Nonlinear optics is a field with new applications being regularly discovered, which leads to a growing interest in computing these properties. In this work, we attempt to determine new methods of computationally determining the properties of biologically relevant systems. We do so through testing a novel finite-field method to compute these properties. To facilitate the computation of molecular energies required for finite-field calculations, we tested a hypergeometric resummation scheme. Together, these projects form a strong step into being able to compute the nonlinear optical properties for larger systems of biological relevance. / Thesis / Master of Science (MSc)

Main objectives of the present dissertation can be divided in two parts. The first part deals with setting up a spectroscopic technique for reliable and accurate measurements of the two-photon absorption (2PA) cross section spectra. In the second part, this firmly established experimental technique together with conventional spectroscopic characterization, quantum-chemical computations and theoretical modelling calculations was combined and therefore used as a tool to gain information for the so-called structure-property relationship through several molecular compounds. / Die Hauptziele der vorliegenden Dissertation lassen sich in zwei Teile gliedern. Der erste Teil befasst sich mit dem Aufbau einer spektroskopischen Technik zur zuverlässigen und genauen Messung der Zwei-Photonen-Absorptionsquerschnittsspektren (2PA). Im zweiten Teil wurde diese fest etablierte experimentelle Technik zusammen mit konventioneller spektroskopischer Charakterisierung, quantenchemischen Berechnungen und theoretischen Modellrechnungen kombiniert und damit als Werkzeug genutzt, um über mehrere molekulare Verbindungen Informationen für die sogenannte Struktur-Eigenschafts-Beziehung zu gewinnen.

The aim of this diploma thesis is to study the optical properties of new -conjugated molecules based on 1,4-di(4'-N, N-diphenylaminostyryl)benzene and their potential application in advanced imaging techniques of biological specimens, the so-called multiphoton microscopy. The thesis focuses mainly on the characterization of their optical properties and the determination of their two-photon absorption cross-section using a unique laser equipment. Furthermore, a suitable methodology for the preparation of nanoparticles from these molecules, their characterization and stability are also developed. The thesis also investigates the influence of structure on the optical properties of these molecules. The relation between the length of the conjugated system and the presence of substituents on the backbone has been shown for the optical properties of the molecules in the solvent, the position and shape of the two-photon absorption spectrum and the value of two-photon absorption cross-section. It has been shown that this substance retains its unique fluorescent properties even in the form of nanoparticles and therefore appears to be a suitable candidate for the observation of biological specimens using multiphoton fluorescence microscopy. The work contributes to the knowledge base for the design of the chemical structure of molecules with desired properties.

Molecular nonlinear optical (NLO) properties are extensively studied using both theory and experiment because of their use in myriad applications. Experimental measurements of the most interesting molecules’ NLO properties are difficult, so experimental data for molecules with desirable NLO properties is scarce. Theoretical tools don’t suffer from the same limitations and can provide significant insights into the physico-chemical phenomena underlying the nonlinear responses, can help in interpreting response behaviour of molecules, and can guide design the materials with desirable response properties. Here, I present my work on developing methods for accurately calculating the NLO properties of molecules using the finite field (FF) approach. The first chapter provides a background for the finite field and electronic structure methods used in this dissertation. Chapter two is a thorough investigation of the finite field method. The limitations of the method are highlighted and the optimal conditions for overcoming its drawbacks and obtaining meaningful and accurate results are described. Chapter three presents the first systematic study of the dependence of optimal field strengths on