Gravitational lensing for interstellar power transmission

Abstract

We investigate the propagation of monochromatic electromagnetic waves through multiple, well-separated, monopole gravitational lenses in the thin-lens/eikonal approximation. For the axially aligned transmitter--lens(es)--receiver geometry, the relevant diffraction integrals can be evaluated analytically, yielding closed-form expressions for the point-spread function (PSF) and for the aperture-averaged gain. A single gravitational lens can enhance transmission when it is used either at the transmitting end or at the receiving end. For a two-lens link, the second lens focuses the signal into a much smaller diffraction pattern; however, for optical wavelengths and metre-scale receiving apertures this fine structure is aperture-averaged, and the averaged additional gain becomes independent of the second lens mass. We estimate photon rates and shot-noise-limited SNRs for these idealized configurations. The results indicate that gravitational lensing can in principle support high-SNR interstellar optical power links, subject to stringent alignment, finite-aperture, transmitter-beam, and coronal-background assumptions.

22 pages, 4 figures