Multimode resonant gravitational-wave antennas: How many modes is enough?

A model for multimode gravitational-wave antennas is presented. A complete sensitivity analysis is carried out for a simplified, but realistic degenerate case. We discuss the optimum configuration, proving that it is set by the two requirements that the last oscillator be light enough to achieve a sufficiently large energy coupling factor β and the mass ratio μ satisfy a simple optimization condition. We show that the constraints imposed by current technology set an optimal number of modes. It is not advantageous to increase the degrees of freedom beyond this value, as this would add thermal noise to the total noise figure, without substantial gain in the efficiency of signal conversion