Resonators modes

If an electric held of the proper frequency is applied across the quartz crystal, the crystal wiU oscillate in a mechanically resonant mode. These condihons correspond to the creation of a standing acoustic shear wave that has a node midpoint between the two faces of the crystal and two antinodes at both faces of the disk. This is depicted schematically in Eig. 21.20b. In an EQCM experiment the crystals are operated at the fundamental resonant frequency that is a function of the thickness of the crystal. A crystal with a thickness of 330pm has a resonant frequency of 5 MHz. Crystals with these characteristics are commercially available. In an EQCM experiment, an alternating electric field of 5 MHz is applied to excite the quartz crystal into... 

Equation 28 states, that co is proportional to t. The effect of the thickness of the gel film on the frequency of the first resonance mode has been investigated. When the buoyancy is taken into account, the experimental results have quantitatively followed Eq. 28. It has been found that the buoyancy plays an important role in the occurrence of the electric field-associated vibration of gel film. The vibration of the gel film in an electric field has thus roughly analyzed as a mechanical bending vibration of a uniform cantilever beam. 

For different acceptors in the same material, the distance between atoms H and Y does not seem however to be the only criterion, and the existence of a LVM of atom Y leads to the coupling of this LVM with the X—H mode resulting in an increased FWHP (As—HBe). In the case of (As—HZn), the resonant mode of Zn couples only weakly with the H atom, hence the smaller FWHP of the As—H mode of this complex. 

In order to understand the physics behind the observed super-high sensitivity, we investigated the optical field distribution in the microtube using cylindrical coordinates z, r, and time-independent field distribution for the resonant mode can be separated into a radial-dependent mode component and an azimuthal-dependent phase term, T lYjexpfiw J, where / is the amplitude of the axial magnetic (TE) or electric (TM) modal field and m is the azimuthal quantization... 

For a given m, there are a series of ko satisfying (8.7), which are referred to as the vth (v = 1,2,3,...) order resonant mode. The radial and tangential components of the electric field for TE modes can be obtained with ... 

Fig. 8.30 (a) Radial electric field intensity distribution of E, and (b) the resonance shift as a function of liquid index change for resonant mode E u. Reprinted from Ref. 68 with permission. 2008 Optical Society of America... 

The unique field penetration into the liquid of a nonevanescent resonant mode like Tlij(7)0 is very promising for the sensing applications. To understand the origin of this behavior and further optimize the devices, a ray optical picture71 is presented. This type of resonant modes exist as if rays are bounced at the liquid/silica interface and confined in the liquid region as plotted in Fig. 8.32. From the viewpoint of ray optics, light is partially reflected (termed ray 1) and partially transmitted when it is... 

The detection limit of the microresonator-based refractive index sensing device is directly related to the g-factor of the resonator and the sensitivity of the resonant mode discussed above. The g-factor of a microtube resonator is determined by the total loss of a resonant mode, including radiation loss, absorption loss, and surface roughness scattering loss. The overall g-factor can be expressed as... 

Fig. 8.36 Radial electric field intensity distribution for the resonant mode E m...

Ling, T. Guo, L. J., A unique resonance mode observed in a prism coupled micro tube resonator sensor with superior index sensitivity, Opt. Exp. 2007, 15, 17427 17432... 

Generally, the resonances in transmission spectrum can overlap. Then, the transmission spectrum of these devices depends on the coupling of resonant mode to the MNF/MNF or MNF/microsphere (microdisk) as well as on the coupling of different WGMs to each other in the MNF/microsphere contact region. 

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