By combining detailed imaging measurements at different tilt angles with simulations of ray emission from prolate-deformed lasing microdroplets, we conclude that the dominant contribution to the laser emission of such three-dimensional dielectric microcavities must come from modes associated with the chaotic region of the ray phase space. As a particularly striking signature, 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 nontangent and displaced from the highest curvature regions owing to the presence of stable orbits. In this paper we present the first experimental evidence for this phenomenon of dynamical eclipsing.
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