A predistortion circuit for a laser sourced optical transmission system, for use with an input RF modulation signal carrying a plurality of subcarriers extending across a predetermined frequency band, comprising: an input port; a splitter having an input connected to the input port and having first, second and third outputs; a combiner having first, second and third inputs and an output; a first signal path connecting the first output of the splitter to the first input of the combiner; a second signal path connecting the second output of the splitter to the second input of the combiner, the second signal path providing precompensation for distortion in the laser source; and a third signal path connecting the third output of the splitter to the third input of the combiner, the third signal path including a second order distortion generator and a differentiator downstream of the second order distortion generator, characterized in that the differentiator has a magnitude response which differs by no more than 1dB, throughout the predetermined frequency band, from a target magnitude response which increases at a rate of 6dB/octave throughout the predetermined frequency band, wherein the differentiator has an insertion loss of no more than 4dB throughout the predetermined frequency band, and wherein the differentiator has a phase response which differs by no more than 4°, throughout the predetermined frequency band, from a target fixed phase shift of 90°, wherein the third signal path further includes a pre-processing filter upstream of the second order distortion generator, the pre-processing filter having a frequency response curve which peaks in magnitude at a particular frequency within the predetermined frequency band, and decreases in magnitude monotonically from the peak to both the high end and low end of the frequency band. an input port; a splitter having an input connected to the input port and having first, second and third outputs; a combiner having first, second and third inputs and an output; a first signal path connecting the first output of the splitter to the first input of the combiner; a second signal path connecting the second output of the splitter to the second input of the combiner, the second signal path providing precompensation for distortion in the laser source; and a third signal path connecting the third output of the splitter to the third input of the combiner, the third signal path including a second order distortion generator and a differentiator downstream of the second order distortion generator, characterized in that the differentiator has a magnitude response which differs by no more than 1dB, throughout the predetermined frequency band, from a target magnitude response which increases at a rate of 6dB/octave throughout the predetermined frequency band, wherein the differentiator has an insertion loss of no more than 4dB throughout the predetermined frequency band, and wherein the differentiator has a phase response which differs by no more than 4°, throughout the predetermined frequency band, from a target fixed phase shift of 90°, wherein the third signal path further includes a pre-processing filter upstream of the second order distortion generator, the pre-processing filter having a frequency response curve which peaks in magnitude at a particular frequency within the predetermined frequency band, and decreases in magnitude monotonically from the peak to both the high end and low end of the frequency band.