molecular descriptors. The first protocol for predicting the optimal field for the second hyperpolarizability is presented and successfully tested, and the dependence of the optimal field strength for the first hyperpolarizability on the molecular structure is investigated. Chapter four is an assessment of various DFT functionals in calculating the second hyperpolarizabilities of organic molecules and oligomers. This study shows the limitations of conventional DFT methods and the importance of electron correlation to response properties. In chapter five we present a new method of calculating NLO properties using a rational function model that is shown to be more robust and have lower computational cost than the traditional Taylor expansion. Finally, chapter six includes a summary of the thesis and an overview of future work. / Thesis / Doctor of Philosophy (PhD)

Femtosecond laser has been an essential tool for nonlinear optics and materials processing at micrometer scale, in which chalcogenide and heavy metal oxide glasses have received special attention not only for their high third-order optical nonlinearities but also due to their transparency up to the infrared regions. Although metallic nanoparticles are expected to improve the optical properties of glasses, there are no enough experimental researches about their influence on the nonlinear refractive index (n2) and nonlinear absorption coefficient (&#946), moreover at femtosecond regime. Based on the scientific and technological interests on highly nonlinear glasses, the goal of this thesis was to apply femtosecond laser pulses in two main domains: (i) at the basis of fundamental science, to study the effect of metallic nanoparticles in the third-order nonlinear optical properties of glasses; and (ii) at the field of applied science, aiming the development of photonic devices, performed by the fabrication of 3D optical waveguides containing metallic nanoparticles. This aim was achieved through the techniques of z-scan and femtosecond laser micromachining, which provided the nonlinear optical characterization and waveguides development, respectively. First, we analyzed the third-order nonlinear optical properties of the GeO2-Bi2O3 glass containing gold nanoparticles, which promoted saturation of the absorption in the region of the surface plasmon resonance band. On the other hand, these gold nanoparticles did not affect the n2 that kept constant in the wavelength range of 480 - 1500 nm. The same features were investigated for a Pb2P2O7-WO3 matrix doped with copper nanoparticles. In contrast to the gold doped ones, these samples showed a slight enhancement of the nonlinear refractive index when the energy of the excitation approaches the surface plasmon band. We also found out that the Pb2P2O7-WO3 matrix is a good host to grow silver nanoparticles by fs-laser micromachining. Similarly, copper nanoparticles were produced in a borosilicate glass using single-step laser processing. The explanation for metallic nanoparticle formation is addressed in this thesis, as well as, its application in waveguides. Thus, we demonstrated the functionality of optical waveguides containing Cu0 or Ag0 nanoparticles. Still based on the technological interests on glasses doped with nanoparticles, we showed a single-step synthesis of silver sulfide nanoparticles in chalcogenide glass, which was carried in partnership with researches at Princeton University. The materials investigated in this PhD work are of great importance for photonics, in which the synthesis of nanoparticles, fabrication of waveguides and nonlinear optical characterization have been performed. / O laser de femtossegundos tem sido uma ferramenta essencial tanto para a óptica não-linear quanto para o processamento de materiais na escala micrométrica, na qual os vidros calcogenetos e óxidos de metais pesados têm recebido atenção especial, não apenas pelas suas elevadas não-linearidades ópticas de terceira ordem, mas também devido à sua transparência até o infravermelho. Embora seja esperado que nanopartículas metálicas melhorem as propriedades ópticas dos vidros, não existe investigações experimentais suficientes sobre a sua influência no índice de refração não linear (n2) e no coeficiente de absorção linear (&#946), sobretudo no regime de femtossegundos. Com base nos interesses científicos e tecnológicos de vidros altamente não-lineares, o objetivo deste trabalho foi