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

Optics Express, Vol. 16, Issue 9, pp. 6251-6259 (2008)

http://dx.doi.org/10.1364/OE.16.006251

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### Abstract

A nonlinear imaging technique with phase object, which can deduce nonlinear 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 nonlinear 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.

© 2008 Optical Society of America

## 1. Introduction

1. G. Boudebs and S. Cherukulappurath, “Nonlinear optical measurements using a 4f coherent imaging system with phase objects,” Phys. Rev. A **69**, 053813 (2004). [CrossRef]

*et al.*have measured dynamic nonlinear absorption and refraction by use of a time-resolved pump-probe system that is based on a Z-scan system [2

2. J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B **11**, 1009–1017 (1994). [CrossRef]

3. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hangan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. **26**, 760–769 (1990). [CrossRef]

## 2. Experiment setup

*λ*=532 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 half-wave 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 32 mm in diameter by the convex lenses

*L*

_{1}and

*L*

_{2}with focal lengths

*f*

_{1}=10 cm and

*f*

_{2}=40 cm, respectively, and then passes through the 4f system, which consists of convex lenses

*L*

_{3}and

*L*

_{4}with equal focal length

*f*

_{3}=

*f*

_{4}=40 cm. As shown in Fig. 2(a), an aperture with a radius of

*R*=1.7mm, PO radius of

_{a}*L*=0.5 mm, and phase retardation of

_{p}*ϕ*=0.4

_{L}*π*is placed at the front focal plane of

*L*

_{3}. It allows only 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 nonlinear sample is placed at the Fourier plane of the 4f system. A charge-coupled 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 1040×1376 pixels and a 4095 gray level. The size of each pixel is 6.4×6.4

*µ*m

^{2}. The PO can modulate the nonlinear phase shift in the nonlinear sample into the amplitude change of the electric field at the CCD plane. Figure 2(b) is the profile of a classical nonlinear 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 nonlinear phase shift inside the nonlinear sample ΔΦ

_{0}. When ΔΦ

_{0}is positive, the image will have an increased intensity inside the PO,

*i.e.*, Δ

*T*>0. Inversely, Δ

*T*<

_{0}when ΔΦ

_{0}is negative. In the measurement, the value of ΔΦ

_{0}can be deduced by fitting the numerically simulated Δ

*T*well with the experimental one. So the nonlinear refraction index

*n*

_{2}can be obtained from ΔΦ

_{0}=

*kn*

_{2}

*I*

_{0}

*L*, where the wave-vector

*k*, the peak intensity

*I*

_{0}, and the sample thickness

*L*are know quantities.

*T*| varies with the ratio of the pump beam radius

*ω*

_{e0}and the probe beam radius

*ω*

_{p0}. The solid curve in Fig. 3 is plotted with the reported parameters of ZnSe

*β*=5.8 cm/GW (TPA coefficient) and

*n*

_{2}=-6.8×10

^{-14}cm

^{2}/

*W*at zero time delay, and the dashed curve is obtained with the parameters of CS

_{2},

*β*=0 cm/GW, and

*n*

_{2}=3.2×10

^{-14}cm

^{2}/

*W*. We can see that both curves reach the highest sensitivity at

*ω*

_{e0}/

*ω*

_{p0}≈1.25. It means that whether or not the nonlinear sample has nonlinear absorption, the highest sensitivity of the nonlinear refraction measurement can reach around

*ω*

_{e0}/

*ω*

_{p0}≈1.25. Figure 4 shows that the sensitivity of nonlinear absorption increases with the value of

*ω*

_{e0}/

*ω*

_{p0}in the TPA measurement in which

*T*is the normalized transmittance at zero time delay. There are two reasons that make us consider that

_{ν}*ω*

_{e0}at two to three times greater than

*ω*

_{p0}is the best choice for the measurement. One reason is that though the sensitivity of nonlinear refraction decreases to about 1.5 times less than the highest sensitivity, the sensitivity of nonlinear absorption increases to about 1.3 times greater. So, both the nonlinear 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.

*L*

_{3}is

*ω*

_{p0}=1.22

*λf*/(2

*R*)≈76

_{a}*µ*m. The pump beam with a spatial Gaussian profile is focused to a spot the size of

*ω*

_{e0}=180

*µ*m (HW1/

*e*

^{2}) 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 4.5°. The peak intensity of the probe beam is approximately 1.5% the intensity of the pump beam.

*En*, which is in proportion to the transmitted energy of the linear image. Similarly, we can get

_{l}*En*and

_{nl}*En*, which are in proportion to the nonlinear transmitted energy and without the sample transmitted energy, respectively, by integrating all of the pixels of the nonlinear image and the no-sample image. The linear transmittance of the sample is

_{ns}*T*=

_{l}*En*/

_{l}*En*. 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 nonlinear transmittance of the sample is

_{ns}*T*=

_{nl}*En*/

_{nl}*En*. The nonlinear absorption coefficient

_{l}*β*can be deduced by fitting the numerically calculated nonlinear transmittance to the experimentally measured

*T*by varying the value of

_{nl}*β*. During the calculation of

*β*, the value of

*n*

_{2}is unknown. But since we know that the nonlinear refraction does not affect the nonlinear transmittance, the value of

*n*

_{2}can be set arbitrarily. After the value of

*β*has been obtained, the nonlinear refractive index

*n*

_{2}, the only 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

1. G. Boudebs and S. Cherukulappurath, “Nonlinear optical measurements using a 4f coherent imaging system with phase objects,” Phys. Rev. A **69**, 053813 (2004). [CrossRef]

_{0}|≤

*π*with ΔΦ

_{0}denoting the on-axis nonlinear phase change at beam waist and small aperture Δ

*T*≈0.406|ΔΦ

_{p-ν}_{0}| in the Z-scan, Δ

*T*is the difference between the peak and valley transmittances [3

_{p-ν}3. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hangan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. **26**, 760–769 (1990). [CrossRef]

*φ*(the phase shift of the PO) and

_{L}*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 0.345 and

*φ*=0.39, we get Δ

_{L}*T*=0.889ΔΦ

_{0}(in Ref. [4

4. J.-L. Godet, H. Derbal, S. Cherukulappurath, and G. Boudebs, “Optimization and limits of optical nonlinear measurements using imaging technique,” Eur. Phys. J. D **39**, 307–312 (2006). [CrossRef]

*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 (0.889/0.406).

