## Abstract

A two-dimensional spectral-shearing interferogram has been acquired instantaneously by frequency- and time-resolved sum-frequency conversion where the phase-matching angle and transverse-delay of crossed-pump beams in a nonlinear crystal serve as frequency-time decomposed imaging. The two spectrally sheared components travel the same path after upconversion. A picoseconds delay-scanned interferogram is accumulated on a 2D image sensor.

© 2011 OSA

## 1. Introduction

Adaptive femtosecond pulse shaping [1,2] is a powerful method used to find an optimal light field for controlling chemical reactions such as non-resonant photoionization. For effective research of ultrafast transient phenomena, shaped-pulse monitoring and adaptive controlling of the light field in a particular time range are required. Spectral shearing interferometry (SSI) is one of the most popular methods for characterizing ultrashort pulses. Since spectral-phase interferometry for direct electric-field reconstruction (SPIDER) [3,4] was reported in 1998, SSI had been developed to extend its applicability. For example, a high-speed version of SPIDER [5] performs single-shot, kilohertz operations. Two-dimensional spectral shearing interferometry (2DSI) [6] uses time-delay scanning to provide zeroth-order phase shift. Several methods record a 2D interferogram onto a 2D sensor: Spatially encoded arrangement (SEA)-SPIDER [7] adopts spatial fringe encoding methods. Filter-SPIDER [8,9] prepares two quasi-monochromatic ancilla fields with spectral filters. Chirped-arrangement (CAR)-SPIDER [10] uses interference between a spatially chirped replica and a laterally inverted one. In a two-dimensional spectral-shearing interferometry resolved in time (2D-SPIRIT) setup [11], two angularly-sheared replicas are frequency-decomposed with a grating, and space–time gating is achieved. These methods support data redundancy and high-repetition-rate operation at the same time. Recently, SSI using two monochromatic collinear fields [12,13] was developed. Only two beam lines were used in this instrument, so we can easily expand it to a 2D-sensor version.

In this paper, we demonstrate SSI with frequency- and time-resolved sum-frequency mixing. This enables measurement at the repetition rate of a 2D sensor. The two spectrally sheared components in the output beam from a sum-frequency crystal are collinear, whereas they travel different paths after upconversion in other 2D methods.

## 2. Frequency- and time-resolved upconverter for spectral shearing interferometer

We use two vertical-focused horizontal-crossed pump beams for two-dimensional resolved-frequency mixing. Frequency decomposition is achieved utilizing phase-match angle dispersion in a nonlinear crystal [14–16]. The 2D interferogram $I(\omega ,\tau )$ is given by

*τ*is delay between a measured pulse and two monochromatic fields, ${\Omega}_{S}$ is shear frequency, and ${\left|E(\omega )\right|}^{2}$ and $\phi (\omega )$ are spectrum and spectral phases of the measured pulse. The phase difference of the two frequency-shifted spectra

*Φ*is detected with a one-dimensional Fourier transform on the delay axis. In the case of $\phi (\omega +{\Omega}_{S})-\phi (\omega )>2\pi $, phase jumps are unwrapped. $\phi (\omega )$ is given by the finite sum of the group-delay dispersion (GDD), i.e., $\left[\phi (\omega +{\Omega}_{S})-\phi (\omega )\right]/{\Omega}_{S}.$

The experimental setup is shown in Fig. 1(a)
. Two monochromatic collinear fields are generated with an air-spaced narrow-gap etalon and a band-pass filter. The frequency difference of the two monochromatic fields, i.e., shear frequency, is 8.2 THz, as shown in Fig. 1(b). A measured pulse is up converted with the sum-frequency mixing of the two monochromatic fields. Figure 1(c) shows the frequency- and time-resolved up converter. An optically uniaxial crystal is used to prevent time-frequency coupling. Delay is given by a crossed-beam transverse position, as shown in the top view. A delay range is given by $D\mathrm{tan}{\theta}_{\text{cross}},$ where *D* is the sensor size and ${\theta}_{\text{cross}}$ is the angle between the measured pulse beam and two monochromatic collinear beams. A 9 mm sensor with a 12° angle covers approximately 3 ps. Note that a delay scanning longer than the coherence time of the two collinear monochromatic fields is invalid. Figure 1(d) shows a two-dimensional shearing interferogram. The two-dimensional interferogram is acquired with a CMOS image sensor (744 × 480 pixels, 6 μm pixel pitch, 8 bit depth). The acquired image is processed for phase retrieval and waveform reconstruction. This setup does not use a prism or grating.

