Principal Investigator David E McClelland Project s05

Department of Physics, Machine VP

Faculty of Science

Co-Investigator Ben D Stanley

Department of Physics, Faculty of Science

Numerical Modelling of Laser Interferometers

Long baseline laser interferometers are currently being designed to detect gravitational waves. In order to enhance the signal, optical schemes known as `light recycling' have been proposed. One scheme in particular, known as dual recycling, was predicted to be tolerant to wave front distortion, a major benefit considering the potential difficulties in this area. Numerical modelling of a simple single pass Michelson system confirmed this ability. However, it was not clear whether the proposed designs, which incorporate Fabry-Perot cavities in the arms of the Michelson interferometer, would be as tolerant.

To explore this question we have developed a numerical simulation of a dual recycling Fabry-Perot Michelson interferometer. Initial results with this simulation indicate that such devices are indeed resilient to geometrically induced (tilts, curvature error) distortions.

What are the basic question addressed?

In an analysis based on Hermite-Gauss spatial modes, the fundamental mode propagating in an interferometer is the TEM00 mode. Various imperfections can scatter light from this mode into higher order spatial modes. For example, tilt on the end mirrors of a Michelson interferometer scatters light primarily into the TEM10,01, modes; curvature mismatch scatters light into the cylindrically symmetric TEM02,20 modes; thermal distortions in mirror substrates and coatings or beam splitters, apart from absorbing power, tend to scatter light primarily into TEM02,20 modes; some imperfections in mirror polishing/coating process have been shown to also scatter light into these modes. At the main beam splitter (see Figure 1) of a Michelson type interferometer, the light in these higher order modes is directed toward the output along with the signal.

Interferometers with no recycling, or power recycling only (no mirror M3 in Figure 1), are very sensitive to distortions. Distorted light easily escapes the system via the beam splitter, and is absorbed in the photodetection system. This reduces the signal to noise ratio (S/N) in 2 ways: firstly, less power circulating in the power recycling cavity reduces the instrument's signal response; secondly, extra light on the photodetectors increases shot noise. This is in contrast to simple 2 mirror cavities. Simple cavities tend to be relatively tolerant to distortions because higher order modes must reflect off low transmission mirrors. There is therefore a tendency for such light to be trapped in the cavity, provided the distorted modes are non-resonant.

Figure 1

This situation is dramatically altered when tuned dual recycling is employed. Meers and Strain proposed that with the introduction of mirror M3, (see Figure 1), much of the distorted light will be reflected back into the interferometer, with the reduction in transmission to the photodetection system being related to the transmittivity T3 of mirror M3 and the resonance condition of this light in the split cavity formed by mirror M3 with the reflecting elements in the interferometer arms (Fabry-Perots (FPs) or delay lines (DL) in Figure 1). This split cavity is known as the signal recycling cavity (SRC). The reflected light can reenter the power recycling cavity (PRC), the split cavity formed by mirror M0 with the reflecting elements in the arms, contributing to the formation of a new normal mode for the system and maintaining the circulating power level. Such behaviour has been coined wavefront healing. Benchtop experiments using an interferometer with no arm FPs, support this scenario in the case of broadband dual recycling. The predictions have been verified for delay line interferometers with various recycling arrangements, using numerical simulations. At low distortions levels, power leakage can be reduced by more than a factor of 10 using dual recycling. Furthermore, it can be shown that the input mode couples effectively into the PRC, whilst the signal mode can be efficiently extracted. This translates directly into a much greater tolerance of wavefront distortions of tuned dual recycling interferometers compared with power recycling instruments .

Though dual recycling delay line interferometers exhibit distortion tolerance, will devices with arm Fabry-Perot cavities be similarly tolerant? In the absence of signal recycling, the presence of wavefront distortion in one of the arm cavities reduces its finesse. Light in higher order spatial modes is reflected toward the beam splitter, where it is ejected from the interferometer. The question to be addressed in this project was whether dual recycling could maintain the power circulating in not only the power recycling cavities, but also in the arm cavities (see Figure 1)? Does the new `normal mode' of the device couple effectively into both arm cavities?

A recycling arrangement similar to dual recycling is resonant sideband extraction (RSE). The configuration is identical to dual recycling with Fabry-Perot arm cavities, the difference arising from the chosen resonance conditions of the coupled cavities. The major advantage of RSE lies in the capacity to store large amounts of optical power in the interferometer arms]. This significantly reduces thermal loading on the main beam splitter. This arrangement can be seen as the most likely way to build an effective broadband recycling interferometer. However, such a system employs much smaller recycling factors. This may then permit light scattered into higher order modes by imperfections, to again leak from the interferometer, reducing the response. The question is: is there an optimum set of mirror reflectivities which keep thermal loading tolerably low but enable wavefront healing to be effective?

What are the results to date and the future of the work?

Preliminary results with a numerical simulation of a dual recycling interferometer with Fabry-Perot arm cavities (Figure 2), indicate that wavefront healing does indeed occur. At a tilt of 15% of the beam divergence applied to mirror M2 (see Fig.2), with R3 set to 0.9, the power level in all cavities is still within 4% of the ideal. This is in contrast to power recycling only (R3 = 0.0), where power levels are down by almost 50%. This translates into maintenance of the response of the dual recycling instrument even in the presence of such large error.