I present in this thesis the design, implementation and measurement results of a narrowband quantum light source based on cavity-enhanced Parametric Down-Conversion (PDC). Spontaneous Parametric Down-Conversion (SPDC) is the workhorse in the field of optical quantum information and quantum computation, yet it is not suitable for applications where deterministic nonlinearities are required due to its low spectral brightness. By placing the nonlinear crystal inside a cavity, the spectrum of down-conversion is actively modified, such that all the non-resonant modes of down-conversion experience destructive interference, while the resonant mode sees constructive interference, resulting in great enhancement in spectral brightness. I design and construct such a cavity-enhanced down-conversion source with record high spectral brightness, making it possible to use cold atoms as the interaction medium to achieve large nonlinearity between photons. The frequency of the photons is tunable and their coherence time is measured to be on the order of 10 nanoseconds, matching the lifetime of the excited state of typical alkali atoms. I characterize extensively the output of the source by measuring the second-order correlation function, quantifying two-photon indistinguishability, performing quantum state tomography of entangled states, and showing different statistics of the source. The unprecedented long coherence time of the photon pairs has also made possible the encoding of quantum information in the time domain of the photons. I present a theoretical proposal of multi-dimensional quantum information with such long-coherence-time photons and analyze its performance with realistic parameter settings. I implement this proposal with the quantum light source I have built, and show for the first time that a qutrit can be encoded in the time domain of the single photons. I demonstrate the coherence is preserved for the qutrit state, thus ruling out any classical probabilistic explanation of the experimental data. Such an encoding scheme provides an easy access to multi-dimensional systems and can be used as a versatile platform for many quantum information and quantum computation tasks.

I present in this thesis the design, implementation and measurement results of a narrowband quantum light source based on cavity-enhanced Parametric Down-Conversion (PDC). Spontaneous Parametric Down-Conversion (SPDC) is the workhorse in the field of optical quantum information and quantum computation, yet it is not suitable for applications where deterministic nonlinearities are required due to its low spectral brightness. By placing the nonlinear crystal inside a cavity, the spectrum of down-conversion is actively modified, such that all the non-resonant modes of down-conversion experience destructive interference, while the resonant mode sees constructive interference, resulting in great enhancement in spectral brightness. I design and construct such a cavity-enhanced down-conversion source with record high spectral brightness, making it possible to use cold atoms as the interaction medium to achieve large nonlinearity between photons. The frequency of the photons is tunable and their coherence time is measured to be on the order of 10 nanoseconds, matching the lifetime of the excited state of typical alkali atoms. I characterize extensively the output of the source by measuring the second-order correlation function, quantifying two-photon indistinguishability, performing quantum state tomography of entangled states, and showing different statistics of the source. The unprecedented long coherence time of the photon pairs has also made possible the encoding of quantum information in the time domain of the photons. I present a theoretical proposal of multi-dimensional quantum information with such long-coherence-time photons and analyze its performance with realistic parameter settings. I implement this proposal with the quantum light source I have built, and show for the first time that a qutrit can be encoded in the time domain of the single photons. I demonstrate the coherence is preserved for the qutrit state, thus ruling out any classical probabilistic explanation of the experimental data. Such an encoding scheme provides an easy access to multi-dimensional systems and can be used as a versatile platform for many quantum information and quantum computation tasks.

