From our polarization dependence study, however, we reveal that each of the four different peaks is actually doubly degenerate in its scattering channels, i.e., two different scattering paths with similar Raman frequency shifts for each peak.
The required parameter variation to achieve a desired frequency shift for the structure is then computed.
A numerical evaluation of an equivalent standing-wave cavity shows a frequency shift for the resonant wave due to an induced nonlinear index of refraction.
The Raman frequency shift for the 1st Stokes wave in this scheme amounts to ~410 cm−1 that is close to the maximum of the Raman gain in a highly Ge-doped silica fiber (420 440 cm−1 depending on the GeO2 concentration28), while the shift for the 2nd Stokes wave ~300 cm−1 is far from the gain maximum.
The calibration result shows surprisingly that, unlike cantilevers, the frequency shift for TFs depends on both the conservative and dissipative forces, which may be ascribed to the complex dynamics.
Using the second order Taylor's expansion series, the required parameter variation to achieve a desired natural frequency shift for the structure is computed through second order differential or binomial equations.
Compared with the complementary split ring resonator (CSRR), complementary single split ring resonator (CSSRR) based sensors, the novel sensor with an optimized MTM exhibits more frequency shift for a tiny variation of the dielectric thickness.
Approximate mode shapes of a rectangular elastic plate are used, enabling the calculation of the damping ratio and frequency shift for the linear case, as well as the complex resistant pressure, for both linear and nonlinear cases.
The mechanism for dual-mode generation within a single device has been discussed, and theoretical calculations based on finite element analysis allowed the fabrication of FBARs whose resonance modes have opposite reactions to temperature changes; one of the modes exhibiting a positive frequency shift for a rise of temperature whilst the other mode exhibits a negative shift.
Both modes exhibit negative frequency shift for a mass load and hence by monitoring simultaneously both modes it is possible to distinguish whether a change in the resonance frequency is due to a mass load or temperature variation (or a combination of both), avoiding false positive/negative responses in gravimetric sensing without the need of additional reference devices or complex electronics.
