Laser-interferometric detectors for gravitational wave backgrounds at 100 MHz: Detector design and sensitivity

Recently, observational searches for gravitational wave background (GWB) have been developed and given direct and indirect constraints on the energy density of GWB in a broad range of frequencies. These constraints have already rejected some theoretical models of large GWB spectra. However, at 100 MHz, there is no strict upper limit from direct observation, though the indirect limit by ${}^2\mathrm{He}$ abundance due to big-bang nucleosynthesis exists. In this paper, we propose an experiment with laser interferometers searching GWB at 100 MHz. We considered three detector designs and evaluated the GW response functions of a single detector. As a result, we found that, at 100 MHz, the most sensitive detector is the design, a so-called synchronous recycling interferometer, which has better sensitivity than an ordinary Fabry-Perot Michelson interferometer by a factor of 3.3 at 100 MHz. When we select the arm length of 0.75 m and realistic optical parameters, the best sensitivity achievable is $h\approx 7.8\times {10}^{-21}{\mathrm{Hz}}^{-1/2}$ at 100 MHz with bandwidth $\sim 2\mathrm{kHz}$.

Figure 1

Synchronous recycling interferometer (SRI).

Figure 2

Fabry-Perot Michelson interferometer (FPMI).

Figure 3

L-shaped cavity Michelson interferometer (LMI).

Figure 4

The optical amplification factor $\alpha (\Omega )$. Parameters are selected $L=0.75\mathrm{m}$, $R_F=0.99$, and $R_E=1$.

Figure 5

GW response function ${\mathcal{T}}_{\mathrm{rms}}(f)$. Vertical lines are plotted at multiples of 100 MHz.

Figure 6

Electric fields of SRI at the recycling mirror.

Figure 7

Electric fields of FPMI.

Figure 8

Electric fields of LMI.