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Nonlinear absorption of a newly synthesized organic inner salt Ge-150 dissolved in four different solvents (DMF, DMSO, acetonitrile and acetone) is investigated by the Z-scan technique with both nanosecond and picosecond pulses. When pulse energy surpasses a threshold and pulse-to-pulse separation is shorter than a characteristic time, all the four solutions show absorption weakening induced by cross-pulse effects in the picosecond regime. However, only two of them (Ge-150 dissolved in DMF and DMSO) show this weakening in the nanosecond regime. By conducting a simple verification experiment, we verify this absorption weakening is induced by solute damage related to solvent effect rather than solute migration. A simple theoretical model is proposed to interpret the experimental phenomenon.
©2010 Optical Society of America
1. Introduction
Reverse saturate absorption (RSA) has important applications for optical limiting devices [1] which can be used to protect the human eyes and sensitive optical components from laser-induced damages. Organic nonlinear optical materials have received considerable attention due to their excellent properties: large third-order susceptibilities associated with fast response time, high damage resistance, variety and processibility [2–6]. In 2004, Wei et al investigated nonlinear absorption of chloroaluminum phthalocyanine solution using Z-scan method with a 19-ps laser pulse. When input pulse energy exceeds a threshold and pulse-to-pulse separation is shorter than a characteristic time, the Z-scan curves show absorption weakening induced by cross-pulse effects and resemble an unsymmetrical “w” [7]. They proposed that this absorption weakening excited by a giant laser pulse is ascribed not just to the saturation of excited state absorption (ESA), but also to the outward migration of the solute molecules at the laser beam center. The saturation of ESA occurs within a single picosecond (ps) laser pulse, while the beam center population decrease due to outward solute migration is sustained much longer than the pulse duration. This pulse-to-pulse cumulative effect affects the RSA and generates these unsymmetrical “w” curves. However, they did not observe similar migration under the excitation of a 2.8-ns laser pulse depositing more energy at the solute molecules [8]. Considering each solute molecule as an oscillator confined within a potential well, they explained, in accordance with the five -level model, that solute molecules excited by a 19-ps pulse retain more translational excess energy to overcome the potential well barrier compared with those excited by a 2.8-ns pulse of equal energy. Thus, solute molecules excited by a 19-ps pulse are more likely to migrate out of the laser beam center, weakening the solution’s absorption in the Z-scan measurements. In 2010, Jin et al found similar solute migration in CuPcTs/DMSO solution in Z-scan experiment with a 21-ps laser pulse and proposed an energy-gradient-induced mass transport theory to interpret their experimental results [9]. Based on this theory, they achieved a good consistency between the numerical simulation and the experimental results. Later, they proposed a two-beam pump-probe Z-scan method to observe the ‘pure’ mass transport phenomenon in CuPcTs/DMSO solution [10]. This method can subtly eliminate the influence of ESA and thermo lens effect. By linear fitting to the curve of peak transmittance versus excited pulse energy, they believed there exists a threshold for excited pulse energy to induce solute migration.