Le travail présenté dans cette thèse est inspiré de précédents résultats sur les modèles de Gaudin ne contenant que des spins-1/2 (ces modèles sont intégrables) qui, par un changement de variable dans les équations de Bethe algébriques, parviennent à simplifier le traitement numérique de ces modèles. Cette optimisation numérique s'effectue par l'intermédiaire d'une construction en déterminant, ne dépendant que des variables précédemment mentionnées, pour chaque produit scalaire intervenant dans l'expression de la moyenne d'une observable à un temps donné. En montrant qu'il est possible d'utiliser la méthode du Quantum Inverse Scattering Method (QISM), même dans un cas où l'état du vide n'est pas état propre de la matrice de transfert, les résultats précédents concernant uniquement des spins-1/2 sont généralisés à des modèles contenant en plus une interaction spin-boson. De fait, cette généralisation a ouvert plusieurs voies de recherche possibles. Premièrement, il est montré qu'il est possible de continuer à généraliser l'utilisation de déterminants pour des modèles de spins décrivant l'interaction d'un spin de norme arbitraire avec des spins-1/2. La méthode permettant d'obtenir la construction des expressions explicites de ces déterminants est donnée. On peut également pousser la généralisation à d'autres modèles de Gaudin dont l'état du vide n'est pas état propre de la matrice de transfert. C'est ce que nous avons fait pour des spins-1/2 en interaction avec un champ magnétique dont l'orientation est arbitraire. Enfin, un traitement numérique de ces systèmes de spins-1/2 interagissant avec un mode bosonique est présenté. L'évolution temporelle de l'occupation bosonique et de l'aimantation locale des spins est ainsi étudiée selon deux Hamiltoniens différents, l'Hamiltonien de Tavis-Cummings et un Hamiltonien type spin central. Cette étude nous apprend que la dynamique de ces systèmes, qui relaxent d'un état initial vers un état stationnaire, conduit à un état superradiant lorsque l'état initial choisi y est favorable / The work presented in this thesis was inspired by precedent results on the Gaudin models (which are integrable) for spins-1/2 only which, by a change of variables in the algebraic Bethe equations, manage to considerably simplify the numerical treatment of such models. This numerical optimisation is carried out by the construction of determinants, only depending on the previously mentioned variables, for every scalar products appearing in the expression of the mean value of an observable of interest at a given time. By showing it is possible to use the Quantum Inverse Scattering Method (QISM), even when the vacuum state is not eigenstate of the transfer matrix, the previous results concerning spins-1/2 only are generalised to models including an additional spin-boson interaction. De facto, this generalisation opened different possible paths of research. First of all, we show that it is possible to further generalise the use of determinants for spin models describing the interaction of one spin of arbitrary norm with many spins-1/2. We give the method leading to the explicit construction of determinants’ expressions. Moreover, we can extend this work to other Gaudin models where the vacuum state is not an eigenstate of the transfer matrix. We did this work for spins-1/2 interacting with an arbitrarily oriented magnetic field. Finally, a numerical treatment of systems describing the interaction of many spins-1/2 with a single bosonic mode is presented. We study the time evolution of bosonic occupation and of local magnetisation for two different Hamiltonians, the Tavis-Cummings Hamiltonian and a central spin Hamiltonian. We learn that the dynamics of these systems, relaxing from an initial state to a stationary state, leads to a superradiant-like state for certain initial states

Pendant ces trois ans, nous nous sommes intéressés à quelques sujets choisis en optique et en électrodynamique quantiques. Le fil rouge de nos interrogations est la fonction d’onde du photon. Les expériences d’optique et d’électrodynamique quantique peuvent-elles être décrites de manière simple, dans l’espace des positions, à l’aide d’une fonction d’onde décrivant le ou les photon(s) impliqués dans l’expérience ? Ce n’est pas entièrement évident :la description usuelle des photons se fait dans l’espace réciproque des vecteurs d’onde. Mais ces expériences gagnent à être décrites par la mécanique ondulatoire en représentation position, comme cela est fait dans les manuels de mécanique quantique pour des situations impliquant des particules massives. De surcroît, une expérience récente[1] a conduit à l’observation de trajectoires de photons uniques à travers un interféromètre à deux fentes d’Young.Pour essayer de décrire formellement ces trajectoires, il est naturel de formuler une mécanique ondulatoire pour les photons. Nous avons donc examiné en détail la construction formelle de la fonction d’onde du photon, un objet qui est resté peu étudié jusqu’aux années 1990. Nous avons également étudié les propriétés de la fonction d’onde du photon en présence de sources, et considéré pour ce faire divers systèmes quantiques ouverts (en interaction). Nous avons vu qu’il existe, en principe, une infinité de possibilités pour le choix de la fonction d’onde du photon.Nous avons mis en évidence un certain nombre de critères sur la base desquels il apparaît que seuls trois choix parmi tous ceux possibles sont intéressants, l’un d’entre eux ramenant à un objet introduit par Glauber [2] pour étudier la détection de la lumière et les corrélations du champ électromagnétique. Nous avons également vu qu’en l’absence de sources l’équation quantique de propagation des photons est formellement identique aux équations de Maxwell.