Recycling in laser-interferometric gravitational-wave detectors.

Laser interferometers may detect gravitational waves by sensing the strain in space produced by their passage. The resultant change in intensity of an interference fringe must be observable against a background noise due to the statistical fluctuations in the number of detected photons. Optimization of the detector sensitivity thus involves devising an optical system which both maximizes the signal and minimizes the noise. This is attempted in the various arrangements known collectively as light recycling. Here, the performance of these systems is quantitatively assessed. Standard or broadband recycling functions essentially by making efficient use of the available light, but it is shown that it may also be made to further enhance the sensitivity within a narrow bandwidth, becoming tuned recycling. This works, as do all the narrow-band variants, by arranging for both the laser light and a gravitational-wave-induced sideband to be resonant in the optical system. The original narrow-band system, resonant recycling, can also be made broadband; the various sensitivity-bandwidth combinations, together with the tuning properties of such a system, are discussed. Furthermore, a new optical arrangement, dual recycling, is proposed. Its optical layout is an extension of standard recycling and its strength lies in its flexibility. It is shown that, relatively simply, it may be made into either a broadband or a narrow-band system, in each case with the same performance as the best of the other schemes. It may be tuned more efficiently and easily over a wide range of frequencies. Uniquely, optimum performance may be obtained with dual recycling without the requirement that the storage time of the optical elements in each arm of the interferometer be comparable with the period of the gravitational wave. This may allow the operation of delay line interferometers down to much lower gravitational-wave frequency and will provide great operational flexibility. Finally, it is shown that dual recycling, together with resonant recycling, is relatively insensitive to imperfections in the geometrical quality of the optical system. When implemented on interferometers with lengths greater than about a kilometer, recycling should allow the attainment of the sensitivity required in order to observe gravitational waves and open up a new window to the Universe.