Figure 2(a)
shows calculated phase-match angle dispersion of a BBO crystal. The phase-match angle is approximately proportional to the SFG frequency. Available bandwidth is given by the product of the angle width and the dispersive slope. We evaluated bandwidth and resolution of the SFG crystal in the instrument experimentally. Spectra of upconverted beams are measured with a spectrometer behind a horizontal slit. A contour plot of the angular dispersive upconverted spectra is shown in Fig. 2(b). Table 1
shows a BBO phase-match type comparison of an acceptance angle, a phase-match angle width $\Delta {\theta}_{PM},$ and linearity for a bandwidth of 60 THz. Linearity is defined as $\Delta {\theta}_{MD}/\Delta {\theta}_{PM},$ where $\Delta {\theta}_{MD}$ is the maximum deviation of the curves as shown in Fig. 2(a) from the 1^{st} order fitting. Type-I was selected because of minimum linearity. For example, $\Delta {\theta}_{MD}$ is 0.04° (1.9%) at type-I, 60 THz bandwidth. In our setup the BBO thickness and $\Delta {\theta}_{PM}$ are 1 mm and ~60 mrad, respectively. The generated sum frequency has a 60 THz bandwidth and a 5.2 THz sensitivity, corresponding to an effective thickness of 0.7 mm. After the SFG crystal, two spectrally sheared components in the upconverted beam are collinear. The far-field pattern for the frequency axis and the near-field pattern for the delay axis are required on the image sensor. The beam divergence of each frequency component is limited by the acceptance angle and thickness of the nonlinear crystal. The far-field range for the frequency axis is given by $n\lambda /2\pi L\Delta {\theta}_{\text{accept}}$ at ~30 mm. On the other hand, half of the fringe period in the shearing interferogram is given by $\pi c/\Omega \mathrm{tan}{\theta}_{\text{cross}}$ at ~0.22 mm at ${\Omega}_{S}/2\pi $ = 8.2 THz. The far-field range for the delay axis is ~76 mm. The distance between the SFG crystal and the image sensor is 33 mm, and we simplify an imaging lens.

Figure 3(a) shows a typical 2D interferogram (exposure time: 1 s). The longitudinal axis is the time delay, and the lateral axis is the fundamental frequency (365 THz shift is given from the sum frequency). A mode-locked Ti:sapphire oscillator (pulse width: ~10 fs; pulse energy: ~6 nJ; repetition rate: 76 MHz) is used as the light source. Figure 3(b) shows the beat spectrum, i.e., the power spectral density (dot) and the phase (triangle) calculated with a 1D fast Fourier transform (FFT) at the center frequency. The estimated power density of the beat between two monochromatic fields is described as a thin curve. The estimated filtering width is 0.40 THz. In fact, the output from the etalon has an exponential-decay waveform, but its tail is soft apertured with the beam profile in the interferogram. The filtering width is broadening (~0.6 THz) and the pedestal is suppressed as compared to the estimation. The delay fringes observed during 2 ps are transform limited because of a flat phase. The delay is proportional to the sensor position. Figure 3(c) shows the spectrum and retrieved phases. The bandwidth of the sum frequency was suppressed with an angular distribution of focused beam. Figure 3(d) shows a reconstructed waveform.

The signal-to-noise ratio of the detector can be improved rapidly with data accumulation because there is no time jitter during upconversion. The delay drift between a measured pulse and two monochromatic collinear fields is evaluated. Figure 4 shows the Allan standard deviation (SD) of group delay at an optical frequency of 377 THz. It shows the delay drift or light source fluctuation during 100 s. The gamma of the Allan deviations is −0.5 because of white noise.

We measure the spectral phase added by synthesized quartz plates for relative accuracy verification. Figure 5(a) shows added spectral phase as a function of the propagation length in the glass. The experiments agree with the calculation from the Sellmeier equation (broken curves) given by

*n*is refractive index, and

*λ*is the wavelength (μm). Coefficients ${B}_{1},$ ${B}_{2},$ ${B}_{3},$ ${C}_{1},$ ${C}_{2},$ and ${C}_{3}$are 0.669422575, 0.434583937, 0.871694723, 0.00448011239, 0.0132847049, and 95.3414824, respectively [17]. When the measured pulse has a smooth GDD, we can evaluate the group delay at above $2\pi /{\Omega}_{S}$ with unwrapping the retrieved phase of the interferogram. Figure 5(b) describes group-delay dispersion as a function of the glass thickness. Note that the spectral phase is averaged for a bandwidth of 8.2 THz. The added second-order spectral phase agrees well with the calculation (36.2 fs

^{2}/rad/mm), as shown in Fig. 5(c).

## 3. Conclusion

A real-time delay-scanned spectral-shearing interferometer with a frequency- and time-resolved up converter has been demonstrated. A 60 THz bandwidth and 2 ps delay range interferogram is accumulated on a 2D image sensor in the video rate. The scanned delay and upconverted bandwidth are 2 ps and 60 THz. The acquisition rate can be improved by use of 10 kHz vision chips [18,19]. This method has single-shot capability. The 2D measurement also allows measuring of the pulse-front tilt along one axis.

## Acknowledgments

Part of this work is supported by the 21st Century Center of Excellence (COE) program from the Ministry of Education, Culture, Science, Sports and Technology.

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