  We have carried out a spectroscopic study on a prototype ferroelectric
nematic material (RM7343) doped with a non-polar chiral compound. The mixture
presents two chiral nematic phases, one conventional (N*) and the other polar
(NF*), whose behaviours under electric fields E are totally different. On the
one hand, the N* phase shows a single reflection band if E is not very high,
while fields perpendicular to the helix of a few V/mm are already sufficient to
produce multiple bands in the NF* phase. On the other hand, the pitch of the
NF* phase grows notably on increasing fields, however remaining practically
constant in the N* phase. Both effects have been explained in terms of the
different type of interaction with E in each phase (ferroelectric in NF* and
dielectric in N*). We argue that the NF* phase behaves as a photonic material
with multiple gaps tunable by small fields, which presents important
potentialities for applications. A study of the bandgaps has been carried out
through the analysis of the dispersion relation of the optical eigenmodes in
the NF* phase under field. Finally, an example of the potentialities of the NF*
phase within the field of nonlinear optics is briefly presented.
