As part of the ongoing world-wide effort in improving time and frequency references, a high accuracy optical frequency standard was developed using the electric quadrupole allowed clock transition at 445 THz (674 nm) in a trapped and laser cooled 88Sr+ion. An ion trap system of the endcap design has been recently evaluated with a fractional frequency uncertainty which surpasses the accuracy of the current realization of the SI second. This thesis seeks to further evaluate the limiting systematic shifts of the device by optimizing a second ion trap reference based on a rf Paul trap design, which was then compared with the endcap trap reference frequency. The comparison of the two ion traps' reference frequencies confirmed an overall offset of -0.36 pm 0.08 Hz at the 445 THz reference frequency corresponding to a fractional frequency offset of 8 x 10^-16.

As part of the ongoing world-wide effort in improving time and frequency references, a high accuracy optical frequency standard was developed using the electric quadrupole allowed clock transition at 445 THz (674 nm) in a trapped and laser cooled 88Sr+ion. An ion trap system of the endcap design has been recently evaluated with a fractional frequency uncertainty which surpasses the accuracy of the current realization of the SI second. This thesis seeks to further evaluate the limiting systematic shifts of the device by optimizing a second ion trap reference based on a rf Paul trap design, which was then compared with the endcap trap reference frequency. The comparison of the two ion traps' reference frequencies confirmed an overall offset of -0.36 pm 0.08 Hz at the 445 THz reference frequency corresponding to a fractional frequency offset of 8 x 10^-16.

Doctor of Philosophy / Department of Physics / Kristan L. Corwin / We have made significant accomplishments in the development of portable frequency standard inside hollow optical fibers. Such standards will improve portable optical frequency references available to the telecommunications industry. Our approach relies on the development of a stabilized Cr:forsterite laser to generate the frequency comb in the near-IR region. This laser is self referenced and locked to a CW laser which in turn is stabilized to a sub-Doppler feature of a molecular transition. The molecular transition is realized using a hollow core fiber filled with acetylene gas. We finally measured the absolute frequency of these molecular transitions to characterize the references. In this thesis, the major ideas, techniques and experimental results for the development and absolute frequency measurement of the portable frequency references are presented. A prism-based Cr:forsterite frequency comb is stabilized. We have effectively used the prism modulation along with power modulation inside the cavity in order to actively stabilize the frequency comb. We have also studied the carrier-envelope-offset frequency (f0) dynamics of the laser and its effect on laser stabilization. A reduction of f0 linewidth from [similar to]2 MHz to [similar to]20 kHz has also been observed. Both our in-loop and out-of-loop measurements of the comb stability showed that the comb is stable within a part in 10^11 at 1-s gate time and is currently limited by our reference signal. In order to develop this portable frequency standard, saturated absorption spectroscopy is performed on the acetylene v1+v3 band near 1532 nm inside different kinds of hollow optical fibers. The observed linewidths are a factor 2 narrower in the 20 um fiber as compared to 10 um fiber, and vary from 20-40 MHz depending on pressure and power. The 70 um kagome fiber shows a further reduction in linewidth to less than 10 MHz. In order to seal the gas inside the hollow optical fiber, we have also developed a technique of splicing the hollow fiber to solid fiber in a standard commercial arc splicer, rather than the more expensive filament splicer, and achieved comparable splice loss. We locked a CW laser to the saturated absorption feature using a Frequency Modulation technique and then compared to an optical frequency comb. The stabilized frequency comb, providing a dense grid of reference frequencies in near-infrared region is used to characterize and measure the absolute frequency reference based on these hollow optical fibers.

Doctor of Philosophy / Department of Physics / Kristan L. Corwin / Current portable near-infrared optical frequency references offer modest accuracy and instability compared to laboratory references. Low pressure reference cells are necessary to realize features narrower than the Doppler broadened overtone transitions, and most setups to date have occurred in free-space. Hollow-core photonic crystal fibers offer a potential alternative to free-space setups through their small cores (~10’s of µm) and low-loss guidance. Furthermore, HC-PCF can be made into fiber cells that could be directly integrated into existing telecommunications networks. Efforts were made to fabricate these fiber cells with a low pressure of molecules trapped inside, but this has proven to be quite challenging. Therefore, investigation of these fibers is conducted by placing the ends of the fiber inside vacuum chambers loaded with acetylene (12C2H2). The linewidths of several P branch transitions (near 1.5 µm) are investigated as a function of acetylene pressure and optical pump power in three different HC-PCFs. Frequency modulation spectroscopy is then implemented on the acetylene-filled HC-PCF to generate sub-Doppler dispersion features that are useful for frequency stabilization using standard servo electronics. Instability and accuracy of this near-IR optical reference were then determined by analysis of heterodyne experiments conducted with frequency combs referenced to a GPS-disciplined rubidium oscillator. The instability and accuracy of this HC-PCF reference are within an order of magnitude of free-space experiments, as expected based on the ratio of linewidths observed in the two experiments. Therefore, HC-PCF has been shown to be suitable for potential frequency references. Further work is necessary to fabricate gas fiber cells with high optical transmission and low molecular contamination.

