  Conventional microlasing of electromagnetic waves requires (1) a high $Q$
cavity and (2) a mechanism for directional emission. Previous theoretical and
experimental work demonstrated that the two requirements can be met with
deformed dielectric cavities that generate chaotic ray dynamics. Is it possible
for a massless Dirac spinor wave in graphene or its photonic counterpart to
exhibit a similar behavior? Intuitively, because of the absence of
backscattering of associated massless spin-1/2 particles and Klein tunneling,
confining the wave in a cavity for a long time seems not feasible. Deforming
the cavity to generate classical chaos would make confinement even more
difficult. Investigating the decay of a spin-1/2 wave from a scalar potential
barrier defined cavity characterized by an effective refractive index $n$ that
depends on the applied potential and the particle energy, we uncover the
striking existence of an interval of the refractive index in which the average
lifetime of the massless spin-1/2 wave in the cavity can be as high as that of
the electromagnetic wave, for both integrable and chaotic cavities. We also
find scaling laws for the ratio between the mean escape time associated with
electromagnetic waves and that with massless spin-1/2 particles versus the
index outside of this interval. The scaling laws hold regardless of the nature
of the classical dynamics. All the results are verified numerically. The
findings provide insights into the emergent field of Dirac electron optics and
have potential applications in developing unconventional electronics using 2D
Dirac materials.
