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Fast simulation of Gaussian-mode scattering for precision interferometry

Brown, D. and Smith, R. J. E. and Freise, A. (2016) Fast simulation of Gaussian-mode scattering for precision interferometry. Journal of Optics, 18 (2). Art. No. 025604. ISSN 2040-8978. doi:10.1088/2040-8978/18/2/025604.

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Understanding how laser light scatters from realistic mirror surfaces is crucial for the design, commissioning and operation of precision interferometers, such as the current and next generation of gravitational-wave detectors. Numerical simulations are indispensable tools for this task but their utility can in practice be limited by the computational cost of describing the scattering process. In this paper we present an efficient method to significantly reduce the computational cost of optical simulations that incorporate scattering. This is accomplished by constructing a near optimal representation of the complex, multi-parameter 2D overlap integrals that describe the scattering process (referred to as a reduced order quadrature). We demonstrate our technique by simulating a near-unstable Fabry–Perot cavity and its control signals using similar optics to those installed in one of the LIGO gravitational-wave detectors. We show that using reduced order quadrature reduces the computational time of the numerical simulation from days to minutes (a speed-up of ≈2750x) while incurring negligible errors. This significantly increases the feasibility of modelling interferometers with realistic imperfections to overcome current limits in state-of-the-art optical systems. While we focus on the Hermite–Gaussian basis for describing the scattering of the optical fields, our method is generic and could be applied with any suitable basis. An implementation of this reduced order quadrature method is provided in the open source interferometer simulation software Finesse.

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Freise, A.0000-0001-6586-9901
Additional Information:© 2016 IOP Publishing Ltd. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 2 September 2015. Accepted 16 November 2015. Published 5 January 2016. We would like to thank GariLynn Billingsley for providing the Advanced LIGO mirror surface maps and for advice and support on using them. We would also like to thank Kent Blackburn, Peter Deiner, Scott Field and Chad Galley for useful discussions and encouragement throughout this project. Some of the computations were carried out using the high performance computing resources provided by Louisiana State University ( and the Extreme Science and Engineering Discovery Environment (XSEDE) [43], which is supported by National Science Foundation grant number ACI-1053575. This work has been supported by the Science and Technology Facilities Council (STFC) Consolidated Grant ST/K000845/1 and the U.S. National Science Foundation under cooperative agreement NSF-PHY-0757058. This document has been assigned the LIGO Laboratory document number LIGO-P1500128.
Funding AgencyGrant Number
Science and Technology Facilities Council (STFC)ST/K000845/1
NSFPHY- 0757058
Subject Keywords:simulation, scattering, gaussian beams, reduced order quadrature
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Other Numbering System NameOther Numbering System ID
LIGO DocumentLIGO-P1500128
Issue or Number:2
Record Number:CaltechAUTHORS:20160211-091906079
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Official Citation:D Brown et al 2016 J. Opt. 18 025604
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64413
Deposited By: Ruth Sustaita
Deposited On:17 Feb 2016 22:40
Last Modified:10 Nov 2021 23:30

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