  For direct imaging of exoplanets, a stellar coronagraph helps to remove the
image of an observed bright star by attenuating the diffraction effects caused
by the telescope aperture of diameter D. The Dual Zone Phase Mask (DZPM)
coronagraph constitutes a promising concept since it theoretically offers a
small inner working angle (IWA \sim \lambda_0/D), good achromaticity and high
starlight rejection, typically reaching a 1e6 contrast at 5 \lambda_0/D from
the star over a spectral bandwidth \Delta\lambda/\lambda_0 of 25% (similar to
H-band). This last value proves to be encouraging for broadband imaging of
young and warm Jupiter-like planets. Contrast levels higher than 1e6 are
however required for the observation of older and/or less massive companions
over a finite spectral bandwidth. An achromatization improvement of the DZPM
coronagraph is therefore mandatory to reach such performance. In its design,
the DZPM coronagraph uses a grey (or achromatic) apodization. We propose to
replace it by a colored apodization to increase the performance of this
coronagraphic system over a large spectral range. This innovative concept,
called Colored Apodizer Phase Mask (CAPM) coronagraph, is defined with some
design parameters optimized to reach the best contrast in the exoplanet search
area. Once this done, we study the performance of the CAPM coronagraph in the
presence of different errors to evaluate the sensitivity of our concept. A 2.5
mag contrast gain is estimated from the performance provided by the CAPM
coronagraph with respect to that of the DZPM coronagraph. A 2.2e-8 intensity
level at 5 \lambda_0/D separation is then theoretically achieved with the CAPM
coronagraph in the presence of a clear circular aperture and a 25% bandwidth.
In addition, our studies show that our concept is less sensitive to low than
high-order aberrations for a given value of rms wavefront errors.
