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We investigate non-Hermitian skin modes in laser arrays with spatiallylocalized excitation. Intriguingly, we observe an unusual threshold behaviorwhen selectively pumping either the head or the tail of these modes: both casesexhibit the same lasing threshold and hence defy the conventional principle ofselective pumping, which aims to maximize the overlap between the pump profileand the target lasing mode. To shed light on this enigma, we reveal apreviously overlooked phenomenon, i.e., energy exchange at non-Hermitiancoupling junctions with the photonic environment, which does not occur withuniform gain or loss. Utilizing a transfer matrix approach, we elucidate themechanism of this anomalous threshold behavior, which is determined by thespecific physical realization of the non-Hermitian gauge field (i.e., usinggain, loss, or their mixture). Finally, we derive a generalized principle ofselective pumping in non-Hermitian arrays, which shows that the decisivespatial overlap is given by the tripartite product of the pump, the lasingmode, and its biorthogonal partner. Our study provides a glimpse into how thetwo forms of non-Hermiticity, i.e., asymmetric couplings and a complex onsitepotential, interact synergetically in laser arrays, which may stimulate furtherexplorations of their collective effects in photonics and related fields.

Non-Hermitian gauged laser arrays with localized excitations: Anomalous threshold and generalized principle of selective pumping