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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 9 — Apr. 27, 2009
  • pp: 7110–7116
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Time-resolved pump-probe technology with phase object for measurements of optical nonlinearities

Junyi Yang, Yinglin Song, Yuxiao Wang, Changwei Li, Xiao Jin, and Min Shui  »View Author Affiliations


Optics Express, Vol. 17, Issue 9, pp. 7110-7116 (2009)
http://dx.doi.org/10.1364/OE.17.007110


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Abstract

A new time-resolved pump-probe system with phase object, which is based on the PO Z-scan technique and the standard pump-probe system, is presented. This new method can simultaneously investigate the dynamic of nonlinear absorption and refraction conveniently. On the other hand, both degenerate and nondegenerate pump and probe beams in any polarization states can be used in this system. The nonlinear optical properties of tetrasulfonated copper phthalocyanine dissolved in dimethyl sulfoxide solution are investigated by using this system.

© 2009 Optical Society of America

1. Introduction

In this paper, we present a time-resolved pump-probe system with phase object, which can overcome all defaults of the above mentioned methods and simultaneously measure the dynamic of nonlinear absorption and refraction conveniently. This system is based on the PO Z-scan technique [7

7. J. Yang and Y. Song, “Direct observation of the transient thermal lensing effect using the PO Z-scan,” Opt. Lett. 34, 157–159 (2009). [CrossRef] [PubMed]

] and the standard pump-probe system. We demonstrate this technique for investigating the optical nonlinearities occurring in tetrasulfonated copper phthalocyanine (CuPcTS) dissolved in dimethyl sulfoxide (DMSO) solution.

2. Experimental setup and Theoretical analysis

As we have depicted in Ref. [7

7. J. Yang and Y. Song, “Direct observation of the transient thermal lensing effect using the PO Z-scan,” Opt. Lett. 34, 157–159 (2009). [CrossRef] [PubMed]

], the trace of PO Z-scan is very different from the valley-peak shape for the positive nonlinear refraction (peak-valley shape for negative nonlinear refraction) in the convention Z-scan, only a single peak shape nearby the lens focus for the positive nonlinear refraction (single valley for the negative nonlinear refraction) is observed in the PO Z-scan. If it extended to the time-resolved pump-probe system by the introduction of a pump beam, we can simultaneously measure the dynamic nonlinear absorption and refraction when the sample is placed at the focus of the lens. The modified time-resolved pump-probe configuration based on the PO Z-scan is shown in Fig. 1(a). By means of the splitter BS1, the laser pulse is separated into two beams: a 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 PO, as shown in Fig. 1(b), is added into the probe branch in front of the lens L1. Here, to simplify the calculation, the PO is placed at the front focal plane of the L1. The PO consists of a glass plate on which a transparent dielectric disc of radius Lp is deposited. The disc has a thickness and index of refraction so that it retards the phase of the incident light. The sample cell is placed at the focal of the lens L1. After getting through sample, the probe beam is separated into two beams and detected by two detectors D1and D2, respectively. A finite aperture is placed in the front of D2. The radius of the aperture in the far field is adjusted to equal to the radius of diffraction transmission beam inside the PO. A variable time delay is introduced into the pump beam path, and the two pulses are recombined at the sample cell with a small angle. The probe waist is smaller than the pump waist. The small angle between the beams and the fact that the probe spot size is considerably smaller than the pump, ensure that the probe could test a uniformly excited region of material in the thin cell. The change of the probe beam energy versus the delay time is recorded after the pump beam.

Fig. 1. (a) The schematic of the improved time-resolved pump-probe system .BS, beam splitter; M1-M3, mirrors; L1-L3, convex lens; D1-D2, energy detector. (b) The schematic of PO.

The initial pump beam incidence on the front face of the sample can be expressed as:

Ie=Ioeωoe2ωe2exp[2r2ωe2(ttd)2τ2]
(1)

where ωe (z) = ω 0e [1 + (z / z 0e)2]1/2 is the pump-beam radius at z. Z is the sample position away from the focus on the axis, z 0e = πω 0e 2/λ is the diffraction length of the beam, ω0e 2 is the pump beam radius at focus, I 0e is the on-axis peak irradiance at focus, td is the time delay between the pump and probe.

For the probe beam, the linearly polarized Gaussian beam of beam waist radius at the entry of the setup can be expressed as:

Ep0(r,t)=E0exp[r2ω02]exp[t22τ2]
(2)

where r is the transverse polar coordinate; ω 0 is the beam waist of the Gaussian beam at the entry of probe beam; E0 denotes the radiation electric field at the focus; τ is the laser pulse width (FWHM).

