Modeling circulating cavity fields using the discrete linear canonical transform

Fabry-Perot cavities are central to many optical measurement systems. In high-precision experiments, such as aLIGO and AdVirgo, coupled cavities are often required, leading to complex optical behavior. We show, for the first time to our knowledge, that discrete linear canonical transforms (LCTs) can be used to compute circulating optical fields for cavities in which the optics have arbitrary apertures, reflectance and transmittance profiles, and shape. We compare the predictions of LCT models with those of alternative methods. To further highlight the utility of the LCT, we present a case study of point absorbers on the aLIGO mirrors and compare it with recently published results.

Interferometer techniques for gravitational-wave detection

Several km-scale gravitational-wave detectors have been constructed worldwide. These instruments combine a number of advanced technologies to push the limits of precision length measurement. The core devices are laser interferometers of a new kind; developed from the classical Michelson topology these interferometers integrate additional optical elements, which significantly change the properties of the optical system. Much of the design and analysis of these laser interferometers can be performed using well-known classical optical techniques; however, the complex optical layouts provide a new challenge. In this review, we give a textbook-style introduction to the optical science required for the understanding of modern gravitational wave detectors, as well as other high-precision laser interferometers. In addition, we provide a number of examples for a freely available interferometer simulation software and encourage the reader to use these examples to gain hands-on experience with the discussed optical methods.

Accelerated convergence method for fast Fourier transform simulation of coupled cavities

Fast Fourier transform (FFT) simulation was used to calculate the power and spatial distribution of resonant fields in optical cavities. This is an important tool when characterizing the effect of imperfect geometry and mirror aberrations. This method is, however, intrinsically slow when the cavities are of relatively high finesse. When this is the case, an accelerated convergence scheme may be used to calculate the steady-state cavity field with a speed that is orders of magnitude faster. The rate of convergence of this method, however, is unpredictable, as many different factors may detrimentally affect its performance. In addition, its use in multiple cavity configurations is not well understood. An in-depth study of the limitations and optimization of this method is presented, together with a formulation of its use in multiple cavity configurations. This work has not only resulted in consistent improvement in performance and stability of the accelerated convergence method but also allows the simulation of optical configurations, which would not previously have been possible.