Parametric excitation can occur when the value of a parameter of an oscillator is modulated at twice the natural frequency of the oscillator. The response grows exponentially and is only limited by a nonlinearity of the system, so large response amplitudes typically occur. However, there is no response unless the parametric drive amplitude is above a threshold value that is dictated by the damping. We investigate parametric excitation in three physical systems. The first involves an acoustic standing wave in a pipe that is driven by a piston at one end. An analysis shows that parametric excitation is not feasible in this system unless one uses a very large-excursion piston (for example, from an aircraft engine). The second system is an inductor-capacitor circuit which can undergo oscillations of the current. An analysis of capacitance modulation with a bank of alternate rotating and stationary parallel plates shows that parametric excitation would be very difficult to achieve. Finally, we describe the construction of a torsional oscillator whose length is modulated. Parametric excitation is successfully demonstrated in this system. A comparison of data to predictions of the standard theory of parametric excitation reveals significant deviations.

Parametric excitation is a fundamental feature of dynamical systems arising across the applied sciences. In this thesis we study the structure of parametric res- onance and its in uence of the global nonlinear dynamics in a number of oscillating systems which arise in engineering contexts. The parametrically excited Helmholtz oscillator and the elliptically excited pen- dulum are two systems where the interaction of regular and parametric excitation are important for a complete understanding of the dynamics. We examine the resonance structure of the Helmholtz oscillator and use the Melnikov function to demonstrate the e ect that the parametric excitation has on the nonlinear dynam- ics. The estimates produced in this analysis are then compared to a numerical study of the engineering integrity. For the elliptically excited pendulum we discuss the quantitative e ects of introducing ellipticity to the pro le of excitation. We go on to examine the e ect of periodic time varying mass in the Helmholtz oscillator and demonstrate that the resonance structure exhibits the phenomenon of coexistence. The evolution of the systems engineering integrity is examined and compared to the purely parametrically excited case. Finally we examine a system incorporating two pendulums on a rigid rig modelled by two linear springs. The parametric resonance in this case is mapped using numerical Floquet theory and the structure of the linear resonance is shown to organise solution space for the nonlinear system.

Thesis (M.S. in Engineering Acoustics)--Naval Postgraduate School, June 2005. / Thesis Advisor(s): Includes bibliographical references (p. 59). Also available online.

Several pulsed optical oscillators (OPOs) based on periodically poled lithium niobate (PPLN) and pumped by single longitudinal mode Ti:sapphire lasers have been developed. These OPOs provide access to important spectroscopic regions in the 1 - 5.5 [mu]m region and can be rapidly turned by varying the pump wavelength. Previously many of the OPOs developed to take advantage of PPLN relied on a combination of period selection and temperature tuning and as a result were slow and cumbersome to tune. This problem my be avoided by using tunable pump sources or acoustically induced strain waves. Several candidate OPO pump sources were characterised. These pump sources with themselves pumped by lasers operating at repetition reates of either 1.5 kHz (high repetition rate) or 10Hz (low repetition rate). High repetition rate systems include: a Ti-sapphire laser, injection seeded by a single longitudinal mode diode laser, several coupled cavity Ti:sapphire lasers with bandwidths less than 100 Ghz and Cr:forsterite lasers narrowed by prisms and étalons. The low repetition rate systems were all coupled cavity Ti:sapphire lasers one of which was single and double pass amplified. Of these it was found that only the high repetition rate injection seeded laser and the low repetition Ti:sapphire lasers were suitable as OPO pump sources. OPOs were characterised at high and low repetition rates. The high repetition rate system exhibited a low threshold of oscillation (18.7 [mu]J) and a low overall efficiency (25%) which was thought to be due to the pulse to pulse variability of the Ti:sapphire bandwidth. The tuning range of the OPO was 932 to 1310 nm (signal) and 1.989 [mu]m to 5.281 [mu]m (idler) using multiple poling periods and only 15 nm of pump tuning. OPO oscillation on two separate signals simultaneously was observed. Two separate low repetition rate systems were investigated; the first was tuned from 1200 to 1600 nm (signal) and from 1600 to 2400 nm (idler) on a single poling period with a high absolute efficiency of 35% and a threshold of 180 [mu]J. The second OPO was tuned from 940 to 1220 nm (signal) and 2.2 to 4.3 [mu]m (idler) on a single poling period. The absolute efficiency of the system was 25% and the threshold was 200 [mu]J. OPO oscillation on two separate signals was investigated using an OPO based on grazing incidence configured cavity. It was found that the signals coupled together through Raman transitions present in lithium niobate and that coupling reduced the efficiency of the device as a whole. The affect of an acoustically induced strain field on the optical nonlinearity of tetragonal ferroelectric materials was investigated. It was found that the optical nonlinear coefficient varies linearly with the cell displacement and as the square root of the acoustic power. A crystal designed to implement a quasi phase matched interaction based on this variation is proposed.