The circular PO of radius Lp having a uniform phase shift φL is placed at the center of the Gaussian beam. The transmittance of the object can be written t(r) = exp(L) if r < Lp and 1 elsewhere. In our case, using the PO, no analytical solution can be found, so we should propagate the probe field from the front object plane of L1. The amplitude of the field at the output of the PO is E p1(r,t) = E p0(r,t)t(r). The adopted procedure to propagate the probe field from the object to the aperture A is achieved with three Fresnel diffraction integrals.

The amplitude of the probe field in the front plane of L1 for PO placed at a distance equal to the focal length of L can be written as:

Ep2=2πiλdexp(iπr2λd)0+r1dr1Ep1exp(iπr12λd)J0(2πrr1λd)
(3)

where d=f is the distance of propagation, r 1 is the radial coordinate in this plane. j 0 is the Bessel function of the first kind of zero order. The phase transformation due to the lenses in the paraxial approximation is expressed by tL=exp(ikr122f). The amplitude of the probe field in the rear plane of L1 can be obtained as: E p2 ' = E p2 tL. The second propagation is performed on a distance d=f where the nonlinear material is placed, the amplitude of the probe field in the front surface of nonlinear materials is defined as Ep. In the material, considering a thin medium and using the slowly varying envelope approximation, we can separate the beam propagating equation into a couple of equations, one for the phase and another for the irradiance, as follows:

Ipz'=α(Ie)Ip
(4)
dϕdz'=kΔn(Ie)
(5)

Here, Ip and ϕ represent the probe irradiance and phase, and z' is the propagation length in sample. α and Δn denote the absorptive coefficient and change of refractive index which are induced by the pump beam. Integration of Ip over the pulse duration and the whole beam cross section gives an energy corresponding to that detected by D 1. The final diffraction is calculated with d=D where the aperture is placed, D is the distance between the aperture and the focal plane we deduce the electric-field at the aperture (Epa). The radius of the aperture in the far field is adjusted to equal to the radius of diffraction transmission beam inside the PO. While integration of irradiance over the pulse duration and the aperture cross section, which gives an energy corresponding to that detected by D2 with an aperture.

3. Experiments and discussion

In this paper, CuPcTs/DMSO solution is used to validate our proposed technique. CuPcTS is synthesized according to the procedure of Weber and Busch [8

8. J. H. Weber and D. H. Busch, “Complexes Derived from Strong Field Ligands. XIX. Magnetic Properties of Transition Metal Derivatives of 4, 4’, 4”, 4”’-Tetrasulfophthalocyanine,” Inorg. Chem. 4, 469–471 (1965). [CrossRef]

]. As shown in Fig. 2, CuPcTs/DMSO exhibit two characteristic absorptions, which are S band (200-400 nm) and Q band (600–800 nm), respectively, because of S0-S1 and S0-S2 transitions. The interesting region of optical nonlinearities for CuPcTs molecules lies in the highly transparent regime between 450 and 550 nm. Consequently, we focused the region near 532 nm for instrumental consideration. The excitation wavelength is chosen to probe the nonlinear absorption at off resonance. The concentration of the CuPcTs/DMSO solution has been prepared to be 2.8 × 10-4 mol/L. An extracted 21-ps FWHM double-frequency pulse (λ = 532 nm) from a Q-switched and mode-locked Nd:YAG laser (EKSPLA, PL2143B) is used as the laser resource. A PO with a radius of Lp = 0.5 mm and a phase retardation of ϕL = 0.5π at 532 nm placed in the center of the Gaussian beam. The sample cell thickness is 2 mm. The focal length of the lens is f = 400 mm. The distance between the aperture and the focal plane is D = 0.8 m, and the radius of the aperture is ra =1 mm. The probe waist (24.5 μm) is two times smaller than the pump waist (50 μm). The energy of the pump beam is 0.49 μJ. The probe peak irradiance was approximately 10% of the pump peak irradiance.

Fig. 2. The UV/Vis spectrum of CuPcTs/DMSO.
Fig. 3. The normalized transmittance as a function of the temporal delay of CuPcTs/DMSO solution. The solid line is the numerical simulated curve.

