Ultrafast Nanoscale Optics Group, University of California, San Diego

Phase Sensitive Detection of Femtosecond Laser Pulses Using Two-Photon Absorption in Silicon CCD Camera

1. Ultrashort pulse detection using nonlinear absorption in semiconductor photodetectors

The traditional approach to ultrashort pulse diagnostics relies on sum-frequency generation in nonlinear optical crystals. However, this method becomes less effective for characterization of broadband optical signals because the efficiency of the wave-mixing process is affected by the nonuniformity of the phase matching across the spectral bandwidth of the measured signal. To overcome this problem, methods based on two-photon absorption in semiconductor materials and photodetectors have been introduced1. The characterization of femtosecond pulses employing two-photon absorption in semiconductor photodetectors has a number of advantages over the methods based on nonlinear wave mixing: (i) semiconductor materials exhibit a nonlinear response in a wide optical frequency range below the bandgap, allowing detection of extremely broadband optical signals without the limitations imposed by the phase matching process; (ii) free electrons generated in the process of nonlinear absorption in a semiconductor photodetector are converted to an electrical current directly, simplifying the detection process; and finally (iii) by using semiconductor detector arrays, simple and reliable single shot characterization systems can be constructed.

In recent years numerous photodetectors have been used to perform both interferometric and intensity correlations of ultrashort laser pulses. The most commonly used apparatus is based on a delay line autocorrelator, which uses mechanical scanning in order to record a multi-shot correlation trace but is therefore incapable of making a single-shot measurement. We have introduced single-shot phase-sensitive methods for ultrashort pulse detection that are based on two-photon absorption in a conventional silicon CCD camera

Interferometric correlation of ultrashort laser pulses is one of the first techniques introduced to extract information about the complex amplitude of an ultrafast optical waveform2. Due to its experimental simplicity in comparison with other phase sensitive techniques, the interferometric correlation method is commonly used for the characterization of ultrashort laser pulses.

Figure 1: Single-shot interferometric correlator. Diffraction grating in the lower arm of the interferometer is telecentrically imaged onto the surface of the CCD, creating a pulse front tilt. The value of the tilt determines the size of the correlation function, decoupling it from the interference fringe spacing, controlled by the incidence angle b of the pulse in the upper arm of the interferometer.

The interferometric correlation I(t) of an ultrashort laser pulse with complex electric field can be obtained by introducing the signal into a Michelson or Mach-Zehnder interferometer with a nonlinear detector (a combination of a nonlinear medium and an intensity detector) at the output. The nonlinear medium responds to the square of the optical field, which is integrated in time by an intensity detector:

Fig. 2. Experimental results: Interferometric correlation (a) for the pulse from the output of the OPA and (b) the pulse stretched by a grating pair. The narrow interference pattern for the stretched pulse indicates the presence of the linear chirp.

The phase sensitivity of the interferometric correlation technique can be best described by considering a linearly chirped pulse. Since the leading and trailing edges of the chirped pulse contain different frequency components, they will not interfere with each other and the correlation trace will not display the interference fringes for the large values of time delay t when the leading edge of the pulse overlaps its trailing edge. Therefore, the interferometric correlation of a linearly chirped pulse will be characterized by an interference pattern that is narrower than the width of the pulse intensity autocorrelation. For linearly chirped gaussian pulses, I(t) can be calculated analytically, and the chirp value can be found by measuring the width of the fringe pattern.

An efficient realization of a single-shot interferometric correlation measurement requires matching the size of the correlation function to the size of the CCD array and matching the spacing of the interference fringes to the resolution of the CCD. In our correlator we employ a technique of creating a pulse front tilt utilizing a dispersive element3 such as a grating or a prism. The experimental setup is shown schematically in Fig.5. The input pulse was derived from the Optical Parametric Amplifier operating at 1.4 μm. We use a 200 lines/mm diffraction grating to introduce the pulse front tilt into the beam in one of the arms of the Mach-Zehnder interferometer. The resulting beam with the tilted pulse front is interfered with the signal from the second arm of the interferometer, introduced at an angle β: A two-photon absorption process in the CCD with successive integration in time generates the interferometric correlation as described by Eq.1:

(2)

,Relation 2 is characterized by two independent time delays across the spatial profile of the beam: xsinθ and xcosβ in amplitude and phase, respectively. Consequently, the width of the correlation function envelope is determined by the value of the pulse front tilt, controlled by both the value of the grating dispersion angle θ and the magnification factor M. The fringe spacing is determined by the value of the angle β, which is set independently such that the interference fringes in the correlation function are resolved by the CCD camera. We use a standard silicon CCD camera (Pulnix TM7-EX) with 640x480 pixel array size, 10 μm pixel size and a linear response in the spectral range of 0.4-1μm. The CCD response as a function of the input optical power at 1.4 μm was measured, verifying the expected quadratic behavior due to the two-photon process.

Fig.3.(left): Sonogram snapshots for (a)-negatively chirped, (b)-transform limited, (c)-positively chirped pulses.

