Time-resolved pump-probe system based on a nonlinear imaging technique with phase object

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1 Time-resolved pump-probe system based on a noinear imaging technique with phase object Yunbo Li, 1 Guangfei Pan, 1 Kun Yang, 1 Xueru Zhang, 1 Yuxiao Wang, 1 Tai-huei Wei, 1 Yinglin Song 1,,* 1 Department of Physics, Harbin Institute of Technology, Harbin 151, China School of Physical Science and Technology, Suzhou University, Suzhou 156, China * ylsong@hit.edu.cn Abstract: A noinear imaging technique with phase object, which can deduce noinear absorption and refraction coefficients by single laser-shot exposure, is expanded to a time-resolved pump-probe system by introducing a pump beam with a variable temporal delay. This new system, in which both degenerate and nondegenerate pump and probe beams in any polarization states can be used, can simultaneously measure dynamic noinear absorption and refraction conveniently. In addition, the sensitivity of this new pump-probe system is more than twice that of the Z-scan-based system. The semiconductor ZnSe is used to demonstrate this system. 8 Optical Society of America OCIS codes: (19.441) noinear optics, parametric processes; (5.58) phase shift; (7.434) noinear optical signal processing. References and links 1. G. Boudebs and S. Cherukulappurath, Noinear optical measurements using a 4f coherent imaging system with phase objects, Phys. Rev. A 69, (4).. J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, Time-resolved Z-scan measurements of optical noinearities, J. Opt. Soc. Am. B 11, (1994). 3. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hangan, and E. W. Van Stryland, Sensitive measurement of optical noinearities using a single beam, IEEE J. Quantum Electron. 6, (199). 4. J.-L. Godet, H. Derbal, S. Cherukulappurath, and G. Boudebs, Optimization and limits of optical noinear measurements using imaging technique, Eur. Phys. J. D 39, (6). 5. J. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, Measurement of nondegenerate noinearities using a two-color Z scan, Opt. Lett. 17, 58 6 (199). 6. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, Determination of bound-electronic and free-carrier noinearities in ZnSe, GaAs, CdTe, and ZnTe, J. Opt. Soc. Am. B 9, (199). 7. X. Zhang, H. Fang, S. Tang, and W. Ji, Determination of two-photon-generated free-carrier lifetime in semiconductors by a single-beam Z-scan technique, Appl. Phys. B 65, (1997). 1. Introduction The noinear-imaging technique with phase object (NIT-PO) is a newly developed technique for measurement of the noinearity of materials [1]. Because the NIT-PO is a single-shot technique and the sample does not need to move during the measurement, it easily can be extended to a time-resolved pump-probe system by the introduction of a pump beam. Since the amplitude and sign of the noinear absorption and refraction coefficients can be extracted from a single laser shot in the NIT-PO, the time-resolved pump-probe system based on the NIT-PO can measure the dynamic noinear absorption and refraction simultaneously. In our time-resolved pump-probe system, the pump and probe beams are crossed at a small angle, so their separation is very easy after they have passed through the sample. This means that the system can be applied to both degenerate and nondegenerate beams in any polarization states. J. Wang et al. have measured dynamic noinear absorption and refraction by use of a time- # $15. USD Received 5 Dec 7; revised 3 Jan 8; accepted 4 Jan 8; published 18 Apr 8 (C) 8 OSA 8 April 8 / Vol. 16, No. 9 / OPTICS EXPRESS 651

