  We investigate non-Hermitian skin modes in laser arrays with spatially
localized excitation. Intriguingly, we observe an unusual threshold behavior
when selectively pumping either the head or the tail of these modes: both cases
exhibit the same lasing threshold and hence defy the conventional principle of
selective pumping, which aims to maximize the overlap between the pump profile
and the target lasing mode. To shed light on this enigma, we reveal a
previously overlooked phenomenon, i.e., energy exchange at non-Hermitian
coupling junctions with the photonic environment, which does not occur with
uniform gain or loss. Utilizing a transfer matrix approach, we elucidate the
mechanism of this anomalous threshold behavior, which is determined by the
specific physical realization of the non-Hermitian gauge field (i.e., using
gain, loss, or their mixture). Finally, we derive a generalized principle of
selective pumping in non-Hermitian arrays, which shows that the decisive
spatial overlap is given by the tripartite product of the pump, the lasing
mode, and its biorthogonal partner. Our study provides a glimpse into how the
two forms of non-Hermiticity, i.e., asymmetric couplings and a complex onsite
potential, interact synergetically in laser arrays, which may stimulate further
explorations of their collective effects in photonics and related fields.
