Ring-down time

The pulses of radiation are said to ring backwards and forwards between the mirrors and the time for the signal to decrease to 1/e of its original value is called the ring-down time of the cavity hence the name cavity ring-down spectroscopy. 

Figure 9.38 Cavity ring-down absorption spectrum of the 0-0 band of the a Ag-X Z system of O2, where k is the reciprocal of the ring-down time. (Reproduced, with permission, from Newman, S. M., Lane, I. C., Orr-Ewing, A. J., Newnham, D. A. and Ballard, J., J. Chem. Phys., 110, 10749, 1999)...

For an RF electric field sensor, bandwidth (speed) is another important requirement. The speed of a resonator is determined by the cavity ring down time r = QX/c. As in any devices using resonating structures, a trade off between sensitivity (which increases with Q) and speed (which decreases when Q increases) has to be made. At the wavelength of 1.55 pm, Q factors of 104 and 106 translates to a sensor bandwidths of 20 GHz and 200 MHz, respectively. 

Thus measurement of the cavity ring down times in the presence and absence of the absorbing gas allows the absorption of the gas to be obtained, and from A = (1 - e aNL) aNL, the concentration of the gas determined. These concentrations as a function of time therefore allow the reaction kinetics of the absorbing species to be determined. 

Without absorbing species between the mirrors (Figure 4a), the ring down time of the optically empty cavity is given by (eq.2) ... 

This technique is critically dependent on the quality of the mirrors and cavity, respectively. Super polishing to <0.05 nm root-mean-square of surface roughness is essential. Under such conditions the arrangement with Pellin—Broca prism exhibits a base ring-down time of about 1 ps and yields a minimum detectable absorbance change of about 32 ppm. A ring-down time of about 800 ns is found for a 1 cm square mini-cavity. 

If an absorbing sample is introduced into the cavity such that the absorption follows Beer s law (Equation (6.2)) for a single pass of the laser pulse through the medium, then this absorption (proportional to the attenuation constant a) simply adds to the per-pass cavity loss, resulting in a shorter ring-down time. Equation (6.4) thus becomes... 

Figure 2 Precision of the initial stabilization of the evolution field. The plot represents the voltage transient recorded with a Hall probe (6 iJ.T/mV) and a 16 bit analogue-to-digital converter. The field level corresponds to a proton Larmor frequency of 3.5 kHz. The fieldcycling relaxometer is described below. This plot demonstrates that the evolution field can be stabilized within 1 digital unit in a ring-down time less than 1 ms.

The total transition and ring-down time from the polarization field to a value of the evolution field. 

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