6.2 Fabry–Pérot length sensing

In Figure 25View Image 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 (88View Equation)),
T T P1∕P0 = -------------1-------------= -1, (103 ) 1 + R1R2 − 2r1r2cos (2kL ) d
we can see that the actual frequency dependence is given by the cos(2kL) term. Writing this term as
( ) cos(2kL ) = cos 2π Lf- , (104 ) c
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 (88View Equation), which gives the slope of the trace shown in Figure 25View Image,
dP1∕P0 − 4T1r1r2k sin (2kL ) ------- = ----------2--------, (105 ) dL d
with d as defined in Equation (103View Equation). This is plotted in Figure 33View Image together with the cavity power as a function of the cavity tuning. From Figure 33View Image we can deduce a few key features of the cavity:
View Image

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.

  Go to previous page Go up Go to next page