With a new aspect in the physics of condensed matters, we have studied temperature dependences with anomalies of the transient photoconductivity in insulators or semiconductors La-Cu-O and Y-Cu-O etc., between 4.2 K and 300 K, especially on the systems close to high- Tc superconductors. Different from submergences in normal photoconductors with decreasing temperature, we observe several unexpected emergences of photoconductivity even for host oxide insulators below temperatures in correspondences with the critical temperatures Tsc of superconductors. The Cu2O-like part in insulators at photoexcitation exhibits behaviors similar to the doped Cu-O based superconductors in the dark, irrespective of variety of crystal symmetry, dimensionality, and huge difference in carrier concentration. Situations are similar for the Bi-O based superconductors. Thus, we speculate that Cu2O or Bi2O3 single crystals themselves at photoexcitation can be the basic substances equivalent to the Cu-O or Bi-O based oxide superconductors. Finally, we proposed that, by combining these photoconductors for the gate materials and relevant superconductors for the source and drain materials, both become effective simultaneously below Tsc, one can fabricate a novel device such as optically controllable FET-type transistors and accumulate them into high density. Therefore, we believe that our discovery of such phenomena reveals a possibility to open a new field in contemporary science and technology to be called `Superconductive Optoelectronics'.