  By combining detailed imaging measurements at different tilt angles with
simulations of ray emission from prolate deformed lasing micro-droplets, we
conclude that the probability density for the lasing modes in a
three-dimensional dielectric microcavity must reside in the chaotic region of
the ray phase space. In particular, maximum emission from such chaotic lasing
modes is not from tangent rays emerging from the highest curvature part of the
rim. The laser emission is observed and calculated to be non-tangent and
displaced from the highest curvature due to the presence of stable orbits. In
this Letter we present the first experimental evidence for this phenomenon of
``dynamical eclipsing''.