So far, nonlinearity of organic salts is seldom studied. Recently, Liu et al studied a series of resonance benzo[a]phenoxazinium salts in acetic acid solution showing strong RSA using Z-scan technique at 532 nm in ns regime [11]. In this paper, we investigate nonlinear absorption of a newly synthesized organic inner salt Ge-150 dissolved in four different solvents (DMF, DMSO, acetonitrile and acetone) by traditional Z-scan technique in ns regime and top-hat Z-scan technique in ps regime. Both in ns and ps regimes, all the four solutions show small RSA when the input energy is very low. Under 21-ps (FWHM) pulse excitation, when the input pulse energy exceeds about 3.3 μJ and the pulse-to-pulse separation is 0.1 s, all the four solutions show absorption weakening. However, when excited by 4-ns (FWHM) pulse, only two of them (Ge-150 dissolved in DMF and DMSO) show this weakening when the input energy reaches about 10 μJ and the pulse repetition frequency is 10 Hz. For another two solutions (Ge-150 dissolved in acetonitrile and acetone), this weakening is not observed even when the input energy is increased to 70 μJ. Up to now, this absorption weakening in ns regime has not been reported yet. The “w” curves induced by absorption weakening get more unsymmetrical as the input energy or the pulse repetition frequency gets higher. Similar to solute migration, the skewing trends of the “w” curves are reversed when the sample is stepped in the opposite direction [7]. As mentioned in [8], it is much harder for solute molecules under ns pulse excitation to retain enough excess energy to migrate outward due to energy dissipation from excited solute molecules to the surrounding solvent molecules. In regard to ns laser pulse, the rate of the accumulation of the kinetic energy is low because the pulse width is much bigger than τthermo of ethanol, and the dissipation of the kinetic energy cannot be neglected [8]. The accumulated kinetic energy is not strong enough to cause the migration of the solute molecule within a ns pulse. However, it seems easy for the two solutions (Ge-150 in DMF and DMSO) to exhibit absorption weakening in ns regime considering that the pulse energy is only 10 μJ and their nonlinear absorption is so small at low input energy. In view of the asymmetric molecular structure of Ge-150 (see Fig. 1 ), we tend to believe that this absorption weakening in caused by optical damage to solute molecules (called solute damage) unlike ClAlPc and CuPcTs. Once the solute molecules in the beam center are damaged, they will no longer induce nonlinear absorption, which will weaken the solution’s absorption. Simultaneously, the diffusion of adjacent fresh solute molecules will weaken this effect caused by solute damage. As this diffusion of solute molecules also takes a certain time, this solute damage induced absorption weakening is also a kind of cross-pulse effect like solute migration.
Since both solute migration and solute damage lead to absorption weakening once input energy surpasses a threshold, nonlinear transmittance increases instead of decreasing around the beam waist as input energy increases. In this way, unlike the case of pure RSA, the sample no longer plays the role of optical limiting devices once the input energy exceeds the threshold. Thus, both solute migration and solute damage contract the scope of application of optical limiting devices and make the sample less valuable.
To attest our guess, we conduct a simple verification experiment. In the experiment, both the linear and nonlinear transmittance of the corresponding solutions changes after they are irradiated by either intense ps or ns pluses. We think the solute damage is caused by the insufficient capability of inter-molecular excess energy dissipation and accumulation of the excess energy in the solute molecules. Based on this idea, we proposed an approximate theoretical model to interpret the experimental results, especially the difference of the four solutions between ns and ps regimes. Finally, a ps time-resolved pump-probe experiment is conducted for Ge-150/DMF solution as a representation of the four solutions and the results clearly show sequential ground and excited states absorption rather than TPA contributes to nonlinear absorption under low intensity.
2. Experimental methods
Preparation of 3-(Dipropylamino)-7-(piperidin-1-yl) phenoxazinium Chloride (1e) (Ge-150) [12] A mixture of 3-(dipropylamino) phenol (1d, 1 mmol) and 90% i-PrOH (20 mL) was stirred at 70 °C in a 50 mL two-neck bottle with distilling apparatus filled with argon. A suspended solution of 1-(3-methoxy-4-nitrosophenyl) piperidine hydrochloride (1c, 1 mmol) and acid (1 mmol) in 90% i-PrOH (20 mL) was injected with syringe into the above mixture in four portions during 45 min. The temperature rose to reflux. When about 20 mL of the solvent was distilled out, 20 mL of 90% i-PrOH was added to the reaction mixture. This procedure was repeated three times during 3-4 h. The dark-blue solution was evaporated, and the residue was purified by column chromatography with silica gel, eluting with CHCl3/MeOH from 10:1 to 10:3 (v/v). The dark-blue solution was evaporated. To a solution of the residue in EtOH or MeOH (2 mL) was added AcOEt (20 mL). After ultrasonication for 10 min, the mixture was filtrated. The powder was washed by AcOEt and Et2O and then dried in vacuum.
