Quantum information science has shown that computers which exploit the quantum nature of particles, namely quantum computers, can outperform contemporary computers in some computational tasks. The fundamental building blocks of a quantum computer are quantum logical gates and quantum bits (qubits). Previous research has shown that the optical approach to quantum computing is promising. However, linear optical quantum computing (LOQC) schemes require a huge amount of resource, which makes large scale LOQC impractical, and hence there have been renewed interests in nonlinear optical quantum computing schemes, where less resource is required. The performance of these quantum gates depends on the properties of the nonlinear media. However, requirements on some of the properties for high performance quantum gates are not fully known. This thesis intends to bridge this gap of knowledge and examines the necessary conditions on several types optical nonlinearities that are common in two-qubit quantum gates schemes. These types of nonlinearities are, namely two-photon absorption, $\chi^{(2)}$ nonlinearity and $\chi^{(3)}$ cross-Kerr nonlinearity. The two-photon absorption based quantum Zeno gate is modeled in this thesis. It is shown that for practical absorbers, the photon loss significantly lowers the quantum fidelity of the Zeno gate. Nevertheless, this thesis proposes to use the Zeno gate for fusing optical cluster states. With the best theoretical estimate of single photon loss in the absorbers, the Zeno gate can outperform linear optical schemes. This thesis also proposes to embed the Zeno gate in the teleportation-type of two-qubit gate, namely GC-Zeno gate, such that the success rate of the gate can be traded off for higher gate fidelity. The effect of some mode matching error and detector inefficiency on the GC-Zeno gate are also considered here. It is shown that the photon loss requirement as well as the mode matching requirement are both stringent for having a fault tolerant GC-Zeno gate. This thesis models some of the properties of a $\chi^{(3)}$ optical medium and explores how they affect the fidelity of the cross-Kerr nonlinearity based quantum gate. This thesis shows that for a cross-Kerr medium with fast time response but negligible wave dispersion, the medium would induce spectral entanglement between the input photons and this significantly lowers the fidelity of the quantum gate. Nevertheless, when the dispersion has a stronger effect than the time response, and if phase noise is negligible, it is possible to achieve a quantum gate with high fidelity. However, the noise is actually significant, and this thesis suggests that spectral filtering can be applied to prohibit the occurrence of the noise. The requirements on employing optical $\chi^{(2)}$ nonlinearity for quantum computing are also examined. This study models the spectral effects of a $\chi^{(2)}$ medium on its efficiency. It is shown in this thesis that since the Hamiltonian of the medium does not commute at different times, the unitary operation should be modeled by a Dyson series, which leads to undesired spectral entanglement that lowers the efficiency of the medium. However, in the case of periodical poling, the unitary operation can be modeled by a Taylor series, where under some phase matching conditions, the medium can have a high efficiency. Furthermore, this thesis proposes a Bell measurement scheme and a quantum gate scheme based on $\chi^{(2)}$ nonlinearity that can always outperform linear optics even when the nonlinearity strength is weak. In the case of sufficiently strong nonlinearity, a quantum gate with high success rate can be achieved. In summary, this thesis models some of the properties of two-photon absorbers, $\chi^{(2)}$ nonlinearity and $\chi^{(3)}$ nonlinearity, and shows that it is possible to achieve the conditions required for high performance quantum gates, however these conditions are experimentally challenging to meet.