À bas nombre de photons, le formalisme de la fonction d’onde peut se révéler très pratique. Nous avons adapté l’approche aux systèmes en interaction, en nous intéressant dans un premier temps à l’électrodynamique quantique1en cavité [3], en particulier aux expériences réalisées par le groupe de Serge Haroche [4]. Nous avons proposé un modèle simple pour la description des photons dans les cavités d’électrodynamique. À l’aide de ce modèle, et de la fonction d’onde du photon, nous avons étudié la propagation des photons s’échappant de la cavité. Nous avons également construit l’équation maîtresse de Lindblad sans introduire de sauts quantiques non unitaires (voir également [5]). Nous nous sommes enfin intéressés à la question de l’évolution spatiotemporelle d’un photon émis lors d’une désexcitation d’un électron atomique. Après avoir étudié soigneusement la dynamique de la désexcitation de l’électron, notamment aux temps très courts [6, 7], nous nous sommes attachés à décrire, aussi rigoureusement que possible, le champ électromagnétique émis. Celui-ci, de manière surprenante, n’évolue pas causalement. Si cela n’est pas entièrement inattendu au vu du théorème de Hegerfeldt, qui stipule [8] que la causalité est exclue pour les systèmes décrits par un Hamiltonien dont le spectre est borné inférieurement, nous avons identifié [9] deux autres sources de non-causalité, l’une, prédite qualitativement par Shirokov [10], et l’autre, entièrement nouvelle à notre connaissance, et dont la compréhension reste à affiner. / During these three years we focused on several topics in quantum otpics and quantum electrodynamics. A central theme in our investigations is that of the photon wave function. Can quantum optics and quantum electrodynamics experiments be described simply, in position space, with the help of a wave function describing the photon(s) featured in the experiment ? The answer to that question is not quite obvious: the usual description of photons takes place in the reciprocal space of wave vectors. But these experiments call for a wave mechanical description in the position representation, as is done in quantum mechanics textbooks in situations featuring massive particles. Moreover, in a recent experiment [1], single photon trajectories through a Young two-slit setup have been observed. In order to try and describe these trajectories formally, it is natural to build a wave mechanical formalism for photons. We therefore studied in detail the formal construction of the photon wave function, an object which was little studied until the 1990s. We also studied the properties of the photon wave function in the presence of sources.To do that, we considered several open (interacting) quantum systems. We saw that there exists in principle an infinite number of possibilities when defining the photon wave function. We emphasised several criteria on the basis of which it appears that only three choices for the wave function are interesting. One of them coincides with an object introduced and used by Glauber [2] to study light detection andthe correlations of the electromagnetic field in the quantum regime. We also saw that, in the absence of sources, the propagation equation for a single photon is formally equivalent to Maxwell’s equations. At low photon numbers, the wave function formalism can be very useful. We adapted it to interacting systems,first, to cavity quantum electrodynamics (QED) [3], in particular to the experiments carried out by Serge Haroche’s group [4]. We proposed a simple model to describe photons in QED cavities. With this model, and with the helpof the photon wave function, we studied the propagation of photons escaping a cavity. We also constructed the Lindblad master equation without introducing nonunitary quantum jumps (also see [5]). We finally investigated the spacetime evolution of a photon which is emitted during the decay of an atomic electron. After having carefully studied the dynamics of the electronic decay, especially at very short times [6, 7], we set out to describe the emitted electromagnetic field as rigorously as possible. This emitted field, surprisingly, does not evolve causally. Though this is not entirely unexpected in view of Hegerfeldt’s theorem, which states [8] that causality is impossible for quantum systems which are described by a Hamiltonian with a spectrum which is bounded by below, we identified [9] two other sources of non causality. One of them was predicted qualitatively by Shirokov [10], while the other one, which is completely new as far as we can tell, is still to be better understood

This thesis describes the development of experimental methods to probe the nanoscale light-matter interactions in photonic and plasmonic nanostructures. The first part of this thesis presents the experimental findings on the temperature evolution of optical properties in important plasmonic materials. Understanding the influence of temperature on the optical properties of thin metal films - the material platforms for plasmonics - is crucial for the design and development of practical devices for high temperature applications in a variety of research avenues, including plasmonics, novel energy conversion technologies and near-field radiative heat transfer. We will first introduce a custom built experimental platform comprising a heating stage integrated into a spectroscopic ellipsometer setup that enables the determination of optical properties in the wavelength range from 370 nm to 2000 nm at elevated temperatures, from room temperature to 900 ^oC. Subsequently, the temperature dependent complex dielectric functions of gold, silver and titanium nitride thin films that were obtained using the above described experimental platform will be presented. Furthermore, the underlying microscopic physical processes governing the temperature evolution and the role of film thickness and crystallinity will be discussed. Finally, using extensive numerical simulations we will demonstrate the importance of incorporating the temperature induced deviations into numerical models for accurate multiphysics modeling of practical high temperature nanophotonic applications.