Ces travaux de thèse portent principalement sur la génération de signal d'horloge haute fréquence. Dans un premier temps, la faisabilité d'un oscillateur à base de BAW y est démontrée par la conception d'un circuit en technologie CMOS 65 nm. Les deux principales innovations sont les performances en terme de stabilité (bruit de phase de -128dBc/Hz à 100kHz de la porteuse) et en précision (implémentation d'une banque de capacités ayant un pas de 0.4ppm) de l'oscillateur. Sa consommation est optimisée (0.9mW). Il est suivi d'un diviseur faible bruit (-140dBc/Hz à 100kHz de la porteuse) délivrant un signal à 500MHz. Dans un second temps, les imperfections des résonateurs BAW sont analysées. Une procédure de calibration comprenant une calibration initiale et une calibration en boucle ouverte est alors proposée. Cette dernière repose sur l'identification et l'utilisation d'un modèle comportemental du dispositif, régulièrement mis à jour grâce à un filtre de Kalman. Une précision de 0.4 ppm est atteinte / This thesis deals with the gigahertz range reference frequency generation. In a first part, this document presents the design of a 500 MHz oscillator in a 65 nm CMOS process using a 2 GHz Bulk Acoustic Wave resonator. A digital frequency control is implemented using a switched capacitor bank in parallel to the resonator. The tuning range is up to 500 kHz with a minimum step of 200 Hz. The oscillator core uses a differential topology and is designed for low phase noise (-128 dBc/Hz at 100 kHz offset) at low power consumption (0.9 mW). It is followed by a low noise divider which provides a 500 MHz output with a phase noise of -139 dBc/Hz at 100 kHz offset from the carrier. In a second part, we consider a method for the calibration of a BAW based frequency reference. In fact, the frequency variations of a BAW oscillator against process, supply, temperature and aging effects make difficult its use as a frequency reference. We propose here a method based on Kalman filtering to identify with high precision a behavioral model of this BAW reference, thus enabling its use in an open loop frequency tuning. A precision of 0.4 ppm is achieved

Microelectromechanical resonators have found widespread applications in timing, sensing and spectral processing. One of the important performance metrics of MEMS resonators is the temperature sensitivity of their frequency. The main objective of this dissertation is the compensation and control of the temperature sensitivity of silicon resonators through engineering of device geometry and structural composition. This has been accomplished through formation of composite platforms or novel geometries based on dispersion characteristics of guided acoustic waves in single crystalline silicon (SCS) microstructures. Furthermore, another objective of this dissertation is to develop efficient longitudinal piezoelectric transduction for in-plane resonance modes of SCS resonators that have lithographically-defined frequencies, to reduce their motional resistance (Rm). A uniformly distributed matrix of silicon dioxide pillars is embedded inside the silicon substrate to form a homogenous composite silicon-oxide platform (SilOx) with nearly perfect temperature-compensated stiffness moduli. Temperature-stable micro-resonators implemented in SilOx platform operating in any desired in- and out-of-plane resonance modes show full compensation of linear temperature coefficient of frequency (TCF). Overall frequency drifts as small as 80 ppm has been achieved over the industrial temperature range (-40°C to 80°C) showing a 40x improvement compared to uncompensated native silicon resonators. A 27 MHz temperature-compensated MEMS oscillator implemented using SilOx resonator demonstrated sub-ppm instability over the industrial temperature range. Besides this, a new formulation of different resonance modes of SCS resonators based on their constituent acoustic waves is presented in this dissertation. This enables engineering of the acoustic resonator to provide several resonance modes with mechanical energy trapped in central part of the resonator, thus obviating narrow tethers traditionally used for anchoring the cavity to the substrate. This facilitates simultaneous piezoelectric-transduction of multiple modes with different TCFs through independent electrical ports, which can realize highly accurate self-temperature sensing of the device using a beat frequency (fb) generated from linear combination of different modes. Piezoelectrically-transduced multi-port silicon resonators implemented using this technique provide highly temperature-sensitive fb with a large TCF of ~8500 ppm/°C showing 100x improvement compared to other Quartz/MEMS counterparts, suggesting these devices as highly sensitive temperature sensors for environmental sensing and temperature-compensated/oven-controlled crystal oscillator (TCXO/OCXO) applications. Another part of this dissertation introduces a novel longitudinal piezoelectric transduction technique developed for implementation of low Rm silicon resonators operating in lithographically defined in-plane modes. Aluminum nitride films deposited on the sidewalls of thick silicon microstructures provides efficient electromechanical transduction required to achieve low Rm. 100 MHz SCS bulk acoustic resonators implemented using this transduction technique demonstrates Rm of 33Ω showing a 100x improvement compared to electrostatically transduced counterparts. Low-loss narrow-band filters with tunable bandwidth and frequency have been implemented by electrical coupling of these devices, showing their potential for realization of truly reconfigurable and programmable filter arrays required for software-defined radios.