Quantum information science has shown that computers which exploit the quantum nature of particles, namely quantum computers, can outperform contemporary computers in some computational tasks. The fundamental building blocks of a quantum computer are quantum logical gates and quantum bits (qubits). Previous research has shown that the optical approach to quantum computing is promising. However, linear optical quantum computing (LOQC) schemes require a huge amount of resource, which makes large scale LOQC impractical, and hence there have been renewed interests in nonlinear optical quantum computing schemes, where less resource is required. The performance of these quantum gates depends on the properties of the nonlinear media. However, requirements on some of the properties for high performance quantum gates are not fully known. This thesis intends to bridge this gap of knowledge and examines the necessary conditions on several types optical nonlinearities that are common in two-qubit quantum gates schemes. These types of nonlinearities are, namely two-photon absorption, $\chi^{(2)}$ nonlinearity and $\chi^{(3)}$ cross-Kerr nonlinearity. The two-photon absorption based quantum Zeno gate is modeled in this thesis. It is shown that for practical absorbers, the photon loss significantly lowers the quantum fidelity of the Zeno gate. Nevertheless, this thesis proposes to use the Zeno gate for fusing optical cluster states. With the best theoretical estimate of single photon loss in the absorbers, the Zeno gate can outperform linear optical schemes. This thesis also proposes to embed the Zeno gate in the teleportation-type of two-qubit gate, namely GC-Zeno gate, such that the success rate of the gate can be traded off for higher gate fidelity. The effect of some mode matching error and detector inefficiency on the GC-Zeno gate are also considered here. It is shown that the photon loss requirement as well as the mode matching requirement are both stringent for having a fault tolerant GC-Zeno gate. This thesis models some of the properties of a $\chi^{(3)}$ optical medium and explores how they affect the fidelity of the cross-Kerr nonlinearity based quantum gate. This thesis shows that for a cross-Kerr medium with fast time response but negligible wave dispersion, the medium would induce spectral entanglement between the input photons and this significantly lowers the fidelity of the quantum gate. Nevertheless, when the dispersion has a stronger effect than the time response, and if phase noise is negligible, it is possible to achieve a quantum gate with high fidelity. However, the noise is actually significant, and this thesis suggests that spectral filtering can be applied to prohibit the occurrence of the noise. The requirements on employing optical $\chi^{(2)}$ nonlinearity for quantum computing are also examined. This study models the spectral effects of a $\chi^{(2)}$ medium on its efficiency. It is shown in this thesis that since the Hamiltonian of the medium does not commute at different times, the unitary operation should be modeled by a Dyson series, which leads to undesired spectral entanglement that lowers the efficiency of the medium. However, in the case of periodical poling, the unitary operation can be modeled by a Taylor series, where under some phase matching conditions, the medium can have a high efficiency. Furthermore, this thesis proposes a Bell measurement scheme and a quantum gate scheme based on $\chi^{(2)}$ nonlinearity that can always outperform linear optics even when the nonlinearity strength is weak. In the case of sufficiently strong nonlinearity, a quantum gate with high success rate can be achieved. In summary, this thesis models some of the properties of two-photon absorbers, $\chi^{(2)}$ nonlinearity and $\chi^{(3)}$ nonlinearity, and shows that it is possible to achieve the conditions required for high performance quantum gates, however these conditions are experimentally challenging to meet.

The two main themes in this thesis are the implementation of interference methods with optically trapped particles for measurements of position and optical phase (optical interferometric metrology) and the optical manipulation of nanoparticles for studies in the assembly of nanostructures, nanoscale heating and nonlinear optics (nanophotonics). The first part of the thesis (chapter 1, 2) provides an introductory overview to optical trapping and describes the basic experimental instrument used in the thesis respectively. The second part of the thesis (chapters 3 to 5) investigates the use of optical interferometric patterns of the diffracting light fields from optically trapped microparticles for three types of measurements: calibrating particle positions in an optical trap, determining the stiffness of an optical trap and measuring the change in phase or coherence of a given light field. The third part of the thesis (chapters 6 to 8) studies the interactions between optical traps and nanoparticles in three separate experiments: the optical manipulation of dielectric enhanced semiconductor nanoparticles, heating of optically trapped gold nanoparticles and collective optical response from an ensemble of optically trapped dielectric nanoparticles.

