The second aspect of the present invention concerns a waveguide having a core for light transmission therethrough, wherein the core is made of a polyimide copolymer including at least two units represented by the formulae [II] and [III] as follows: ##STR3## wherein each of R1 and R2 is a tetravalent organic group selected from the group consisting of ##STR4## with the proviso that R1 and R2 are di