<div><br></div><div>The second part of this thesis focuses on the development of experimental techniques to quantify the nanoscale steady-state energy distributions of plasmonic hot-carriers. Such hot-carriers have drawn significant research interest in recent times due to their potential in a number of applications including catalysis and novel photodetection schemes circumventing bandgap. However, direct experimental quantification of steady-state energy distributions of hot-carriers in nanostructures, which is critical for systemic progress, has not been possible. Here, we show that transport measurements from suitably chosen single molecular junctions can enable the quantification of plasmonic hot-carrier distributions generated via plasmon decay. The key idea is to create single molecule junctions - using carefully chosen molecules featuring sharp molecular resonances - between a plasmonic nanostructure and the gold tip of a scanning tunneling microscope, and quantify the hot-carrier distributions form the current flowing through the molecular junctions with and without plasmonic excitation at various voltage biases. Using this approach, we reveal the fundamental role of surface-scattering assisted absorption - Landau damping - and the contributions of different plasmonic modes towards hot-carrier generation in tightly confined nanostructures. The approach pioneered in this work can potentially enable nanoscale experimental quantification of plasmonic hot-carriers in key nanophotonic and plasmonic systems.<br></div>

Chromophore is a molecule or a part of a molecule which is responsible for its appearance color. This definition has been evolving over time with the progress of science. Contemporary scientific advances have expanded its meaning: to an inclusive level, chromophore is an irreducible collective of fundamental particles, which can represent the photophysical (optical physical) properties of the macroscopic matter. Previous studies have already found that the same molecule can have different photophysical properties under different condensed states. Therefore, it is straight forward to conclude that the definition of chromophore should take such extrinsic influencing interactions of this given molecule into consideration, thus simply taking the smallest unit such as a molecule is not accurate. A good example is quantum dots. Same species of quantum dots possess the identical smallest chemical unit but can emit very differently due to quantum confinement effect, thus defining the smallest unit as the chromophore is apparently fallacious. In solid polymeric compositions, the chemical unit or building blocks may differ from the spectroscopic unit depending on how these chemical units interacts within their ensemble to evolve new properties such as a new transition dipole. As thus, understanding the evolution of photophysical behaviors between the targeted unit and neighbors is of much importance to determine whether they should be considered as one chromophore or many. This requires a thorough understanding towards the evolution of photophysical properties of a collective, and the construction of such collective will need to pay extra attention to, as any structural factor could have changed some photophysical interactions of the collective. The introductory chapter discusses the material platform and fundamental photophysics investigated in this dissertation. Chromophore assembly (CA) as a sylloge of several classes of self-assembled materials, including metal-organic frameworks (MOFs), covalent-organic frameworks (COFs), porous organic polymers (POPs). Among them, MOF-based CAs (MOF-CAs) featuring with the ease of synthesis, demonstrate incomparable promises to construct such collective with several appealing characteristics, including component diversity, chemical stability, structural porosity, and post-synthetic versatility (Chapter 1.1). As for here, the main target to achieve using these assemblies is to understand the interaction between adjacent chemical monomeric units, therefore their spatial arrangements are of the paramount importance. As modern theory discovered, both ordered and random systems can be very important for novel quantum material developments. Both crystalline and amorphous arrangements of monomeric units can be achieved by adopting different classes of materials. MOF-CAs could achieve the precise control of spatial arrangement including distance, direction, and dihedral angle by its crystalline structures, whereas porous organic polymer-based CAs (POP-CAs) could feature a total randomness. Photophysics, as the research topic targeting the firsthand knowledge gained by interrogating the information provided by the propagating light after its interaction with matters, could provide crucial knowledge of the targeted matter. Hence, photophysical properties could provide fundamental understanding of the targeted matter (Chapter 1.2). State-of-the-art spectroscopic methods and instrumentation have made it possible to critically examine new structures to correlate photophysics with the chemical structure of their assemblies. By combining multiple spectroscopic techniques along with theoretical study, several correlations between the electronic properties of the matter, such as structural features, have been investigated. To illustrate, some unique topology-dependent photophysical behaviors found in chromophore assemblies are introduced (Chapter 1.3). In this dissertation, the feasibility of using specific types of MOF-CAs to conduct unique photophysical studies has been carefully chosen and verified (Chapter 2). Next, with the help of first principles computations, the nature of