This thesis examines second-order optical nonlinear wave mixing processes in domain-disordered quasi-phase matching waveguides and evaluates their potential use in compact, monolithically integrated wavelength conversion devices. The devices are based on a GaAs/AlGaAs superlattice-core waveguide structure with an improved design over previous generations. Quantum-well intermixing by ion-implantation is used to create the quasi-phase matching gratings in which the nonlinear susceptibility is periodically suppressed. Photoluminescence experiments showed a large band gap energy blue shift around 70 nm after intermixing. Measured two-photon absorption coefficients showed a significant polarization dependence and suppression of up to 80% after intermixing. Similar polarization dependencies and suppression were observed in three-photon absorption and nonlinear refraction. Advanced modeling of second-harmonic generation showed reductions of over 50% in efficiency due to linear losses alone. Self-phase modulation was found to be the dominant parasitic nonlinear effect on the conversion efficiency, with reductions of over 60%. Simulations of group velocity mismatch showed modest reductions in efficiency of less than 10%. Experiments on second-harmonic generation showed improvements in efficiency over previous generations due to low linear loss and improved intermixing. The improvements permitted demonstration of continuous wave second-harmonic generation for the first time in such structures with output power exceeding 1 µW. Also, Type-II phase matching was demonstrated for the first time. Saturation was observed as the power was increased, which, as predicted, was the result of self-phase modulation when using 2 ps pulses. By using 20 ps pulses instead, saturation effects were avoided. Thermo-optically induced bistability was observed in continuous wave experiments. Difference frequency generation was demonstrated with wavelengths from the optical C-band being converted to the L- and U-bands with continuous waves. Conversion for Type-I phase matching was demonstrated over 20 nm with signal and idler wavelengths being separated by over 100 nm. Type-II phase matched conversion was also observed. Using the experimental data for analysis, self-pumped conversion devices were found to require external amplification to reach practical output powers. Threshold pump powers for optical parametric oscillators were calculated to be impractically large. Proposed improvements to the device design are predicted to allow more practical operation of integrated conversion devices based on quasi-phase matching superlattice waveguides.

This thesis deals with the investigation of the first hyperpolarizabilities (β) of a large number of molecules linked to other molecules either covalently or noncovalently. Chapter 1 gives a brief introduction to supramolecular chemistry and Nonlinear Optics (NLO). A survey of literature pertinent to noncovalently interacting supramolecular assembly and their NLO properties as well as NLO properties of oligomeric systems has been presented. The scope of the present investigation has been described at the end of the chapter. Chapter 2 discusses all the methods used in carrying out this thesis work. The first hyperpolarizabilities (β) of all the compounds have been measured by the hyper Rayleigh scattering (HRS) technique; the experimental details of which are written in this chapter. Various spectroscopic techniques such as NMR, IR, UV-Vis, etc. that were used in the investigation have been presented. The subsequent chapters 3-5 deal with the actual results obtained in this work. In chapter 3 first hyperpolarizabilities of o-, m-, and p-aminobenzoic acids and their oligomers viz., dimer, trimer and tetramer (covalently linked) have been studied. The compounds are synthesized and characterized by various spectroscopic methods and their β values have been measured by HRS. The hyperpolarizability increases in going from the monomer to the dimer but decreases subsequently from the dimer to the trimer to the tetramer. This unexpected trend in β has been attributed to the formation of molecular aggregates in the trimers and tetramers. Further evidences of aggregation come from the results of1H NMR spectroscopy and conductivity measurements. In chapter 4, synthesis, characterization and HRS investigation to probe the formation, dissociation and binding constants of hydrogen bonded supramolecular complexes (noncovalent interaction) formed in solution between 6-amino-2-(pivaloylamino)pyridine and ferrocene functionalized barbituric acid and 5-methoxy-N,N′-bis(6-amino-2-pyridinyl)-1,3-benzenedicarboxamide and ferrocenyl barbituric acid have been described. From the HRS data the stoichiometry of the supramolecular complexes has been determined and compared to that from the NMR data. Some of the complex stoichiometries that are measured by HRS have not been seen in the NMR data and vice versa. The results have been rationalized in terms of the strengths and weaknesses of various spectroscopic methods as applied to this problem. Many fold increase in the β value has been realized in the supramolecular complex formation process. Depolarized HRS experiments have been carried out to obtain structural information on the complexes. In the last chapter the synthesis, characterization and measurements on the first hyperpolarizabilities of unsubstituted tetraphenylporphyrin and its metallated complexes have been presented. Synthesis of supramolecular complexes of ferrocenyl barbituric acid with functionalized porphyrin compounds has been carried out although the amount of the final complex was insufficient for HRS measurements. This chapter ends with a perspective for the future work in the direction.