3-(Dipropylamino)-7-(piperidin-1-yl)phenoxazinium Chloride (1e) (Ge-150):Yield 51%, mp 154-155 °C. IR ν (neat, cm−1): 2936, 2873, 1595, 1490, 1400, 1153. UV-vis (CHCl3), λ (nm) (log ε/Lmol−1cm−1): 657 (5.00), 264 (4.48). 1H NMR (270 MHz, CD3OD)δppm: 1.05 (t, J = 7.4 Hz, 6H), 1.72 1.86 (m, 10H), 3.65 3.71(m, 4H), 3.89 (br, 4H), 6.91 (d, J = 2.6 Hz, 1H), 7.11 (d, J = 2.6Hz, 1H), 7.37 (dd, J = 9.7, 2.6 Hz, 1H), 7.52 (dd, J = 9.7, 2.6 Hz, 1H), 7.76 (br, 1H), 7.79 (br, 1H). 13C NMR (68 MHz, CD3OD) δppm: 11.4, 22.1, 25.2, 27.6, 50.9, 55.0, 97.6, 97.9, 118.6, 118.7, 135.3, 135.5, 135.8, 150.7, 151.0, 158.0, 158.1. MS (ESI+), m/z: 364.1 [M-Cl]+. Anal. Calcd for C23H30ClN3O·2H2O: C, 63.36; H, 7.86; N, 9.64. Found: C, 63.39; H, 7.62; N, 9.42. The molecular structure is shown in Fig. 1 and its synthese step is shown in Fig. 2 . As is shown in Fig. 3 , a strong linear absorption peak is located at 650 nm in the linear absorption spectrum of Ge150/DMF. The concentration of Ge-150 dissolved in DMF, DMSO, acetonitrile and acetone is 1.5 × 10−4 mol/L, 1.5 × 10−4 mol/L, 2.3 × 10−4 mol/L and 1.7 × 10−4 mol/L, respectively, giving the same linear transmittance 70% (surface reflection included). The solution is contained in 2 mm thick quartz cuvette.
For the ns Z-scan experiment, a frequency-doubled and Q-switched Nd:YAG laser (Continuum Surelite II-10) emitting 4 ns (FWHM) laser pulse with a wavelength of 532 nm is employed as the laser source. The experimental setup is the same as that in ref [7–9]. This mature technique has been introduced in detail in ref [13]. and we do not give unnecessary details here. The laser pulse with approximate Gaussian spatial profile is focused to have a beam waist of , corresponding to a diffraction length (z 0) of 3.4 mm.
For the ps top-hat Z-scan experiment, the 21 ps (FWHM) double frequency laser pulse at 532 nm is emitted from the Q-switched and mode-locked Nd:YAG laser (EKSPLA, PL2143B). The laser beam is expanded and subsequently passes a circular aperture to generate a top-hat beam. The top-hat beam Z-scan technique is invented by Zhao et al which can overcome the instability of spatial profile of laser beam and its sensitivity is a factor of 2.5 greater than that with Gaussian beams [14]. The experimental setup is similar to that in ref [15]. and we do not say more than is needed here. The diameter of the circular aperture A1 is 9.2 mm and the radius of Airy spot on the focal plane is also about 24 μm [16].
The experimental setup for the ps time-resolved pump-probe experiment is similar to that in ref [17]. In the experiment, the angle between the pump and the probe beams is about.The beam waist of the pump and the probe beams are 50 μm and 29 μm, respectively. The Ge-150/DMF solution as a representation is prepared to have a linear transmittance of 68% and contained in a 2 mm thick quartz cuvette. The input energy of pump beam is 11.7 μJ, giving a peak intensity of 14.1 GW/m2. The peak intensity of the probe beam is approximately 8% of the peak intensity of the pump beam.
