Stellar coronagraphs help to remove the image of an observed bright star by attenuating the diffraction effects caused by a telescope aperture. We pursue our efforts on circular phase mask coronagraphs since these promising concepts provide small inner working angle, high starlight rejection ability, clear 360° discovery space in the coronagraphic images and good suitability to aperture geometry. These properties led us to propose in 2009 the Roddier & Roddier phase mask coronagraph as a possible upgrade for GTC-FRIDA to increase the instrument capabilities to image faint substellar mass companions. To allow broadband imaging of these companions, the dual zone phase mask (DZPM) coronagraph (Soummer et al. 2003) has been proposed, theoretically reaching a $10^6$ contrast at $\5lambda/D$ over a spectral bandwidth $\Delta\lambda/\lambda$ of 25% (similar to H-band).

We now investigate achromatization improvement of the circular phase mask coronagraphs to enlarge the capabilities of these concepts to work in broad spectral bands. 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. Our concept, called Colored Apodizer Phase Mask (CAPM) coronagraph, allows us to obtain a contrast gain of 2.5 mag with respect to DZPM coronagraph performance and reach a $2.2 10^{-8}$ intensity level at $5\lambda/D$ over a 25% bandwidth. We also analyse different effects that can alter the performance of our concept, such as aberrations, mask imperfections and Lyot stop misalignment. This innovating CAPM coronagraph could find its place in a possible GTC exoplanet imager to follow VLT-SPHERE and Gemini-Planet Imager.