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Response from the displacement ( $x$ ) of the cavity to the relative intensity ( $RIN$ ):

$RIN(x) = \frac{1}{1 + \left(\frac{x}{HWHM}\right)^2} \simeq 1 -\left(\frac{x}{HWHM}\right)^2$

Fluctuation in a certain frequency:

$RIN(A\cos\omega t) \simeq 1 -\left(\frac{A\cos\omega t}{HWHM}\right)^2 = 1 - \frac{1}{2}\left(\frac{A}{HWHM} \right)^2 - \frac{1}{2}\left(\frac{A}{HWHM} \right)^2 \cos2\omega t$

Amplitude of response at the second harmonics of the original frequency:

$RIN \,at \,2\omega = - \frac{1}{2}\left(\frac{A}{HWHM} \right)^2 = -2\left(\frac{A}{FWHM} \right)^2$