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.