Figure 3 gives the results of the PO pump-probe for CuPcTs/DMSO solution. The curve of the nonlinear refraction is directly obtained from the closed aperture configuration. The experimental results show that both nonlinear absorption and nonlinear refraction of this solution have rapid optical response, which indicated the nonlinear absorption and nonlinear refraction mechanism of CuPcTs/DMSO solution is excited-state nonlinearity. According to our previously work [7

7. J. Yang and Y. Song, “Direct observation of the transient thermal lensing effect using the PO Z-scan,” Opt. Lett. 34, 157–159 (2009). [CrossRef] [PubMed]

], the transient thermal-lensing effect has little influence on the nonlinear refraction at the focus of the probe beam, so the signal of the nonlinear refraction in Fig. 3 only generate from the excited-state nonlinearity although the delay time is to about 2 ns. For metal phthalocyanine (MPc) it is most appropriate to use a five-level model to interpret the experimental results. The negative delay time means that the probe beam arrive at the sample before the pump beam, that is, the pump beam has no effect on the probe beam. And the nonlinearity of the sample induced by the probe beam can be neglected because of the weak intensity of the probe beam, so initially the normalized transmittance is 1. For the nonlinear absorption results shown in Fig. 3, when the delay time near zero, the absorption of the solution increases as a function of time in a manner consistent with the temporal integration of the pump pulse, the instant drop of the probe is dominant due to the excited single state absorption, which has larger cross-sections than the ground state. Once the pump pulse has passed through the sample, the normalized transmittance has not any change and remains a long low transmittance tail. This behavior is may be induced by the absorption and the long life time of the first excited singlet state or attributed to the absorption and the long life time of the excited triplet state which has the same absorption cross-section to the first excited singlet state. However, the long unchanged normalized transmittance tail of the nonlinear refraction indicates that there is maybe only the first excited-state contributes to the nonlinear refraction. Meanwhile, the normalized transmittance is larger than 1, which indicates that the nonlinear refraction is a self-focusing refraction.

According to the discussion above, the typical five energy-level model can be simplified as a three level model which consists of the ground state S0, the first singlet excited-sate S1, and the higher singlet excited-state S2 to describe the process of optical nonlinearities of CuPcTs/DMSO solution under our experimental conditions. And this three level model should be satisfied with the conditions as follow. The lifetime τS 1, of the first excited-state S1 is very long and the population relaxation from this state to the ground state S0 can be neglected. The lifetime of the higher excited singlet state S2 is very short, from this state the population relaxes very rapidly back to S1, so this relaxation process can also be neglected under our experimental conditions, which have little influence on the results, because the valley bottom of the pump-probe result is behind the zero delay time about 30ps, which gives the population of the higher excited-state enough time to relax to the first excited-state after the pump beam has passed though the sample. In this case, the population-change rates of the states are:

{dN0dt=σ0IeħωN0N1=N00N0
(6)

Accompanying each of the absorptions, there is instantaneous refraction according to the Kramers–Kronig relation. Thus, the absorptive coefficient α and change of refractive index Δn in Eqs. (4) and (5) can be expressed by:

α=σ0N0+σ1N1
(7)
Δn=Δη1N1
(8)

Here, σ 0 is the ground-state absorption cross section, σ 1 is the excited-state absorption cross section from the excited-state S1; Δη 1 (=η 1-η 0) denote the contrast of the refractive index between the S1 and S0. N 00 represents the initial number densities of states S 0, N 0, N 1 represent the number densities of states S0, S1, respectively.

Based on the Eqs.(1)–(8), good theoretical fitting lines are shown in Fig. 3 and obtained by using a single set of parameters σ 1 = 89.5×10-22 m2, Δη 1 = 4.3×1021 m2. Here, σ 0 = 7.1 × 1022 m2, which is provided by the linear absorption measurements, the linear transmittance measurements is 79%.

In order to ascertain the results obtained by the proposed method, we have investigated the optical nonlinearities of CuPcTs/DMSO solution by using the top-hat technique under the 4ns pulse excitation at the wavelength of 532 nm. The top-hat Z-scan arrangement is similar to that in Ref. [9

9. W. zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993). [CrossRef]

].The laser beam was expanded with a diameter of about 70 mm and subsequently illuminated a circular aperture A1 with a diameter of 8 mm to generate a top-hat beam, and then was focused by a lens with the focal length of f = 400 mm , producing an Airy spot of 28 μm in radius on the focal. Here, the input beam energy is 0.31 μJ. The transmittance of the samples is measured with and without an aperture A2 in the far-field. The diameter of A2 is 3.3 mm. Fig. 4 shows the experimental results. Obviously, the nonlinear absorption of this solution is reverse saturation absorption, and the nonlinear refraction is positive, which is consistent with the results of the PO pump-probe system. By using the theory of the top-hat Z-scan and the parameters obtained by the PO pump-probe system, the good theoretical fitting lines are obtained and shown in Fig. 4. It implies that the PO pump-probe system is a credible method to investigate the nonlinear optical properties of materials.

