Nonlinear absorption in CuPc-doped PMMA thin film in the femtosecond regime: Experimental and theoretical studies

The nonlinear absorption (NLA) properties of copper phthalocyanine (CuPc)-doped polymethylmethacrylate (PMMA) thin film in the femtosecond regime were investigated both experimentally and theoretically. The open-aperture (OA) Z-scan measurements of the film were carried out by femtosecond laser pulse. A transition from saturable absorption (SA) to reverse saturable absorption (RSA) was observed as the excitation intensity is increased. The rate equation analysis based on an developed efficient energy level model was performed and the intensity dependence of level populations was obtained, which reveals the source of NLA. The results show that the transition from SA to RSA is ascribed to the fifth-order effect of excited-state absorption (ESA) induced by two-photon absorption (TPA) process. Furthermore, it is found that the CuPc-doped PMMA thin film possesses a large fifth-order coefficient (β (5)) of 0.24×10−21cm3/W2. It indicates that the CuPc-doped PMMA thin film could be a promising candidate for optical limiting material. © 2008 Optical Society of America OCIS codes: (160.4330) Nonlinear optical materials; (190.7110) Nonlinear optics: Ultrafast nonlinear optics; (190.4710) optical nonlinearites in organic materials. References and links 1. X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nature Photon. 2, 185 (2008). 2. Osamu Wada, “Femtosecond all-optical devices for ultrafast communication and signal processing,” New J. Phys. 6, 183 (2004). 3. G. S. He, J. D. Bhawalkar, C. F. Zhao, and P. N. Prasad, “Optical limiting effect in a two-photon absorption dye doped solid matrix,” Appl. Phys. Lett. 67, 2433 (1995). 4. R. Hagen and T. Bieringer, “Photoaddressable Polymers for Optical Data Storage,” Adv. Mater. 13, 1805-1810 (2001). 5. I. Wang, M. Bouriau, P. L. Baldeck, C. Martineau, and C. Andraud, “Three-dimensional microfabrication by two-photon-initiated polymerization with a low-cost microlaser,” Opt. Lett. 27, 1348-1350 (2002). 6. M. Hanack, D. Dini, M. Barthel, and S. Vagin, “Conjugated Macrocycles as Active Materials in Nonlinear Optical Processes: Optical limiting effect with phthalocyanines and related compounds,” Chem. Record. 2, 129-148 (2002). 7. A. Santhi, Vinu V. Namboodiri, P. Radhakrishnan, and V. P. N. Nampoori, “Spectral dependence of third order nonlinear optical susceptibility of zinc phthalocyanine,” J. Appl. Phys. 100, 053109 (2006). 8. G. de la Torre, P. Vaaquez, F. Agullo-Lopez, and T. Torres, “Role of structural factors in the nonlinear optical properties of phthalocyanines and related compounds,” Chem. Rev. 104, 3723 (2004). #98382 $15.00 USD Received 8 Jul 2008; revised 26 Aug 2008; accepted 26 Aug 2008; published 2 Sep 2008 (C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 14571 9. J. W. Perry, K. Mansour, I. Y. S. Lee, X. Wu, P. V. Bedworth, C. T. Chen, et al. “Organic optical limiter with a strong nonlinear absorptive response,” Science 273, 1533 (1996). 10. N. Venkatram, D. Narayana Rao, L. Giribabu, and S. Venugopal Rao, “Nonlinear optical and optical limiting studies of alkoxy phthalocyanines in solutions studied at 532 nm with nanosecond pulse excitation,” Appl. Phys. B 91, 149-156 (2008). 11. M. C. Larciprete, R. Ostuni, A. Belardini, M. Alonzo, G. Leahu, E. Fazio, C. Sibilia, and M. Bertolotti, “Nonlinear optical absorption of zinc-phthalocyanines in polymeric matrix,” Photonics and Nanostructures Fundamentals and Applications 5, 73-78 (2007). 12. C. Li, J. Si, M. Yang, R. Wang, and L. Zhang, “Excited-state nonlinear absorption in multi-energy-level molecular systems,” Phys. Rev. A 51, 569-575 (1995). 13. T.-H. Wei, T.-H. Huang, and T.