Optical source generation has attracted significant attention recently, especially in fiber optical communications. Today there is a growing a demand for optical source generation beyond conventional telecommunication wavelength bands. However, high quality and versatile optical source is generally not available over those wavelength bands due to the lack of efficient gain medium. Thanks to fiber optical parametric amplifier (FOPA), which is based on the third order nonlinear susceptibility of optical fibers, offers ultrafast response, wide-gain bandwidth, high gain and large frequency detune from the pump, serves as a promising candidate for signal amplification over those wavelength bands. By using the corresponding fiber optical parametric oscillator (FOPO) configuration, widely tunable source from continuous-wave (CW) to sub-picosecond pulses can be potentially generated to serve different applications from communication to biomedical imaging. In this thesis, we first demonstrate an all-fiber widely-tunable picosecond FOPO using highly-nonlinear fiber (HNLF). The tuning range is as wide as 250 nm, which is higher than previous picosecond FOPOs reported in the 1550-nm region. Second, time-dispersion tuning of the FOPO is investigated with fixed pump wavelength. It is a relatively simple and economic approach, and there will be no filter induced cavity loss. We then describe using FOPO to generated nearly-transform limited sub-picosecond pulses with a 60-nm tuning range. Another FOPO with a tuning range of 440-nm with dispersion-shifted fiber (DSF) as the gain medium is proposed and demonstrated. Compared with FOPOs demonstrated using HNLF as the gain medium, the use of DSF offers two key advantages: a wider tuning range and a narrower linewidth. In addition to picosecond FOPO, CW FOPO is also of great interest in fiber optical communications and biomedical imaging. We also demonstrate an all-fiber CW single-longitudinal-mode (SLM) FOPO with tuning range covers the S and L bands. SLM oscillation with a side-mode suppression ratio greater than 43 dB is achieved, which has been extended to 1-μm region under stable operation. Apart from static tuning, dynamic wavelength tuning of the FOPO is also discussed in this thesis with a cumulative speed exceeds 4,000,000 nm/s, which is higher than previous work reported in wavelength-swept FOPOs. The high-speed swept source would be useful in biomedical imaging and sensing applications. The amplification of the sub-picosecond pulses of the FOPO output is also investigated, for the first time to our knowledge, by using a fiber optical parametric chirped pulse amplifier(FOPCPA).The totally fiber-integrated nature of the whole system allows complete self-alignment and further integration to other fiber-based systems. All these research effort will show the versatility of FOPO techniques for generating wide range of optical sources for varies applications. These schemes may be useful in generating CW and short pulse for potential optical communication and biomedical imaging in non-conventional wavelength bands. / published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

No description available.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 92-95).

Thesis (Ph.D.) - University of St Andrews, October 2007.

