We report an optical study of CaAlSi, a superconductor which displays both the crystal structure of MgB_2 and the electronic band structure of intercalated graphites. The reflectivity of a CaAlSi single crystal was measured down to subterahertz frequencies and to 3.3 K, with the use of coherent synchrotron radiation. A single superconducting gap in the hexagonal planes and two gaps along the c axis were found and measured consistently with the structure of the CaAlSi Fermi surface. The normal-state optical conductivity is also anisotropic: in the ab plane, the plasma frequency is larger by more than a factor of 2 than along the c axis. An analysis of the ab-plane spectral weight in comparison with the corresponding quantity in a cuprate such as La_(2-x)Sr_xCuO_4 shows that in CaAlSi the correlation effects are negligible.
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