  Raman scattering excitation (RSE) is an experimental technique in which the
spectrum is made up by sweeping the excitation energy when the detection energy
is fixed. We study the low-temperature ($T$=5~K) RSE spectra measured on four
high quality monolayers (ML) of semiconducting transition metal dichalcogenides
(S-TMDs), $i.e.$ MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$, encapsulated in
hexagonal BN. The outgoing resonant conditions of Raman scattering reveal an
extraordinary intensity enhancement of the phonon modes, which results in
extremely rich RSE spectra. The obtained spectra are composed not only of
Raman-active peaks, $i.e.$ in-plane E$'$ and out-of-plane A$'_1$, but the
appearance of 1$^{st}$, 2$^{nd}$, and higher-order phonon modes is recognised.
The intensity profiles of the A$'_1$ modes in the investigated MLs resemble the
emissions due to neutral excitons measured in the corresponding PL spectra for
the outgoing type of resonant Raman scattering conditions. Furthermore, for the
WSe$_2$ ML, the A$'_1$ mode was observed when the incoming light was in
resonance with the neutral exciton line. The strength of the exciton-phonon
coupling (EPC) in S-TMD MLs strongly depends on the type of their ground
excitonic state, $i.e.$ bright or dark, resulting in different shapes of the
RSE spectra. Our results demonstrate that RSE spectroscopy is a powerful
technique for studying EPC in S-TMD MLs.
