Critical coupling

Journal bearing eccentricity Bearing damage Rotor-bearing system critical Coupling critical Structural resonances Thrust bearing damage... 

On their way from the source to the resonator the intensity of the microwaves must be attenuable for two reasons (1) full power may be too much for the sample leading to saturation (treated in Chapter 4) or (2) it may be impossible to critically couple the cavity at full incident power (e.g., because the sample contains too much water). Therefore, the main waveguide contains an attenuator, usually of the dissipative, rotary-vane type. Dissipative means that the eliminated power is converted to heat and is not reflected as radiation to the source. Rotary vane means that it contains a section of circular waveguide, in which a flat piece of material is located that can be rotated over an angle 0, where 0 = 0 means no attenuation and 0 = 90° causes full attenuation. The amount of attenuation is expressed in decibels, a non-SI,... 

Tune for critical coupling (zero the dip in the scope mode cf. Figure 2.8d). 

FIGURE 2.8 Tuning mode patterns. The scope mode shows a dip when the frequency of the microwave fits into the resonator. This dip has maximal depth when the spectrometer is tuned (with the adjustable iris) to be reflectionless, that is, when the resonator is critically coupled to the bridge. Shown patterns are (a) off resonance, (b) slightly off resonance, (c) either under- or over-coupled, (d) critically coupled, (e) asymmetry from out-of-phase reference. 

If x = 1, critical coupling is obtained and the dip depth attains its maximum value of 100% the microresonator is said to be undercoupled if x < 1 and overcoupled for x > 1. While the coupling loss remains constant, the effective intrinsic loss can be changed by interaction of the evanescent fraction (/) of the WGM with the surrounding medium. The effective loss coefficient can then be written as a = a +/aa f /as, where the three terms denote true intrinsic loss, absorption (and perhaps also scattering) by the analyte, and absorption in the solvent (or ambient). 

Cai, M. Painter, O. Vahala, K. J., Observation of critical coupling in a fiber taper to a silica microsphere whispering gallery mode system, Phys. Rev. Lett. 2000, 85, 74 77... 

Fig. 9.16 The calculated output spectrum of a silicon waveguide ring resonator sensor at critical coupling (t a) and for t 0.8a. The assumed ring radius is R 150 pm...

The ability to measure small index perturbations, (I/Ven. depends on the depth (i.e., the extinction ratio at resonance) and width of these resonances. The depth and width in turn depend on the relative values of the coupling coefficient t and the resonator loss a. Figure 9.16 shows typical ring resonator spectra calculated for two different loss values. The maximum extinction ratio is obtained at critical coupling when t = a, and the output intensity at resonance is exactly zero. The width of the resonances depends on the total round trip resonator loss, at, which is the product of waveguide losses within the ring (a) and coupling loss (t) at the coupler. 

Yariv, A., Critical coupling and its control in optical waveguide ring resonator systems, IEEE Photonics Technol. Lett. 2002, 14, 483 485... 

Fig. 13.23 (a) Transmission power of microtoroid resonator near the condition of critical coupling (inset shows the MNF/microtoroid sensor), (b) Single photon counting events C(t) as a function of time t after the release of the cold atom cloud at t 0. Reprinted from Ref. 48 with permission. 2008 Nature Publishing Group... 

Phase Matched and Critical Coupling to Droplet Resonators... 

After sample insertion, the cavity is tuned to achieve critical coupling, so that the microwave power stored in the cavity is maximized while its dissipation is minimized. Tuning generally involves two steps roughtuning to approximately match the microwave frequency to the cavity resonance frequency followed by fine-tuning to establish critical coupling. 

The critical potential may now be determined by plotting the coupling current versus the corrosion potential, as shown in Fig. 15. The horizontal line, which represents the critical coupling current (3 nA), intersects the coupling current versus ECP correlations at potentials ranging from —0.40 V he f°r an ECL of 0.1 to —0.15Vshe f°r an ECL of 50 cm. The origin of the dependence of CGR on ECL is that, as the ECL increases, the potential drop down the crack increases... 

Fig. 15 Plots of coupling current versus ECP (corrosion potential) for a range of ECLs extending from 0.1 to 50 cm for the conditions shown in the figure. The horizontal line corresponds to the calculated critical coupling current, as determined from Fig. 14, which defines the critical potential, Eicscc for stress corrosion cracking [54].

Hoffmann-Ostenhof et al. [64] have proved that M Xr) has a square-integrable eigenfunction corresponding to a threshold energy E(XC) = They noted that the existence of a bound state at the critical coupling constant Xc implies that for X < Xc, E(X) approaches E(XC) = linearly in (A, — Xc) as... 

Modeling Dislocation Cores. In an earlier section, we belabored the critical coupling of structure and properties, and this is another arena within which modeling can produce valuable insights. One of our insights concerning the importance of structure was that of the role of lattice defects in governing many... 

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