Using a novel two-beam technique developed to greatly enhance quadrupolar contributions to the second-order nonlinear polarization, we performed a nonlinear spectroscopic study of silicon nanocrystals implanted in an SiO₂ matrix.

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In recent years, second harmonic generation (SHG) microscopy has revolutionised the field of biological imaging by offering a new means of visualising the fine structures of collagen tissues with excellent image penetration while minimising photodamage. This project involves the design and construction of a SHG microscope that is built around a compact femtosecond fibre laser for collagen imaging. Operating at 1032 nm, the microscope has demonstrated a penetration depth of beyond 320 microns in collagen, which is considerably superior to depths of 250 to 300 microns achievable with a conventional SHG microscope coupled to a Ti:sapphire excitation laser. The imaging characteristics of the microscope have been tested with a modified sample of bovine pericardium. The results indicate the microscope is polarisation-sensitive to the tissue structure and is capable to detecting signal changes at 10 μm resolution. This thesis will describe in detail, to our best knowledge, the first SHG microscope equipped with a compact and robust all-fibre femtosecond 1032 nm laser source.

Second Harmonic Generation (SHG) microscopy has undergone rapid transformation as an imaging tool for research due to its noninvasive properties that provides high resolution images for quantitative analysis. Extensive research has been performed to study the type of materials compatible with SHG but the effects of varying laser wavelengths on SHG efficiency is still poorly understood. The aim of this project is to design and build a scanning laser SHG microscope that is optimised for a 1030 nm giant chirp oscillator (GCO) designed by the University of Auckland. The project has shown that this wavelength is capable of producing SHG in collagen tissues of thickness up to 100 µm. We used nonlinear crystals and collagen samples to acquire signals and high resolution 2D images. The images were found to be of excellent quality with resolutions of up to a few microns to allow accurate measurements of the size and orientation of the fibrillar structures.

Information regarding the structure and function of living tissues and cells is instrumental to the advancement of cell biology and biophysics. Nonlinear optical microscopy can provide such information, but only certain biological structures generate nonlinear optical signals. Therefore, structural specificity can be achieved by introducing labels for nonlinear optical microscopy. Few studies exist in the literature about labels that facilitate harmonic generation, coined "harmonophores". This thesis consists of the first major investigation of harmonophores for third harmonic generation (THG) microscopy. Carotenoids and chlorophylls were investigated as potential harmonophores. Their nonlinear optical properties were studied by the THG ratio technique. In addition, a tunable refractometer was built in order to determine their second hyperpolarizability (γ). At 830 nm excitation wavelength, carotenoids and chlorophylls were found to have large negative γ values however, at 1028 nm, the sign of γ reversed for carotenoids and remained negative for chlorophylls. Consequently, at 1028 nm wavelength, THG signal is canceled with mixtures of carotenoids and chlorophylls. Furthermore, when such molecules are covalently bonded as dyads or interact within photosynthetic pigment-protein complexes, it is found that additive effects with the γ values still play a role, however, the overall γ value is also influenced by the intra-pigment and inter-pigment interaction. The nonlinear optical properties of aggregates containing chlorophylls and carotenoids were the target of subsequent investigations. Carotenoid aggregates were imaged with polarization-dependent second harmonic generation and THG microscopy. Both techniques revealed crystallographic information pertaining to H and J aggregates and β-carotene crystalline aggregates found in orange carrot. In order to demonstrate THG enhancement due to labeling, cultured cells were labeled with carotenoid incorporated liposomes. In addition, Drosophila melanogaster larvae muscle as well as keratin structures in the hair cortex were labeled with β-carotene. Polarization-dependent THG studies may be particularly useful in understanding the structural organization that occurs within biological structures containing carotenoids and chlorophylls such as photosynthetic pigment-protein complexes and carotenoid aggregates in plants and alga. Further, artificial labeling with carotenoids and chlorophylls may be useful in clinical applications since they are nontoxic, nutritionally valuable, and they can aid in visualizing structural changes in cellular components.