3. Results and discussion
3.1 ns Z-scan
As shown in Fig. 4 , when input energy is 2.0 μJ, Ge150/DMF solution shows small RSA. When the input energy comes to 10.1 μJ, nonlinear absorption weakening emerges and the Z-scan curve changes to an unsymmetrical “w” shape. The “w” curve gets more unsymmetrical as the input energy increases to a much higher energy 35.0 μJ. Figure 5 shows the normalized transmittance at the beam waist (z = 0) versus input energy Ein. This normalized transmittance first monotonically decreases due to RSA and then suddenly increases after Ein surpasses 10.1 μJ. In the experiment, the sample is stepped from the -z side of the beam waist to the + z side and the pulse-to-pulse separation is 0.1 s. Similar to the solute migration [7], as shown in Fig. 6 , when the sample is stepped in the opposite direction, the skewing trend of the “w” curve is reversed. Besides, as shown in Fig. 7 , at a fixed input energy (22.4 μJ), the “w” curves get more unsymmetrical as the pulse repetition frequency gets higher. When the pulse repetition frequency decreases to 1 Hz, the “w” curve has nearly become symmetrical. Based on the experimental results, we can draw a conclusion that there exists a threshold for the absorption weakening induced by cross-pulse cumulative effect.
Fig. 4 Open aperture transmittance curves obtained in the ns Z-scan for Ge-150/DMF solution with different input energy, the solid lines are theoretical fits.
Fig. 6 The open-aperture Z-scan curves of Ge-150/DMF solution at 35.0 μJ when stepped in two opposite direction. Square: -z side to the + z side; asterisks: + z side to the -z side.
Fig. 7 The open aperture Z-scan curves of Ge-150/DMF solution at 22.4 μJ with different pulse repetition frequency.
As shown in Fig. 8 , nonlinear absorption of Ge-150/DMSO solution shows a similar characteristic as that of Ge-150/DMF. Compared with Ge-150/DMF, it requires a much higher input energy (about twice) for Ge-150/DMSO to show the same degree of absorption weakening (see circles in Fig. 8). For Ein = 10.0 μJ, the transmittance curve has become a little unsymmetrical (see triangles in Fig. 8) showing a feeble absorption weakening.
Fig. 8 Open aperture transmittance curve obtained in the ns Z-scan for Ge-150/DMSO solution with different energy Ein.
The results of nonlinear absorption for Ge-150/acetonitrile and Ge-150/acetone solution are shown in Fig. 9 and Fig. 10 , respectively. Unlike Ge-150/DMF and Ge-150/DMSO, this two solutions show pure RSA even the input energy comes up to 70.0 μJ. For simply, we only display the results under 35.0 μJ. No absorption weakening is observed and the nonlinear transmittance at z = 0 decreases monotonically as input energy increases.
Fig. 9 Open aperture transmittance curve obtained in the ns Z-scan for Ge-150/acetonitrile solution with different energy.
Fig. 10 Open aperture transmittance curve obtained in the ns Z-scan for Ge-150/acetone solution with different energy.
3.2 ps top-hat Z-scan
Unlike in ns regime, in ps regime, the four solutions show very similar nonlinear characteristic, as shown in Fig. 11 –14 . Similar to ns regime, they all show small RSA at low input energy. However, when the input energy surpasses about 2 μJ and pulse-to-pulse separation is 0.1 s, they all show absorption weakening. In the experiment, the sample is also stepped from the -z side of the beam waist to the + z side. When the sample is stepped in the opposite direction, the skewing trend of the “w” curve is reversed and this “w” curve gets less unsymmetrical as the input energy and pulse repetition frequency get smaller. We can say that this absorption weakening with a threshold in both ns and ps regime is induced by cross-pulse effects. It is interesting that only Ge-150/DMF and Ge-150/DMSO solutions show this absorption weakening in ns regime, indicating the influence of solvent effects which will be detailedly discussed in the theoretical model section.
Fig. 11 Open aperture transmittance curve obtained in the ps top-hat Z-scan for Ge-150/DMF solution with different input energy, the solid lines are theoretical fits.
Fig. 14 Open aperture transmittance curve obtained in the ps top-hat Z-scan for Ge-150/acetone solution with different input energy.
Fig. 12 Open aperture transmittance curve obtained in the ps top-hat Z-scan for Ge-150/DMSO solution with different input energy.
Fig. 13 Open aperture transmittance curve obtained in the ps top-hat Z-scan for Ge-150/acetonitrile solution with different input energy.
3.3 ps time-resolved pump-probe experiment
The results of ps time-resolved pump-probe experiment for Ge-150/DMF solution are shown in Fig. 15 , indicating a positive nonlinear absorption. Although the signs of the absorption coefficients are the same for TPA and RSA (sequential ground and excited states absorption), they exhibit different response times. As a kind of transient process, the effect of TPA disappears once the laser pulse has passed (dozens of picoseconds after zero-delay time) and the normalized transmittance recovers to the constant one. The generation process of RSA is also rapid like TPA, however it has much slower recovery process. Thus the nonlinear absorption of Ge150/DMF is initiated by sequential ground and excited states absorption rather than TPA. Since nonlinear dynamics is not our emphasis in this paper, we will not discuss it any more.
3.4 Verification experiment for solute damage
In order to verify the absorption weakening is caused by solute damage rather than solute migration, we performed a simple verification experiment in both ns and ps regimes.
In ns regime, as shown in Fig. 4, the absorption weakening appears in the extent around the beam waist () at 10.1 μJ for Ge-150/DMF solution. For a Gaussian beam traveling in the + z direction, the area of the beam in this extent () is less than . Suppose the height of the solution is only 2 mm and the width of the quartz cuvette is about 8 mm, the cross sectional area of the solution in the + z direction is at least 16 mm2, which is hundredfold big of the incident beam on the sample. In other words, the damaged solute molecules in once Z-scan are only a little of the whole solute population even though the solute molecules within the beam area are all damaged. Once the solute molecules within the beam area are damaged, the uniformity of the solution is broken. The non-uniformity of the solution will cause the diffusion of other solute molecules to recover the uniformity of the solution in a characteristic time. If the pulse-to-pulse separation is less than this characteristic time, the later coming pulse will experience this solute population decrease and the absorption weakening occurs. Unlike solute migration, the damaged solute molecules in the solution are unrecoverable and are different from the intact solute molecules. If we irradiate the solution located at the beam waist with pulse energy of 10.1 μJ and repetition frequency of 10 Hz for a long time, the damaged solute molecules in the solution will accumulate to a certain degree and the properties including linear and nonlinear properties of the solution will be different from the fresh solution. It is noteworthy that the irradiated solution has to rest for a period of time (tens of seconds) to eliminate the influence of solute migration [7]. Moreover, several different solution positions are measured to eliminate the influence of cuvette surface. Simultaneously, we prepare another same fresh solution and keep it from irradiation for the same time as the irradiated one.
For simplicity, we give the results of Ge-150/DMF solution as an example. Before the experiment, fresh Ge-150/DMF solution is prepared and contained in a thin quartz cuvette with a thickness of 1 mm. The solution with a height of 5 mm is placed at 1.7 mm left of the beam waist. Here, we intentionally let the sample deviate from the beam waist a little to obtain bigger beam area to shorten the time for irradiation. The linear transmittance of the fresh solution is 74%.
First, the linear transmittance of the fresh solution is measured and Z-scan experiment is conducted at two input energy, one low and another high. Then the solution is irradiated by laser pulse of 10 Hz with energy of 10.1 μJ in ns regime and 2.5 μJ in ps regime respectively. After dozens of hours, we stop irradiating and let the solution rest for a while (tens of seconds). Then, the linear transmittance and nonlinear absorption of the solution are measured again under the same condition as for the fresh solution. In ns regime, the solution is irradiated for 47 hours altogether. After irradiated, the volume of the solution has not decreased but its linear transmittance has increased from 74% to 80%. Moreover, as shown in Fig. 16 , nonlinear absorption of the irradiated solution is much smaller than the fresh solution for both 2.6 μJ and 9.5 μJ. The experimental results in the ps regime are similar to the ns regime and are shown in Fig. 17 . The solution is irradiated for 70 hours in all in ps regime. After irradiated, the linear transmittance has increased from 74% to 86% with the solution volume unchanged. Nonlinear absorption of the irradiated solution is also much smaller than the fresh solution for both 0.6 μJ and 2.5 μJ.
