We present an optical spectroscopy study on Bi_(2)Se_(3),Bi_(2)Te_(3),Sn-doped Bi_(2)Te_(3) and Cu-intercalated Bi_(2)Se_(3) crystals grown by self-melting.We find that the plasma edge of Bi_(2)Se_(3) slightly shifts to lower energy with decreasing temperature.The Cu-intercalated Bi_(2)Se_(3) shows a superconducting transition near 3.1 K.Optical spectroscopy measurement shows that the plasma edge shifts substantially to higher frequency 1250 cm^(-1) indicating that Cu-doping supplies extra electrons to the system and further shifts the chemical potential up.Furthermore,our measurement reveals that the plasma edge of Bi_(2)Te_(3),Sn doped Bi_(2)Te_(3-δ)Sn_(δ)(δ=0.67%)and Cu-intercalated Bi_(2)Se_(3) shift slightly to higher energies with decreasing temperature.Combined with the band calculation,we attribute the blue-shift primarily to the reduction of effective mass of carriers with decreasing temperature.The optical data yield useful information about the bulk electronic band structure of the superconducting doped topological insulator Cu_(x)Bi_(2)Se_(3)(x=0.14).