aplicar pulsos laser de femtossegundos em dois domínios principais: (i) na campo da ciência fundamental, para estudar o efeito de nanopartículas metálicas nas propriedades ópticas não lineares de terceira ordem destes materiais; e (ii) no domínio da ciência aplicada, visando o desenvolvimento de dispositivos fotônicos, realizado pelo fabricação de guias de onda tridimensionais contendo nanopartículas metálicas. Este objetivo foi alcançado através das técnicas de varredura-z e microfabricação com laser de femtossegundos, que proporcionaram a caracterização óptica não-linear e o desenvolvimento de guias de onda, respectivamente. Primeiramente, foram investigadas as propriedades ópticas não-lineares de terceira ordem do vidro GeO2-Bi2O3 contendo nanopartículas de ouro, as quais promoveram saturação da absorção na região da banda de ressonância de plásmon. Por outro lado, essas nanopartículas não afetaram o n2, que se manteve constante no intervalo de comprimento de onda 480 - 1500 nm. As mesmas características foram investigadas para uma matriz Pb2P2O7-WO3 dopada com nanopartículas de cobre. Em contraste com os vidros dopados com ouro, estas amostras apresentaram um ligeiro aumento do índice de refração não linear quando a energia de excitação está próxima da banda de ressonância de plásmon. Observou-se ainda que a matriz Pb2P2O7-WO3 é ideal para a obtenção de nanopartículas de prata através da microfabricação com laser de femtossegundos. Similarmente, nanopartículas de cobre foram produzidas em vidro de borosilicato usando somente uma varredura a laser. A explicação para a formação de nanopartículas metálicas é abordada nesta tese, bem como sua aplicação em guias de onda. Deste modo, demonstrou-se a funcionalidade de guias de onda ópticos compostos por nanopartículas de Cu0 e Ag0. Ainda com base nos interesses tecnológicos em vidros dopados com nanopartículas, demonstrou-se uma síntese de nanopartículas de sulfeto de prata em vidro calcogeneto usando o processamento de única etapa, realizada em parceria com pesquisadores da Universidade de Princeton. Os materiais investigados neste trabalho de doutorado são de grande importância para aplicações em fotônica, em que a síntese de nanopartículas, a fabricação de guias de onda e a caracterização óptica não-linear foram realizadas.

Η εφεύρεση του laser έδωσε την δυνατότητα μελέτης της αλληλεπίδρασης ύλης-φωτός σε υψηλές εντάσεις ακτινοβολίας με αποτέλεσμα να οδηγηθούμε σε φαινόμενα κατά τα οποία οι συνήθεις οπτικές παράμετροι δε μπορούν να θεωρηθούν σταθερές, αλλά εξαρτώνται από την ένταση. Σε αυτή την περίπτωση, η συχνότητα δύναται να μεταβληθεί κατά την διάδοση της ακτινοβολίας σε ένα μέσο, ενώ η αρχή της επαλληλίας κυμάτων παραβιάζεται. Ο κλάδος της μη γραμμικής οπτικής μελετά φαινόμενα αλληλεπίδρασης της ύλης με ακτινοβολίες υψηλής έντασης. Αυτά τα φαινόμενα προέρχονται από την μεταβολή των οπτικών ιδιοτήτων της ύλης λόγω ισχυρών ηλεκτρικών πεδίων και η μη γραμμικότητα αυτών των φαινόμενων έγκειται στο ότι η απόκριση του υλικού είναι μη γραμμική συνάρτηση της έντασης της ακτινοβολίας. Οι θεμελιώδεις φυσικές αρχές που διέπουν τα μη γραμμικά φαινόμενα έχουν πλέον πλήρως αποσαφηνιστεί και το ενδιαφέρον έχει πια στραφεί στην μελέτη των μη γραμμικών οπτικών ιδιοτήτων διαφόρων υλικών. Σκοπός των ερευνών αυτών αποτελεί η εύρεση υλικών με μεγάλη μη γραμμική απόκριση, που θα μπορούσαν να χρησιμοποιηθούν σε διάφορες εφαρμογές στις οπτικές τηλεπικοινωνίες και στην οπτική επεξεργασία της πληροφορίας (π.χ. ως οπτικοί διακόπτες). Σε αυτήν την εργασία λοιπόν μέσω των τεχνικών ΟΚΕ και Z-Scan, ασχοληθήκαμε με την μελέτη της μη γραμμικής απόκρισης μιας σειράς παραγώγων φουλλερενίων, οι οπτικές ιδιότητες των οποίων είναι άμεσα συνδεδεμένες με την δομή τους και τον τρόπο σύνδεσης των επιμέρους ενώσεων από τις οποίες αποτελούνται.