-C. Wen, “Mechanism of reverse saturable absorption in chloro-aluminum phthalocyanine solution studied with Z-scan,” Chem. Phys. Lett. 314, 403-410 (1999). 14. L. Edwards and M. Gouterman, “Porphyrins XV. Vapor absorption spectra and stability: Phthalocyanines,” J. Mol. Spectrosc. 33, 292-310 (1970). 15. F. Li, Q. Zheng, G. Yang, N. Dai, and P. Lu, “Spectrum of copper phthalocyanine: Experiments and semiempirical quantum chemical calculations” Physica B 403, 1704-1707 (2008). 16. T. Basova et al., “Spectral characterization of thin films of vanadyl hexadecafluorophthalocyanine VOPcF16,” Surf. Sci. (2008), doi:10.1016/j.susc.2008.04.044. 17. 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 (1990). 18. G. Yang, W. Wang, L. Yan, H. Lu, G. Yang, and Z. Chen, “Z-scan determination of the large third-order optical nonlinearity of Rh:BaTiO3 thin films deposited on MgO substrates,” Opt. Commun. 209, 445-449 (2002). 19. M. Fakis, G. Tsigaridas, I. Polyzos, V. Giannetas, P. Persphonis, I. Spiliopoulos, and J. Mikroyannidis, “Intensity dependent nonlinear absorption of pyrylium chromophores,” Chem. Phys. Lett. 342, 155 (2001). 20. S. M. OFlaherty, S. V. Hold, Y. Chen, M. Hanack, and W. J. Blau, “Reverse saturable absorption based optical limiting properties of Indium and Gallium phthalocyanines and naphthalocyanines,” Proc. SPIE 4991, 183 (2003). 21. S. Hughes, G. Spruce, J. M. Burzler, R. Rangel-Rojo, and B. S. Wherrett, “Theoretical analysis of the picosecond, induced absorption exhibited by chloroaluminum phthalocyanine,” J. Opt. Soc. Am. B 14, 400-404 (1997). 22. N. K. M. Naga Srinivas, S. Venugopal Rao, and D. Narayana Rao, “Saturable and reverse saturable absorption of Rhodamine B in methanol and water,” J. Opt. Soc. Am. B 20, 2471 (2003). 23. T. H. Wei, T. H. Huang, H. D. Lin, and S. H. Lin, “Lifetime determination for high-lying excited states using Z scan,” Appl. Phys. Lett. 67, 2266 (1995). 24. R. L. Sutherland, M. C. Brant, J. E. Rogers, J. E. Slagle, D. G. McLean, and P. A. Fleitz, “Excited-state characterization and effective three-photon absorption model of two-photon-induced excited-state absorption in organic push-pull change-transfer chromophores,” J. Opt. Soc. Am. B 22, 1939 (2005). 25. J. M. Nunzi and F. Charra, “Intensity-dependent Two-photon-enhanced degenerate nonlinearity of polydiacetylene,” Nonlin. Opt. 1, 19-30 (1991). 26. J. M. Nunzi and F. Charra, “Picosecond two-photon absorption effects on index variation gratings in polydiacetylenes,” Nonlin. Opt. 2, 131-148 (1992). 27. A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinhardt, P. Roderer, and A. G. Dillard, “Thirdand fifth-order optical nonlinearities in organic materials,” Chem. Phys. Lett. 228, 646 (1994). 28. T. C. Lin, G. S. He, Q. Zheng, and P. N. Prasad, “Degenerate two-/three-photon absorption and optical powerlimiting properties in femtosecond regime of a multi-branched chromophore,” J. Mater. Chem. 16 2490 (2006). 29. M. Drobizhev, A. Rebane, Z. Suo, and C. W. Spangler, “One-, twoand three-photon spectroscopy of -conjugated dendrimers: cooperative enhancement and coherent domains,” J. Lumin. 111, 291 (2005). 30. C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, “Dynamic and steady-state behavior of reverse saturable absorption in metallophthalocyanine,” Phys. Rev. A 49, 1149-1157 (1994). 31. S. Venugopal Rao, S. Singh, B. S. DeCristofano, and D. Narayana Rao, ”Theoretical and experimental study of the excited state dynamics in reverse saturable absorbers using Z-scan technique,” http://www.standrews. ac.uk/ scnlo/icol.pdf. 32. B. Aneeshkumar, P. Gopinath, C. P. G. Vallabhan, V. P. N. Nampoori, and P. Radhakrishnan, “Optical-limiting response of rare-earth metallophthalocyanine-doped copolymer matrix,” J. Opt. Soc. Am. B 20, 1486 (2003).


Introduction
In recent years, there is great interest in understanding the optical nonlinearities of dyes for widespread applications in optical switches [1], optical signal-processing devices [2], optical limiting [3], optical data storage [4] and three-dimensional micro fabrication [5].Among all the applications of nonlinear optical properties, optical limiting is one of the most promising prop-erties for practical use, such as protection of human eyes and optical sensors [6].The nonlinear absorption (NLA) phenomena can be of either two types: saturable absorption (SA), in which the absorption coefficient decreases with increasing intensity, and reverse saturable absorption (RSA), in which the absorption coefficient increases with increasing intensity.RSA can occur when the absorption cross-section of excited states exceeds the ground state cross-section, while for SA to happen at least one of the excited state cross-sections would need to be smaller than the ground state cross-section.
Metallophthalocyanines exhibit large ultrafast non-resonant nonlinear optical responses due to the large two-dimensional π-conjugated systems.It has attracted considerable attentions owing to its potential optical and electrical applications [7][8][9].The NLA properties in these materials are usually characterized by z-scan technique in the nanosecond and picosecond regimes [10][11][12][13].To our knowledge, few studies have been devoted to the NLA properties in the femtosecond regime.In contrast to the nanosecond or picosecond pulse, the fs pulse can be compared with the lifetimes of the higher upper excited states in the molecule system, which will play an important role in the NLA.Moreover, owing to the extremely strong excitation intensity, it can be predicted that some novel NLA phenomena would happen if these materials are excited by the femtosecond laser.Therefore, on further research, the ultrafast nonlinear response is quite essential for understanding the source of NLA in the femtosecond regime and their practical applications.
In this paper, the nonlinear optical properties of the copper phthalocyanine (CuPc)-doped polymethylmethacrylate (PMMA) thin film were studied using a femtosecond laser by performing an open-aperture (OA) Z-scan measurement.On the other hand, in order to reveal the source of the observed NLA response, an efficient energy level model was developed based on which a theoretical rate equation analysis was carried out.Our studies show that the CuPc-doped PMMA thin film is a promising candidate for optical limiting applications in the femtosecond regime.

Experiment
To prepare the CuPc-doped PMMA thin film, 1 wt.%PMMA was first dissolved in chloroform.Subsequently, CuPc was added according to the weight ratio (3 : 7) of CuPc to PMMA, and thoroughly mixed ultrasonically.Then the mixed solution was spin-coated onto the cleaned quartz substrate (thickness 0.3 mm) at a rotating speed of 6500 r/min.Finally, the film was annealed at 150 • C for 3 hours, and then a sample of 200 nm thickness was obtained.The linear absorption spectra for the mixed solution and the film were measured with a UV-visible spectrometer (HITACHI U-3310), and the results are shown in Fig. 1(a) and Fig. 1(b), respectively.It can be seen that both of them have two typical ground-state absorption bands: the Q band (600-900 nm) and the B band (300-400 nm), which originate from ππ * transition.Figure 1(a) has an intense and sharp absorption peak at 658 nm.It is in agreement with other reports [14,15], showing that it is monomer solution.Compared with Fig. 1(a), Fig. 1(b) shows that the Q band is split into two distinct bands (Davido splitting), and the peaks are slightly red shifted due to the aggregation effect and annealing treatment [16].
