LIGO Document P1000032-v4

[Thesis] On Non-Gaussian Beams and Optomechanical Parametric Instabilities in Interferometric Gravitational Wave Detectors

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Direct detection of gravitational radiation, predicted by Einstein's
general theory of relativity, remains one of the most exciting
challenges in experimental physics. Due to their relatively weak
interaction with matter, gravitational waves promise to allow
exploration of hitherto inaccessible objects and
epochs. Unfortunately, this weak coupling also hinders detection
with strain amplitudes at the Earth estimated to be of order

Due to their wide bandwidth and theoretical sensitivity,
kilometre-scale Michelson style interferometers have become the
preferred instrument with which to attempt ground based detection. A
worldwide network of first generation instruments has been
constructed and prodigious volumes of data recorded. Despite each
instrument approaching or having reached its design sensitivity, a
confirmed detection remains elusive.

Planned upgrades to these instruments aim to increase strain
sensitivity by an order of magnitude, commencing the era of second
generation detectors. Entry into this regime will be accompanied by
an entirely new set of challenges, two of which are addressed in
this work.

As advanced interferometers are commissioned, instrumental artifacts
will give way to fundamental noise sources. In the region of peak
sensitivity it is expected that thermal noise in the
interferometers' dielectric mirror coatings will be the principal
source of displacement noise. Theory suggests that increasing the
spot size of laser light incident on these mirrors will reduce the
measured thermal noise. In the first part of this work we examine
one method of realising larger spots.

By adopting non-spherical mirrors in the interferometers' arms it is
possible to create resonators which support a wide, flat-topped
field known as the mesa beam. This beam has been shown to
theoretically reduce all forms of mirror thermal noise without being
significantly more difficult to control. In this work we investigate
these claims using a bespoke prototype mirror. The first results
regarding a non-Gaussian beam created in a manner applicable to a
gravitational wave interferometer are presented.

A common theme among all second generation interferometer designs is
the desire to maximise circulating power. This increased power is
partnered by commensurately increased thermal perturbations. Since
the attractive properties of the mesa beam are produced by the fine
structure of its supporting mirrors, it is important that we
understand the effects absorption of stored optical power could have
on mesa fields. In the second part of this work we report on
numerical evaluations of measured thermal noise and mesa beam
intensity profile as a function of absorbed power.

Increased optical power also has less obvious consequences. As a
result of radiation pressure, there exists a pathway between optical
energy stored in an interferometer's arms and mechanical energy
stored in the acoustic modes of its test masses. Under appropriate
conditions, this coupling can excite one or more test masses to such
a degree that interferometer operation becomes impossible. In the
final part of this work we determine whether it is possible to
mitigate these parametric instabilities using electrostatic
actuators originally designed to control the position and
orientation of the test masses.

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