**3.1 Optics schematics of a multifunctional autocorrelator**

A multifunctional autocorrelator can be realized by use of a precise translation stage and a lock-in amplifier. The optical schematic is shown in Fig. 10(a). BS1 and BS2 are two 30/70 beam splitters coated with 450 nm - 1150 nm board bandwidth film, and M1 and M2 are two sliver roof mirrors. M2 was mounted on a translation stage (M405-DG, Physik Instrument GmbH), the resolution of which can reach 8.5 nm to provide a fine enough optical delay. We place a chopper (SR540, Stanford Research Systems Inc.) in the inlet of the incident pulse, and the output of a two-photon detector (G1115, Hamamatsu Photonics Corp.) is fed into a lock-in amplifier (SR830, Stanford Research Systems Inc.) to improve the SNR. Our homemade experimental setup of the multifunctional autocorrelator is shown in Fig. 10(b).

Fig. 10. Schematic of the versatile autocorrelator. M1, M2: Roof mirror; BS1, BS2: Beam splitter. (a) Optical schematic, (b) experimental setup.

The interferometric autocorrelation and intensity autocorrelation can be easily switched by tuning the scanning speed of the translation stage and the time constant of the lock-in amplifier. When the ratio of the central wavelength of the measured pulse *<sup>c</sup>* to the time constant of the lock-in amplifier *ct* is much less than two times of the scanning speed of the translation stage *<sup>s</sup> v* , i.e., / 2 *cc s t v* , the measurement result shows an intensity

pulses to generate a distinctive autocorrelation trace. The chirp and phase of the ultrashort optical pulse are reflected in the interferometric trace; however, the vibration range is limited in several hundred micrometers, which results in a limitation of measurement range with this technique. Therefore, a multifunctional autocorrelator, which can realize both

Meshulach *et al* have demonstrated a third-harmonic generation (THG) autocorrelator for ultrashort optical pulses measurement [12]. They used an ordinary glass slide as the THG source, and a pair of 32:1 THG interferometric autocorrelation trace and intensity autocorrelation trace were obtained. However, THG needs the input pulse have enough high energy, and the generated signal always has a low SNR in week energy conditions. In this letter, we demonstrate a second-harmonic generation (SHG) autocorrelator. We use a two-photon detector as the source of SHG. The setup is simplified, and the sensitivity is

A multifunctional autocorrelator can be realized by use of a precise translation stage and a lock-in amplifier. The optical schematic is shown in Fig. 10(a). BS1 and BS2 are two 30/70 beam splitters coated with 450 nm - 1150 nm board bandwidth film, and M1 and M2 are two sliver roof mirrors. M2 was mounted on a translation stage (M405-DG, Physik Instrument GmbH), the resolution of which can reach 8.5 nm to provide a fine enough optical delay. We place a chopper (SR540, Stanford Research Systems Inc.) in the inlet of the incident pulse, and the output of a two-photon detector (G1115, Hamamatsu Photonics Corp.) is fed into a lock-in amplifier (SR830, Stanford Research Systems Inc.) to improve the SNR. Our homemade experimental setup of the multifunctional autocorrelator is shown in Fig. 10(b).

Fig. 10. Schematic of the versatile autocorrelator. M1, M2: Roof mirror; BS1, BS2: Beam

amplifier. When the ratio of the central wavelength of the measured pulse

The interferometric autocorrelation and intensity autocorrelation can be easily switched by tuning the scanning speed of the translation stage and the time constant of the lock-in

constant of the lock-in amplifier *ct* is much less than two times of the scanning speed of the

*t v* , the measurement result shows an intensity

*<sup>c</sup>* to the time

splitter. (a) Optical schematic, (b) experimental setup.

translation stage *<sup>s</sup> v* , i.e., / 2 *cc s*

interferometric autocorrelation and intensity autocorrelation, is desirable.