several electronic excited states as a function of different extent of Van der Waals or electronic interaction in MOF-CAs is unveiled, and experimentally studied with several environmental variates (Chapter 3). The knowledge was then articulated to devise a strategy to improve resonance energy transfer process in MOF-CAs. Here, low electronic symmetry of linker and directionally aligned transition dipoles of their collective ensembled are found beneficial to improve such photophysical process in a bottom-up manner (Chapter 4). Then, a series of MOFs were rationally designed to examine the feasibility and extent of a nonlinear excitonic process, singlet fission, to promote the generation of carriers usable for many applications including light-harvesting applications. The outcome demonstrated MOF-CA is a powerful tool to design such materials and is more capable in terms of its tunability (Chapter 5). At last, a set of randomly oriented CAs in POP were examined for underlying excited state dynamic process that highlights a thermal activated delayed fluorescence (TADF) involving S1 and low-lying T2 excited states (Chapter 6). This dissertation has highlighted unique yet tunable excited-state features and photophysical processes within the well-defined molecular ensemble realized via porous frameworks. These photophysical properties differ from those of their respective molecular system in their solubilized forms. Studies in this dissertation demonstrates a reliable platform to investigate multibody chromophore systems and suggested several valuable discoveries and lights the way for the study of novel chromophore assembly systems.

Physics and potential applications of femtosecond laser pulses interacting with matter have captured interest in various fields, such as nonlinear optics, laser micromachining, integrated optics, and solar cell technologies. On the one hand, such ultrashort intense pulses make them practical elegant tools to be utilized for direct structuring of materials with high accuracy and numerous potential applications. On the other hand, studying the fundamental aspects and nonlinear nature of such interactions opens new remarkable venues for various unique investigations. In recent years, the emerging topic of structured light (also known as twisted or optical vortex light), i.e., a beam of light with a twisted wave-front that can carry orbital angular momentum (OAM), has attracted the attention of many researchers working in the field of light-matter interaction. Such beams offer various applications from classical and quantum communication to imaging, micro/nano-manipulation, and modification of fundamental processes involved in light-matter interactions, e.g., absorption and emission. Nevertheless, the fabrication of complex structures, controlled modification, and achieving a high spatial resolution in material processing still remain in the spotlight. Moreover, the fundamental role of orbital angular momentum in the nonlinear absorption of materials, particularly in solids, has yet remained a subject of debate. Addressing these points was the main motive behind this dissertation. To accomplish this objective and investigate new aspects of structured light-matter interaction, I conducted various experiments, the results of which are presented in this work. The general idea was to study the interaction of femtosecond laser radiation, having a structured phase and polarization, with the matter in two aspects: (i) surface morphology modification and (ii) nonlinear absorption of solids. In this regard, I studied surface processing of crystalline silicon and CVD diamond with femtosecond laser vortex pulses generated by a birefringent phase-plate, known as q-plate, in single and multiple pulse irradiation regimes, respectively. The characterization of the modified region was performed using optical microscopy, scanning electron microscopy (SEM), and atomic force microscopy (AFM). I demonstrated that upon irradiation of a single vortex pulse on silicon, a nano-cone structure is formed within the ablated crater, whose height was independent of the helicity of the twisted light. However, for a linearly polarized vortex pulse, the height of the nano-cone decreases at higher pulse energies. The dynamics of nano-cone formation and the role of polarization were also investigated by simulating the mass transport function in this process. Moreover, using superimposed vortex beams, we fabricated complex patterns containing several nano-cones, by single-shot irradiation on the silicon surface. My experimental results offer an ability to actively control and manipulate material, in terms of the nanocones position, in two dimensions with an ultra-high resolution. I further proceeded with our experiments in the multiple pulse regime on a diamond target. By irradiation of a high number of superimposed vortex pulses, I was able to imprint complex polarization states of structured light on the target surface in the form of periodic nano-ripples. This procedure enabled us to not only generate spatially varying nano-gratings but also directly visualize and study very complex states of polarization. Besides these surface structuring, I carried out experimental studies to investigate the response of bulk material to an incident circularly polarized vortex beam that carries orbital angular momentum. The experimental results reveal, for the first time, that such an interaction can produce a differential absorption that gives rise to helical dichroism. We demonstrate that this response is sensitive to the handedness and degree of the twist in the incident vortex beam. Such a dichroism effect may be attributed to the excitation of dipole-forbidden atomic transitions, e.g., electric quadrupole transitions. However, this explanation is not absolute and remains open to further research and investigations.

