Modified Design of Novel Variable-Focus Lens for VHFGW

The present author previously published a paper at STAIF 2006 detailing the design of a novel variable- focus lens for use with very-high frequency gravitational waves (VHFGW, typically around 3GHz). Such a lens would be invaluable in the design of advanced GW optics for communications applications since focusing would be achievable electrically with no moving parts. The design was based upon the published calculations of Li and Torr (in 1992 and 1993) claiming to show that GWs propagate inside superconductors with a phase velocity reduction by a factor n ~ 300× and a corresponding wavenumber increase. Successful demonstration of this lens would also confirm the controversial Li and Torr result. Type II superconductors do not completely expel large magnetic fields, but instead allow vortices of magnetic flux to channel the magnetic field through the material. Within these vortices, the superconductor is magnetically quenched and so has properties similar or identical to those of non-superconductors. Varying the applied magnetic field varies the proportion of material quenched and superconducting. For GW wavelengths significantly larger than the typical vortex separation, the GW propagation through a type II superconductor is therefore dependent upon the applied magnetic field. Since a conventional optical lens may be regarded as a position-dependent phase shifter, and the VHFGW phase-shift depends upon the applied magnetic field, the design of a VHFGW lens therefore reduces to producing a suitable applied magnetic field variation that gives a technologically-useful spatial variation of phase shift. In this paper, a modified method of producing the required magnetic field is introduced, as well as a more detailed discussion of the VHFGW propagation through the superconducting material with an applied field.