Although the calculation here is for a simple Michelson interferometer, similar arguments apply to the more sophisticated systems with arm cavities, power recycling and signal recycling discussed earlier and lead to the same conclusions. Frequency stabilisation is also important in other applications such as in high resolution optical spectroscopy , optical frequency standards [223, 312] and fundamental quantum measurements . The best reference cavities, such as those developed by the Ye  and Hänsch  groups, have reported a frequency stability performance of around 10–16, which is broadly equivalent to that achieved for ground-based gravitational-wave detectors when scaling by cavity length.
Typically, and ignoring possible ameliorating effects of the power recycling cavity on beam geometry fluctuations, this will mean that the beam positional fluctuations of the laser need to be suppressed by several orders of magnitude. The two main methods of reducing beam geometry fluctuations are 1) passing the input beam through a single mode optical fibre  and 2) using a resonant cavity as a mode cleaner [270, 288, 317, 83].
Passing the beam through a single mode optical fibre helps to eliminate beam geometry fluctuations, as deviations of the beam from a Gaussian TEM00 mode are equivalent to higher-order spatial modes, which are thus attenuated by the optical fibre. However, there are limitations to the use of optical fibres, mainly due to the limited power-handling capacity of the fibres; care must also be taken to avoid introducing extra beam geometry fluctuations from movements of the fibre itself.
A cavity may be used to reduce beam geometry fluctuations if it is adjusted to be resonant only for the TEM00 mode of the input light. Any higher order modes should thus be suppressed . The use of a resonant cavity should allow the handling of higher laser powers and has the additional benefits of acting as a filter for fast fluctuations in laser frequency and power [288, 317]. This latter property is extremely useful for the conditioning of the light from some laser sources as will be discussed below.
From Equation (7) it can be seen that the photon-noise limited sensitivity of an interferometer is proportional to where is the laser power incident on the interferometer, and where is the wavelength of the laser light. Thus, single frequency lasers of high output power and short wavelength are desirable. With these constraints in mind, laser development started on argon-ion lasers and Nd:YAG lasers. Argon-ion lasers emitting light at 514 nm were used to illuminate several interferometric gravitational-wave detector prototypes, see, for example, [287, 264]. However, their efficiency, reliability, controllability and noise performance has ruled them out as suitable laser sources for current and future gravitational wave detectors.
Nd:YAG lasers, emitting at 1064 nm or frequency doubled to 532 nm, present an alternative. The longer (infrared) wavelength may initially appear less desirable than the 514 nm of the argon-laser and the frequency doubled 532 nm, as more laser power is needed to obtain the same sensitivity. In addition, the resulting increase in beam diameter leads to a need for larger optical components. For example in an optical cavity the diameter of the beam at any point is proportional to the square root of the wavelength  and to keep diffractive losses at each test mass below 1 × 10–6, it can be shown that the diameter of each test mass must be greater than 2.6 times the beam diameter at the test mass. Thus, the test masses for gravitational wave detectors have to be 1.4 times larger in diameter for infrared than for green light. However, Nd:YAG sources at 1064 nm have demonstrated some compelling advantages, in particular the demonstration of scaling the power up to levels suitable for second generation interferometers ( 200 W) combined with their superior efficiency [286, 306, 200]. Frequency-doubled Nd:YVO lasers at 532 nm have currently only been demonstrated to powers approaching 20 W and have not been actively stabilised to the levels needed for gravitational-wave detectors . An additional problem associated with shorter wavelength operation is the potential for increased absorption, possibly leading to photochemistry (damage) in the coating materials, in addition to increased scatter. For this reason, all the initial long-baseline interferometer projects, along with their respective upgrades, have chosen some form of Nd:YAG light source at 1064 nm.
