<title>Direct ultrashort-pulse retrieval in frequency-resolved optical gating using wavelets and a neural network</title>

Abstract

Frequency-resolved optical gating (FROG) is a method for measuring the intensity and phase of an ultrashort laser pulse. The technique involves producing a `FROG trace,' which is a type of spectrogram of the pulse, and an iterative phase-retrieval algorithm that determines the intensity and phase of the laser pulse. Although the iterative FROG algorithm performs well, it requires a minute or more to converge for complex pulse shapes. For many applications more rapid retrieval is important, and it is therefore desirable to have a direct, i.e., non- iterative, computational method capable of inverting the highly non-linear and complex function that relates the pulse intensity and phase to its experimental FROG trace. In previous work we showed that a neural network can retrieve simple pulses rapidly and directly. Unfortunately, this approach involved feature extraction by computing the integral moments of the FROG trace, making it particularly sensitive to the presence of additive noise. Using parallel-processing hardware, we are now able to use FROG traces of limited size without any feature extraction as input for a neural net. This gives us the opportunity to compare the network performance using raw data with other representations of the FROG traces. Particularly interesting seemed a representation of the traces in terms of their wavelet coefficients, because the wavelet transform is known for its noise-insensitivity and the compression of most information about a given signal in only a small number of wavelet coefficients, making it therefore appealing for feature extraction in signal processing applications. We found, however, that a representation of the FROG trace in terms of its Lemarie-wavelet coefficients did not yield convergence despite many attempts, and hence is not suitable as an input signal for simple neural networks. Fortunately,--and surprisingly--use of no feature extraction appears quite promising.