where
are the relative power fluctuations of the laser, and
is the offset from the null fringe position for an
interferometer of arm length
L
. From calculations of the effects of low frequency seismic
noise for the initial designs of long baseline detector [51
] it can be estimated that the rms motion will be of the order
of
m when the system is operating. Taking strains of around
at 300 Hz, as shown in the lower curve in Fig.
3
for LIGO 2, as typical of that desired for upgraded
detectors, requires power fluctuations of the laser not to
exceed
To achieve this level of power fluctuations typically requires the use of active stabilisation techniques of the type developed for argon ion lasers [79].
Hence to achieve the target sensitivity used in the above calculation using a detector with arms of length 4 km, maximal fractional frequency fluctuations of
are required.This level of frequency noise may be achieved by the use of appropriate laser frequency stabilisation systems involving high finesse reference cavities [51].
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.
A typical beamsplitter misalignment of
radians means that to achieve sensitivities of the level
described above using a detector with 3 or 4 km arms, and
50 bounces of the light in each arm, a level of beam geometry
fluctuations at the beamsplitter of close to
at 300 Hz is required.
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 [67] and 2) using a resonant cavity as a modecleaner [85,
93
,
109
,
10
].
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 [85]. 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 [93,
109]. This latter property is extremely useful for the
conditioning of the light from some laser sources as will be
discussed below.
Nd:YAG lasers, emitting at 1064 nm or frequency doubled
to 532 nm, present an alternative. The longer wavelength is
less desirable than the 514 nm of the argon-laser, 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 [61] and to keep diffractive losses at each test mass below
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.
Nd:YAG sources do however have some compelling advantages, and in
particular the potential for scaling Nd:YAG laser designs up to
levels of 100 W or more [91
] combined with their superior efficiency, has led all the long
baseline interferometer projects to choose some form of Nd:YAG
light source.
Compact sources of lower powers of Nd:YAG light have been available for several years in the form of monolithic diode-pumped ring lasers [59]. Investigations have shown that the technical noise associated with these lasers may be well controlled and reduced to levels comparable to those needed for gravitational wave interferometer sources [58, 39, 21, 81, 44]. Different approaches to obtaining high powers of low-noise Nd:YAG light have been studied. They all have in common the use of a stable lower power laser as a master oscillator.
One approach is to use a lower power Nd:YAG master oscillator
to injection lock a higher power Nd:YAG slave laser, with the
length of the slave laser cavity being locked to the frequency of
the light from the master oscillator [25,
72,
42]. Up to 20 W of single frequency laser light have been
obtained using this method [91], which has the desirable feature that the higher power slave
laser light has noise properties which are for the most part
dominated by those of the master laser light [36]. This is desirable since it is typically easier to apply active
noise reduction techniques to stabilise the lower power master
lasers. Injection locked systems of this type are being developed
for use by the VIRGO, TAMA 300 and GEO 600 projects,
each of which requires
10 W of laser light for initial operation.
However to adapt this technique for producing still higher powers from the slave laser requires care, since the light power needed from the master oscillator also increases. To meet this requirement systems have been proposed in which a series of lasers are successively injection locked.
An alternative scheme has been developed for use by the LIGO project [106]. Light from a master laser is passed through diode-pumped Nd:YAG amplification stages in a master oscillator/power amplifier (MOPA) configuration. This approach has the advantage of allowing a very high continous light power to be obtained using multiple amplification stages, without the need for multiple cavity locking schemes. However the effects of this design configuration on the noise properties of the amplified light must be addressed.
In particular, to obtain high performance from the modulation techniques discussed in section 5.1 it is necessary that at the modulation frequency, the power fluctuations of the laser light used must be shot noise limited in the amount of light detected at the interferometer output (typically up to a few Watts).
Previous studies of the noise properties of optical amplifiers
have shown that in a given output power of light from an optical
amplifier, power fluctuations exist which are in excess of those
obtained from a shot noise limited laser of the same output
power [45]. This gain dependent excess noise arises from the beating of
the spontaneous emission from the amplifier with the light being
amplified. Measurements of this excess noise at rf modulation
frequencies have been made using a free space Nd:YAG linear
optical amplifier system [101]. For this type of light source to be suitable for use in an
interferometric gravitational wave detector, it is necessary to
reduce these high frequency power fluctuations; a suitable
technique is to pass the light through a resonant cavity similar
to that used to spatially filter the input laser light as
described in section
5.4.1
[109]. Above the corner frequency
of the cavity, power and frequency fluctuations of the laser
light are reduced by a factor
where
f
is the frequency at which the fluctuation occurs, and
Thus the excess power noise introduced by the amplification process may be reduced to an appropriate level. The noise properties of saturated free space Nd:YAG optical amplifiers remain to be experimentally evaluated.
As mentioned earlier, a light source with the potential to combine the increased efficiency of solid state lasers with the advantage of using shorter wavelength light is a frequency doubled Nd:YAG laser. While single frequency powers in excess of 10 W are obtainable, sources of frequency-controllable doubled light of an acceptable power level have still to be proven in terms of long term reliability, but are likely to become available in the future.
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Gravitational Wave Detection by Interferometry (Ground
and Space)
Sheila Rowan and Jim Hough http://www.livingreviews.org/lrr-2000-3 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |