Direct Ultrashort-Pulse Retrieval Using Frequency-Resolved Optical Gating and a Computational Neural Network

Frequency-Resolved Optical Gating (FROG) is a method for measuring the time-dependent intensity and phase of an ultrashort laser pulse. In FROG a nonlinear autocorrelation signal is frequency-resolved by a spectrometer to produce a "FROG trace", which is a type of spectrogram of the pulse [1]. The FROG trace, a two-dimensional image (intensity vs. frequency and delay) is then input into a phase-retrieval-based iterative algorithm [2], that determines the intensity and phase of the laser pulse. Although the FROG algorithm performs well, it requires a minute or more to converge for complex pulse shapes. It is therefore desirable in many situations to have a direct (i.e., non-iterative) computational method capable of quickly inverting the highly non-linear and complex function that relates the ultrashort pulse intensity and phase to its experimental FROG trace. In this work, we show that computational neural networks can directly obtain the intensity and phase of a pulse from its FROG trace in less than one second, independent of the pulse shape. Our demonstration using a serial personal computer is a proof of this principle, utilizing a set of pulses defined by only five parameters. Because neural networks now take advantage of very simple, fast, and powerful parallel-processing hardware, however, future waveform recovery, even in the general case of arbitrary pulses, could be nearly instantaneous.