A 50 K dual-mode sapphire oscillator and whispering spherical mode oscillators

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    Abstract

    [Truncated abstract] This thesis is split into two parts. In part one; A 50 K dual mode oscillator, the aim of the project was to build a 50 K precision oscillator with frequency stability on the order of 1014 from 1 to 100 seconds. A dual-mode temperature compensation technique was used that relied on a turning point in the frequency-temperature relationship of the difference frequency between two orthogonal whispering gallery modes in a single sapphire crystal. A cylindrical sapphire loaded copper cavity resonator was designed, modelled and built with a turning point in the difference frequency between an E-mode and H-mode pair at approximately 52.5 K . . . The frequencies and Q-factors of whispering spherical modes in the 3-12 GHz range in the fused silica resonator are measured at 6, 77 and 300 K and the Q-factor is used to determine the loss tangent at these temperatures. The frequency and Q-factor temperature dependence of the TM2,1,2 whispering gallery mode at 5.18 GHZ is used to characterise the loss tangent and relative permittivity of the fused silica from 4-300 K. Below 22 K the frequency-temperature dependence of the resonator was found to be consistent with the combined effects of the thermal properties of the dielectric and the influence of an unknown paramagnetic impurity, with a spin resonance frequency at about 138 ± 31 GHz. Below 8 K the loss tangent exhibited a 9th order power law temperature dependence, which may be explained by Raman scattering of Phonons from the paramagnetic impurity ions. A spherical Bragg reflector resonator made from multiple concentric dielectric layers loaded in a spherical cavity that enables confinement of field in the centre of the resonator is described. A set of simultaneous equations is derived that allow the calculation of the required dimensions and resonance frequency for such a resonator and the solution is confirmed using finite element analysis. A spherical Bragg reflector resonator is constructed using Teflon and free-space as the dielectric materials. A Q-factor of 22,000 at 13.87 GHz was measured and found to compare well with the design values.
    Original languageEnglish
    QualificationDoctor of Philosophy
    Publication statusUnpublished - 2007

    Fingerprint

    sapphire
    oscillators
    resonators
    Q factors
    tangents
    whispering gallery modes
    Bragg reflectors
    temperature dependence
    simultaneous equations
    silicon dioxide
    impurities
    spin resonance
    temperature compensation
    frequency stability
    theses
    teflon (trademark)
    cavity resonators
    phonons
    thermodynamic properties
    permittivity

    Cite this

    @phdthesis{6152a004901e4d9aaac8424819a98d44,
    title = "A 50 K dual-mode sapphire oscillator and whispering spherical mode oscillators",
    abstract = "[Truncated abstract] This thesis is split into two parts. In part one; A 50 K dual mode oscillator, the aim of the project was to build a 50 K precision oscillator with frequency stability on the order of 1014 from 1 to 100 seconds. A dual-mode temperature compensation technique was used that relied on a turning point in the frequency-temperature relationship of the difference frequency between two orthogonal whispering gallery modes in a single sapphire crystal. A cylindrical sapphire loaded copper cavity resonator was designed, modelled and built with a turning point in the difference frequency between an E-mode and H-mode pair at approximately 52.5 K . . . The frequencies and Q-factors of whispering spherical modes in the 3-12 GHz range in the fused silica resonator are measured at 6, 77 and 300 K and the Q-factor is used to determine the loss tangent at these temperatures. The frequency and Q-factor temperature dependence of the TM2,1,2 whispering gallery mode at 5.18 GHZ is used to characterise the loss tangent and relative permittivity of the fused silica from 4-300 K. Below 22 K the frequency-temperature dependence of the resonator was found to be consistent with the combined effects of the thermal properties of the dielectric and the influence of an unknown paramagnetic impurity, with a spin resonance frequency at about 138 ± 31 GHz. Below 8 K the loss tangent exhibited a 9th order power law temperature dependence, which may be explained by Raman scattering of Phonons from the paramagnetic impurity ions. A spherical Bragg reflector resonator made from multiple concentric dielectric layers loaded in a spherical cavity that enables confinement of field in the centre of the resonator is described. A set of simultaneous equations is derived that allow the calculation of the required dimensions and resonance frequency for such a resonator and the solution is confirmed using finite element analysis. A spherical Bragg reflector resonator is constructed using Teflon and free-space as the dielectric materials. A Q-factor of 22,000 at 13.87 GHz was measured and found to compare well with the design values.",
    keywords = "Atomic clocks, Oscillators, Electric, Nonlinear oscillators, Frequencies of oscillating systems, Dielectric resonator oscillators, Sapphire oscillators, Temperature control, Whispering gallery modes",
    author = "James Anstie",
    year = "2007",
    language = "English",