This thesis examines second-order optical nonlinear wave mixing processes in domain-disordered quasi-phase matching waveguides and evaluates their potential use in compact, monolithically integrated wavelength conversion devices. The devices are based on a GaAs/AlGaAs superlattice-core waveguide structure with an improved design over previous generations. Quantum-well intermixing by ion-implantation is used to create the quasi-phase matching gratings in which the nonlinear susceptibility is periodically suppressed. Photoluminescence experiments showed a large band gap energy blue shift around 70 nm after intermixing. Measured two-photon absorption coefficients showed a significant polarization dependence and suppression of up to 80% after intermixing. Similar polarization dependencies and suppression were observed in three-photon absorption and nonlinear refraction. Advanced modeling of second-harmonic generation showed reductions of over 50% in efficiency due to linear losses alone. Self-phase modulation was found to be the dominant parasitic nonlinear effect on the conversion efficiency, with reductions of over 60%. Simulations of group velocity mismatch showed modest reductions in efficiency of less than 10%. Experiments on second-harmonic generation showed improvements in efficiency over previous generations due to low linear loss and improved intermixing. The improvements permitted demonstration of continuous wave second-harmonic generation for the first time in such structures with output power exceeding 1 µW. Also, Type-II phase matching was demonstrated for the first time. Saturation was observed as the power was increased, which, as predicted, was the result of self-phase modulation when using 2 ps pulses. By using 20 ps pulses instead, saturation effects were avoided. Thermo-optically induced bistability was observed in continuous wave experiments. Difference frequency generation was demonstrated with wavelengths from the optical C-band being converted to the L- and U-bands with continuous waves. Conversion for Type-I phase matching was demonstrated over 20 nm with signal and idler wavelengths being separated by over 100 nm. Type-II phase matched conversion was also observed. Using the experimental data for analysis, self-pumped conversion devices were found to require external amplification to reach practical output powers. Threshold pump powers for optical parametric oscillators were calculated to be impractically large. Proposed improvements to the device design are predicted to allow more practical operation of integrated conversion devices based on quasi-phase matching superlattice waveguides.

Pas de résumé en français / Being compared with oxide glasses, chalcogenide glasses have fine infrared transmissivity and higher optical nonlinearity, and also could be drawn into optical fibers. So chalcogenide glasses and fibers have potential wide applications in the fields of all-optical information processing, infrared lasers, nonlinear optical devices, and so on, the studies of their optical nonlinearity are one of the attractive subjects in the area of optoelectronics at present. The main purpose of this paper is to improve the stability and enhance the intensity of nonlinearity in chalcogenide glasses and fibers by means of exploring new glass compositions, optimizing the external field poling method, designing and fabricating fibers with special structures, all of these will promote their real applications. The main results are concluded as follows . The glass-forming region of GeS2-GA2S3-AgX (X=Cl, Br, I) and GeS2-Ga (In)2S3-CuI systems were determined , the maximal content of the additive halides are 70% and 12% respectively. In both two systems glasses, with the increasing addition of halides, the thermal stability reduce, density and linear refractive index increase, the ultraviolet cut-off edges shift to longer wavelength, while the infrared cut-off edges keep almost the same. 30GeS2 35Ga2S3 35AgCl and 47.5GeS2 17.5Ga2S3 35AgCl surface- and bulk-crystallized glasses that contain AgGaGeS4 nonlinear optical crystallites were prepared. Obvious second harmonic generation (SHG) could be observed in these crystallized glasses, and their intensity relate to the distribution and size of the precipitated AgGaGeS4 crystals, the maximal second-order nonlinearity coefficients is as high as 12.4pm/V. These crystallized glasses have good chemical and SHG stability. For GeS2-Ga (In)2S3-CuI systems glasses, due to their small glass-forming region, they are not suit for the preparation of crystallized glasses that contain CuGaS2 or CuInS2 nonlinear optical crystals. According to the structural studies of two system glasses, the main structural units of theses glasses are [YS4-xXx] (Y=Ge, Ga, In. X=Cl, Br, I) mixed anion tetrahedrons, they form a three-dimensional glassy network through bridging sulphur bonds. When the contents of halides MX(M=Ag, Cu. X=Cl, Br, I) are low, some [XxS3-xGe(Ga)S3-xXx] (X=Cl, Br, I) mixed ethane-like structural units exist in the glass network, and they will gradually transform to [YS4-xXx] (Y=Ge, Ga, In. X=Cl, Br, I) mixed anion tetrahedrons with the increasing content of halides, till totally disappear. Both two system glasses have ultrafast (~150fs) third-order optical nonlinearity and reverse saturation absorption, they belong to self-focusing medium. The third-order optical nonlinearity mainly originate from the distortion of electron cloud of Y-X (Y=Ge, Ga, In, X=Cl, Br, I, S) bonds in the structural units. For GeS2-GA2S3-AgX (X=Cl, Br, I) system glasses, the largest nonlinear susceptibility n2 is 10.50x10-18 m/W, the smallest figure of merit (FOM) is 0.606. In addition, the relation of n2 with n0 do not obey Miller’s rule, but in accordance with the structural variation. Among the glass compositions with different additive halogens, Br-containing glasses have relatively best third-order nonlinearities. For GeS2-Ga (In)2S3-CuI system glasses, the largest nonlinear susceptibility n2 is 9.37x10-18 m/W, the smallest figure of merit (FOM) is 2.237. High purity AS2S3 glass performs and low loss single index fibers with diameter of 100~400µm that drawn form these performs were prepared, the transmission losses between 2~6 µm is only 0.5dB/m. AS2S3 tapered fibers have a uniform diameter of taper wasit, fine surface smoothness, and sharp taper transition part.

