  We study the increasing stability of an inverse source problem for the
Helmholtz equation from limited-aperture far field data at multiple wave
numbers. The measurement data are givenby the far field patterns
$u^\infity(\hat{x},k)$ for all observation directions in some neighborhood of a
fixed direction $\hat{x}$ and for all wave numbers k belonging to a finite
interval $(0,K)$. In this paper, we discuss the increasing stability with
respect to the width of the wavenumber interval $K>1$. In three dimensions we
establish stability estimates of the $L^2$-norm and $H^{-1}$-norm of the source
function from the far field data. The ill-posedness of the inverse source
problem turns out to be of H\"older type while increasing the wavenumber band
K. We also discuss an analytic continuation argument of the far-field data with
respect to the wavenumbers at a fixed direction.
