Triple optical autocorrelation of femtosecond optical pulses was realized simply with third-harmonic-generation technique. This optical technique provides complete knowledge of transient pulse intensity variation directly in time domain. Only analytic calculation is needed to obtain the pulse-shape from data without direction-of-time ambiguity. Combined with a spectral measurement and the Gerchberg-Saxton algorithm, except for pulses with complete temporal and spectral symmetry that will cause a twofold ambiguity, exact phase variation in time can also be retrieved through an iterative calculation with an O(n) complexity.

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Because electronic devices (streak camera etc.) are too slow to measure temporal evolution of ultrashort optical pulses, many techniques were developed to retrieve temporal pulse shape. Most of them extract the temporal intensity either by assuming an analytic pulse shape (autocorrelation) or with the help of spectral measurements (including FROG' and SPIDER.') AU of these techniques rely on either interference or various nonlinear effect including second harmonic generation and optical Kerr effect. However, in the later 1960 it was shown that a triple correlation is sufficient to determine the temporal intensity of a laser pulse3 with a direct mathematical calculation. In this report, we demonstrate direct temporal intensity measurement of ultrashort optical pulses using a novel third-harmonic-generation (THG) based triple correlation method. Using THG process in a single GaN thin film, the optical pulse intensity profile from a modelocked Cr:forsterite laser was directly obtained with the background free triple correlation trace without any spectral information and pulseshape assumption. This is different from the previous demonstration4 where triple correlation was obtained through a complex combination of second-harmonic generation and sum-frequency-generation. In order to retrieve the corresponding phase information, a simple genetic algorithm was also developed for the first time based on the direct optical spectrum measurement with improved O(n) complexity than O(nZ) in. ' An optical pulse with intensity I(t) can be expanded in frequency domain v as as shown in Fig. 1. By varying the time delay between pulses t , and t2 and recording the selected THG signals with a detector, the backgroundfree triple correlation I ( t ) = 1 I(v)exp(-i2xvt)dv = Ij(v)lexp(ia(v) -i2xvt)dv(1) G3 (q,tZ) = I I(t)Z(t+ q ) l ( t + t,)dt ( 2 )was directly measured. Then we can use bispec- trum G 3 (vI,vZ), the Fourier transform of triple correlation function, to calculate li(v)l and a(v),' and thus determine the I(t) using equation (1). Figure 2 shows two examples of the obtained triple correlation traces of ultrashort laser pulses where Il(v)l and a ( v ) are magnitude and phase of the optical pulse intensity I(t) in the spectral domain. After beam splitting, three mutual parallel and equal distance laser pulses were focused on the THG crystal and THG signal with three fundamental frequency photon contributed from three individual pulses was spatially selected with an iris according to momentum conservation law n w CMPl Fig. 1. Diagrammatic representation of THG based triple correlation.---.

Comparisons between second-harmonic-generation based freguency resolved optical gating (SHG FROG) and triple-oplical autocorrelation for direct pulse-shape measurement (TOAD). have been made by computer simulation and experimenls. Results show fhat TOAD has better accuracy than FROG.