Bolometric Interferometry is a technology currently under development that
will be first dedicated to the detection of B-mode polarization fluctuations in
the Cosmic Microwave Background. A bolometric interferometer will have to take
advantage of the wide spectral detection band of its bolometers in order to be
competitive with imaging experiments. A crucial concern is that interferometers
are presumed to be importantly affected by a spoiling effect known as bandwidth
smearing. In this paper, we investigate how the bandwidth modifies the work
principle of a bolometric interferometer and how it affects its sensitivity to
the CMB angular power spectra. We obtain analytical expressions for the
broadband visibilities measured by broadband heterodyne and bolometric
interferometers. We investigate how the visibilities must be reconstructed in a
broadband bolometric interferometer and show that this critically depends on
hardware properties of the modulation phase shifters. Using an angular power
spectrum estimator accounting for the bandwidth, we finally calculate the
sensitivity of a broadband bolometric interferometer. A numerical simulation
has been performed and confirms the analytical results. We conclude (i) that
broadband bolometric interferometers allow broadband visibilities to be
reconstructed whatever the kind of phase shifters used and (ii) that for
dedicated B-mode bolometric interferometers, the sensitivity loss due to
bandwidth smearing is quite acceptable, even for wideband instruments (a factor
2 loss for a typical 20% bandwidth experiment).Comment: 13 pages, 14 figures, submitted to A&