New family of light beams and mirror shapes for future LIGO interferometers

Abstract

Advanced LIGO's present baseline design uses arm cavities with Gaussian light beams supported by spherical mirrors. Because Gaussian beams have large intensity gradients in regions of high intensity, they average somewhat poorly over fluctuating bumps and valleys on the mirror surfaces (thermal noise). Flattopped light beams (mesa beams) are being considered as an alternative because they average over thermal noise more effectively. However, the proposed mesa beams are supported by nearly-flat mirrors, which experience a very serious tilt instability. In this paper we propose an alternative configuration in which mesa-shaped beams are supported by nearly-concentric spheres, which experience only a weak tilt instability. The tilt instability is analyzed for these mirrors in a companion paper by Savov and Vyatchanin. We also propose a one-parameter family of light beams and mirrors in which, as the parameter varies continuously from 0 to , the beams and supporting mirrors get deformed continuously from the nearly-flat-mirrored mesa configuration (FM) at 0, to the nearly-concentricmirrored mesa configuration (CM) at . The FM and CM configurations at the endpoints are close to optically unstable, and as moves away from 0 or , the optical stability improves.

Pass-through Mach-Zehnder topologies for macroscopic quantum measurements

“…Taking into account, that this gain is cumulative with the other proposed methods of reducing the coating thermal noise: in particular, broadened laser beams [42], better coating materials [43], coating structure optimization [44,45], it is quite possible that together all these methods will allow to push the coating thermal noise below the quantum noise.…”

Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO

“…These optical axes are readily recognized to be the generators of hyperboloids (see, e.g, [9], Fig. 1(b)).…”

“…The BT construction [9], which generalizes the original idea in [3], is based on the superposition of minimumspreading GBs launched from a circular equivalent aperture of radius R 0 at the waist plane (z 0), with optical axes pointing along the unit vector u r 0 =L cos 0 ÿ cos 0 ÿ x r 0 =L sin 0 ÿ sin 0 ÿ ŷ ẑ. These optical axes are readily recognized to be the generators of hyperboloids (see, e.g, [9], Fig.…”

“…Specifically, the FM and CM beams belong to the class of flattened beams introduced in [10], and can therefore be represented in terms of the rapidly-converging GaussLaguerre (GL) beam expansions derived therein. Based on this observation, we extend the approach in [10] to accommodate the more general family of BT hyperboloidal beams [9]. This leads to a generalization (we limit the analysis here to the dominant eigenmode) of the FM-CM duality relations in [7,8], which involves fractional Fourier transforms of complex order.…”

“…Remarkably, the nearlyflat (FM) and nearly-concentric mesa (CM) configurations were found to be connected through a duality relation [7,8], which allows a one-to-one mapping between all the corresponding eigenmodes. The geometrical construction underlying FM and CM beams [3], based on coherent superposition of minimum-spreading Gaussian beams (GBs), was further generalized by Bondarescu and Thorne [9], in terms of a one-parameter family of ''hyperboloidal'' beams which allows continuous spanning from the FM to the CM configurations, and including the standard GB case. This paper elaborates on the analytic structure of the Bondarescu-Thorne (BT) hyperboloidal beams, building on a number of results from the applied optics literature concerning flat-top beams, which have most likely not come to the attention of the gravitational-wave community.…”