  We report an optical spectroscopy study on the single crystal of
Na$_2$Ti$_2$As$_2$O, a sister compound of superconductor BaTi$_2$Sb$_2$O. The
study reveals unexpectedly two density wave phase transitions. The first
transition at 320 K results in the formation of a large energy gap and removes
most part of the Fermi surfaces. But the compound remains metallic with
residual itinerant carriers. Below 42 K, another density wave phase transition
with smaller energy gap scale occurs and drives the compound into
semiconducting ground state. These experiments thus enable us to shed light on
the complex electronic structure in the titanium oxypnictides.
