Frequency-resolved optical grating (FROG) is a technique for measuring the intensity and phase of ultrashort laser pulses. In FROG, a spectrogram of the pulse is produced from which the intensity and phase of the pulse's electric field is then retrieved using an iterative algorithm. This iterative algorithm performs well for all types of pulses, but it sometimes requires more than a minute to converge, and faster retrieval is desired for many applications. As a faster alternative, we therefore employed a neural network to invert the function that relates the pulse intensity and phase to its FROG trace. In previous work, we showed that a neural network can retrieve simple pulses, described by four or six parameters, rapidly and directly. In this contribution, we discuss our latest attempts to train an artificial neural network for more complex pulse shapes.
We present results of second harmonic generation (SHG) frequency-resolved optical gating (FROG) measurements on the mid-IR free-electron laser (FEL) at the Stanford Picosecond FEL Center. These are the first SHG FROG measurements performed in the mid-IR or on an FEL. The observed pulses have an optical wavelength near 5 micrometers , and the field profiles reconstructed from the FROG trace exhibit narrow-line absorption and free-induction decay caused by atmospheric water vapor. The SHG FROG signal is easier to isolate than for the polarization gate geometry; hence the SHG traces are not corrupted by a residual background. The experiment used only 10% of the full laser power, and the spectrum and autocorrelation were quickly calculated from the FROG trace, demonstrating the feasibility of using SHG FROG as a real-time diagnostic for the FEL facility.
We extend the Frequency-Resolved Optical Gating (FROG) technique to the measurement of the time-dependent intensity and phase of arbitrary ultraweak ultrashort pulses. We accomplish this by combining FROG with spectral interferometry. Spectral interferometry (SI) yields the phase difference between an unknown and a known pulse (the latter characterized with FROG). SI is a linear-optical method and hence is very sensitive. We demonstrate the combination of these two techniques by measuring the intensity and phase of a train of pulses 42 zeptojoules in energy (1/5 of a photon per pulse).
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.
Frequency-resolved optical gating (FROG) is a technique for measuring ultrashort laser pulses that involves producing a spectrogram of the pulse and then retrieving the intensity and phase of the electric field using a phase-retrieval algorithm. Since noise on experimental FROG traces reduces the performance of the retrieval algorithm, removing the noise is crucial. In previous work we have shown that subtracting the mean of the noise, optimized lowpass filtering, and suppression of the corners of the trace provides an efficient tool for denoising FROG traces. The recent development of wavelet noise-reduction techniques for signal and image processing now provides a new method for attacking this problem. We apply a two- dimensional discrete wavelet transform to the noisy FROG trace, threshold the wavelet coefficients, and perform the inverse wavelet transform to regain the trace. In combination with other noise-filtering methods, this efficiently removes noise from the trace and improves the algorithm's ability to retrieve the intensity and phase of the pulse accurately, especially in fairly low-noise situations, where extremely high accuracy is desired. In addition to wavelet- coefficient thresholding, we also investigate the possibility of using a geometrical scheme for filtering the wavelet coefficients, thus combining data compression and noise reduction.
Frequency-resolved optical gating (FROG) is a technique that allows the determination of the intensity and phase of ultrashort laser pulses. In FROG, a spectrogram of the pulse, the so- called FROG trace, is produced, from which the intensity and phase is then retrieved using an iterative algorithm. This algorithm performs well for all types of pulses, but it sometimes requires more than a minute to converge, and more rapid retrieval is important for many applications. It is therefore desirable to have a non-iterative computational method capable of inverting the function that relates the pulse intensity and phase to its FROG trace. In previous work, we showed that a neural network can retrieve simple pulses rapidly and directly. This original approach involved feature extraction by computing the lowest-order 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 (32 X 32 pixel) without any feature extraction as input for a neural net. In addition, FROG traces of 64 X 64 pixel size, typical for experimental data, can be used in conjunction with a more noise-insensitive feature extraction method.
The common computations of wave phenomena, in particular, of diffraction suffer from several drawbacks which are in- herent to the approximations applied. These are circumvented when replacing Kirchhoff s formula by the Chapman-Kolmo- gorov equation. The discrete analogue of this new representation of Huygens' principle is a physically based, one-step, ex- plicit algorithm which may be realized as a electrical network, a correlated random walk, or a cellular automaton.
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