Quantum Noise in a Fabry-Perot Interferometer Including the Influence of Diffraction Loss of Light

Shoki Iwaguchi,Taigen Morimoto,Tomotada Akutsu,Izumi Watanabe,Yuta Michimura,Rika Yamada,Koji Nagano,Masaki Ando,Seiji Kawamura,Mitsuru Musha,Tomohiro Ishikawa,Kentaro Komori,Takeo Naito

doi:10.3390/galaxies9010009

Abstract

The DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) is designed to detect gravitational waves at frequencies between 0.1 and 10 Hz. In this frequency band, one of the most important science targets is the detection of primordial gravitational waves. DECIGO plans to use a space interferometer with optical cavities to increase its sensitivity. For evaluating its sensitivity, diffraction of the laser light has to be adequately considered. There are two kinds of diffraction loss: leakage loss outside the mirror and higher-order mode loss. These effects are treated differently inside and outside of the Fabry-Perot (FP) cavity. We estimated them under the conditions that the FP cavity has a relatively high finesse and the higher-order modes do not resonate. As a result, we found that the effects can be represented as a reduction of the effective finesse of the cavity with regard to quantum noise. This result is useful for optimization of the design of DECIGO. This method is also applicable to any FP cavities with a relatively small beam cut and the finesse sufficiently higher than 1.

Highlights

The DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) is designed to detect gravitational waves at frequencies between 0.1 and 10 Hz
The coefficient of the diffraction loss is defined as Di, which is given by Equation (7)
The reflectivity and transmissivity influenced by the diffraction loss are defined as the effective reflectivity reff and the effective transmissivity teff for each mirror in the cavity. reff and teff are given by Equations (8)

Summary

Introduction

The DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) is designed to detect gravitational waves at frequencies between 0.1 and 10 Hz. The recent observation of the cosmic microwave background (CMB) by the Planck satellite and other electromagnetic observations reduced the upper limit for primordial gravitational waves significantly [2,3] This reduction of the upper limit requires further improvement of the target sensitivity of DECIGO [4]. We have been trying to improve the sensitivity by optimizing various parameters of DECIGO, such as the arm length, the laser power and the diameter, reflectivity, and mass of the mirrors For this optimization, we have to treat the diffraction loss of light in a Fabry-Perot (FP) cavity properly; we should treat the diffraction loss differently from other optical lossrelated quantities such as absorption and transmission.

Treatment of Diffraction Loss in a FP Cavity

Quantum Noise Including Diffraction Loss

Quantum Noise in DECIGO

Summary