  We theoretically analyze a quasi-two-dimensional system of fermionic polar
molecules in a harmonic transverse confining potential. The renormalized energy
bands are calculated by solving the Hartree-Fock equation numerically for
various trap and dipolar interaction strengths. The inter-subband excitations
of the system are studied in the conserving time-dependent Hartree-Fock (TDHF)
approximation from the perspective of lattice modulation spectroscopy
experiments. We find that the excitation spectrum consists of both
inter-subband particle-hole excitation continuums and anti-bound excitons,
arising from the anisotropic nature of dipolar interactions. The excitonic
modes capture the majority of the spectral weight. We also evaluate the
inter-subband transition rates in order to investigate the nature of the
excitonic modes and find that they are anti-bound states formed from
particle-hole excitations arising from several subbands. Our results indicate
that the excitonic effects are present for interaction strengths and
temperatures accessible in current experiments with polar molecules.
