5.1 Power recycling

It can be shown that an optimum signal-to-noise ratio in a Michelson interferometer can be obtained when the arm lengths are such that the output light is very close to a minimum (this is not intuitively obvious and is discussed more fully in [133]). Thus, rather than lock the interferometer to the side of a fringe as discussed above in Section 4.4.1, it is usual to make use of a modulation technique to operate the interferometer close to a null in the interference pattern. An electro-optic phase modulator placed in front of the interferometer can be used to phase modulate the input laser light. If the arms of the interferometer are arranged to have a slight mismatch in length this results in a detected signal, which, when demodulated, is zero with the cavity exactly on a null fringe and changes sign on different sides of the null providing a bipolar error signal; this can be fed back to the transducer controlling the interferometer mirror to hold the interferometer locked near to a null fringe (this is the RF readout scheme discussed in Section 5.4).

In this situation, if the mirrors are of very low optical loss, nearly all of the light supplied to the interferometer is reflected back towards the laser. In other words the laser is not properly impedance matched to the interferometer. The impedance matching can be improved by placing another mirror of correctly chosen transmission – a power recycling mirror – between the laser and the interferometer so that a resonant cavity is formed between this mirror and the rest of the interferometer; in the case of perfect impedance matching, no light is reflected back towards the laser [131, 278]. There is then a power build-up inside the interferometer as shown in Figure 10View Image. This can be high enough to create the required kilowatts of laser light at the beamsplitter, starting from an input laser light of only about 10 W.

View Image

Figure 10: The implementation of power recycling on a Michelson interferometer with Fabry–Pérot cavities.

To be more precise, if the main optical power losses are those associated with the test mass mirrors – taken to be A per reflection – the intensity inside the whole system considered as one large cavity is increased by a factor given by (πL )∕(cA τ), where the number of bounces, or light storage time, is optimised for signals of timescale τ and the other symbols have their usual meaning. Then:

( λhA )1∕2 detectable strain in time τ = -------- . (11 ) 4πLP τ2

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