Estimate of diffraction from Gaussian Beam in Li-Baker HFGW detector

Recent experimentation and speculation about the design of a sensitive detector for high-frequency gravitational waves (HFGW) has centered around a number of principles. Those detectors that have been built so far have not yet realized sensitivity sufficient to investigate the cosmic high-frequency relic gravitational wave background, analogous to the cosmic microwave background. A proposal for a more sensitive HFGW detector due to Baker and based upon a principle first enunciated by Li and co-workers has become known as the Li-Baker detector. Its possible design details are currently the subject of scientific debate. One significant aspect concerns the diffraction of microwave power from the intrinsic transmitter producing a microwave beam. This beam is required for interaction with the gravitational waves to be detected and diffraction will not be distinguishable from photons produced by interaction with the HFGW. This means that diffraction is potentially a source of shot noise at the microwave receivers and, if extreme, may also swamp the receivers. In this paper some estimates of this diffraction are obtained. These estimates show that the Li-Baker detector must be designed in such a way that the diffraction reaching the microwave receivers is reduced as far as possible by employing a suitable geometry and highly absorbent walls for the interaction volume.