**3.1 Optics schematics of a multifunctional autocorrelator** 

improved.

autocorrelation trace; When the ratio of the central wavelength *<sup>c</sup>* to the time constant of the lock-in amplifier *ct* is greatly larger than two times of the scanning speed of the translation stage *<sup>s</sup> v* , i.e., / 2 *cc s t v* , the measurement performs as an interferometric autocorrelation trace.

In section 2.2, we have measured the spectral interferogram of an ultrashort optical pulse train emitted from a Ti:sapphire laser (Micra-5, Coherent Inc.). In this section, we measure the autocorrelations of the same laser pulse with our home-made autocorrelator. By tuning the scanning speed of the translation stage and the time constant of the lock-in amplifier, both interferometric autocorrelation and intensity autocorrelation have been obtained. Figure 11(a) shows the intensity autocorrelation, and Fig. 11(b) shows the interferometric autocorrelation.

Fig. 11. Measured autocorrelation of Ti:sapphire laser pulses. (a) Interferometric autocorrelation, (b) intensity autocorrelation.

The intensity autocorrelation in Fig. 11(a) shows an autocorrelation width (FWHM) of 30 fs, and the corresponding pulses width is nearly 20 fs. And the interferometric autocorrelation in Fig. 11(b) shows the autocorrelation width and the chirp information. The interferometric autocorrelation has such a high SNR that the two wings of the interferometric trace can be clearly distinguished, which is useful in complete characterization of the ultrashort optical pulses.

From Fig. 11, we can see that the simulated autocorrelations are in good agreement with the simulated ones (in Fig. 6(b) and 6(a)). The deviation is within ±1 fs, which gives a proof of the reliability for both the techniques.

#### **3.2 Measurement of a strongly chirped pulse**

This autocorrelation setup is suitable for characterization of various ultrashort optical pulses, including strongly chirped pulses and fiber laser pulses. We use a 25-mm-thick SF 10 glass bulk to stretch the ultrashort optical pulses emitted from the Ti:sapphire laser. The chromatic dispersion of SF 10 glass is 156 fs2 calculated with Sellmeier coefficient. And the width of critical pulse can be gotten with the equation:

$$T\_c = 2\sqrt{\ln 2 \times \left| \vec{\phi} \right|} = 104 \text{ fs.}$$

For a 15 fs nearly transform-limited ultrashort optical pulse, the output pulse width from the SF 10 glass is:

$$t\_{p,out} = \left[1 + \left(T\_c \sqrt{t\_p}\right)^4\right]^{1/2} \cdot t\_p = 720 \text{ fs.}$$

The pulses were stretched in temporal range with a great quadratic chirp, which can also be well characterized with the autocorrelator. The intensity autocorrelation and the interferometric autocorrelation were shown in Fig. 12(a) and 12(b), respectively.

Fig. 12. Measured autocorrelation of the Ti:sapphire laser pulses stretched by a SF 10 glass bulk. (a) Interferometric autocorrelation, (b) intensity autocorrelation.

In Fig. 12(a), the intensity autocorrelation clearly shows the width of the broadened pulses. We can clearly discern the pulses width and the chirp of the pulses with the two autocorrelation traces, even if they have a great chirp. The intensity autocorrelation in Fig. 12(a) shows an autocorrelation width (FWHM) of 1100 fs, and the corresponding pulses width is 720 fs assuming a Sech2-shaped pulses, which can agree well with the calculation of the stretched pulse. From Fig. 12(b), we can see that the interferometric autocorrelation shows the interference range is very narrow, and the two wings uplift, which demonstrated the great quadratic chirp generated from the dispersion of the SF 10 glass.

With the intensity autocorrelation and interferometric autocorrelation, both pulse width and phase information of the pulses were presented. Another advantage of this technique is that the space of the interferometric fringes can be used as a ruler to calibrate the time axis of the intensity autocorrelation. That is to say, this autocorrelator setup can self-calibrate with the two autocorrelation traces. This autocorrelation setup can give an accurate autocorrelation width of the pulses; however, a ratio factor should be assumed from autocorrelation width to pulse width. The ratio factor of different pulse waveforms varies greatly; therefore, unsuitable factor may generate great error in pulse width determination with autocorrelation.