Στο πρώτο μέρος αυτής της εργασίας παρατίθενται οι βασικότερες έννοιες της μη γραμμικής οπτικής και περιγράφονται ορισμένα πολύ σημαντικά μη γραμμικά φαινόμενα. Στο δεύτερο μέρος παρουσιάζονται οι τεχνικές ΟΚΕ και Z-Scan οι οποίες χρησιμοποιήθηκαν για την μελέτη των μη γραμμικών οπτικών παραμέτρων των δειγμάτων των παραγώγων των φουλλερενίων στο πειραματικό μέρος της εργασίας αυτής και στη συνέχεια αναλύεται ο τρόπος επεξεργασίας των πειραματικών δεδομένων. Τέλος στο τρίτο μέρος περιγράφονται τα πειράματα που διεξήχθησαν, τα αποτελέσματα καθώς και τα συμπεράσματα που προέκυψαν. / The development of lasers has been a turning point in the history of science. It gave birth to the new field of nonlinear optics (NLO), which is the study of the interaction between intense light radiation and matter. In this regime, the response of matter cannot be considered linearly dependent on the intensity of the applied field, giving rise to significant new types of behavior and a wide spectrum of novel phenomena. Nonlinear optics has now become a rapidly growing field. It is at the forefront of progress in the area of photonics and optoelectronics. This vast development necessitates new materials with large nonlinearities, suitable for NLO applications in the laser and the optical communication technologies (e.g. optical switches). In that context, fullerenes have justifiably attracted considerable interest due to their intriguing physical and chemical properties; the extensive delocalization of their charge, as well as, their small reorganization energy can give rise to fast and high nonlinear optical response. Inevitably, the interest of the scientific community has now turned to the study of sophisticatedly altered fullerene derivatives. Depending on their ability to act as excellent electron acceptors, fullerenes are one of the most prominent chromophores that have been incorporated into multi-component molecular structures. Novel synthetic methods that enable the chemical modification of pristine molecules with electron donating moieties have been developed. This chemical functionalization of fullerenes can result in strong donor-acceptor interactions and photo-induced electron transfer, invigorating their nonlinear optical response. Their potential usage, which can range from photonics and photovoltaics implementations to applications in the biomedical area, is the main driving force of all this research. In the present study, the measurements were performed via the Z-Scan and the Optical Kerr Effect (OKE) techniques. The third order nonlinear susceptibility χ(3) and the second order hyperpolarizability γ of the derivatives were determined employing 4 ns and 35 ps laser pulses respectively, at excitation wavelength of 532 nm. In that respect, the main aim of the current study is threefold. Firstly, to provide a complete overview of the third order nonlinear parameters determined. Secondly, to briefly discuss the linkage between the observed nonlinearities with the molecular structures of the examinant hybrids, as well as, the possible effect of photo-induced charge transfer. Lastly, to shed light upon the role of the different pulse duration in the measurements and the dominant contributing physical processes related. Consequently, the first part of this work provides some basic concepts of nonlinear optics and the physical processes related with it. Then reference will be made to the experimental techniques used, including the fundamental background of the data analysis procedure. Finally, the nonlinearities observed in the picosecond and nanosecond regime are presented.

Femtosecond laser has been an essential tool for nonlinear optics and materials processing at micrometer scale, in which chalcogenide and heavy metal oxide glasses have received special attention not only for their high third-order optical nonlinearities but also due to their transparency up to the infrared regions. Although metallic nanoparticles are expected to improve the optical properties of glasses, there are no enough experimental researches about their influence on the nonlinear refractive index (n2) and nonlinear absorption coefficient (&#946), moreover at femtosecond regime. Based on the scientific and technological interests on highly nonlinear glasses, the goal of this thesis was to apply femtosecond laser pulses in two main domains: (i) at the basis of fundamental science, to study the effect of metallic nanoparticles in the third-order nonlinear optical properties of glasses; and (ii) at the field of applied science, aiming the development of photonic devices, performed by the fabrication of 3D optical waveguides containing metallic nanoparticles. This aim was achieved through the techniques of z-scan and femtosecond laser micromachining, which provided the nonlinear optical characterization and waveguides development, respectively. First, we analyzed the third-order nonlinear optical properties of the GeO2-Bi2O3 glass containing gold nanoparticles, which promoted saturation of the absorption in the region