The OA z-scan is a popular technique for studying NLA of both organic and inorganic materials.This technique, which is described in detail elsewhere [17], has the advantage that it immediately indicates the sign and type of nonlinearity [18].In our experiment, the laser source used for the measurement was a Ti:sapphire regenerative amplifier (Spitfire, Spectra-Physics, 800 nm, 50 fs, 1 kHz).The sample was scanned along the optic axis (the z-direction) through the focus of the lens, which has a focal length of 250 mm, while the energy transmitted through an aperture in the far field was recorded as a function of the sample position.The radius of the beam waist ω 0 was 30 μm. z 0 = πω 2 0 /λ is the Rayleigh length.The value of z 0 of the beam was calculated to be 3.8 mm, much longer than the thickness of either the 0.3-mm thick quartz substrates or the film.The reference beam energy and the transmitted beam energy were measured by a dual-channel energy meter (Molectron model # EPM 2000 with model # J8LP heads) simultaneously.We performed the OA z-scan measurements both on the CuPc-doped PMMA film and the pure PMMA film, validating that the measured NLA phenomena originate from CuPc only.

Theory
When a light propagates through a nonlinear absorption material, the intensity transmitted through the sample is given by the Beer's law equation where I is the intensity, z the penetration depth inside the nonlinear medium and α the absorption coefficient.When a very high irradiance laser beam propagates through a nonlinear absorption material, third-and fifth-order absorptive phenomena need to be considered.In this case, the absorption coefficient α can be written as [19] α where α 0 is the linear absorption coefficient, β (3) and β (5) the third-(TPA) and fifth-order nonlinear absorption coefficient, respectively.If we define Δα = α − α 0 , Eq. ( 2) can be expressed as The dynamic process of NLA can be investigated by the light-propagation equation and the rate equation based on a multi-level energy model for the organic molecular system.In the multi-level energy model, the contributions of each excited state to the NLA of the materials are different when excited by laser with nanosecond (ns), picosecond (ps) and femtosecond (fs) pulse.For the nanosecond laser, the pulse width is much longer than the upper excited states lifetimes and the contributions of the upper excited states to the NLA can be neglected.So the NLA process in the nanosecond regime is usually described by a three-level model involving the ground state, the first excited singlet state and the first excited triplet state [7,8,20].For the picosecond laser, the pulse width is much shorter than τ ISC (the intersystem-crossing lifetime, usually several tens of nanoseconds for dyes) so that contributions of the triplet states to NLA can be ignored.Hence the NLA process in the picosecond regime is described by a three-level model involving the ground state, the first excited singlet state and the second excited singlet state [21,22].However, the above two models become inapplicable in understanding the NLA behaviors in the femtosecond regime.Since the laser pulse width in femtosecond regime can be compared with the higher excited state lifetimes (usually several hundreds of femtoseconds for dyes [23]), contributions of the higher excited states to the NLA become significant and can not be neglected.Therefore, a new energy level model in femtosecond regime needs to be developed.
Figure 2 illustrates a developed four-level model, in which the ground state S 0 , the first excited singlet state S 1 , the second excited singlet state S 2 and the higher excited singlet state S n are considered, and all triplet states are ignored.Since CuPc belongs to the C 4 v point group, its corresponding electronic state symmetries are A 1 for the S 0 band, E for the S 1 band and E for the S 2 band.One-photon excitation A 1 (S 0 ) → E(S 1 ) is thus dipole allowed, so is the Twophoton excitations A 1 (S 0 ) → E(S 2 ).For the NLA excited by the fs laser pulse, the contribution of TPA from S 0 to S 2 is greater than that of OPA from S 0 to S 1 , namely, the TPA from S 0 to S 2 is predominated.Moreover, One-photon absorption (OPA) is between the states of opposite parities while TPA occurs between states of even parties, so TPA from S 1 to S n is not allowed.Hence, the system mainly simultaneously absorbs two photons, promoting an electron from S 0 to S 2 .Subsequently, from S 2 , the electron will be promoted to S n by absorbing another single photon, resulting in excited-state absorption (ESA) induced by two-photon absorption (TPA) [24,25,26,27].The rate equations for describing the time variation of the population density in each energy level are Taking into account only TPA from S 0 to S 2 and OPA from S 2 and S n , and the linear absorption at the wavelength studied is considered negligible, the intensity transmitted through sample is given by [19] with Where τ is the pulse duration; n 0 , n 1 , n 2 and n 3 represent the number densities of states S 0 , S 1 , S 2 and S n , respectively; hν is the incident photon energy; I 0 is the peak intensity at the focal point.The first-term on the right-hand side is corresponding to the third-order nonlinear effect since it varies as I 2 .The TPA contributes to the intensity variation with an absorption coefficient β (3) .While the second-term arises from ESA.Since this term varies as I 3 , ESA is related to the fifth-order nonlinearity with a absorption coefficient β (5) .Comparing the Eqs.( 2) and ( 8) the fifth-order absorption coefficient can be related to the ESA cross-section σ 2 via β (3) and β (5) can be extracted from the OA z-scan curves, and the ESA cross-section σ 2 can be calculated from Eq. ( 10).

