Analytical study of the optical spectrum shift in a modulating channel

In this work, an analytical model of the frequency shift experienced by an optical signal passing through a traveling wave modulating channel is derived. The model starts from the well-known coupled-mode theory but holds for an arbitrary temporal envelope of the optical signal and for any time dependence of the slowly varying modulating field; it provides an analytical and accurate explanation of various effects such as those due to losses or microwave-optical group velocity mismatch. The practical example of a modulated optical Gaussian pulse is provided.