  Diffraction gratings are famous for their ability to exhibit, near a Wood
anomaly, an arbitrarily large angular dispersion, e.g., with respect to the
incidence angle or wavelength. For a diffraction grating under incidence by a
plane wave at a fixed frequency, by rotating the incidence angle at a given
angular velocity, the field propagated by a nonzero diffraction order will
rotate at increasingly fast angular velocity as the incidence angle approaches
the angle where Wood anomaly occurs. Such a fast rotating diffracted field has
the potential to generate a substantial Doppler shift. Indeed, under the
assumption of a grating with infinite extent, the expression for the
instantaneous frequency shift perceived by an observer, who is looking into the
light radiated by the diffraction order, is derived and it is in full agreement
with the prediction from an interpretation based on the Doppler shift generated
by a rotation of light sources. In particular the classical (non-relativistic)
Doppler shift can take arbitrarily high values as the incidence angle
approaches a Wood anomaly. It is also found that gratings of a finite size can
have a similar property. In order to have a physically detectable frequency
shift, it is important to use a grating which can maintain a significant
reflectance into higher diffraction orders near their Wood anomaly cut-off.
Interestingly, we have found that the geometry of the nanostructures of a
\emph{Morpho} butterfly wing scale is aptly suited for such a function because
it can strongly reflect into higher diffraction orders while minimising the
reflection into the specular order.