2 resolved pump-probe system that is based on a Z-scan system [,3]. Numerical simulation shows that the sensitivity of our time-resolved pump-probe system is more than twice that of the Z-scan-based ssystem. In this paper, we demonstrate the time-resolved pump-probe system based on the NIT-PO for a standard sample of ZnSe at the wavelength of 53 nm. The bound electronic noinear refraction and two-photon absorption (TPA) as well as the twophoton-generated free-carrier refraction and absorption of ZnSe are measured.. Experiment setup Fig. 1. Schematic of time-resolved pump-probe system based on noinear-imaging technique with phase object. BS is beam splitter; M 1 -M 3 are mirrors; L 1 -L 5 are convex lenses; A is aperture with phase object; tf is natural filter; NL is noinear material. The experimental arrangement of a time-resolved pump-probe system based on the NIT-PO is shown schematically in Fig. 1. The extracted -ps FWHM double-frequency pulse ( λ = 53 nm ) from a Q-switched and mode-locked Nd:YAG laser is separated into two beams: an intense pump beam and a much weaker probe beam. In our experiments, the polarization of the pump beam is adjusted perpendicular to that of the probe beam by a halfwave plate. A variable time delay is introduced into the pump path. The probe branch of the arrangement is a NIT-PO system. The probe beam is first expanded from 8 to 3 mm in diameter by the convex lenses L 1 and L with focal lengths f 1 = 1 cm and f = 4 cm, respectively, and then passes through the 4f system, which consists of convex lenses L 3 and L 4 with equal focal length f3 = f4 = 4 cm. As shown in Fig. (a), an aperture with a radius of R a = 1.7 mm, PO radius of L p =.5 mm, and phase retardation of φl =.4π is placed at the front focal plane of L 3. It allows oy a small portion of the expanded probe beam to pass through at the central part. Since the size of the aperture is very small compared with the expanded probe beam, the part of the beam illuminated inside the aperture can be seen as a top-hat beam. The noinear sample is placed at the Fourier plane of the 4f system. A chargecoupled device (CCD) camera is used to collect the probe beam at the rear focal plane of L 4. The CCD camera (Imager QE of Lavision Company in Germany) has pixels and a 495 gray level. The size of each pixel is μm. The PO can modulate the noinear phase shift in the noinear sample into the amplitude change of the electric field at the CCD plane. Figure (b) is the profile of a classical noinear image. We define the difference between the mean value of the intensity inside the PO and the one outside as Δ T. The amplitude of Δ T increases with the noinear phase shift inside the noinear sample ΔΦ. When ΔΦ is positive, the image will have an increased intensity inside the PO, i.e., Δ T >. Inversely, Δ T < when ΔΦ is negative. In the measurement, the value of ΔΦ can be deduced by fitting the numerically simulated Δ T well with the experimental one. So the # $15. USD Received 5 Dec 7; revised 3 Jan 8; accepted 4 Jan 8; published 18 Apr 8 (C) 8 OSA 8 April 8 / Vol. 16, No. 9 / OPTICS EXPRESS 65

3 noinear refraction index n can be obtained from ΔΦ = knil, where the wave-vector k, the peak intensity I, and the sample thickness L are know quantities. Fig.. (a) Schematic of aperture with PO. (b) Profile of numerical simulated noinear image ΔΦ >. In our system, the relative sizes of the pump and probe beams inside the noinear sample should be considered, because they are main factors with which to decide the sensitivity of the measurement. We do the numerical simulation using the parameters in the above paragraph. Figure 3 shows that Δ T varies with the ratio of the pump beam radius ω e and the probe beam radius ω p. The solid curve in Fig. 3 is plotted with the reported parameters of ZnSe 14 β = 5.8 cm/gw (TPA coefficient) and n = cm / W at zero time delay, and the 14 dashed curve is obtained with the parameters of CS, β = cm/gw, and n = 3. 1 cm / W. We can see that both curves reach the highest sensitivity at ωe / ωp 1.5. It means that whether or not the noinear sample has noinear absorption, the highest sensitivity of the noinear refraction measurement can reach around ωe / ωp 1.5. Figure 4 shows that the sensitivity of noinear absorption increases with the value of ωe / ω p in the TPA measurement in which T v is the normalized transmittance at zero time delay. There are two reasons that make us consider that e ω at two to three times greater than ω p is the best choice for the measurement. One reason is that though the sensitivity of noinear refraction decreases to about 1.5 times less than the highest sensitivity, the sensitivity of noinear absorption increases to about 1.3 times greater. So, both the noinear absorption and the refraction can reach relatively high sensitivity. Another more important reason is that when a larger pump beam is used, the probe beam can detect a relatively homogeneous area. Thus, the error caused by misalignment of the pump and probe beams will be smaller than when they have approximately the same radii. In the experiment, the Airy radius of the probe beam at the focal plane of L 3 is ωp = 1. λ f /( Ra) 76 μm. The pump beam with a spatial Gaussian profile is focused to a spot the size of ωe = 18 μm (HW1/e ) onto the sample by lens L 5. Considerable care was taken to ensure accurate spatial overlap of the pump and the probe beams within the sample with the aid of a pinhole. The small angle between the pump beam and the probe beam is # $15. USD Received 5 Dec 7; revised 3 Jan 8; accepted 4 Jan 8; published 18 Apr 8 (C) 8 OSA 8 April 8 / Vol. 16, No. 9 / OPTICS EXPRESS 653

