  In this work, we introduce the platform of plasmonic Doppler grating (PDG) to
experimentally investigate the enhancement effect of plasmonic gratings in the
input and output beams of nonlinear surface-enhanced coherent anti-Stokes Raman
scattering (SECARS). PDGs are designable azimuthally chirped gratings that
provide broadband and spatially dispersed plasmonic enhancement. Therefore,
they offer the opportunity to observe and compare the overall enhancement from
different combinations of enhancement in individual input and output beams. We
first confirm PDG's capability of spatially separating the input and output
enhancement in linear surface-enhanced fluorescence and Raman scattering. We
then investigate spatially resolved enhancement in nonlinear SECARS, where
coherent interaction of the pump, Stokes, and anti-Stokes beams is enhanced by
the plasmonic gratings. By mapping the SECARS signal and analyzing the
azimuthal angle-dependent intensity, we characterize the enhancement at
individual frequencies. Together with theoretical analysis, we show that while
simultaneous enhancement in the input and output beams is important for SECARS,
the enhancement in the pump and anti-Stokes beams plays a more critical role in
the overall enhancement than that in the Stokes beam. This work provides an
insight into the enhancement mechanism of plasmon-enhanced spectroscopy, which
is important for the design and optimization of plasmonic gratings. The PDG
platform may also be applied to study enhancement mechanisms in other nonlinear
light-matter interactions or the impact of plasmonic gratings on the
fluorescence lifetime.
