IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 38, NO. 11, NOVEMBER 2002 1529 Characterization of Ultrashort Optical Pulses With Third-Harmonic-Generation Based Triple Autocorrelation Tzu-Ming Liu, Yin-Chieh Huang, Gia-Wei Chern, Kung-Hsuan Lin, Yu-Chueh Hung, Chih-Jie Lee, and Chi-Kuang Sun, Senior Member, IEEE Abstract—We present a method to obtain complete information of femtosecond pulses. By measuring triple-optical autocorrelation directly with third-harmonic generation, without spectral informa- tion, a temporal pulse shape can be obtained by analytical calcula- tion without direction-of-time ambiguity. Combining the resulting optical pulse shape with its corresponding optical spectrum, the exact phase and color variations in time can all be recovered with a Gerchberg–Saxton algorithm through an iterative calculation with an complexity. Index Terms—Pulse characterization, third-harmonic genera- tion, triple correlation. I. INTRODUCTION T HE ULTRASHORT optical pulse is an increasingly im- portant tool for many fields, from basic physics, chemistry, and biomedicine to applications including micro-machining and high-bandwidth optical communications. Its short optical dura- tion allows us to study and utilize ultrafast time-domain events. Therefore, for most of these temporal applications, measuring the ultrashort optical pulse shape is a crucial diagnosis. Recent advances in ultrafast technology have pushed optical pulse du- ration below 5 fs, which is so fast that electronic devices (streak camera, etc.) are too slow to measure the evolution. Many tech- niques were developed to characterize the temporal pulse shape [1]–[5]. By far, the most common mean to evaluate femtosecond optical pulses is optical autocorrelation measurement based on second-harmonic generation (SHG) [1], [2]. An incident pulse is split into two replicas with relative temporal delay. These two pulses are then recombined in an SHG crystal. Thus, the gener- ated SHG signal, with one photon contributed from each pulse, is usually detected with a photomultiplier tube and the variation of detected photocurrent with delay yields the pulse autocorre- lation function (1) Manuscript received April 24, 2002; revised July 23, 2002. The work of T.-M. Liu was supported by SIS Corporation. This work was supported by the National Science Council of Taiwan, R.O.C., under Grant 90-2112-M-002-051. T.-M. Liu, Y.-C. Huang, G.-W. Chern, K.-H. Lin, and C.-K. Sun are with the Department of Electrical Engineering and Graduate Institute of Electro-Op- tical Engineering, National Taiwan University, Taipei 10617, Taiwan, R.O.C. (e-mail: sun@cc.ee.ntu.edu.tw). Y.-C. Hung and C.-J. Lee are with Department of Electrical Engineering, Na- tional Taiwan University, Taipei 10617, Taiwan, R.O.C. Digital Object Identifier 10.1109/JQE.2002.804268. A proper measurement of autocorrelation can provide estima- tion on the pulse duration, and with the aid of high-order non- linearity [3]–[5], some pulse asymmetry information can also be extracted without direction-of-time ambiguity. However, the complete temporal optical pulse shape cannot be determined directly from these previously proposed two-arm correlations [1]–[5] due to limited information in the measurements. To obtain the exact optical pulse shape, an extra dimension of information is required for measurement. In the late 1960s, Blount et al. had proposed that by measuring the triple-cor- relation function, the temporal intensity of a pulse can be analytically calculated without direction-of-time ambiguity [6]. Moreover, computer simulation also showed that this suggested method is quite insensitive to noise [7]. This proposed triple-op- tical autocorrelation has been implemented previously with a cascade of SHG and sum frequency generation [8]. However, for pulse-formation dynamic study and other applications including optical coherent controls [9]–[11], we not only need the complete knowledge of pulse intensity variation in time, but also the color variation in time. As a Fourier correspondence in frequency-time transformation, determination of color variation in time means phase reconstruction of the measured optical pulses. Just like several other proposed methods (including frequency-resolved optical gating (FROG) [12], SPIDER [13], photodiode-based phase-retrieval ultrafast waveform measure- ments [14], [28] and phase and intensity from correlation and spectrum only (PICASO) [15], [16]), temporal data itself is not enough to provide color (or phase) variation information and extra spectral measurement is needed. In this paper, we add spectral information into triple-optical-autocorrelation measurements to make the triple-autocorrelation method capable of providing a complete knowledge of laser pulses. With the measured temporal intensity of an optical pulse and its corresponding spectral intensity obtained with a spectrom- eter, exact intensity and phase variations in time can all be recovered with the Gerchberg–Saxton (GS) algorithm through an iterative calculation with an complexity. We have employed a single-staged third-harmonic-generation (THG) based triple-optical autocorrelation for direct pulse-shape measurement (TOAD), which is different from the two-staged implementation previously demonstrated [8], [17]. With these established procedures, optical pulse shapes can be directly calculated from TOAD measurement, and its phase variation can be exactly retrieved thereafter. 0018-9197/02$17.00 © 2002 IEEE