4 4.5. The peak intensity of the probe beam is approximately 1.5% the intensity of the pump beam. Fig. 3. Absolute value of Δ T varies with ratio of pump and probe beam radii ωe / ω p in third-order noinear refraction measurement of samples with (ZnSe) and without (CS ) noinear absorption. Fig.4. Noinear absorption signal 1 varies with ratio of pump and probe beam radii ωe / ω p, in which v Tv T is normalized transmittance at zero time delay. In the NIT-PO system, three images are needed to deduce the noinear absorption and refraction coefficients of the sample. The first image is a linear image, which is obtained when a neutral filter is placed before the noinear sample to attenuate the laser intensity that is too weak to induce the noinearity. The second one is a noinear image, which is obtained by placing the same neutral filter, which was used before, after the noinear material. The last one is a no-sample image, which is acquired by taking away the noinear material while leaving the neutral filter in the optical setup. We integrate all of the pixels of the linear image to get En, which is in proportion to the transmitted energy of the linear image. Similarly, we can get l En and En ns, which are in proportion to the noinear transmitted energy and # $15. USD Received 5 Dec 7; revised 3 Jan 8; accepted 4 Jan 8; published 18 Apr 8 (C) 8 OSA 8 April 8 / Vol. 16, No. 9 / OPTICS EXPRESS 654

