An optical resonant modulator includes an optical ring resonator and an optical loop that is coupled to the optical ring resonator by two couplers. The optical ring resonator can have a hybrid design in which the ring resonator is formed on an electro-optically passive material and the optical loop is formed on an electro-optically active material. An amplification section can be inserted between the electro-optically passive and the electro-optically active sections. In analog applications, an optical resonator includes a Mach Zehnder interferometer section having an input and an output, with a feedback path coupling the output to the input. Applications of the optical modulator of the invention, and a method for modulating an optical signal also are disclosed.