1. Introduction

Various techniques were used for measurements of the nonlinear optical properties (NLO), such as the degenerate four-wave mixing (DFWM) technique [1], Z-scan technique [2], and the nonlinear-imaging technique with phase object (NIT-PO) [3]. Thereinto, Z-scan technique is the most popular and standard tool because of some salient features such as simplicity and high sensitivity. This technique gives quick determinations of the sign and magnitude of the nonlinear susceptibility, simultaneously. However, the mechanisms of optical nonlinearities of materials are often complicated by the presence or the competition of two or more nonlinear mechanisms. These techniques mentioned above can not distinguish between these different nonlinearities easily. J. Wang et al. have determined the temporal response of the nonlinear absorption and refraction by use of a time-resolved pump-probe system that is based on the Z-scan system [4]. However, this method can not investigate the dynamics of nonlinear absorption and nonlinear refraction simultaneously and it is complicated to determine the dynamics of nonlinear refraction. A closed-aperture Z scan at a fixed time delay must be done firstly to determine the transmittance peak and valley Z positions. Then, two sets of data were obtained with the sample fixed at the position of the peak and at the Z position of the valley, respectively. According to the difference between these two sets of data, the dynamics of nonlinear refraction could be determined. This method also has inevitable experimental error due to these two sets of data obtained in different time and the fluctuation of the energy and the instability of spatial distribution of the laser beam. Meanwhile, it is difficult to separate the pump beam from the probe beam when measure the degenerate nonlinear response of a material. T. Xia et al. have investigated the nonlinear response in inorganic metal cluster Mo₂Ag₄S₈(PPh₃)₄ solutions by using a standard pump-probe system[5].In this 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. However, this method is only used to measure the nonlinear absorption response and can not measure the nonlinear refraction response. Recently, a time-resolved pump-probe system which is based on the NIT-PO system has been presented [6].This new system can simultaneously measure dynamic nonlinear absorption and refraction. However, in this method, the phase object and CCD must be placed in the focal plane of the lens, and the requirement of the CCD is high, so the experiment is relatively difficult and costly. When do this experiment, it must record at least hundreds of image for different delay time. When one wants to investigate the dynamic of nonlinear refraction for longer delay time, for example, in Ref.5, the more images must be acquired. In addition, the quantity of the images is also related to the precision of the step. The shorter step, the more images must be acquired. These need a lot of time and storage space. And then, it must extract the information of nonlinear absorption and nonlinear refraction by dealing with each image. ΔT The useful images and (the difference between the mean value of the intensity inside the PO and the one outside) must be extracted from the original CCD images manually which induce some inevitable experimental error, so the manage procedure is also complicated and time-consuming. Furthermore, this method can not obtain the final results of the materials in time because it must wait to the images treatment, then it can not adjust the experiment timely, such as the zero delay time determination, the effectiveness of experimental results.

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] 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], 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.

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

where ω_e (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, ω_0e ² is the pump beam radius at focus, I _0e is the on-axis peak irradiance at focus, t_d 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:

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 φ_L is placed at the center of the Gaussian beam. The transmittance of the object can be written t(r) = exp(iφ_L) if r < L_p 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:

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 $t_L=\exp \left(\frac{-ik{r}_1^2}{2f}\right)$. The amplitude of the probe field in the rear plane of L₁ can be obtained as: E _p2 ^' = E _p2 t_L. 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 E_p. 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:

Here, I_p 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 I_p 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 (E_pa). 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]. 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 L_p = 0.5 mm and a phase retardation of ϕ_L = 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 r_a =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.

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

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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], 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 τ_{S 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:

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:

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].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.

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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.