Within this thesis, photo-induced mechanisms of the light-matter interaction are investigated in tailored and photofunctional materials that differ significantly in their optical and structural properties. The individual coupling mechanisms in congruently melted, nominally undoped or iron doped lithium niobate crystals as well as in structurally disordered photoswitchable molecules embedded into a solid state polymer are examined in particular by the principle of holographic grating recording and transient absorption spectroscopy which provide new insight into a variety of material response properties. In case of photoswitchable ruthenium sulfoxide compounds, the underlying mechanism can be unambiguously assigned to a photochromic material response evoked by a photochemical reaction, i.e., a non-instantaneous, local ligand isomerisation. Comparable results are obtained for iron-doped, oxidized lithium niobate where holographic grating recording is related to the photophysical generation of transient excitonic states whose photochromic properties are characterized by targeted ns-pump, supercontinuum probe spectroscopy. In the event of nominally undoped lithium niobate, the holographic amplification of two sub-picosecond pulses is attached to the phenomenon of two-beam coupling on a self-induced dynamic grating. By correlating the individually obtained mechanisms of the light-matter interaction and the light-induced material response, generally accepted conclusions on a microscopic level can be achieved. A major influence of the internal structure and orientation of the excited states, i.e., an appropriate threedimensional structural arrangement, is deduced as a prerequisite for the formation of light-induced, macroscopic refractive index changes while absorption and microscopic refractive index alterations linked via the Kramers-Kronig relation are unaffected. In systems featuring a random distribution of excited states, an orientational order might be achieved as a consequence of linear polarized light, i.e., by polarization structuring. Moreover, if the photorefractive effect can be ruled out, the material response in lithium niobate can be solely assigned to a local alteration of the transient electronic states, i.e., to the photochromic properties of polarons and/or excitonic states, which is in particular comparable to the linkage isomerism of molecular photoswitchable molecules. In addition, the influence of structural parameters on the light-matter/surface interaction is studied on the μm-scale by analyzing the diffraction phenomenon arising from a relief grating. A considerable impact on the surface grating assisted coupling is determined by the transition from cw-lasers to ultrashort laser pulses which enables interference quenching. However, this phenomenon is of no consequence in case of selfinduced holographic gratings.

We report on the investigation and observation of Bloch surface wave polaritons, resulting from the interaction between excitons in ZnO and a Bloch surface wave supported by a distributed Bragg reflector (DBR), for temperatures up to 430 K. The samples were fabricated using pulsed laser deposition and consist of a DBR made of 6.5 layer pairs of yttrica-stabilized zirconia and Al2O3 with a ZnO surface layer. We measured the reflectivity of transverse electric modes using a SiO2 prism in Kretschmann–Raether configuration, giving access to high in-plane momenta. Whereas the lower polariton branch was clearly observable, the upper polariton branch was not visible, due to the strong absorption in ZnO above the excitonic resonance. By employing a coupled oscillator model for the interaction between the bare surface mode and exciton, we derived a corresponding Rabi splitting between 100–192 meV at 294 K, which decreases with increasing temperature.

This work derives a nonlinear optical spatio-temporal instability. It is a perturbative analysis that begins from Maxwell’s equations and its constituent relations to derive a vectorial nonlinear wave equation. In fact, it is a new theoretical method that has been developed that builds on previous aspects of nonlinear optics in a more general way. The perturbation in the wave equation derived is coupled with its complex conjugate which has been taken for granted so far. Once decoupled it gives rise to a second-order equation and thus a true instability regime because the wavevector can become complex. The solution obtained for the perturbation that co-propagates with the driving laser is a generalization to modulation and filamentation instability, extending beyond the nonlinear Schrodinger and nonlinear transverse diffusion equations[1][2]. As a result of this new mechanism, new phenomena can be explored. For example, the Kerr Nonlinear Instability can lead to exponential growth, and hence amplification. This can occur even at wavelengths that are typically hard to operate at, such as into far infrared wave- lengths. This provides a mechanism for obtaining amplification in the far infrared from a small seed pulse without the need for population inversion. The analysis provides the basic framework that can be extended to many different avenues. This will be the subject of future work, as outlined in the conclusion of this thesis.