  One recent breakthrough in the field of magnonics is the experimental
realization of reconfigurable spin-wave nanochannels formed by magnetic domain
wall with a width of $10-100$ nm [Wagner \emph{et al}., Nat. Nano. \textbf{11},
432 (2016)]. This remarkable progress enables an energy-efficient spin-wave
propagation with a well-defined wave vector along its propagating path inside
the wall. In the mentioned experiment, a micro-focus Brillouin light scattering
spectroscopy was taken in a line-scans manner to measure the frequency of the
bounded spin wave. Due to their localization nature, the confined spin waves
can hardly be detected from outside the wall channel, which guarantees the
information security to some extent. In this work, we theoretically propose a
scheme to detect/eavesdrop on the spin waves inside the domain-wall nanochannel
via nonlinear three-magnon processes. We send a spin wave in one magnetic
domain to interact with the bounded mode in the wall. Two kinds of three-magnon
processes, i.e., confluence and splitting, are expected to occur. The
confluence process is conventional. We predict a stimulated three-magnon
splitting (or "magnon laser") effect: the presence of a bound magnon
propagating along the domain wall channel assists the splitting of the incident
wave into two modes, one of which is identical to the bound mode in the
channel. Micromagnetic simulations confirm our theoretical analysis. These
results demonstrate that one is able to uniquely infer the spectrum of the
spin-wave in the domain-wall nanochannel once we know both the injection and
the transmitted waves.
