Abstract：The origin of fast radio bursts (FRBs) is still unknown. Multi-wavelength observations during the FRB phase would be essential to identify the counterpart of an FRB and to constrain its radiation mechanism and environment. In this report, I will discuss the coherent curvature radiation by bunches as the radiation mechanism of FRBs. We find that the curvature radiation spectra of the bunches are characterized by a multisegment broken power law, with the break frequencies depending on bunch properties and trajectory configuration. Next, I will discuss the brightness of the ``fast optical bursts'' (FOBs) associated with FRBs and the prospects of detecting them. A joint observation between optical and radio telescopes would be essential to observe FOBs and further constrain the FRB environment.