5 without the sample transmitted energy, respectively, by integrating all of the pixels of the noinear image and the no-sample image. The linear transmittance of the sample is Tl = E / Enns. Note that the energy loss because of the reflection of the front and rear surfaces of the sample cell in the linear image should be considered. The noinear transmittance of the sample is T = En / E. The noinear absorption coefficient β can be deduced by fitting the numerically calculated noinear transmittance to the experimentally measured T by varying the value of β. During the calculation of β, the value of n is unknown. But since we know that the noinear refraction does not affect the noinear transmittance, the value of n can be set arbitrarily. After the value of β has been obtained, the noinear refractive index n, the oy unknown parameter, can be deduced by fitting the numerically calculated Δ T to the experimentally calculated one. More details about the measurement can be found in Ref. [1]. In our time-resolved pump-probe system based on the NIT-PO, a neutral filter is used in the probe beam to attenuate the intensity of the probe beam at the Fourier plane weakly enough so as to avoid noinearity. First, a linear image and a no-sample image are obtained when the pump beam is blocked. The linear transmittance of the material is Tl = E / Enns. Then the pump beam is unblocked, and a series of noinear images are taken while the temporal delay is scanning. For each noinear image at a different temporal delay, En and Δ T are extracted. By plotting En as a function of time delay t d, we obtain a curve that reveals noinear absorption alone. On the other hand, the curve Δ T versus t d exhibits noinear refraction as well as noinear absorption, if present. It is very difficult to extract a signal that is produced by pure noinear refraction alone. So, first we have to analyze the normalized curve of En versus t d to obtain the photophysical parameters of noinear absorption. With the parameters related to noinear absorption already known, the parameters of noinear refraction can be obtained by fitting the curve of Δ T versus t d. In addition to the time-resolved pump-probe system based on the NIT-PO, a time-resolved pump-probe system can also be realized based on a Z-scan. Because the pump beams of the two kinds of systems are both tightly focused Gaussian beams, the sensitivities of the pumpprobe system are determined by the probe beams. By comparing the sensitivity of the NIT-PO and the Z-scan, we conclude that the time-resolved pump-probe system based on the NIT-PO has higher sensitivity than the system based on a Z-scan. For small noinear phase shift ΔΦ π with ΔΦ denoting the on-axis noinear phase change at beam waist and small aperture ΔTp v.46 ΔΦ in the Z-scan, Δ Tp v is the difference between the peak and valley transmittances [3]. On the other hand, the sensitivity of the NIT-PO is determined by ϕ L (the phase shift of the PO) and ρ (the ratio of the radii of the PO and the aperture). The sensitivity increases with the decrease of ρ. Considering the conveniently achievable ρ of.345 and ϕ L =.39, we get Δ T =.889ΔΦ (in Ref. [4]), where Δ T is the difference between the mean intensity within the PO radius on the CCD camera and that outside of the PO radius. So the sensitivity of NIT-PO is more than twice that of the Z-scan (.889/.46). 3. Measurement and discussion As described in Ref. [], the optical noinearities contained in the semiconductor ZnSe have two mechanisms: an ultrafast bound electronic noinearity that can be regarded as instantaneous, and a much slower TPA-induced free-carrier noinearity that has a long recovery time determined by the free-carrier lifetime. A time-resolved study of these processes can identify and characterize the various contributions. The change of the absorption coefficient and refractive index induced by the bound electronic effect are: # $15. USD Received 5 Dec 7; revised 3 Jan 8; accepted 4 Jan 8; published 18 Apr 8 (C) 8 OSA 8 April 8 / Vol. 16, No. 9 / OPTICS EXPRESS 655

6 Δ αb = β Ie, 1 Δ n = n I, b where I e is the irradiance of the pump beam, β is the TPA coefficient, and n is the noinear refractive index. The factor comes from weak-wave retardation [5]. The freecarrier absorption and refraction naturally depend on the density of the photo-generated carriers ( Δ N ) produced by TPA Δ α f = σδ Nt (), 3 Δ n = ηδ N() t, 4 f where η denotes the change of the refractive index per unit carrier density and σ is known as the free-carrier absorption cross-section. In the pump-probe experiment, the probe beam is very weak compared with the excitation beam, so the TPA of the pump beam can be seen as the oy source of the carrier generation. The carrier-generation rate is given by dδn β ΔN = Ie, 5 dt ħω τ where τ r is the carrier lifetime. By invoking slowly varying envelope approximation and thin-sample approximation [], the propagation of the pump and probe beams in the sample can be described as di p dz die dz e e e r = αi β I, 6 = Δ, 7 αi βii σ α NI p e p p dφ p ω nie η N dz c where I p and φ p are the intensity and phase of the probe beam and α is the linear absorption coefficient of ZnSe. The linear refraction index of ZnSe is.7 at 53 nm, the sample thickness is mm, and the linear transmittance is.55 (this includes the surface loss of the sample). During the measurement, the energy of a single pump pulse is 1.48 μ J, and it produces a peak intensity of.1 GW/cm. The CCD camera is very sensitive to background light, so the experiments are done in a darkroom. Before the experiments, the background light is eliminated by the software. The energy fluctuation of the laser is ±3%. Five images are taken at each temporal delay. Figures 5(a) and 5(b) are the linear image and noinear image at the zero time delay, respectively. It can be found that both the PO and the aperture are in nearly circular symmetry, whether for the linear image or the noinear image, so we use polar coordinates in the numerical simulation to simplify the calculation. En and Δ T are extracted from each noinear image. During the extraction, the pixels below counts are set to to reduce the background noise. The mean intensity of the background light is 4. counts, and the mean intensity of the laser spot is above 8 counts. The normalized curve of En versus t d is = + Δ, 8 # $15. USD Received 5 Dec 7; revised 3 Jan 8; accepted 4 Jan 8; published 18 Apr 8 (C) 8 OSA 8 April 8 / Vol. 16, No. 9 / OPTICS EXPRESS 656