Experimental results on the measurement of the interferometric correlation are shown in Fig.6. We first investigate the pulse derived from the output of the OPA. The shape of the correlation function (see Fig.6a) shows characteristic features of a pulse that is close to transform-limited (the fringe pattern extends over the full range of the correlation peak all the way to the background level). The FWHM of the intensity autocorrelation function for the signal in Fig.6a, extracted by filtering out the zero-frequency component of the interferometric correlation, is about 150 fs. This result is in good agreement with the value of 125 fs obtained from the measured power spectrum width assuming a transform limited gaussian pulse. To investigate the performance of our method further, we use a pair of gratings to introduce a linear chirp to the input signal. The resulting correlation trace is shown in Fig.6b. The envelope of the correlation function becomes wider due to the stretching of the input pulse in time, while the interference pattern fills only the central part of the envelope indicating the presence of the linear chirp in the waveform. The peak-to-background ratio in our measurements matched the theoretically predicted value of 8 to 1.

Fig.4. (right): Spectrum of the signal together with the spectral phase (solid line) extracted from the sonogram of the Fig.7a. Quadratic spectral phase calculated from the grating stretcher geometry is shown for comparison (dashed line).

3 Single-shot sonogram generation

Although interferometric correlation provides certain information about the pulse phase, complete reconstruction of the complex amplitude, if possible, requires complicated iterative processing of the data. Additionally interferometric correlation is a symmetric function and therefore has an intrinsic uncertainty about the direction of time axis. A different method that allows easy reconstruction of the complex amplitude of the ultrashort laser pulse without ambiguity in the direction on time is based on generation and analysis of the sonogram5. The Sonogram W(t,ω)of a complex amplitude signal p(t) is defined as:

Here is a Fourier amplitude of the signal and G(ω)is a window function in the frequency domain. The sonogram displays the temporal position of different spectral components and intuitively describes the dependence of the signal frequency versus time. It can be seen from Eq.3 that in order to generate a sonogram experimentally one needs to apply a spectral filter to the signal with subsequent time resolved detection of the intensity of a selected spectral component. Frequently used multi-shot sonogram arrangement consists of a spectral filter introduced into one of the arms of the scanning delay autocorrelator. In this section we discuss the modification of our interferometric correlation system in order to provide single-shot detection of a sonogram of an ultrashort laser pulse.

By inspecting an arrangement for generating a tilted pulse front in Fig.1 one observes that the pulse diffracted from the grating is spectrally decomposed in the back focal plane of the cylindrical lens f1. The spectral filter in Eq.3 can be implemented by installing a narrow slit in this plane. The two-photon process in the CCD in this case produces a cross correlation function between the original pulse and the spectrally filtered signal. A set of such cross correlation functions for every spectral component of the original signal constitutes a sonogram. Changing the central wavelength of the spectral filter can be achieved by moving the slit across the spectral decomposition plane. We can however exploit an unused degree of freedom in y-direction, perpendicular to the plane of the picture in Fig.5. In this case a moving slit is replaced by a rectangular slit oriented at a 45° and a spatial mode of the beam is expanded in y-directions. At each vertical position y the slit selects a different spectral component; the cross correlation function on the surface of the CCD shows its temporal position, therefore generating a sonogram in a single shot.

Figure 3 shows experimentally obtained CCD snapshots of the sonograms for negatively chirped, transform limited and positively chirped pulses. As expected, the linear chirp causes sonogram to rotate with the direction of the rotation depending upon the sign of the chirp. The group delay dφ(ω)/dω of the original temporal signal (where φ(ω) is the spectral phase) can be determined from the relative temporal position of the correlation peak for each spectral component. The spectral phase φ(ω) is then obtained by integration (see Fig.4).

References

1. D.T. Reid, W. Sibbett, J.M. Dudley, L.P. Barry, B. Thomsen, J.D. Harvey, “Commercial semiconductor devices for two photon absorption autocorrelation of ultrashort light pulses”. Applied Optics, 37, 8142-8144, (1998).
2. J.-C.M. Diels, J.J. Fontaine, I.C. McMichael, F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy”. Applied Optics, 24, 1270-1282, (1985)
3. G. Szabo, Z. Bor, A. Muller, “Phase-sensitive single-pulse autocorrelator for ultrashort laser pulses”. Optics Lett., 13, 746-748, (1998)
4. D.Panasenko, Y.Fainman “Interferometric correlation of infrared femtosecond pulses with two-photon conductivity in a silicon CCD”. Applied Optics (2002).
5. J. L .A. Chilla and O. E. Martinez, “Direct determination of the amplitude and the phase of femtosecond light pulses,” Optics Lett., 16, 39-41 (1991)
6. D. Panasenko,Y. Fainman. “Single-shot generation of femtosecond laser pulse sonogram using two-photon conductivity in a silicon CCD”, presented at Conference on Lasers and Electro-Optics, Long Beach, May 19-24, 2002, paper CMR-2