Orbital angular momentum (OAM) is a property of light that is widely used for applications in bioimaging, optical communication and optical manipulation, but is mainly limited to the infrared and visible spectra. Developing a table-top source of Extreme Ultraviolet (XUV) light containing an arbitrary amount of OAM is yet to be achieved. We accomplish this by exploiting high-harmonic generation (HHG), a process whereby an infrared pump beam produces high order harmonics. We experimentally demonstrate the conservation of OAM in HHG by measuring harmonics of order n containing n times the OAM of the pump (n = 11, 13, 15 in our experiment). These results agree with our theoretical model. We also show theoretically how to manipulate the HHG process to impart an arbitrary amount of OAM to the di fferent harmonics. We hence show the way to a table-top and flexible source of XUV light containing orbital angular momentum.

Over the last decade it has become increasingly popular to provide large public areas with gracefully designed 'flexible' staircases. One inherent characteristic of this type of construction is a low stiffness to mass ratio and hence a low natural frequency when compared to more traditional designs. A number of staircases have been found to be dynamically responsive to pedestrian traffic resulting in costly repairs. The objective of this thesis was to investigate the differences between human induced loading on floors with that on stairs. Experimental work carried out on a purpose built staircase showed that forces up to 3 times the static body weight were generated during fast descents while forces up to 2.5 times the static body weight were generated during fast ascents. The work also showed that first harmonic values generated while ascending were slightly higher than for descending whilst second harmonic values were up to 3 times greater for fast descents than for fast ascents. When compared with floor testing, stair testing produced first harmonic values nearly 2.5 times greater with second, third and fourth harmonic values nearly 3 times greater. The harmonic results for the flat testing were also incorporated into a new mathematical expression to predict peak accelerations on simply supported floors and footbridges. The experimental results were duplicated analytically by developing a computer program to calculate the vertical ground reaction forces from body segment positional data. Following a Newtonian approach, the predicted first harmonic values were 20% to 30% lower than actual while the second harmonic values were approximately the same. Monte Carlo simulation techniques were also used to model the effects of group loading on stairs. The simulations predicted enhancement factors (a multiplier on single subject loading) of 3 to 6 for smaller groups(< 9 people) and 4 for larger groups(> 25 people). If the experimental/analytical results are combined with the group loading predictions, the harmonic values for groups ascending or descending flexible staircase could be substantially increased. These results demonstrate that loading data from floors is highly inappropriate for staircase design.

Implementation of the ultrasonic second harmonic generation has typically been restricted to simple setups such as through-transmission or Rayleigh surface waves. Recent research has evaluated the second harmonic generation in P- and SV- waves reflected from a stress-free surface to enable the single-sided interrogation of a specimen. This research considers the second harmonic generation in an aluminum specimen, which is analytically evaluated using an approach based on the perturbation method. Here, the model is chosen to mimic an experimental setup where a longitudinal wave is generated at an oblique angle and the reflected wave is detected using a set of wedge transducers. Due to mode conversion at the interface of the wedge and the specimen, it is necessary to evaluate longitudinal and shear waves, determining all second harmonic waves generated in the bulk and at the stressfree boundary. The theoretically developed model is then implemented in a commercial finite element code, COMSOL, using increasing fundamental wave amplitudes for different values of third order elastic constants. The results of this computational model verify the analytical approach and the proposed measurement setup, taking into account assumptions and approximations of the solution procedure. Furthermore, the computational model is used to draw important conclusions relevant to the experimental setup, including the need to avoid evolving surface waves and interactions with diffracted waves. These numerical results are used to develop a recommendation for the measurement position and incident angle. Finally, the nonlinearity of two different aluminum specimens is measured with the suggested measurement setup and the results confirm the feasibility of the single-sided determination of the acoustic nonlinearity using reflected bulk waves.