Interactions of light and mirrors: Advanced techniques for modelling future gravitational wave detectors Daniel David Brown A thesis submitted for the degree of Doctor of Philosophy Astrophysics and Space Research Group School of Physics and Astronomy College of Engineering and Physical Sciences University of Birmingham Compiled: Friday 12th February, 2016 University of Birmingham Research Archive e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. ii Abstract As of yet, a direct observation of gravitational waves has eluded science’s best efforts to detect them. The second generation of ground based interferometric grav- itational wave detectors, offering ten times the sensitivity of their predecessors, are now just beginning to come online. With these fully operational the community ex- pects that within the next few years we will finally observe the first direct detection of a gravitational wave. To achieve this feat, the interferometers must reach a displacement sensitivity of 20 =1 10− m pHz around 100Hz. The second generation of detectors aiming to reach this,∼ such as Advanced LIGO in the USA, employ a variety of techniques to overcome the limits of previous detectors, for example improved interferometer mirrors and bet- ter seismic isolation systems. The new optical designs rely on using multiple coupled optical cavities whose primary aim is to increase the laser power interacting with the gravitational wave signal. This comes at the cost of creating a more complex sys- tem. The suspended optical components in the presence of high laser powers produce a complex optomechanical system involving thermal distortion of the optics and ra- diation pressure effects. Furthermore, imperfections in the detector, such as mirror surface defects or misaligned optics, can have a significant impact on its behaviour and sensitivity. To design and operate these detectors the combination of the afore- mentioned effects must be understood and prepared for. Numerical models are vital to this effort, allowing us to explore new parameter spaces for designs and troubleshoot- ing unexpected results as the detectors are commissioned. The work presented in this thesis is aimed at using numerical models to improve the designs of future gravita- tional wave detectors and for a more effective commissioning of current ones, with a particular focus on the Advanced LIGO detectors. The main tool used throughout this work is FINESSE; a program originally de- veloped more than 10 years ago and already popular within the gravitational wave community. Its primary aim was to provide a tool to better understand the behaviour of the first generation of gravitational wave detectors. However, neither FINESSE nor other simulation packages provided the means to model realistic second generation detectors. In particular none of the tools could effectively model all of the following key effects: radiation pressure effects, distortions of the laser beam, quantum fluc- tuations of the optical fields, interferometer control signal and noise projections. As part of my work I have implemented these features into FINESSE for the benefit of the wider gravitational wave community and other interested parties. With these new features I have used FINESSE to directly support the Advanced LIGO project including a study into the interferometer behaviour in the presence of a combination of beam clipping and mode-mismatch experienced at one of the LIGO detectors. I also studied how similar imperfections in the system leads to an effect called ‘mode hopping’. The effectiveness of numerical modelling of realistic systems is in many cases lim- ited by the computation time. I have investigated the use of a reduced-order quadra- ture technique to reduce the computational cost of calculating spatial overlap integrals of Hermite-Gaussian mode. This technique was successfully applied to optical mode coupling calculations in FINESSE and resulted in a speed improvement of around three orders of magnitude. This significant reduction allows for new parameter spaces to be efficiently explored. The described method is generic and could also be applied to other numerical models using Gaussian modes or beam shapes. One of the challenges in the design of future gravitational wave detectors are un- stable mechanical oscillations of the test masses: also known as parametric instabil- ities. These are present due to the use of low loss mirror substrate materials and a high intracavity laser power inducing an undesirable optomechanical feedback. I have shown a new method to reduce these parametric instabilities by using purely optical means—previously only mechanically damping has been successfully demonstrated and explored. The described method opens up new avenues to explore advanced op- tical configurations with higher circulating power. Finally, the susceptibility of waveguide grating mirrors to lateral displacement phase shifts coupling in to the reflected beam was investigated. Waveguide grating mirrors offer reduced thermal noise that limits the mid-range of many detectors’ sen- sitivities. These devices incorporate grating structures that typically exhibit a strong coupling between lateral displacements to the phase of diffracted orders. It was demonstrated using a finite-difference time-domain model to solve Maxwell’s equa- tions that such a coupling does not affect waveguide grating mirrors, to the level of numerical errors. Acknowledgements Over the last four years I have met some fantastic people. Whether you were guid- ing me to become a better physicist, sympathising with me when having yet another missing conjugate or minus sign in FINESSE to hunt down, or distracting me from it all: you have my thanks. None of this would have been possible without my supervisor Andreas Freise. You have given me the opportunity to work on exciting problems and projects I would have never even considered, and the chance to travel around the world presenting my work in the process. You have been a great supervisor, and no doubt we will continue making computer games long into the future. Paul Fulda and Charlotte Bond, thank you for battling FINESSE with me! It has been a both great fun and a privilege working with you both on all the various projects over the years; and all the fun times had outside of work. You both taught me a great deal and if it was not for your bug reports (no matter how late at night they came in) and feature requests FINESSE would be half the tool it is today. My thanks also goes out to all my colleagues, past and present, at Birmingham; it has been a pleasure to work with you all and you have made the group here a great place to work. David Stops, thanks for the countless times you have helped me with all manner of computer based problems—whether it was the computers at fault or me for breaking things. To Jan Harms, Rebecca Palmer and Haixing Miao, your knowledge of physics and abilities to teach me about all manner of complex problems amazes me to this day. Without your help the quantum features of FINESSE would have taken much longer to surface. A big thanks must also go to Rory Smith who opened my eyes to the seemingly ‘magical’ abilities of reduced order modelling techniques. The LIGO-VIRGO collaboration has been a great team of international scientists to work with. I have many great memories of all the interesting conferences (both content and destinations) and being able to be part of one of the most exciting exper- iments being undertaken in the world today. My thanks is also extended to Garilynn Billingsley for all the help with LIGO maps over the years for all our simulations at Birmingham. To my friends: Simon ‘Weasel’ Jones, Stas ‘Brains’ Kuzmierkiewicz, Chris ‘El rat’ Bradley, Emily ‘Gnasher’ Nash, Charlotte ‘Chops’ Roberts, Lilly ‘the pink’ Pye, Jamie ‘Curtains!’ Pugh and Sayo ‘Lemon drizzle’ Taiwo. Thank you for all the distractions from work, the Snobs escapades, and all the horrendous in-jokes—all of which I am sure there will be plenty more of in the future. I would not be where I am today without my family. To my Mum who has always been there to offer guidance and help me out (especially with proof reading this the- sis), Dad for the terrible puns and jokes but always sound advice, to my Brother, and the extended stepfamily: I have come along way with all your support and encour- agement. Finally, my little sister, Sofia. Thank you for all the late night chats on dinosaurs, hamsters and endangered animals, and generally keeping me young at heart. I hope that one day—when you are grown up—you can look over all this and understand some of the seemingly strange science I was always getting up to! Statement of Originality This thesis reports on my own research work conducted during my PhD at the Univer- sity of Birmingham between September 2011 and September 2015. Chapter1 begins with a brief introduction to gravitational wave detectors. This provides background on interferometer optics and the noise sources relevant to the work reported in this thesis. Chapter2 outlines the use of a technique called reduced order quadrature for computing the optical scattering in interferometers. This work was carried out by myself and Rory Smith and as of September 2015 has been submitted for publication under the name Fast simulation of Gaussian-mode scattering for precision interferometry. Chapter3 presents a new idea using optical feedback to provide a broadband re- duction in unstable mechanical modes (parametric instabilities) in the mirrors of grav- itational wave detectors.