of the surface plasmon resonance band. On the other hand, these gold nanoparticles did not affect the n2 that kept constant in the wavelength range of 480 - 1500 nm. The same features were investigated for a Pb2P2O7-WO3 matrix doped with copper nanoparticles. In contrast to the gold doped ones, these samples showed a slight enhancement of the nonlinear refractive index when the energy of the excitation approaches the surface plasmon band. We also found out that the Pb2P2O7-WO3 matrix is a good host to grow silver nanoparticles by fs-laser micromachining. Similarly, copper nanoparticles were produced in a borosilicate glass using single-step laser processing. The explanation for metallic nanoparticle formation is addressed in this thesis, as well as, its application in waveguides. Thus, we demonstrated the functionality of optical waveguides containing Cu0 or Ag0 nanoparticles. Still based on the technological interests on glasses doped with nanoparticles, we showed a single-step synthesis of silver sulfide nanoparticles in chalcogenide glass, which was carried in partnership with researches at Princeton University. The materials investigated in this PhD work are of great importance for photonics, in which the synthesis of nanoparticles, fabrication of waveguides and nonlinear optical characterization have been performed. / O laser de femtossegundos tem sido uma ferramenta essencial tanto para a óptica não-linear quanto para o processamento de materiais na escala micrométrica, na qual os vidros calcogenetos e óxidos de metais pesados têm recebido atenção especial, não apenas pelas suas elevadas não-linearidades ópticas de terceira ordem, mas também devido à sua transparência até o infravermelho. Embora seja esperado que nanopartículas metálicas melhorem as propriedades ópticas dos vidros, não existe investigações experimentais suficientes sobre a sua influência no índice de refração não linear (n2) e no coeficiente de absorção linear (&#946), sobretudo no regime de femtossegundos. Com base nos interesses científicos e tecnológicos de vidros altamente não-lineares, o objetivo deste trabalho foi aplicar pulsos laser de femtossegundos em dois domínios principais: (i) na campo da ciência fundamental, para estudar o efeito de nanopartículas metálicas nas propriedades ópticas não lineares de terceira ordem destes materiais; e (ii) no domínio da ciência aplicada, visando o desenvolvimento de dispositivos fotônicos, realizado pelo fabricação de guias de onda tridimensionais contendo nanopartículas metálicas. Este objetivo foi alcançado através das técnicas de varredura-z e microfabricação com laser de femtossegundos, que proporcionaram a caracterização óptica não-linear e o desenvolvimento de guias de onda, respectivamente. Primeiramente, foram investigadas as propriedades ópticas não-lineares de terceira ordem do vidro GeO2-Bi2O3 contendo nanopartículas de ouro, as quais promoveram saturação da absorção na região da banda de ressonância de plásmon. Por outro lado, essas nanopartículas não afetaram o n2, que se manteve constante no intervalo de comprimento de onda 480 - 1500 nm. As mesmas características foram investigadas para uma matriz Pb2P2O7-WO3 dopada com nanopartículas de cobre. Em contraste com os vidros dopados com ouro, estas amostras apresentaram um ligeiro aumento do índice de refração não linear quando a energia de excitação está próxima da banda de ressonância de plásmon. Observou-se ainda que a matriz Pb2P2O7-WO3 é ideal para a obtenção de nanopartículas de prata através da microfabricação com laser de femtossegundos. Similarmente, nanopartículas de cobre foram produzidas em vidro de borosilicato usando somente uma varredura a laser. A explicação para a formação de nanopartículas metálicas é abordada nesta tese, bem como sua aplicação em guias de onda. Deste modo, demonstrou-se a funcionalidade de guias de onda ópticos compostos por nanopartículas de Cu0 e Ag0. Ainda com base nos interesses tecnológicos em vidros dopados com nanopartículas, demonstrou-se uma síntese de nanopartículas de sulfeto de prata em vidro calcogeneto usando o processamento de única etapa, realizada em parceria com pesquisadores da Universidade de Princeton. Os materiais investigados neste trabalho de doutorado são de grande importância para aplicações em fotônica, em que a síntese de nanopartículas, a fabricação de guias de onda e a caracterização óptica não-linear foram realizadas.