    }

    TY - THES

    T1 - A 50 K dual-mode sapphire oscillator and whispering spherical mode oscillators

    AU - Anstie, James

    PY - 2007

    Y1 - 2007

    N2 - [Truncated abstract] This thesis is split into two parts. In part one; A 50 K dual mode oscillator, the aim of the project was to build a 50 K precision oscillator with frequency stability on the order of 1014 from 1 to 100 seconds. A dual-mode temperature compensation technique was used that relied on a turning point in the frequency-temperature relationship of the difference frequency between two orthogonal whispering gallery modes in a single sapphire crystal. A cylindrical sapphire loaded copper cavity resonator was designed, modelled and built with a turning point in the difference frequency between an E-mode and H-mode pair at approximately 52.5 K . . . The frequencies and Q-factors of whispering spherical modes in the 3-12 GHz range in the fused silica resonator are measured at 6, 77 and 300 K and the Q-factor is used to determine the loss tangent at these temperatures. The frequency and Q-factor temperature dependence of the TM2,1,2 whispering gallery mode at 5.18 GHZ is used to characterise the loss tangent and relative permittivity of the fused silica from 4-300 K. Below 22 K the frequency-temperature dependence of the resonator was found to be consistent with the combined effects of the thermal properties of the dielectric and the influence of an unknown paramagnetic impurity, with a spin resonance frequency at about 138 ± 31 GHz. Below 8 K the loss tangent exhibited a 9th order power law temperature dependence, which may be explained by Raman scattering of Phonons from the paramagnetic impurity ions. A spherical Bragg reflector resonator made from multiple concentric dielectric layers loaded in a spherical cavity that enables confinement of field in the centre of the resonator is described. A set of simultaneous equations is derived that allow the calculation of the required dimensions and resonance frequency for such a resonator and the solution is confirmed using finite element analysis. A spherical Bragg reflector resonator is constructed using Teflon and free-space as the dielectric materials. A Q-factor of 22,000 at 13.87 GHz was measured and found to compare well with the design values.

    AB - [Truncated abstract] This thesis is split into two parts. In part one; A 50 K dual mode oscillator, the aim of the project was to build a 50 K precision oscillator with frequency stability on the order of 1014 from 1 to 100 seconds. A dual-mode temperature compensation technique was used that relied on a turning point in the frequency-temperature relationship of the difference frequency between two orthogonal whispering gallery modes in a single sapphire crystal. A cylindrical sapphire loaded copper cavity resonator was designed, modelled and built with a turning point in the difference frequency between an E-mode and H-mode pair at approximately 52.5 K . . . The frequencies and Q-factors of whispering spherical modes in the 3-12 GHz range in the fused silica resonator are measured at 6, 77 and 300 K and the Q-factor is used to determine the loss tangent at these temperatures. The frequency and Q-factor temperature dependence of the TM2,1,2 whispering gallery mode at 5.18 GHZ is used to characterise the loss tangent and relative permittivity of the fused silica from 4-300 K. Below 22 K the frequency-temperature dependence of the resonator was found to be consistent with the combined effects of the thermal properties of the dielectric and the influence of an unknown paramagnetic impurity, with a spin resonance frequency at about 138 ± 31 GHz. Below 8 K the loss tangent exhibited a 9th order power law temperature dependence, which may be explained by Raman scattering of Phonons from the paramagnetic impurity ions. A spherical Bragg reflector resonator made from multiple concentric dielectric layers loaded in a spherical cavity that enables confinement of field in the centre of the resonator is described. A set of simultaneous equations is derived that allow the calculation of the required dimensions and resonance frequency for such a resonator and the solution is confirmed using finite element analysis. A spherical Bragg reflector resonator is constructed using Teflon and free-space as the dielectric materials. A Q-factor of 22,000 at 13.87 GHz was measured and found to compare well with the design values.

    KW - Atomic clocks

    KW - Oscillators, Electric

    KW - Nonlinear oscillators

    KW - Frequencies of oscillating systems

    KW - Dielectric resonator oscillators

    KW - Sapphire oscillators

    KW - Temperature control

    KW - Whispering gallery modes

    M3 - Doctoral Thesis

    ER -