Resonator quality factor

The sinc fiinction describes the best possible case, with often a much stronger frequency dependence of power output delivered at the probe-head. (It should be noted here that other excitation schemes are possible such as adiabatic passage [9] and stochastic excitation [fO] but these are only infrequently applied.) The excitation/recording of the NMR signal is further complicated as the pulse is then fed into the probe circuit which itself has a frequency response. As a result, a broad line will not only experience non-unifonn irradiation but also the intensity detected per spin at different frequency offsets will depend on this probe response, which depends on the quality factor (0. The quality factor is a measure of the sharpness of the resonance of the probe circuit and one definition is the resonance frequency/haltwidth of the resonance response of the circuit (also = a L/R where L is the inductance and R is the probe resistance). Flence, the width of the frequency response decreases as Q increases so that, typically, for a 2 of 100, the haltwidth of the frequency response at 100 MFIz is about 1 MFIz. Flence, direct FT-piilse observation of broad spectral lines becomes impractical with pulse teclmiques for linewidths greater than 200 kFIz. For a great majority of... 

The sharpness of the frequency response of a resonant system is conunonly described by a factor of merit, called the quality factor, Q=v/Av. It may be obtained from a measurement of the frill width at half maxuuum Av, of the resonator frequency response curve obtained from a frequency sweep covering the resonance. The sensitivity of a system (proportional to the inverse of tlie minimum detectable number of paramagnetic centres in an EPR cavity) critically depends on the quality factor... 

The formal definition of this quality factor, Q, is the amount of power stored in the resonator divided by the amount of power dissipated per cycle (at 9.5 GHz a cycle time is l/(9.5 x 109) 100 picoseconds). The dissipation of power is through the resonator walls as heat, in the sample as heat, and as radiation reflected out of the resonator towards the detector. The cycle time is used in the definition because the unit time of one second would be far too long for practical purposes within one second after the microwave source has been shut off, all stored power has long been dissipated away completely. 

Good X-band resonators mounted into a spectrometer and with a sample inside have approximate quality factors of 103 or more, which means that they afford an EPR signal-to-noise ratio that is over circa three orders of magnitude better than that of a measurement on the same sample without a resonator, in free space. This is, of course, a tremendous improvement in sensitivity, and it allows us to do EPR on biomolecules in the sub-pM to mM range, but the flip side of the coin is that we are stuck with the specific resonance frequency of the resonator, and so we cannot vary the microwave frequency, and therefore we have to vary the external magnetic field strength. 

Niehusmann, J. Vorckel, A. Bolivar, P. H. Wahlbrink, T. Henschel, W. Kurz, H., Ultra high quality factor silicon on insulator microring resonator, Opt. Lett. 2004, 29, 2861 2863... 

Abstract The self-organized and molecularly smooth surface on liquid microdroplets makes them attractive as optical cavities with very high quality factors. This chapter describes the basic theory of optical modes in spherical droplets. The mechanical properties including vibrational excitation are also described, and their implications for microdroplet resonator technology are discussed. Optofluidic implementations of microdroplet resonators are reviewed with emphasis on the basic optomechanical properties. 

Freely suspended liquid droplets are characterized by their shape determined by surface tension leading to ideally spherical shape and smooth surface at the subnanometer scale. These properties suggest liquid droplets as optical resonators with extremely high quality factors, limited by material absorption. Liquid microdroplets have found a wide range of applications for cavity-enhanced spectroscopy and in analytical chemistry, where small volumes and a container-free environment is required for example for protein crystallization investigations. This chapter reviews the basic physics and technical implementations of light-matter interactions in liquid-droplet optical cavities. 

The ajTnbol Q is employed here to denote the quality factor of a resonant circuit, i.e., circulating energy divided by rate of energy loss. 

Here, ks is the Boltzmann constant (1.38 x 10-23 J/K), T is the absolute temperature (300 K at room temperature), B is the bandwidth of measurement [typically about 1000 Hz for direct current (dc) measurement], /o is the resonant frequency of the cantilever, and Q is the quality factor of the resonance, which is related to damping. It is clear from Eq. (12.8) that lower spring constant, K, produces higher thermal noise. This thermal motion can be used as an excitation technique for resonance frequency mode of operation. 

Vibration isolation 237—250 critical damping 239 pneumatic systems 250 quality factor, Q 239 resonance excitation 241 stacked plate-elastomer system 249 transfer function 240 Virus 341 Viton 250, 270, 272 Voltage-dependent imaging 16, 17 Si(lOO) 17 Si(lll)-2X1 16 Volterra equation 310 Vortex 334 W... 

Microwaves. Among the lowest frequencies of interest in collisional absorption are radio- and microwaves. As will be seen below, the absorption coefficient a is extremely small at low frequencies because absorption falls off to zero frequency as of2 see Chapter 5 for details. As a consequence, it has generally been necessary to use sensitive resonator techniques for the measurement of the loss tangent, tan <5 = s"/s, where s and s" are the real and imaginary part of the dielectric constant. The loss tangent is obtained by determination of the quality factors Qa, Qo, of the cavity with and without the gas filling, as (Dagg 1985)... 

Replacing the field plates of Fig. 14.7 with the resonant microwave cavity shown in Fig. 15.4 allowed an increase in the circulating microwave power by Q, the quality factor, of the cavity.8 The cavity is a piece of WR-90 (X band) waveguide 20 cm long which is closed at both ends. The inside dimensions of the cavity are... 

Q q R i l, i 2 Rb Rd Rg RP Ro r rc S Electric charge (As), heat (J), quality factor of a resonator Heat per unit area (J m-2), integer coefficient Radius of a (usually) spherical object (m), gas constant Two principal radii of curvature (m) Radius of a spherical bubble (m) Radius of a spherical drop (m) Radius of gyration of a polymer (m) Radius of a spherical particle (m) Size of a polymer chain (m) Radius (m), radial coordinate in cylindrical or spherical coordinates Radius of a capillary (m) Entropy (J K-1), number of adsorption binding sites per unit area (mol m-2), spreading coefficient (Nm-1)... 

---