Fig. 16 Open aperture transmittance curve obtained in the ns Z-scan for fresh and irradiated Ge-150/DMF solution with low and high input energy. (a) 2.6 μJ (b) 9.5 μJ
Fig. 17 Open aperture transmittance curve obtained in the ps top-hat Z-scan for fresh and irradiated Ge-150/DMF solution with low and high input energy. (a) 0.6 μJ (b) 2.5 μJ
As the linear transmittance of the irradiated solution has increased with its volume unchanged, the intact solute molecules per unit volume have decreased. In other words, some solute molecules are permanently damaged when irradiated by high energy and high repetition frequency laser pulse. As new solute molecules will diffuse to occupy the position of the damaged solute molecules within the interval of the laser pulse, the next incident laser pulse will damage other new molecules. After irradiated for a long time, a large portion of the solute molecules have been damaged and the linear transmittance and nonlinear absorption of the whole solution changes. Properties of another fresh solution without irradiation are also measured and no differences are found. Furthermore, the linear transmittance of the irradiated solution remains the same after statically placed for 7 days. Thus, this verification experiment verifies that the absorption weakening in both ns and ps regimes is induced by solute damage.
4. Theoretical model
In this section, we try to build a simple model to interpret our experimental results.
As Ge-150 is an organic molecule, we use a five-level model to describe its optical response. We take Ge-150/DMF solution in the ns regime as an example. A Gaussian pulse with a spatially and temporally Gaussian distribution of intensity is written as
where I 00 is the peak intensity, is the beam radius, τ is the pulse width (HW e−2 M). The sample position z originates from the beam waist with and Zmax is the farthest distance the sample is moved. is the diffraction length of the beam and λ is the wavelength. The arguments r and t stand for the lateral and temporal distributions of I. Here, t is defined in the interval instead of to facilitate the numerical calculation.In ns regime, the five-level model can be simplified to a three-level model. The detailed description of this model is given in ref [18]. and the corresponding rate equations are given by
where NSi and denote the population density and life time for the state Si respectively. is the absorption cross section of the ground state S 0. ℏ is the Planck constant and ω is the angular frequency of the laser pulse.The nonlinear absorption in the sample can be described by the Beer’s law equation:
where is the depth of light penetration into the sample. α denotes the absorption coefficient, which is the function of I. For z = -Zmax, the sample experiences the first coming laser pulse, the initial population of the ground state is , where is the initial solution concentration.As to ESA induced RSA, α increases with the increase of generalized fluence [19]:
Through the three one-photon absorption and subsequent relaxations related to Eqs. (2)–(4), most of the energy absorbed within a pulse is converted to the excess energy of the Ge-150 molecule in the ps order [7]. The excess energy redistributes, as a result of anharmonicity, among various vibrations in the solute molecules and turns into intramolecular heat [20]. The intramolecular heat eventually dissipates into the phonon bath and raises the solution temperature since molecular vibrations are ultimately coupled to thermal phonons in the solution. The time for the heat to transfer from the solute molecules throughout the surrounding solvent molecules is referred to as the local thermal equilibrium time τtherm [20]. In this case, the fluence should satisfy the following equation simultaneously:To facilitate the numerical calculation, the sample is divided into NL layers. The space between two layers is , where L is the sample thickness. The intramolecular heat absorbed by solute molecules per unit volume at the depth and different radial position in the sample can be measured by absorbed photon numbers:where is the fluence value just after the first pulse passes.Suppose a solute molecule is damaged when it absorbs more than Na photons and the probability of damage satisfies a normal distribution in accordance with the laser intensity distribution. The damaged solute molecules no longer possess nonlinear absorption. That is:
with , (). is the probability of solute damage when a solute molecule absorbs np photons.In this case, the residual undamaged solute molecules just after the first pulse passes are:
Under our experimental condition, the time interval τp-p between two pulses is 0.1 s. Similar to solute migration, if the nonequilibrium distribution of solute molecules does not return to its equilibrium in τp-p we have to integrate the Fick’s law equation from to [7]:where is the population at the beginning of the diffusion and Dmd is the mass diffusion coefficient. Then, for the next coming pulse, the initial solute concentration distribution at the depth in the solution equals to the solute concentration at the end of the diffusion .Next we will give some results of the theoretical calculation by using the model. The solid lines in Fig. 4 and Fig. 11 are theoretical fits for Ge-150/DMF solution at different input energy. The parameters used are: ,,, ,,, , , . is obtained by the concentration and linear transmittance of the solution. Actually, it is impossible to obtain all the parameters simultaneously based on the experimental results; however, we achieved satisfactory accordance between theoretical calculations and the experimental results for different input energy in both ns and ps regimes by using the same parameters. By fitting the Z-scan curves of Ge-150/DMF solution at 22.4 μJ with different pulse repetition frequency simultaneously (Fig. 7), we find appropriate damage threshold Na = 7, indicating a solute molecule may be damaged when it absorbs more than seven photons. Figure 18 shows the theoretical calculation of open aperture transmittance curves at 10.1 μJ when the sample is stepped in two opposite directions, which is in agreement with the results shown in Fig. 6. This is interesting because we can directly judge the stepping direction of the sample according to the experimental curves.
Fig. 18 Theoretical open aperture transmittance curves in ns Z-scan for Ge-150/DMF solution at 10.1 μJ when stepped in two opposite directions. Square: -z side to the + z side; asterisks: + z side to the -z side.
Figure 19 shows theoretical transmittance curves in ns Z-scan for Ge-150/DMF solution at 10.1 μJ with different τtherm. We can see that the “w” curves due to absorption weakening get more unsymmetrical as τtherm increases, indicating more solute molecules are damaged as τtherm increases. According to Eq. (7), as τtherm increases, less heat in the solute molecules will transfer throughout the surrounding solvent molecules within the time of the laser pulse. In this case, more heat will accumulate in the solute molecules and they are more likely to be damaged when the heat in them exceeds the damage threshold. In ns regime, the pulse width τ is ns (HW 1/e2). By approximately fitting to the experimental results, we obtain τtherm = 3.7 ns, which is comparable with the ns pulse duration. As shown in Fig. 19, in ns regime, when τtherm ≥ 3 ns > τ, the “w” curve becomes more unsymmetrical as τtherm increases, while when τtherm < 2 ns < τ, the “w” curve becomes symmetrical and the transmittance value keeps unchanged as τtherm further decreases. In the latter case, we cannot see the influence of solute damage on nonlinear absorption except common transition from RSA to SA. In the ps regime, since 3.7 ns is much bigger than the ps pulse width (ps), we can see obvious absorption weakening induced by solute damage (see Fig. 20 ) at 2.4 μJ. In fact, as shown in Fig. 21 , τtherm = 200 ps is long enough for solute damage to happen in ps regime at 2.4 μJ. Until τtherm decreases to 20 ps which is comparable with the ps pulse width, absorption weakening is no longer observed. Similarly, as the way used in ref [21], we estimate the solvent-solvent time (τs-s) for DMF is 168 ps (0.945 g/cm3 and 73.09 g/mol), which is much bigger than that for methanol and ethanol [8,20,21].
Fig. 19 Theoretical open aperture transmittance curves in ns Z-scan for Ge-150/DMF solution at 10.1 μJ with different τtherm.
Fig. 20 Theoretical open aperture transmittance curves in ps Z-scan for Ge-150/DMF solution at 2.4 μJ with different.
