  We consider the high-frequency Helmholtz equation with a given source term,
and a small absorption parameter $\a>0$. The high-frequency (or:
semi-classical) parameter is $\eps>0$. We let $\eps$ and $\a$ go to zero
simultaneously. We assume that the zero energy is non-trapping for the
underlying classical flow. We also assume that the classical trajectories
starting from the origin satisfy a transversality condition, a generic
assumption. Under these assumptions, we prove that the solution $u^\eps$
radiates in the outgoing direction, {\bf uniformly} in $\eps$. In particular,
the function $u^\eps$, when conveniently rescaled at the scale $\eps$ close to
the origin, is shown to converge towards the {\bf outgoing} solution of the
Helmholtz equation, with coefficients frozen at the origin. This provides a
uniform version (in $\eps$) of the limiting absorption principle. Writing the
resolvent of the Helmholtz equation as the integral in time of the associated
semi-classical Schr\"odinger propagator, our analysis relies on the following
tools: (i) For very large times, we prove and use a uniform version of the
Egorov Theorem to estimate the time integral; (ii) for moderate times, we prove
a uniform dispersive estimate that relies on a wave-packet approach, together
with the above mentioned transversality condition; (iii) for small times, we
prove that the semi-classical Schr\"odinger operator with variable coefficients
has the same dispersive properties as in the constant coefficients case,
uniformly in $\eps$.
