Enhancement of sensitivity and bandwidth of gravitational wave detectors using fast-light-based white light cavities

The effect of gravitational waves (GWs) has been observed indirectly, by monitoring the change in the orbital frequency of neutron stars in a binary system as they lose energy via gravitational radiation. However, GWs have not yet been observed directly. The initial LIGO apparatus has not yet observed GWs. The advanced LIGO (AdLIGO) will use a combination of improved techniques in order to increase the sensitivity. Along with power recycling and a higher power laser source, the AdLIGO will employ signal recycling (SR). While SR would increase sensitivity, it would also reduce the bandwidth significantly. Previously, we and others have investigated, theoretically and experimentally, the feasibility of using a fast-light-based white light cavity (WLC) to circumvent this constraint. However, in the previous work, it was not clear how one would incorporate the white light cavity effect. Here, we first develop a general model for Michelson-interferometer-based GW detectors that can be easily adapted to include the effects of incorporating a WLC into the design. We then describe a concrete design of a WLC constructed as a compound mirror, to replace the signal recycling mirror. This design is simple, robust, completely non-invasive, and can be added to the AdLIGO system without changing any other optical elements. We show a choice of parameters for which the signal sensitivity as well as the bandwidth are enhanced significantly over what is planned for the AdLIGO, covering the entire spectrum of interest for gravitational waves.