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A study of the nonlinear vibrations of metallic cantilever beams and plates subjected to transverse harmonic excitations is presented. Both experimental and theoretical results are presented. The primary focus is however on the transfer of energy between widely spaced modes via modulation. This phenomenon is studied both in the presence and absence of a one-to-one internal resonance. Reduced-order models using Galerkin discretization are also developed to predict experimentally observed motions. A good qualitative agreement is obtained between the experimental and numerical results. Experimentally the energy transfer between widely spaced modes is found to be a function of the closeness of the modulation frequency to the natural frequency of the first mode. The modulation frequency, which depends on various parameters like the amplitude and frequency of excitation, damping factors, etc., has to be near the natural frequency of the low-frequency mode for significant transfer of energy from the directly excited high-frequency mode to the low-frequency mode. An experimental parametric identification technique is developed for estimating the linear and nonlinear damping coefficients and effective nonlinearity of a metallic cantilever beam. This method is applicable to any single-degree-of-freedom nonlinear system with weak cubic geometric and inertia nonlinearities. In addition, two methods, based on the elimination theory of polynomials, are proposed for determining both the critical forcing amplitude as well as the jump frequencies in the case of single-degree-of-freedom nonlinear systems. An experimental study of the response of a rectangular, aluminum cantilever plate to transverse harmonic excitations is also conducted. Various nonlinear dynamic phenomena, like two-to-one and three-to-one internal resonances, external combination resonance, energy transfer between widely spaced modes via modulation, period-doubled motions, and chaos, are demonstrated using a single plate. It is again shown that the closeness of the modulation frequency to the natural frequency of the first mode dictates the energy transfer between widely spaced modes. / Ph. D.

Hybrid quantum dot /organic semiconductor systems are of great interest in optoelectronic and photovoltaic applications, because they combine the robust and tunable optical properties of inorganic semiconductors with the processability of organic thin films. In particular, cadmium selenide (CdSe) quantum dots coordinated with oligo-(phenylene vinylene) ligands have displayed a number of hybrid optical properties that make them particularly well-suited to these applications. When probed on an individual particle level, these so-called CdSe-OPV nanostructures display a number of surprising photophysical characteristics, including strong quenching of fluorescence from coordinating ligands, enhanced emission from the CdSe quantum dot core, suppression of fluorescence intermittency, and photon antibunching, all of which make them attractive in the applications described above. By correlating fluorescence properties with atomic force microscopy, the effects of ligands on quantum dot luminescence are elucidated. In addition, recent studies on individual CdSe-OPV nanostructures have revealed a strong electronic coupling between the coordinating ligands and the nanocrystal core. These studies have shown that excitations in the organic ligands can strongly affect the electronic properties of the quantum dot, leading to linearly polarized optical transitions (both in absorption and emission) and polarization-modulated shifts in band edge emission frequency. These polarization effects suggest exciting new uses for these nanostructures in applications that demand the robust optical properties of quantum dots combined with polarization-switchable control of photon emission.

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Cesium lead halide perovskite quantum dots (PQDs) provide an extraordinary solution-based method to fabricate high-performance solar cells, luminescent lightemitting devices, highly coherent single-photon quantum sources, and studying quantum mechanisms for quantum computing technologies. In these applications, characterizing heterogeneity and observing coupling between dots is critical. In this thesis, we use double-nanohole (DNH) optical tweezers to realize single trapping for PQDs in solution. We can estimate the size of an individual dot by studying thermal fluctuations and correlate it to emission energy shifts from quantum confinement. Based on single trapping experiment, we also use the same setup to capture a second dot by using the DNH tweezer and observe a systematic red-shift of 1.1 ± 0.6 meV in the emission wavelength upon multiple repeated measurements. Theoretical analysis shows that the experiment results are consistent with Förster resonant energy transfer (FRET), which has been proposed to obtain entanglement between colloidal quantum dots for quantum information applications. The value of the FRET is quite large when compared with the confined quantum dots and it is exciting for FRET to generate entanglement for quantum information processing applications (e.g. quantum logic gates). In the thesis, we have proved that our method allows for in-situ sizing of individual PQDs for the first time, which is relevant for improving the growth process and does not require expensive techniques. It also enables future work to search and select two dots that are nominally identical. Optical trapping with DNHs fabricated using colloidal lithography can be used to control PQD growth in-situ and enables further studies of the coupling of quantum dots at a small distance with quantum information applications. / Graduate

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