Pseudo-arbitrary sideband generation by phase modulation calculated with iterative phase retrieval

A method for arbitrarily tailoring amplitude and phase of sidebands generated with a phase shifting electro-optic modulator (EOM) is presented. The technique is extremely simple experimentally, requiring only a single EOM driven by an arbitrary waveform generator. The required time domain phase modulation is calculated using an iterative phase retrieval algorithm, which takes into account the desired spectrum (both amplitude and phase), and other physical constraints. The algorithm works consistently and finds solutions which accurately recreate the desired spectrum. Since EOMs only modulate phase, the solutions will usually match the desired spectrum over the specified range by redistributing optical power to regions of the spectrum that are unspecified. This basic Fourier limitation is the only in-principle limit to the arbitrariness of the spectrum tailoring. An experimental demonstration of the technique is performed, which shows complex spectra can be generated with high accuracy.