Grid-based simulation program for gravitational wave interferometers with realistically imperfect optics

Abstract

[prd,twocolumn,groupedaddress,showpacs,floatfix, nofootinbib]We describe an optical simulation program that models a complete, coupled-cavity interferometer like those used by the Laser Interferometer Gravitational-Wave Observatory (LIGO) Project. A wide variety of interferometer deformations can be modeled, including general surface roughness and substrate inhomogeneities, with no a priori symmetry assumptions about the nature of interferometer imperfections. Several important interferometer parameters are optimized automatically to achieve the best possible sensitivity for each new set of perturbed mirrors. The simulation output data set includes the circulating powers and electric fields at various points in the interferometer, both for the main carrier beam and for its signal-sideband auxiliary beams, allowing an explicit calculation of the shot-noise-limited gravitational-wave sensitivity of the interferometric detector to be performed. Here we present an overview of the physics simulated by the program, and demonstrate its use with a series of runs showing the degradation of LIGO performance caused by realistically-deformed mirror profiles. We then estimate the effect of this performance degradation upon the detectability of astrophysical sources of gravitational waves. We conclude by describing applications of the simulation program to LIGO research and development efforts.

Detector description and performance for the first coincidence observations between LIGO and GEO

“…The first is an FFT-based optical propagation code [31] that models the powerrecycled Michelson interferometer with FabryPerot arms. This code was used to develop the specifications for the interferometer optics, and has been used in comparisons with commissioning data to evaluate the performance of the optics as installed.…”

Simulating a Dual-Recycled Gravitational Wave Interferometer with Realistically Imperfect Optics

“…4. We note that this procedure only computes relative signal amplitudes, not absolute GW-signal strengths; the latter would require us to assume and model a specific GW-detection scheme for DR interferometers. Although we have used the FFT program to model the control system for the Initial-LIGO detector [29,30], we have not yet explicitly modeled any of the (complex and stillevolving) detection schemes being considered for Advanced-LIGO, and for other DR interferometers [e.g., 21,24,27,41,[51][52][53]. Nevertheless, the relative GW-response curves generated from these simulations are very informative about essential features of DR interferometer performance.…”

“…Our numerical model incorporates a wide variety of optical imperfections, such as mirror surface roughness and substrate inhomogeneities, finite aperture sizes, and losses to due absorption and high-angle scattering. Our tool for this work is a pixelized-grid-based numerical simulation program [29,30], which has been developed and used for a variety of modeling studies conducted by the LIGO group [e.g., [31][32][33][34], and by other collaborating GW groups [35][36][37]. With this program, we will be able to more realistically estimate how DR performs in optical environments as similar as possible to those of the real advanced detectors.…”

Accelerated convergence method for fast Fourier transform simulation of coupled cavities

“…However, this solution may only be applied for a few specific optical configurations. A "global relaxation" scheme was proposed in [8,9] whereby steady-state fields for each cavity are determined simultaneously in order to minimize a specially weighted sum of the iteration errors for all relaxed fields. However, this system is also reported to have instabilities that are heavily configuration dependent.…”