Produire et faire interagir entre eux des photons optiques de façon contrôlée sont deux conditions nécessaires au développement de communications quantiques à longue distance, et plus généralement au traitement quantique d’information codée sur des photons. Cette thèse présente une étude expérimentale de solutions possibles a ces deux problèmes, en utilisant la conversion des photons en excitations collectives (polaritons) dans un nuage d’atomes froids, placé dans le mode d’une cavité optique de faible finesse (~100). Dans un premier temps, des polaritons entre états atomiques fondamentaux sont utilisés pour « mettre en mémoire » une excitation unique dans le nuage. Celle-ci est ensuite convertie efficacement en un photon unique, dont le champ est analysé par tomographie homodyne. La fonction de Wigner de l’état à un photon est reconstruite a partir des données expérimentales, et présente des valeurs négatives, démontrant que les degrés de liberté de ce photon (mode spatio-temporel et état quantique) sont complètement contrôlés. Dans un second temps, les photons sont couplés à des polaritons impliquant des états de Rydberg. Les fortes interactions dipolaires entre ces derniers se traduisent par des non-linéarités optiques dispersives très importantes, qui sont caractérisées dans un régime d’excitation classique. Ces non-linéarités peuvent être amplifiées jusqu’à ce qu’un seul photon suffise à modifier totalement la réponse du système, permettant en principe de générer des interactions effectives entre photons. / Controllably producing optical photons and making them interact are two key requirements for the development of long-distance quantum communications, and more generally for photonic quantum information processing. This thesis presents experimental studies on possible solutions to these two problems, using the conversion of the photons into collective excitations (polaritons) in a cold atomic cloud, inside the mode of a low-finesse optical cavity (~100). Firstly, ground-state polaritons are used to store a single excitation in the cloud memory. This polariton is then efficiently converted into a single photon, whose field is characterized via homodyne tomography. The single photon state’s Wigner function is reconstructed from the experimental data and exhibits negative values, demonstrating that the photon’s degrees of freedom (spatio-temporal mode and quantum state) are well controlled. Secondly, photons can be coupled to polaritons involving Rydberg states. The strong dipolar interactions between these give rise to very strong optical dispersive nonlinearities, that are characterized in a classical excitation regime. These nonlinearities can be amplified until a single photon is enough to modify the entire system’s response, allowing in principle for the generation of effective photon-photon interactions.