The objective of the work presented in this thesis is to implement high-Q silicon capacitive micromechanical resonators operating in the HF, VHF and UHF frequency bands. Several variations of a fully silicon-based bulk micromachining fabrication process referred to as HARPSS have been developed, characterized and optimized to overcome most of the challenges facing application of such devices as manufacturable electronic components. Several micromechanical structures for implementation of high performance capacitive silicon resonators covering various frequency ranges have been developed under this work. Design criteria and electromechanical modeling of such devices is presented. Under this work, HF and VHF resonators with quality factors in the tens of thousands and RF-compatible equivalent electrical impedances have been implemented successfully. Resonance frequencies in the GHz range with quality factors of a few thousands and lowest motional impedances reported for capacitive resonators to date have been achieved. Several resonator coupling techniques for implementation of higher order resonant systems with possibility of extension to highly selective bandpass filters have been investigated and practically demonstrated. Finally, a wafer-level vacuum sealing technique applicable to such resonators has been developed and its reliability and hermeticity is characterized.

Optical frequency standards are necessary tools for accurate measurement of time and length. In practice these standards are stabilised laser systems locked to a known frequency reference. These references are typically the resonant frequencies of the atoms of an absorption medium that have been theoretically calculated to a high degree of accuracy. This thesis describes a combination of experimental and theoretical research performed on modulation transfer spectroscopy (MTS)--a technique used to frequency stabilise a laser in order to produce an accurate frequency reference--with emphasis placed on developing techniques and procedures to overcome the limitations found in existing MTS stabilised laser systems. The focus of the thesis is to generate a highly accurate frequency reference by researching the system parameters that will increase the signal to noise ratio and improve the accuracy of the reference through refinement of the signal structure. The early theoretical interpretation of MTS was effectively a low absorption approximation that occurs at low pressures. This approximation ignores the depletion of beam energy through absorption and is a distinct limitation of the theoretical model in its ability to accurately predict the influence of a range of system parameters on signal strength and structure. To overcome this limitation a 3-D (or volumetric) analysis was developed and is presented here for the first time. This volumetric model is a measure of two depleted beams interacting collinearly in an absorbing medium of iodine and is described to accurately predict the signal maximum as a function of pressure for all wavelengths. This model was found to be more accurate in predicting the influence of system parameters on the signal strength and structure, including that of pump beam intensity, pressure, saturation parameter, cell length and modulation parameters. The volumetric model is a novel approach to MTS theory but is more complex computationally than the traditional low pressure model and therefore more difficult to implement in many situations. To overcome this problem a hybrid model was developed as a combination of the low pressure and volumetric models. The comparison between the rigorous volume model and the hybrid model indicate that there is a deviation in the signal strength at high pressures. However, the agreement was very good in the pressure regimes that are commonly used to realise actual frequency references. Comparison of the hybrid model to experimental data was performed over a range of different wavelengths (532 nm, 543.5 nm, 612 nm and 633 nm) and found to be in close agreement. This gives confidence in the model to accurately predict signal strength and structure in any situation. Three mechanisms have been identified that limit the accuracy of frequency references due to the creation of residual amplitude modulation (RAM) where it shifts the frequency of the reference. The influence of RAM is included in the hybrid model as a ratio of the amplitude modulated and frequency modulated components of the saturating beam. These RAM production mechanisms result from the modulation of the saturating beam, the overlap of the beams in the medium, and the differential absorption of the sidebands in the medium. While the first mechanism has been previously reported the latter two are discussed here in detail for the first time. RAM generated by the modulators used (acousto-optic or electro-optic modulators) was typically of the order of 10% to 12%, depending on the excursion of the created sidebands. RAM generated by an asymmetric beam overlap with the modulators used was found to be as large as 30%. A combination of these two independent mechanisms can be used to provide a "RAM-free" state of the system by using one to cancel the effects of the other. The third RAM generation process--medium induced RAM--is difficult to remove but through a careful combination of absorption related parameters--namely, pump intensity, cell length, pressure and detector phase--the effects of RAM can be removed, leading to a distortion free MTS signal. Further investigation into the predictions provided by the hybrid model shows that there is a complex relationship between cell length and the optimum pressure required for maximum signal strength, such that longer cell lengths will not necessarily improve the signal strength. This is contrary to conventional thinking and is important in the MTS design process to reduce unnecessary costs and improve the signal to noise ratio and frequency accuracy. Optimisation of frequency stabilised laser systems using MTS are generally performed using trial and error. Comparison of these optimum parameter values to those predicted by the hybrid model show that for popular wavelengths such as 532 nm they are similar. In addition, the hybrid model is able to predict the frequency shifts that arise within the system parameters used and has shown that existing systems being used at 532 nm, 633 nm and 778 nm could improve their signal to noise ratio and accuracy through a variation in the parameters. A methodology based on the hybrid model is presented that can be used to calculate the optimum parameters for maximum signal strength and a "RAM-free" state for any wavelength. This systematic approach can therefore be used to guide the design of actual frequency stabilised laser systems prior to and during the design process.