This thesis describes the development and applications of single-frequency, continuously tunable, continuous-wave (cw), optical parametric oscillators (OPOs). Two doubly-resonant OPOs (DROs) are presented, one providing tunable light around 1?m, the other specifically designed as a spectroscopic source for methane near 1649nm. Once stabilised, the frequency-selective nature of the DRO ensures operation on a single mode-pair without the need for additional intracavity frequency-selective components. Both DROs are smoothly tunable by smoothly tuning the pump laser. The 1mum DRO is based on a bulk KTP crystal cut for near-degenerate, type-II, critical phase-matching (theta= 90°, ϕ = 37°). Angle tuning the crystal provides coarse tuning of the output frequencies over a range of ~50nm. Small perturbations to the OPO cavity is sufficient to cause a systematic mode-hop and provides a method of tuning across the phase-matching bandwidth (~0.5THz). This DRO is demonstrated as a spectroscopic source by recording the absorption spectrum of cesium molecules near 1050nm. The DRO as a potentially compact source of tunable light is demonstrated by using a frequency-doubled microchip laser as the pump source. The output consists of a single pair of signal and idler modes even when using a multilongitudinal-mode pump laser. Smooth tuning of the output frequencies is achieved by temperature tuning the pump laser. The 1.65mum DRO is based on periodically poled KTiOPO4 (PPKTP). The suitability of PPKTP for cw OPOs was first assessed by a difference frequency generation experiment from which the effective d33 coefficient was estimated to be ~5mum/V. The idler wavelength is coarsely tuned at a rate of 0.73nm/°C by varying the crystal temperature. A combination of computer modelling and experimental observation is used to study the dynamic behaviour of a DRO. The numerical model calculates the time required for the OPO to build-up from the parametric fluorescence and is in excellent agreement with experimental observations.

In this thesis the use of high spatial- and spectral-quality diode-laser pump sources for solid-state lasers and continuous-wave optical parametric oscillators (cw OPOs) is investigated. While diode lasers are potentially attractive, compact, low-cost pump sources for solid-state lasers and cw OPOs, the difficulty in obtaining moderate output powers, while retaining high spatial beam quality and spectral purity, often limits the potential of such lasers in these applications. Techniques for obtaining high-power, high spatial- and spectral-quality output from diode lasers are reviewed and the design, development and characterisation of an injection-locked broad-area diode-laser system is described. This system produced output powers of &ap;400mW in a near-diffraction-limited beam (M2&ap;w1.3) and with a spectral width of < 30MHz. The injection-locked system was used as the pump source for a quasi-three-level 946-nm Nd:YAG laser. End-pumped solid-state lasers of this type can offer potentially efficient, low-threshold operation if a near-diffraction limited pump source is used allowing optimal overlap with the laser mode. A model, including pump beam quality effects, is developed for such lasers and used to highlight the advantages of a near- diffraction-limited pump source, especially in the case of the 946-nm Nd:YAG transition which suffers from low gain and significant reabsorption losses. A 946-nm Nd: YAG laser pumped by the injection-locked system is described, yielding cw output powers up to 120mW with a 46% slope efficiency, performance comparable to Ti:sapphire- or dye-laser pumping, and 27ns Q-switched pulses having peak powers of 180W. 50W, 20ns pulses at 473nm were obtained by second-harmonic generation in KNbOs. The performance and relative merits of various cw OPO configurations, in the context of diode-laser pumping, are discussed and the development of a doubly- resonant OPO (DRO) based on periodically-poled lithium niobate is described. When pumped by the injection-locked system, this device showed a threshold of 25mW and .tuning of the outputs over 1.15- 1.25 mum at the signal and 2.3-2.65 mum at the idler was obtained by variation of crystal temperature, PPLN grating period and pump wavelength. When pumping with a 100mW single-mode diode laser, a 15mW OPO threshold was observed while retaining a similar tuning range. This represented the first demonstration of a cw DRO directly pumped by a single-mode diode laser. The achievement of such spectral coverage while pumping with this source points to the potential of such systems as compact, tunable sources in the near-to mid-infrared.