  Femtolensing is a gravitational lensing effect in which the magnification is
a function not only of the positions and sizes of the source and lens, but also
of the wavelength of light. Femtolensing is the only known effect of
$(10^{-13}-10^{-16} M_{\sun})$ dark-matter objects and may possibly be
detectable in cosmological gamma-ray burst spectra. We present a new and
efficient algorithm for femtolensing calculations in general potentials. The
physical-optics results presented here differ at low frequencies from the
semi-classical approximation, in which the flux is attributed to a finite
number of mutually coherent images. At higher frequencies, our results agree
well with the semi-classical predictions. Applying our method to a point-mass
lens with external shear, we find complex events that have structure at both
large and small spectral resolution. In this way, we show that femtolensing may
be observable for lenses up to $10^{-11}$ solar masses, much larger than
previously believed. Additionally, we discuss the possibility of a search for
femtolensing of white dwarfs in the LMC at optical wavelengths.
