Comparison of iterative Fourier transform and simulated annealing pulse-retrieval algorithms for frequency-resolved optical gating

Abstract

Frequency-resolved optical gating (FROG) is a general technique for simultaneously measuring the intensity I(t) and phase φ(t) of arbitrary ultrashort pulses. The basic method involves spectrally resolving the signal pulse of an autocorrelation-type experiment in an instantaneously responding nonlinear medium. The result is a plot of intensity over frequency and delay, commonly referred to as the FROG trace I_FROG(ω,τ), defined as
I_FROG(ω,τ) = | ∫ E(t) g(t − τ) e^−iωt dt |²,
where the gate g(t − τ) is dependent on the response of the nonlinear medium and the time-dependent amplitude E(t) = Re{I(t)^1/2e^iφ(t)}. Among the earliest implementations of the FROG were the polarization-gated (PG) and second-harmonic generation (SHG). In PG FROG, the gate is introduced by one ofthe pulses through the electronic Kerr effect and is a real quantity ofthe form | E(t − τ) |². In contrast, the SHG FROG utilizes two-wave mixing in crystals (e.g. KDP and BBO) and introduces a complex gate E(t − τ).
The FROG trace is touted to be, in itself, an informative and visually intuitive representation ofthe pulse. However, by recasting the problem as that of a two-dimensional phase retrieval, it can be shown that the full pulse field is uniquely determined by the FROG trace and a pulse-retrieval algorithm may be applied to retrieve I(t) and φ(t) .
In this study we concentrate on iterative-Fourier transform (ITF) and simulated annealing (SA) pulse-retrieval algorithms for PG and SHG FROG. Kane commented on the use of SA for FROG traces, but to the authors' knowledge, this is the first time that an SA phase retrieval-algorithm has been implemented. We compare the performance of the algorithms in terms of rms error in the FROG traces. Different FROG traces were calculated for chirped and self-phase modulated optical pulses.