#### **3.3 Measurement of a fiber laser pulse**

The autocorrelator also performs excellently in characterization of fiber lasers pulses. We measured a photonic crystal fiber laser (Ultrafast Laser Laboratory, Tianjin University) [13] with this autocorrelator. The output average power of the laser is 500 mW, central

For a 15 fs nearly transform-limited ultrashort optical pulse, the output pulse width from

The pulses were stretched in temporal range with a great quadratic chirp, which can also be well characterized with the autocorrelator. The intensity autocorrelation and the

Fig. 12. Measured autocorrelation of the Ti:sapphire laser pulses stretched by a SF 10 glass

In Fig. 12(a), the intensity autocorrelation clearly shows the width of the broadened pulses. We can clearly discern the pulses width and the chirp of the pulses with the two autocorrelation traces, even if they have a great chirp. The intensity autocorrelation in Fig. 12(a) shows an autocorrelation width (FWHM) of 1100 fs, and the corresponding pulses width is 720 fs assuming a Sech2-shaped pulses, which can agree well with the calculation of the stretched pulse. From Fig. 12(b), we can see that the interferometric autocorrelation shows the interference range is very narrow, and the two wings uplift, which demonstrated

With the intensity autocorrelation and interferometric autocorrelation, both pulse width and phase information of the pulses were presented. Another advantage of this technique is that the space of the interferometric fringes can be used as a ruler to calibrate the time axis of the intensity autocorrelation. That is to say, this autocorrelator setup can self-calibrate with the two autocorrelation traces. This autocorrelation setup can give an accurate autocorrelation width of the pulses; however, a ratio factor should be assumed from autocorrelation width to pulse width. The ratio factor of different pulse waveforms varies greatly; therefore, unsuitable factor may generate great error in pulse width determination with

The autocorrelator also performs excellently in characterization of fiber lasers pulses. We measured a photonic crystal fiber laser (Ultrafast Laser Laboratory, Tianjin University) [13] with this autocorrelator. The output average power of the laser is 500 mW, central

bulk. (a) Interferometric autocorrelation, (b) intensity autocorrelation.

the great quadratic chirp generated from the dispersion of the SF 10 glass.

interferometric autocorrelation were shown in Fig. 12(a) and 12(b), respectively.

4 12 , [1 ( ) ] *p out cp p t Tt t* =720 fs.

the SF 10 glass is:

autocorrelation.

**3.3 Measurement of a fiber laser pulse** 

wavelength is 1060 nm, and pulse repeat frequency is 25 MHz. The intensity autocorrelation and the interferometric autocorrelation traces were shown in Fig. 13(a) and 13(b), respectively.

Fig. 13. Measured autocorrelations of photonic crystal fiber laser pulses. (a) Interferometric autocorrelation, (b) intensity autocorrelation.

Figure 13(a) gives a desirable intensity autocorrelation, which can clearly show the pulse width. The intensity autocorrelation applied a fast scanning of the translation stage; it is therefore much timesaving and suitable for fast measurement. The interferometric autocorrelation was shown in Fig. 13(b). The interferometric trace can be clearly discerned even the scanning length has extended to 1200 fs. From Fig. 13(b), we can see the dispersion compensation is acceptable except for a slight quadratic chirp. The interferometric autocorrelation trace in Fig. 13(b) gives phase information of the optical pulses, which is useful for the developing and optimizing of the laser.

This autocorrelator is based on a translation stage; therefore, the measurement range is related to the translation range of the stage. The stage we chosen has a translation range of 50 mm; therefore, the measurement range of the autocorrelator is 110 ps. By use of a twophoton detector and a lock-in amplifier, this autocorrelation has a higher sensitivity than THG one. The pulses with a 10 mW average power can be well measured.