## 3. Measurement and discussion

2. J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B **11**, 1009–1017 (1994). [CrossRef]

*I*is the irradiance of the pump beam,

_{e}*β*is the TPA coefficient, and

*n*

_{2}is the nonlinear refractive index. The factor 2 comes from weak-wave retardation [5

5. J. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z scan,” Opt. Lett. **17**, 258–260 (1992). [CrossRef] [PubMed]

*N*) produced by TPA

*η*denotes the change of the refractive index per unit carrier density and

*σ*is known as the free-carrier absorption cross-section.

*τ*is the carrier lifetime.

_{r}2. J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B **11**, 1009–1017 (1994). [CrossRef]

*I*and

_{p}*ϕ*are the intensity and phase of the probe beam and

_{p}*α*is the linear absorption coefficient of ZnSe.

*µ*J, and it produces a peak intensity of 0.10 GW/cm

^{2}. 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 nonlinear 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 nonlinear image, so we use polar coordinates in the numerical simulation to simplify the calculation.

*En*and Δ

_{nl}*T*are extracted from each nonlinear image. During the extraction, the pixels below 20 counts are set to 0 to reduce the background noise. The mean intensity of the background light is 4.2 counts, and the mean intensity of the laser spot is above 800 counts. The normalized curve of

*En*versus

_{nl}*t*is shown in Fig. 6. The division on of Δ

_{d}*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.

1. G. Boudebs and S. Cherukulappurath, “Nonlinear optical measurements using a 4f coherent imaging system with phase objects,” Phys. Rev. A **69**, 053813 (2004). [CrossRef]

*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 0.99), so it is difficult to deduce the lifetime of the free carrier accurately. Fortunately, the recovery in the curve Δ

*T*versus

*t*(Fig. 7) is clear to see. The lifetime of the free carrier can be obtained from

_{d}*τ*=2.5 ns. Numerical simulate of the curve in Fig. 6 once again by substituting

_{r}*β*and

*τ*, and the free-carrier absorption cross-section is obtained from

_{r}*σ*=6.6×10

^{-17}cm

^{2}. Then we use a similar method of determining

*β*and

*σ*, and it is easy to obtain the nonlinear refractive index

_{α}*n*

_{2}=-6.4×10

^{-14}cm

^{2}/W and

*η*=-9.5×10

^{-21}cm

^{3}by numerical simulating Fig. 7. The photophysical parameters measured in the use of our pump-probe 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

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 nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B **9**, 405–414 (1992). [CrossRef]

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**, 549–554 (1997). [CrossRef]

*τ*through use of the indirect Z-scan measurement technique.

_{r}## 4. Conclusion

## Acknowledgments

## References and links

1. | G. Boudebs and S. Cherukulappurath, “Nonlinear optical measurements using a 4f coherent imaging system with phase objects,” Phys. Rev. A |

2. | J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B |

3. | M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hangan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. |

4. | J.-L. Godet, H. Derbal, S. Cherukulappurath, and G. Boudebs, “Optimization and limits of optical nonlinear measurements using imaging technique,” Eur. Phys. J. D |

5. | J. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z scan,” Opt. Lett. |

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 nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B |

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 |

**OCIS Codes**

(050.5080) Diffraction and gratings : Phase shift

(070.4340) Fourier optics and signal processing : Nonlinear optical signal processing

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: December 5, 2007

Revised Manuscript: January 23, 2008

Manuscript Accepted: January 24, 2008

Published: April 18, 2008

**Citation**

Yunbo Li, Guangfei Pan, Kun Yang, Xueru Zhang, Yuxiao Wang, Tai-Huei Wei, and Yinglin Song, "Time-resolved pump-probe system based on a nonlinear imaging technique with phase object," Opt. Express **16**, 6251-6259 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-9-6251

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### References

- G. Boudebs and S. Cherukulappurath, "Nonlinear optical measurements using a 4f coherent imaging system with phase objects," Phys. Rev. A 69, 053813 (2004). [CrossRef]
- J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, "Time-resolved Z-scan measurements of optical nonlinearities," J. Opt. Soc. Am. B 11, 1009-1017 (1994). [CrossRef]
- M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hangan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760-769 (1990). [CrossRef]
- J.-L. Godet, H. Derbal, S. Cherukulappurath, and G. Boudebs, "Optimization and limits of optical nonlinear measurements using imaging technique," Eur. Phys. J. D 39, 307-312 (2006). [CrossRef]
- J. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, "Measurement of nondegenerate nonlinearities using a two-color Z scan," Opt. Lett. 17, 258-260 (1992). [CrossRef] [PubMed]
- 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 nonlinearities in ZnSe, GaAs, CdTe, and ZnTe," J. Opt. Soc. Am. B 9, 405-414 (1992). [CrossRef]
- 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, 549-554 (1997). [CrossRef]

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