The knowledge of geometry of molecular complexes formed via molecular association in solution through weak interactions is always important to understand the origin of stability and function of an array of molecules, supramolecular assemblies, and macromolecular networks. Simple 1:1 molecular complexes are very useful in this regard as they provide a model to understand both the nature of these interactions and their structural implications. Several weak noncovalent forces from long range (van der Waal’s, electrostatic, induction, dispersion) to short range (charge transfer) govern the geometry, that is, relative orientation of the two molecules in such a complex. On one hand, we find 1:1 electron donor acceptor (EDA) complexes such as naphthalene-tetracyanobenzene, hexamethylbenzene-chloranil etc. which stack parallel or in slipped parallel geometry in their crystals. On the other, benzene dimer has been found to stabilize in T shaped geometry in all its three physical states. In this thesis, I focus on 1:1 EDA complexes in solution. A good volume of literature is available which deals with the optical studies on the formation of such complexes. It has been suggested that the nature of the intermolecular interactions stabilizing these complexes in the gas phase or in their crystals is modified by the presence of solvent-solute interactions in solution thus bringing in difference in the solution geometry. However, the existing experimental techniques, both optical and magnetic, are unable to determine the exact geometries of 1:1 EDA complexes in solution. This opens an opportunity to probe their geometry in solution. The quadratic nonlinearity or first hyperpolarizability (β) of a molecule is a measure of the change in dipole moment (or polarization) in the second order of the applied electrical field and thus has a purely electronic origin. It is a tensorial property and can be resolved in components along the three dimensions. The number of β components and the nonlinear optical anisotropies in a typical donor-acceptor type dipolar molecule, defined as (equation) (where1, 2, 3 axes define the molecular frame, 1 being the direction along the principal axis of symmetry and pointing from the acceptor toward the donor), are determined by the symmetry /structure of the molecule. It has been shown theoretically that the 1:1 EDA complexes possess large hyperpolarizabilities. In the case of pNA dimers calculation revealed that the geometry of the dimer and its symmetry is important for obtaining the correct estimate of β from its tensorial components. Therefore, it should be possible to use the values of tensorial β components to construct the unknown geometry of such complexes. Experimentally macroscopic depolarization ratios (D and D′) in the laboratory fixed frame (XYZ, X being the direction of polarization and Z the direction of propagation of the incident light), are measured from the polarization resolved intensities of second harmonic scattering from molecules in solution using the hyper-Rayleigh scattering technique. The depolarization ratios are correlated to the anisotropy parameters, u and v through a co-ordinate transformation. In this thesis I, have first, characterized the quadratic nonlinear optical property of a variety of 1:1 electron donor acceptor complexes and used the values of u and v obtained from depolarized hyper-Rayleigh scattering to deduce their geometry in solution. Chapter 1 provides an introduction to the 1:1 electron donor acceptor complexes, their relevance to chemistry and biology. It also contains an introduction to nonlinear optical processes in molecules. The objective of the present work and scope of the investigation carried out in this thesis is presented in this chapter. Chapter 2 describes the details of the experimental polarization resolved HRS technique. The geometrical model adopted for the analysis of the HRS data has also been introduced and the method of analysis has been described in detail in this chapter. Chapter 3 presents the measurement of β values of two series of 1:1 EDA complexes of variously substituted methylbenzenes donors with tetrachloro-p-benzoquinone (CHL) and dicyanodichloro-p-benzoquinone (DDQ) acceptors at 1064 nm. In agreement with recent theoretical results we find large first hyperpolarizabilities for these complexes. The β values are greater than that of the typical push-pull molecule p-nitroaniline (pNA). We also find that in general β decreases with decrease in the donor strength. Chapter 4 presents the β values for the two series of EDA complexes of CHL and DDQ acceptors at 1907 nm. The values of β are less in magnitude at 1907 nm than that at 1064 nm which is due to the dispersion effect in β. In Chapter 5 and 6, it is described how depolarized hyper-Rayleigh scattering can be utilized to probe geometries of 1:1 complexes in solution. Chapter 5 concentrates mainly on 1:1 EDA complexes of CHL and DDQ and TCNB (tetracyanobenzene), while chapter 6 contains examples of other 1:1 molecular complexes where the noncovalent interactions are much weaker, such as in benzene-naphthalene, benzene-methoxybenzene, benzene-hexafluorobenzene and benzene-chlorobenzene pairs. We find the geometry of 1:1 EDA complexes in solution in terms of tilt angle (θ) and twist angle (ϕ) between the donor and acceptor pairs. The angle θ varies from 29°-47° for different pairs of EDA complexes, while ϕ varies within 34° and 38°. We find that the geometry of 1:1 EDA complexes in solution is different (twisted and tilted cofacial and twisted ‘V’) from those in the crystalline or gaseous states (cofacial), if known. We find that both benzene-naphthalene and benzene-chlorobenzene pairs assume twisted ‘T’ shape geometry with θ = 82° and 85°, respectively, and φ = 38°, while benzene-hexafluorobenzene assumes a twisted ‘V’ shape. A strong solvent effect is seen in the geometry of the benzene- methoxybenzene complex. The tilt angle is 55° when chloroform is used as a solvent and it is 82° without chloroform. Chapter 7 is the concluding chapter where the main work done in this thesis is summarized and future directions are presented.