1. An all-optical NOT gate comprising: first and second optical input media configured to receive respective first and second optical input signals, the first optical input signal having constant continuous wave (CW) light, and the second optical input signal having amplitude-modulated data with a binary logic level; a combining medium optically coupled to the first and second optical input media, the combining medium configured to receive and combine the first and second optical input signals to produce a combined signal; and a nonlinear element configured to receive the combined signal, the nonlinear element comprising an optical resonator having a resonant frequency tuned relative to the frequency of at least one of the first and second optical input signals so that the nonlinear element is configured to discriminate the combined signal to output the CW light as an optical output signal with a high logic level if the second optical input signal has a low logic level, and the nonlinear element configured to discriminate the combined signal to output substantially no light as the optical output signal with a low logic level if the second optical input signal has a high logic level, the nonlinear element configured to generate the optical output signal to have a binary logic level that is amplitude-modulated with the amplitude of the high logic level determined substantially by the amplitude of the CW light, whereby the nonlinear element is configured to perform a NOT logic operation on the binary logic level of the second optical input signal to generate the optical output signal; and an optical output medium optically coupled to receive and output the optical output signal from the nonlinear element, the first and second optical input media, combining medium, nonlinear element and optical output medium formed at least in part in a photonic crystal, the first and second optical input media, the combining medium, and the optical output medium defined at least in part by the absence of structures in the photonic crystal, and the nonlinear element optically positioned between an output side of the combining medium and an input side of the optical output medium.