. The electronic mechanism is due to the electrons of a material experiencing a non-parabolic potential well due a strong electric field and occurs on the sub-femtosecond timescale. The nuclear or vibrational effect results from the motion of the nuclei of the atoms and typically occurs on the order of a few hundred femtoseconds. Finally the reorientational nonlinearity is due to the alignment of the molecule to the electric field, which alters the polarizability of the molecule and typically occurs on the scale of a few picoseconds. There are other mechanisms can induce nonlinear optical effects such as thermal effects and electrostriction, but these effects typically occur on much larger timescales than we are interested in, and hence will not be a major focus of this dissertation. In the nonlinear characterization techniques section, we describe previous research into the field of nonlinear optical characterization techniques, describing the techniques used to characterize the nonlinear properties of materials, their applications and limitations. We will trace the development of two recently developed techniques for nonlinear spectroscopy − the Dual Arm iii Z-Scan and the Beam Deflection techniques. The Dual Arm Z-Scan technique is an enhancement of the standard Z-Scan technique that allows for the measurement of small nonlinear signals in the presence of large background signals. This technique allows for the measurement of materials under certain conditions not previously measureable using the standard Z-Scan technique, such materials with low damage thresholds, poor solubility and thin films. In addition to the Dual Arm Z-Scan, we have developed a new method for characterizing nonlinear refraction, the Beam Deflection technique, which is a variation of the photothermal beam deflection technique previously used to measure very weak absorption signals. This technique offers relative ease of use, the ability to measure the absolute magnitude and sign of both the real and imaginary parts of � (3) simultaneously with high sensitivity. We fully develop the theory for materials with instantaneous and non-instantaneous nonlinearities, with nonlinear absorption and group velocity mismatch. We also demonstrate the power of this technique to separate the isotropic and reorientational contributions of liquids by examining the temporal response and polarization dependences. Lastly, we summarize our conclusions and describe two promising future research directions that would benefit from the Dual Arm Z-Scan and Beam Deflection techniques

In this dissertation, we propose numerical techniques to explain physical phenomenon of nonlinear photonic crystal fiber (PCF). We explain novel physical effects occurred in PCF subjected to very short duration pulses including soliton. To overcome the limitations in the analytical formulation for PCF, an accurate and efficient numerical analysis is required to explain both linear and nonlinear physical characteristics. A vector finite element based model was developed to precisely synthesize the guided modes in order to evaluate coupling coefficients, nonlinear coefficient and higher order dispersions of PCFs. This finite element model (FEM) is capable of evaluating coupling length of directional coupler implemented in dual core PCF, which was supported by existing experimental results. We used the parameters extracted from FEM in higher order coupled nonlinear Schrödinger equation (HCNLSE) to model short duration pulses including soliton propagation through the PCF. Split-step Fourier Method (SSFM) was used to solve HCNLSE. Recently, reported experimental work reveals that the dual core PCF behaves like a nonlinear switch and also it initiates continuum generation which could be used as a broadband source for wavelength division multiplexing (WDM). These physical effects could not be explained by the existing analytical formulae such as the one used for the regular fiber. In PCF the electromagnetic wave encounters periodic changes of material that demand a numerical solution in both linear and nonlinear domain for better accuracy. Our numerical approach is capable of explaining switching and some of the spectral features found in the experiment with much higher degree of design freedom. Numerical results can also be used to further guide experiments and theoretical modeling.