Fig. 21 Theoretical open aperture transmittance curves in ns Z-scan for Ge-150/DMF solution at 10.1 μJ with different τp-p.
Similarly, by numerical simulation, we can estimate τtherm and τs-s for other three solvents as shown in Table 1 . On the one hand, τtherm of all the four solvents are much bigger than the ps pulse width, so all the four solutions show cross-pulse effects induced absorption weakening in the ps regime. On the other hand, compared with acetonitrile and acetone, τtherm of DMF and DMSO is much bigger and is comparable with the width of ns pulse, thus, the two solutions (Ge-150 in DMF and DMSO) still show this absorption weakening in the ns regime. That is why the four solutions show different characteristic between ns and ps regimes.
Table 1. and obtained from the solute damage model for different solvents
Equation (11) reflects the process of solute damage is a kind a cumulative effect related to τp-p and Dmd. Similar to ref [7], we define the time for nonequilibrium distribution of solute molecules to return to its equilibrium as τmd, which is called diffusion time constant. If τp-p ≥ τmd, every laser pulse will experience the same solution concentration and the nonlinear transmittance curve is symmetrical about the beam waist. Conversely if τp-p < τmd, the next coming pulse will experience the decrease of solute molecules caused by the previous pulse and this kind of cumulative effect will produce the absorption weakening. Figure 21 shows the theoretical calculation of open aperture transmittance curves in ns Z-scan at 10.1 μJ with different τp-p. We can see that more solute molecules are damaged as τp-p gets shorter. When τp-p increases to 10 s, nonlinear absorption curve has completely become symmetrical, indicating no cumulative effect induced solute damage remain. Contrary to τp-p, Dmd plays the opposite effects on solute damage. The bigger Dmd is, the more intact solute molecules will diffuse to occupy the position where solute molecules are damaged in τp-p . This will weaken the cross-pulse effect induced absorption weakening. So, this model is suitable to describe the solvent effect induced solute damage of Ge-150 molecules in both ns and ps regimes.
5. Conclusion
Nonlinear absorption of a newly synthesized organic inner salt Ge-150 dissolved in four solvents (DMF, DMSO, acetonitrile and acetone) is investigated by traditional Z-scan technique in ns regime and top-hat Z-scan technique in ps regime. When pulse energy is small, all the four solutions show common RSA in both ns and ps regimes. When pulse energy surpasses a threshold and pulse-to-pulse separation is shorter than a characteristic time, all the four solutions show absorption weakening induced by cross-pulse effects in ps regime. However, in ns regime, only two of them (Ge-150 dissolved in DMF and DMSO) show this weakening. When one of the conditions is not satisfied, absorption weakening is not observed. In view of the asymmetric molecular structure of Ge-150, we tend to believe that this absorption weakening is caused by solute damage rather than solute migration. By conducting a simple verification experiment, we verify our guess as both the linear and nonlinear transmittance of the corresponding solutions change after they are irradiated by either intense ps or ns pluses. Based on the idea that the solute damage is a result of insufficient capability of inter-molecular excess energy dissipation and the excess energy accumulation in the solute molecules, we proposed a simple theoretical model to interpret the experimental phenomenon. By approximately fitting to the experimental results, we obtained the local thermal equilibrium time and solvent-solvent time for the four solvents. As the local thermal equilibrium time of all the four solvents is much bigger than the width of ps pulse, all the four solutions show absorption weakening in ps regime. Moreover, the local thermal equilibrium time of DMF and DMSO is comparable with the width of ns pulse, thus the two solutions (Ge-150 dissolved in DMF and DMSO) show this weakening in ns regime. A ps time-resolved pump-probe experiment is performed and the results indicate the nonlinear absorption of the four solutions at low intensity is initiated by sequential ground and excited state absorption rather than TPA.
Acknowledgments
We acknowledge the support from the Ministry of Science and Technology of China for the International Collaboration on Scientific Research (2009DFA50620).
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