Determining the phase-energy coupling coefficient in carrier-envelope phase measurements

For f-to-2f interferometers based on white-light generation in sapphire plates, the accuracy of the carrier-envelope (CE) phase measurement and stabilization is affected by the laser energy fluctuation. The coupling coefficient between the CE phase and the laser energy has been determined by modulating the pulse energy in an in-loop f-to-2f interferometer while measuring the CE phase variation with an out-loop interferometer. When the total spectral phase measured by the in-loop interferometer was locked, a 1% change in laser energy caused a 160 mrad shift in the CE phase of the output pulses.