Is there a quad problem among optical gravitational lenses?

Most of optical gravitational lenses recently discovered in the Sloan Digital Sky Survey Quasar Lens Search (SQLS) have two-images rather than fourimages, in marked contrast to radio lenses for which the fraction of four-image lenses (quad fraction) is quite high. We revisit the quad fraction among optical lenses by taking the selection function of the SQLS into account. We find that the current observed quad fraction in the SQLS is indeed lower than, but consistent with, the prediction of our theoretical model. The low quad fraction among optical lenses, together with the high quad fraction among radio lenses, implies that the quasar optical luminosity function has a relatively shallow faint end slope. May 2007 SLAC-PUB-12535 Submitted to New Journal of Physics Is there a quad problem among optical gravitational lenses? 2