By nature discrete solitons represent self-trapped wavepackets in nonlinear periodic structures and result from the interplay between lattice diffraction (or dispersion) and material nonlinearity. In optics, this class of self-localized states has been successfully observed in both one-and two-dimensional nonlinear waveguide arrays. In recent years such lattice structures have been implemented or induced in a variety of material systems including those with cubic (Kerr), quadratic, photorefractive, and liquid-crystal nonlinearities. In all cases the underlying periodicity or discreteness leads to new families of optical solitons that have no counterpart whatsoever in continuous systems. In the first part of this dissertation, a theoretical investigation of linear and nonlinear optical wave propagation in semi-infinite waveguide arrays is presented. In particular, the properties and the stability of surface solitons at the edge of Kerr (AlGaAs) and quadratic (LiNbO3) lattices are examined. Hetero-structures of two dissimilar semi-infinite arrays are also considered. The existence of hybrid solitons in these latter types of structures is demonstrated. Rabi-type optical transitions in z-modulated waveguide arrays are theoretically demonstrated. The corresponding coupled mode equations, that govern the energy oscillations between two different transmission bands, are derived. The results are compared with direct beam propagation simulations and are found to be in excellent agreement with coupled mode theory formulations. In the second part of this thesis, the concept of parity-time-symmetry is introduced in the context of optics. More specifically, periodic potentials associated with PT-symmetric Hamiltonians are numerically explored. These new optical structures are found to exhibit surprising characteristics. These include the possibility of abrupt phase transitions, band merging, non-orthogonality, non-reciprocity, double refraction, secondary emissions, as well as power oscillations. Even though gain/loss is present in this class of periodic potentials, the propagation eigenvalues are entirely real. This is a direct outcome of the PT-symmetry. Finally, discrete solitons in PT-symmetric optical lattices are examined in detail.

This work is divided into two main parts. In the first part (chapters 2-7) we consider the nonlinear response of nano-particle colloidal systems. Starting from the Nernst-Planck and Smoluchowski equations, we demonstrate that in these arrangements the underlying nonlinearities as well as the nonlinear Rayleigh losses depend exponentially on optical intensity. Two different nonlinear regimes are identified depending on the refractive index contrast of the nanoparticles involved and the interesting prospect of self-induced transparency is demonstrated. Soliton stability is systematically analyzed for both 1D and 2D configurations and their propagation dynamics in the presence of Rayleigh losses is examined. We also investigate the modulation instability of plane waves and the transverse instabilities of soliton stripe beams propagating in nonlinear nano-suspensions. We show that in these systems, the process of modulational instability depends on the boundary conditions. On the other hand, the transverse instability of soliton stripes can exhibit new features as a result of 1D collapse caused by the exponential nonlinearity. Many-body effects on the systems' nonlinear response are also examined. Mayer cluster expansions are used in order to investigate particle-particle interactions. We show that the optical nonlinearity of these nano-suspensions can range anywhere from exponential to polynomial depending on the initial concentration and the chemistry of the electrolyte solution. The consequence of these inter-particle interactions on the soliton dynamics and their stability properties are also studied. The second part deals with linear and nonlinear properties of optical nano-wires and the coupled mode formalism of parity-time (PT) symmetric waveguides. Dispersion properties of AlGaAs nano-wires are studied and it is shown that the group velocity dispersion in such waveguides can be negative, thus enabling temporal solitons. We have also studied power flow in nano-waveguides and we have shown that under certain conditions, optical pulses propagating in such structures will exhibit power circulations. Finally PT symmetric waveguides were investigated and a suitable coupled mode theory to describe these systems was developed.