7 shown in Fig. 6. The division of Δ T by the mean intensity of the linear image is shown in Fig. 7. Each data in the two curves is an average of five images. Fig. 5. (a) Linear image in the experiment. (b) Noinear image at zero temporal delay in the pump-probe experiment. Next we deduce the photophysical parameters of ZnSe by numerically simulating the experimental curves. Eqs. (1) (8) as well as the beam propagation described in Ref. [1] are used in the simulation, including a Fourier transform from the input plane of the 4f system to the sample and an inverse Fourier transform from the sample to the CCD plane. The curve in Fig. 6 oy relates to noinear absorption. The sharp valley at the zero temporal delay is the result of TPA, and the slow recovery after the pump beam has passed through is the absorption of the free carrier. The depth of the valley at the zero time delay is maiy dependent on the TPA, and the free-carrier absorption has very little contribution. So the TPA coefficient β = 5.4 cm/gw can be obtained by fitting the valley at zero temporal delay. The free-carrier absorption in Fig. 6 is very small (normalized transmittance reduces to about.99), so it is difficult to deduce the lifetime of the free carrier accurately. Fortunately, the recovery in the curve Δ T versus t d (Fig. 7) is clear to see. The lifetime of the free carrier can be obtained from τ r =.5 ns. Numerical simulate of the curve in Fig. 6 once again by substituting β and τ r, and the free-carrier absorption cross-section is obtained from 17 σ = cm. Then we use a similar method of determining β and σ α, and it is easy to obtain the noinear refractive index n = cm /W and η = cm by numerical simulating Fig. 7. The photophysical parameters measured in the use of our pumpprobe system are in agreement with the ones reported in earlier literature (listed in Table 1). The differences between the values of η in our paper and the ones in Refs. 6 and 7 may be caused by the overestimation of the lifetime of the free carrier τ r through use of the indirect Z-scan measurement technique. # $15. USD Received 5 Dec 7; revised 3 Jan 8; accepted 4 Jan 8; published 18 Apr 8 (C) 8 OSA 8 April 8 / Vol. 16, No. 9 / OPTICS EXPRESS 657

8 Table 1. Comparison of the Photophysical Parameters Obtained in This Paper with Those in Earlier Literature β n (cm/gw) (cm / W) σ (cm ) η τ (ns) 1 3 ( 1 cm ) Method This paper Pump-probe Ref. 5.8±1 (-6.8±1.4) Pump-probe Ref Z-scan Ref ± ±. Z-scan Ref Z-scan Fig. 6. Normalized transmittance as function of temporal delay of ZnSe. Dots are experiment results and line is numerically simulated curve. Fig. 7. ΔT as function of temporal delay. Dots are experiment results and line is numerically simulated curve. # $15. USD Received 5 Dec 7; revised 3 Jan 8; accepted 4 Jan 8; published 18 Apr 8 (C) 8 OSA 8 April 8 / Vol. 16, No. 9 / OPTICS EXPRESS 658

9 4. Conclusion In this paper, we introduce a time-resolved pump-probe system based on the NIT-PO. Dynamic noinear absorption and refraction can be measured simultaneously in this system. This system is suitable for noinearity measurement of both degenerate and nondegenerate beams in any polarization state. In addition, the sensitivity of our time-resolved pump-probe system based on the NIT-PO is more than twice that of the Z-scan-based system. Acknowledgments We gratefully acknowledge support by the National Natural Science Fund of China grant , the Program for New Century Excellent Talents in University grant NCET-4-333, and the Excellent Youth Fund of Heilongjiang Province grant JC-4-4. # $15. USD Received 5 Dec 7; revised 3 Jan 8; accepted 4 Jan 8; published 18 Apr 8 (C) 8 OSA 8 April 8 / Vol. 16, No. 9 / OPTICS EXPRESS 659