High-Frequency Gravitational Wave Optics

R. Clive Woods
Department of Electrical and Computer Engineering and Microelectronics Research Center, Iowa State University

Abstract: It is generally assumed that in free space the velocity of a high-frequency gravitational wave (HFGW) is the same as that of light and so the free space wavelength of an HFGW at 3GHz will be ~10cm. Li and Torr have previously published calculations claiming to show that gravitational waves propagate inside a superconductor with phase velocity reduced by ~300× and wavenumber increased by ~300×. Inside a superconductor, the corresponding HFGW wavelength at 3GHz will therefore be ~300µm. The present paper discusses the technical consequences of this surprising result. Harris and Kowitt independently claimed that the Li and Torr result is not credible, and their refutations are reviewed; their objections appear not to be tenable. It is shown here for the first time that this result has major consequences for the design of instruments to generate and detect gravitational waves, in particular HFGWs having wavelengths on the same order as the dimensions of typical superconductive components. In particular, such a large mismatch in HFGW propagation impedance inevitably results in large Fresnel reflections from superconductor-air interfaces. This will cause a number of design problems in equipment proposed for HFGW generation and detection. For example, the superconductor thickness used in HFGW detectors will be critical. However, for practical designs of HFGW lenses using superconductors, a material is suggested here that is suitable for use as an “optical blooming” coating. It is shown that it may also be possible to use unique optical designs and geometries to obtain HFGW resonators and focusing reflectors.