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A perturbation theory has been developed to calculate the transfer of electric field amplitude and phase ripples from the first harmonic to either the second harmonic or the third harmonic. The theory is restricted to steady-state conversion processes. In the case of small phase gradients, the real and imaginary parts of the output harmonic ripple are related to the real and imaginary parts of the input perturbation by a 2 multiplied by 2 matrix. To confirm the validity of the perturbation theory, we have performed an initial set of experiments on the Optical Sciences Laser to investigate the transfer of a weak ripple from the first harmonic to the second harmonic.

<title>Perturbation theory for frequency doubling and tripling of electric field amplitude and phase ripples</title>