Time Dependent Density Functional Theory offers a good accuracy/computational cost ratio among different methods used to predict the electronic structure for molecules of practical interest. The Coupled Electronic Oscillator (CEO) formalism was recently shown to accurately predict Nonlinear Optical (NLO) properties of organic chromophores when combined with Time Dependent Density Functional Theory. Unfortunately, CEO does not lend itself easily to interpretation of the structure activity relationships of chromophores. On the other hand, the Sum Over States formalism in combination with semiempirical wavefunction methods has been used in the past for the design of simplified essential states models. These models can be applied to optimization of NLO properties of interest for applications. Unfortunately, TD-DFT can not be combined directly with SOS because state-to-state transition dipoles are not defined in the linear response TD approach. In this work, a second order CEO approach to TD-DFT is simplified so that properties of double excited states and state-to-state transition dipoles may be expressed through the combination of linear response properties. This approach is termed the a posteriori Tamm-Dancoff approximation (ATDA), and validated against high-level wavefunction theory methods. Sum over States (SOS) and related Two-Photon Transition Matrix formalism are then used to predict Two-Photon Absorption (2PA) profiles and anisotropy, as well as Second Harmonic Generation (SHG) properties. Numerical results for several conjugated molecules are in excellent agreement with CEO and finite field calculations, and reproduce experimental measurements well.

Lasers are increasingly used for a wide range of different applications for both civil and military purposes. Due to the distinct properties of laser light, use of lasers often comes with a risk of damage to the human eye and other optical sensors. Therefore, an effective laser protection is needed. 2D-materials is a relatively new class of materials, which have shown to possess many unique properties compared to its bulk counterparts. Some 2D-materials exhibit nonlinear optical (NLO) properties, and specifically optical power limiting (OPL) effects, and have therefore been researched for laser protection applications. In this work, two different 2D-materials, MXene Ti3C2 and graphene oxide (GO), have been combined with a hybrid organic-inorganic polymer, a so called melting gel (MG), to synthesise nanocomposites possessing OPL effects for laser protection applications. Different methods of incorporating the 2D-materials in the polymer matrix as well as the effect on optical properties of different concentrations of 2D-materials were investigated. The prepared nanocomposites were characterised using optical microscopy, spectroscopy and OPL measurements in order to investigate and quantify their linear and nonlinear optical properties. The MG was optically clear, mechanically stable and easy to synthesise, which makes it a suitable candidate as a matrix for a laser protection nanocomposite. Additionally, it was possible to dope the MG with the two different 2D-materials to create nanocomposites showing desirable optical properties in the visible spectrum. However, many samples showed signs of clustered 2D-particles indicating that the dispersion could be improved. Finally, OPL measurements, performed at 532 nm, showed that the MG itself exhibited OPL effects, both 2D-materials showed a stronger OPL effect than the non-doped MG and that GO-doped samples gave a better protection than the MXene samples.

Thin-film materials from μm thickness down to single-atomic-layered 2D materials play a central role in many novel electronic and optical applications. Coherent, nonlinear optical (NLO) μ-spectroscopy offers insight into the local thickness, stacking order, symmetry, or electronic and vibrational properties. Thin films and 2D materials are usually supported on multi-layered substrates leading to (multi-) reflections, interference, or phase jumps at interfaces during μ-spectroscopy, which all can make the interpretation of experiments particularly challenging. The disentanglement of the influence parameters can be achieved via rigorous theoretical analysis. In this work, we compare two self-developed modeling approaches, a semi-analytical and a fully vectorial model, to experiments carried out in thin-film geometry for two archetypal NLO processes, second-harmonic and third-harmonic generation. In particular, we demonstrate that thin-film interference and phase matching do heavily influence the signal strength. Furthermore, we work out key differences between three and four photon processes, such as the role of the Gouy-phase shift and the focal position. Last, we can show that a relatively simple semi-analytical model, despite its limitations, is able to accurately describe experiments at a significantly lower computational cost as compared to a full vectorial modeling. This study lays the groundwork for performing quantitative NLO μ-spectroscopy on thin films and 2D materials, as it identifies and quantifies the impact of the corresponding sample and setup parameters on the NLO signal, in order to distinguish them from genuine material properties.