<p> The interaction of light with semiconductors provides essential insight into their electronic and photonic properties. Excitons, excited electron-hole pairs, determine the optical response of nanomaterials and act as nanoscale energy carriers, making excitonic materials excellent candidates for optoelectronic, photovoltaic, and quantum devices. Unique phenomena can be brought about by using excitonic materials as building blocks in designing new systems and taking advantage of excitons’ dimensionality. For example, growing quantum dots into highly ordered arrays enhances exciton transport due to the strong dipolar coupling between excitons. Alternatively, forming vertical heterostructures between monolayer transition metal dichalcogenides introduces moiré superlattices, which localize the excitons introducing nonlinear interactions that be exploited for quantum information processing. Understanding these complex excitonic systems requires experimental tools capable of high spatial and temporal resolutions.</p> <p><br></p> <p>This thesis aims to contribute to understanding the complex excitons and charges formed at nanoscale interfaces with ultrafast techniques. In the discussed work, we take advantage of the 100s of fs time resolution and 10s of nm spatial precision to visualize exciton migration and dynamics associated with complex excitonic systems. First, we introduce the optical techniques needed to help us understand the fundamental photophysics of the studied systems (Chapter 2). Next, we provide an example of how we can use these methods to understand exciton coherence in perovskite quantum dot solids exhibiting superradiance (Chapter 3) and enhanced exciton transport (Chapter 4) due to low disorder and strong dipolar coupling. We also characterize and explore the behavior of highly excited excitons, Rydberg states, in transition metal dichalcogenides (Chapter 5). Then, we examine the properties of heterostructures formed between two monolayers of transition metal dichalcogenides exhibiting moiré superlattices and investigate the nonlinear exciton-exciton interactions modulated by the moiré potentials (Chapter 6). We also explore charge carrier behavior at interfaces of two different excitonic materials in molybdenum disulfide-single-wall carbon nanotube heterojunctions containing one- and two-dimensional excitons (Chapter 7). Finally, we visualize and quantify charge carrier migration across an alloyed cadmium sulfide and cadmium selenide lateral heterojunction (Chapter 8). We hope to give the reader a better understanding of these complex systems and open up new possibilities for their efficient use through the results presented in this thesis. </p>

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.

Nonlinear frequency conversion provides essential tools for generating new colors and quantum states of light. Conventional nonlinear crystals have the problem of relative lower nonlinear susceptibilities, which result in the large footprint of devices and low efficient. Transition metal dichalcogenides possess huge nonlinear susceptibilities; further, 3R-stacked transition metal dichalcogenide crystals possess aligned layers with broken inversion symmetry, representing ideal candidates to boost the nonlinear optical gain with minimal footprint. Here we report the second-order nonlinear processes of 3R-MoS2 along the ordinary and extraordinary directions. Along the ordinary axis, by measuring the thickness-dependent second-harmonic generation, we present the first measurement of the second harmonic-generation coherence length of 3R-MoS2 and achieve record nonlinear optical enhancement from a van der Waals material, >104 stronger than a monolayer. It is found that 3R-MoS2 slabs exhibit similar conversion efficiencies of lithium niobate, but within 100-fold shorter propagation lengths. Furthermore, along the extraordinary axis, we achieve broadly tunable second-harmonic generation from 3R-MoS2 in a waveguide geometry, revealing the coherence length in such a structure. We characterize the full refractive-index spectrum and quantify its birefringence with near-field nanoimaging. In order to bring 3R-MoS2 into the application field, we have developed two fabrication methods: low-cost femtosecond laser etching and cleanroom nanolithography-based processes. The femtosecond laser writing setup offers a rapid, residue-free, and in-situ method for patterning grating structures. On the other hand, the cleanroom process can provide structures with higher resolution. The cleanroom fabrication process is based on SF6 RIE and E-beam lithography, which can narrow down the minimum linewidth to ~120nm. To achieve mode matching in waveguiding second-order nonlinear conversion, we utilized the mode dispersion relation calculated by an anisotropic model to find the overlapping of wavevectors among different photon energies. We proposed a molybdenum disulfide on silicon nitride structure (MOSS) to further unleash the potential of 3R-MoS2 in optical parametric conversion. Photonic structure optimization was performed using the Lumerical FDTD simulator, achieving a 90% coupling efficiency from SiN to 3R-MoS2 with a taper structure. With a taper length of 50μm, we successfully maintained a single mode of excitation wave in MoS2, which could provide a monotonoic mode source for nonlinear conversion. Our work highlights the potential of 3R-stacked transition metal dichalcogenides for integrated photonics, providing critical parameters, developing high-resolution fabrication processes, and offering initial designs for highly efficient on-chip nonlinear optical devices including periodically poled structures, optical parametric oscillators and amplifiers, and quantum circuits.