In Figure 25 we have plotted the circulating power in a Fabry–Pérot cavity as a function of the laser
frequency. The steep features in this plot indicate that such a cavity can be used to measure
changes in the laser frequency. From the equation for the circulating power (see Equation (88)),
we can see that the actual frequency dependence is given by the term. Writing this term as
we can highlight the fact that the cavity is in fact a reference for the laser frequency in relation to the cavity
length. If we know the cavity length very well, a cavity should be a good instrument to measure the
frequency of a laser beam. However, if we know the laser frequency very accurately, we can use an optical
cavity to measure a length. In the following we will detail the optical setup and behaviour of a cavity used
for a length measurement. The same reasoning applies for frequency measurements. If we make use of the
resonant power enhancement of the cavity to measure the cavity length, we can derive the sensitivity of the
cavity from the differentiation of Equation (88), which gives the slope of the trace shown in Figure 25,
with as defined in Equation (103). This is plotted in Figure 33 together with the cavity power
as a function of the cavity tuning. From Figure 33 we can deduce a few key features of the
cavity:
The cavity must be held as near as possible to the resonance for maximum sensitivity. This is the
reason that active servo control systems play an important role in modern laser interferometers.
If we want to use the power directly as an error signal for the length, we cannot use the cavity
directly on resonance because there the optical gain is zero. A suitable error signal (i.e., a
bipolar signal) can be constructed by adding an offset to the light power signal. A control
system utilising this method is often called DC-lock or offset-lock. However, we show below
that more elegant alternative methods for generating error signals exist.
The differentiation of the cavity power looks like a perfect error signal for holding the
cavity on resonance. A signal proportional to such differentiation can be achieved with a
modulation-demodulation technique.
Figure 33: The top plot shows the cavity power as a function of the cavity tuning. A tuning of
360° refers to a change in the cavity length by one laser wavelength. The bottom plot shows the
differentiation of the upper trace. This illustrates that near resonance the cavity power changes very
rapidly when the cavity length changes. However, for most tunings the cavity seems not sensitive at
all.