Reconstructing Ultrashort Pulses: Frequency Resolved Optical Gating and Phase Space Functions

In the following paper, I compare and contrast methods of measuring the amplitude and phase of a short optical pulse over time with techniques that attempt a similar measurement of a optical field over space. Both approaches benefit from considering the energy of an optical wave in a phase space representation, whether in a joint time-frequency representation for short pulses or a space-spatial frequency representation for beam characterization. I will first present a summary of the common pulse characterization method termed frequency-resolved optical gating (FROG), examining it’s reconstruction algorithm in the context of similar algorithms used in the spatial domain. I will then connect the output of a FROG measurement, a spectrogram, with a common output of spatial measurement setups, the Wigner distribution. Specifically, I will show that a FROG’s spectrogram is equivalent to the convolution of the Wigner distribution of the pulse with the Wigner distribution of the pulse’s gate. Finally, I will apply the insights gained between temporal and spatial phase measurements to modify FROG’s reconstruction algorithm, allowing for noise reduction as well as the possibility of integrating prior knowledge into the spectrogram’s decomposition each iteration.