Fig. 4. (a) Open aperture top-hat Z-scan of CuPcTs/DMSO for 4ns with the energy of 0.31 μJ . (b) The nonlinear refraction curves of CuPcTs/DMSO for 4ns with the energy of 0.31 μJ. The solid lines are the theoretical fitting to the experimental results.

4. Conclusions

We have proposed a new time-resolved PO pump-probe system, which can simultaneously measure dynamic nonlinear absorption and refraction conveniently. This system is based on the PO Z-scan technique and the standard pump-probe system. We have demonstrated that this new technique is capable of providing information simultaneously on the excited-state absorptive and refractive dynamics of the material system. The experimental results show that this presented method is an effective way to investigate the nonlinear optical properties of materials.

References and links

1.

A. Yariv and D. M. Pepper, “Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1, 16–18 (1977). [CrossRef] [PubMed]

2.

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

3.

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

4.

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]

5.

T. Xia, A. Dogariu, K. Mansour, D. J. Hagan, A. A. Said, E. W. Van Stryland, and S. Shi, “Nonlinear response and optical limiting in inorganic metal cluster Mo2Ag4S8(PPh3)4 solutions,” J. Opt. Soc. Am. B 15, 1497–1501 (1998). [CrossRef]

6.

Y. Li, G. Pan, K. Yang, X. Zhang, Y. Wang, T.-h. Wei, and Y. Song, “Time-resolved pump-probe system based on a nonlinear imaging technique with phase object,” Opt. Express 16, 6251–6259 (2008). [CrossRef] [PubMed]

7.

J. Yang and Y. Song, “Direct observation of the transient thermal lensing effect using the PO Z-scan,” Opt. Lett. 34, 157–159 (2009). [CrossRef] [PubMed]

8.

J. H. Weber and D. H. Busch, “Complexes Derived from Strong Field Ligands. XIX. Magnetic Properties of Transition Metal Derivatives of 4, 4’, 4”, 4”’-Tetrasulfophthalocyanine,” Inorg. Chem. 4, 469–471 (1965). [CrossRef]

9.

W. zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993). [CrossRef]

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(190.4360) Nonlinear optics : Nonlinear optics, devices
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

ToC Category:
Nonlinear Optics

History
Original Manuscript: March 5, 2009
Revised Manuscript: April 9, 2009
Manuscript Accepted: April 13, 2009
Published: April 14, 2009

Citation
Junyi Yang, Yinglin Song, Yuxiao Wang, Changwei Li, Xiao Jin, and Min Shui, "Time-resolved pump-probe technology with phase object for measurements of optical nonlinearities," Opt. Express 17, 7110-7116 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9-7110


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References

  1. A. Yariv and D. M. Pepper, "Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing," Opt. Lett. 1, 16-18 (1977). [CrossRef] [PubMed]
  2. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlineari-ties using a single beam," IEEE J. Quantum Electron. 26, 760-769 (1990). [CrossRef]
  3. G. Boudebs and S. Cherukulappurath, "Nonlinear optical measurements using a 4f coherent imaging system with phase objects," Phys. Rev. A. 69, 053813 (2004). [CrossRef]
  4. 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]
  5. T. Xia, A. Dogariu, K. Mansour, D. J. Hagan, A. A. Said, and E. W. Van Stryland, S. Shi, "Nonlinear response and optical limiting in inorganic metal cluster Mo2Ag4S8 (PPh3)4 solutions," J. Opt. Soc. Am. B 15, 1497-1501 (1998). [CrossRef]
  6. Y. Li, G. Pan, K. Yang, X. Zhang, Y. Wang, T.-h. Wei, and Y. Song, "Time-resolved pump-probe system based on a nonlinear imaging technique with phase object," Opt. Express 16, 6251-6259 (2008). [CrossRef] [PubMed]
  7. J. Yang and Y. Song, "Direct observation of the transient thermal lensing effect using the PO Z-scan," Opt. Lett. 34, 157-159 (2009). [CrossRef] [PubMed]
  8. J. H. Weber and D. H. Busch, "Complexes Derived from Strong Field Ligands. XIX. Magnetic Properties of Transition Metal Derivatives of 4, 4’, 4", 4"’-Tetrasulfophthalocyanine," Inorg. Chem. 4, 469-471 (1965). [CrossRef]
  9. W. Zhao and P. Palffy-Muhoray, "Z-scan technique using top-hat beams," Appl. Phys. Lett. 63, 1613-1615 (1993). [CrossRef]

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