As an example, the laser power is being upgraded from 10 W in initial LIGO to 180 W for Advanced LIGO to improve the SNR of the shot-noise–limited regime. This power will be delivered by a three stage injection-locked oscillator scheme [120, 237, 157, 144]. The first stage uses a monolithic non-planar ring oscillator (NPRO) to initially produce 2 W of output power. This output is subsequently amplified by a four-head Nd:YVO laser amplifier to a power of 35 W , which is in turn delivered into an injection locked Nd:YAG oscillator to produce 200 W of output power .
Other laser developments are being pursued, such as high-power–fibre lasers, which are currently being investigated by the AEI in Germany  and prototyped for Advanced VIRGO by Gréverie et al. in France . Fibre amplifiers show great potential for extrapolation to higher laser powers in addition to lower production costs.
Third-generation interferometric gravitational-wave detectors, such as the Einstein Telescope, require input laser powers of around 500 W at 1064 nm in order to achieve their high-frequency shot-noise–limited sensitivities . Low-frequency sensitivity is expected to be achieved through the use of separate low-power interferometers with silicon optics operating at cryogenic temperatures [269, 262]. Longer wavelengths are proposed here due to excessive absorption in silicon at 1064 nm and the expected low absorption (less than 0.1 ppm/cm) at around 1550 nm . Worldwide laser developments may provide new baseline light sources that can provide different wavelength and power options for future detectors. However, the stringent requirements on the temporal and spatial stability for gravitational-wave detectors are beyond that sought in other laser applications. Therefore, a dedicated laser-development program will be required to continue beyond the second-generation interferometers in order to design and build a laser system that meets third-generation requirements, as discussed in more detail in .
Another key area of laser development, targeted at improving the sensitivity of future gravitational-wave detectors, is in the use of special optical modes to reduce thermal noise. It can be shown that the amplitude of thermal noise associated with the mirror coatings is inversely proportional to the beam radius . The configuration within current interferometers is designed to inject and circulate TEM00 optical modes, which have a Gaussian beam profile. To keep diffraction losses suitably low for this case ( 1 ppm), a beam radius of a maximum size 35% of the radius of the test mass mirror can be used. The thermal noise could be further reduced if optical modes are circulated that have a larger effective area, yet not increasing the level of diffraction losses. This would be possible through the use of higher-order Laguerre-Gauss beams, and other “exotic” beams, such as mesa or conical beams. A more in-depth discussion of how these optical schemes can be implemented and the potential increase in detector sensitivity attainable can be found in .
Despite the very-low levels of optical absorption in fused silica at 1064 nm, thermal loading due to high-levels of circulating laser powers within advanced gravitational-wave detectors will cause significant thermal loading. In the case of Advanced LIGO, thermal lensing will be most significant in the input test masses of the Fabry–Pérot cavities, where the beam must transmit through the substrate in addition to the high-power within the cavity being incident on the coating surfaces. Thermal distortion in the optics will be sensed by Hartmann sensors and coupled to two schemes of thermal compensation. Firstly, ring resistance heaters will be installed around the barrel of the input mass in order to compensate for the beam heating the central region of the optics, as demonstrated for radius of curvature tuning in GEO600 . Secondly, a flexible CO2 laser based system will be used to deposit heat onto the reaction mass (otherwise called the compensation plate) for the input test mass, as demonstrated in initial LIGO [209, 308]. The laser beam shape and intensity can be easily modified from outside with the vacuum system and can therefore adapt to non-uniformities in the absorption and other changes in the interferometer’s thermal state.
It should also be noted that energy can couple from the optical modes resonating in the interferometer Fabry–Pérot cavities and the acoustic modes of the test masses. When there is sufficient coupling between these optical and mechanical modes, and the mechanical modes have a suitably high-quality factor, then mechanical resonances can be ‘rung-up’ by the large circulating laser power to the point where the interferometer is no longer stable, a phenomenon called parametric instabilities . Mechanical dampers that are tuned to damp at high-frequency yet not significantly increasing thermal noise at low-frequency are being considered in possible upgrades to advanced detectors, in addition to other schemes, such as active feedback to damp problematic modes provided through the electrostatic actuators.
Living Rev. Relativity 14, (2011), 5
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