  Future instruments need efficient coronagraphs over large spectral ranges to
enable broadband imaging or spectral characterization of exoplanets 1e8 fainter
than their star. Several solutions were proposed. Pupil apodizers can attenuate
the star intensity by a 1e10 factor but they transmit a few percents of the
planet light only. Cascades of phase/amplitude masks can both attenuate the
starlight and transmit most of the planet light but the number of optics to
align is not a practical solution for an instrument. Finally, vector phase
masks can be used to detect faint sources close to bright stars but they
require the use of high quality circular polarizers and as for the previous
solution, this leads to a complex instrument with numerous optics to align and
stabilize. We propose simple coronagraphs that need one scalar phase mask and
one binary Lyot stop only providing high transmission for the planet light
(>50%) and high attenuation of the starlight over a large spectral bandpass
(~30%) and a 360 degree field-of-view. From mathematical considerations, we
find a family of 2D-phase masks optimized for an unobscured pupil. One mask is
an azimuthal wrapped vortex phase ramp. We probe its coronagraphic performance
using numerical simulations and laboratory tests. From numerical simulations,
we predict the wrapped vortex can attenuate the peak of the star image by a
factor of 1e4 over a 29% bandpass and 1e5 over a 18% bandpass with transmission
of more than 50% of the planet flux at ~4 lambda/D. We confirm these
predictions in laboratory in visible light between 550nm and 870nm. We also
obtain laboratory dark hole images in which exoplanets with fluxes that are
3e-8 times the host star flux could be detected at 3sigma. Taking advantage of
a new technology for etching continuous 2D-functions, new type of masks can be
easily manufactured opening new possibilities for broadband coronagraphy.
