  Typical nanoparticle-based plasmonic index sensors detect the spectral shift
of localized surface plasmon resonance (LSPR) upon the change of environmental
index. Therefore, they require broadband illumination and spectrometers. The
sensitivity and flexibility of nanoparticle-based index sensors are usually
limited because LSPR peaks are usually broad and the spectral position cannot
be freely designed. Here, we present a fully designable index sensing platform
using a plasmonic Doppler grating (PDG), which provides broadband and azimuthal
angle-dependent grating periodicities. Different from LSPR, the PDG index
sensor is based on the momentum matching between photons and surface plasmons
via the lattice momentum of the grating. Therefore, index change is translated
into the variation of in-plane azimuthal angle for photon-to-plasmon coupling,
which manifests as directly observable dark bands in the reflection image. The
PDG can be freely designed to optimally match the range of index variation for
specific applications. In this work, we demonstrate PDG index sensors for large
(n = 1.00 to 1.52) and small index variation (n = 1.3330 to 1.3650). The tiny
and nonlinear index change of water-ethanol mixture has been clearly observed
and accurately quantified. Since the PDG is a dispersive device, it enables
on-site and single-color index sensing without a spectrometer and provides a
promising spectroscopic platform for on-chip analytical applications.
