Dispersion-corrected frequency-resolved optical gating

100% reliable algorithm for second-harmonic-generation frequency-resolved optical gating

We demonstrate a novel algorithmic approach for the second-harmonic-generation (SHG) frequency-resolved optical gating (FROG) ultrashort-pulse-measurement technique that always converges and, for complex pulses, is also much faster. It takes advantage of the Paley-Wiener Theorem to retrieve the precise pulse spectrum-half the desired information-directly from the measured trace. It also uses a multi-grid approach, permitting the algorithm to operate on smaller arrays for early iterations and on the complete array for only the final few iterations. We tested this approach on more than 25,000 randomly generated complex pulses with time-bandwidth products up to 100, yielding SHG FROG traces to which noise was added, and have achieved convergence to the correct pulse in all cases. Moreover, convergence occurs in less than half the time for extremely large traces corresponding to extremely complex pulses.

High-speed "multi-grid" pulse-retrieval algorithm for frequency-resolved optical gating

We use an algorithmic technique called "multi-grid" to improve the speed of convergence of the cross-correlation frequency-resolved-optical-gating (XFROG) pulse-retrieval algorithm for very complex pulses. The multi-grid approach uses a smaller trace (N/4 × N/4) drawn from the original N × N trace for initial iterations, yielding poorer resolution and range, but proceeding ~16 times faster for such iterations. The pulse field rapidly retrieved from this smaller array then provides the initial guess for the larger, full array, significantly reducing the number of iterations required on the full array. We first find that, for simple pulses and their resulting simple traces, the original generalized-projections FROG and XFROG algorithms already converge in less time than is required to plot the retrieved pulse, so speed improvements for them appear irrelevant in general. Considering therefore only complex pulses and their resulting complex traces, we adapted the multi-grid algorithm to XFROG, the technique used for complex pulses whenever possible. We show that extending multi-grid to even smaller arrays is not helpful, but intermediate-size arrays of N/2 × N/2 are, further reducing the number of iterations on the full array and further decreasing convergence time. We obtain a factor of ~7 improvement in speed for very complex pulses with time-bandwidth products of 50 to 90. This approach does not require modifications to the algorithm itself and so can be used in conjunction with essentially all FROG algorithms for improved speed. And it retains FROG's ability to determine the pulse-shape stability in multi-shot measurements.

Pulse retrieval algorithm for interferometric frequency-resolved optical gating based on differential evolution

A novel algorithm for the ultrashort laser pulse characterization method of interferometric frequency-resolved optical gating (iFROG) is presented. Based on a genetic method, namely, differential evolution, the algorithm can exploit all available information of an iFROG measurement to retrieve the complex electric field of a pulse. The retrieval is subjected to a series of numerical tests to prove the robustness of the algorithm against experimental artifacts and noise. These tests show that the integrated error-correction mechanisms of the iFROG method can be successfully used to remove the effect from timing errors and spectrally varying efficiency in the detection. Moreover, the accuracy and noise resilience of the new algorithm are shown to outperform retrieval based on the generalized projections algorithm, which is widely used as the standard method in FROG retrieval. The differential evolution algorithm is further validated with experimental data, measured with unamplified three-cycle pulses from a mode-locked Ti:sapphire laser. Additionally introducing group delay dispersion in the beam path, the retrieval results show excellent agreement with independent measurements with a commercial pulse measurement device based on spectral phase interferometry for direct electric-field retrieval. Further experimental tests with strongly attenuated pulses indicate resilience of differential-evolution-based retrieval against massive measurement noise.