A new technique for generating an error signal for locking a second-harmonic generation (SHG) enhancement cavity is presented. The calculations are developed within a linear system framework treated with a Laplace transform. The error-signal generation is based on FM sidebands, but it differs from the Pound–Drever–Hall technique by performing the modulation on the (assumed) electro-optic active nonlinear crystal in the cavity. This new technique for generating the error signal has some advantages over the former one in that (i) the shape of the error signal is independent of the relative phase of the rf signal between the photodiode and the local oscillator; (ii) it provides a handy, high-bandwidth actuator to improve the cavity lock, which can improve the average SHG power; and (iii) it decreases cost and complexity by not requiring an external electro-optical modulator. The specific case of SHG in is treated as an example of the feasibility of the technique.
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