We measured the polarized optical conductivity of URu$_2$Si$_2$ from room temperature down to 5 K, covering the Kondo state, the coherent Kondo liquid regime, and the hidden-order phase. The normal state is characterized by an anisotropic behavior between the ab plane and c axis responses. The ab plane optical conductivity is strongly influenced by the formation of the coherent Kondo liquid: a sharp Drude peak develops and a hybridization gap at 12 meV leads to a spectral weight transfer to mid-infrared energies. The c axis conductivity has a different behavior: the Drude peak already exists at 300 K and no particular anomaly or gap signature appears in the coherent Kondo liquid regime. When entering the hidden-order state, both polarizations see a dramatic decrease in the Drude spectral weight and scattering rate, compatible with a loss of about 50 % of the carriers at the Fermi level. At the same time a density-wave like gap appears along both polarizations at about 6.5 meV at 5 K. This gap closes respecting a mean field thermal evolution in the ab plane. Along the c axis it remains roughly constant and it fills up rather than closing.
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