Results and discussion
In order to explore the intensity dependence of NLA of the CuPc-doped PMMA thin film, the sample is scanned at the same position with increasing and decreasing the intensity.As shown in Fig. 3(a) to (j), at the beginning, there is no transmission variation at low intensity of 1.36× 10 12 W /cm 2 .When the excitation intensity is increased at 2.83× 10 12 W /cm 2 , it exhibits an increase of transmittance at positions close to the focus, a typical SA effect.When the excitation intensity increases to be 10.6 × 10 12 W/cm 2 , it still exhibits a SA effect.However it shows a trend of transition from SA to RSA, because the transmittance has a sudden decrease at the position of focus.When the excitation intensity increases to be 13.4 × 10 12 W/cm 2 , it completely shows a decrease of the transmittance at positions close to the focus, that is, it completely transit from SA to RSA.When the excitation intensity increases to be 19.8 × 10 12 W/cm 2 , it still exhibits a RSA effect.Then decreasing the excitation intensity to be 7.78 × 10 12 W/cm 2 , it completely transits from RSA back to SA.Finally, the excitation intensity decreases to the low intensity of 1.36 × 10 12 W /cm 2 again, there is no transmission variation in the scan.Concisely, the OA z-scan curves reveal a transition from SA to RSA while increasing the excitation intensity.And the transition from RSA back to SA while decreasing the excitation intensity indicates the sample is not damaged.In order to obtain the nonlinear absorption coefficient Δα, we fit the transmission z-scan curves by the well-established formula [17]  Here, L e f f = [1 − exp(−α 0 L)]/α 0 is the effective thickness of the films, L is the film thickness.
In order to obtain the relationship of nonlinear absorption coefficient and the excitation intensity, we plot Δα/I versus I, which is shown in Fig. 4. It comprises of two distinct responses.At low intensities a constant negative coefficient is observed which means that a pure third-order effect is present, corresponding to β (3) .When the excitation intensities exceed a critical value, the dependence becomes linear with a positive slope.This suggests that a higher order effect, that is, the fifth-order effect becomes predominated, which contributes to the RSA, when the excitation intensity increased above the critical intensity of I = 10.6 × 10 12 W /cm 2 .The slope of this linear increase section corresponds to β (5) .According to this procedure, the nonlinear absorption coefficients of the sample are determined as β (3) = −3.22×10−9 cm/W , β (5)  = 0.24×10 −21 cm 3 /W 2 .We find that our β (5) values are two orders of magnitude higher than those reported in organic molecules with femtosecond excitation [28,29].In addition, the ESA cross-section σ 2 can be calculated from Eq. ( 10), which is 7.41 ×10 −19 cm 2 .Furthermore, in order to reveal the source of the observed NLA process theoretically, we carry out a rate equation analysis based on the above energy level model and obtain the intensity dependence of level populations.The laser parameters are set according to that in our experiment (800 nm, 50 fs, 1 kHz).In the previous research works [30,31], some of the photophysical Fig. 4. Intensity dependence of NLA coefficient for the CuPc-doped PMMA thin film.The solid line is guide to the eye.parameters of CuPc have been reported, which are σ 0 = 2 × 10 −18 cm 2 , σ 1 = 3.5 × 10 −17 cm 2 , τ 1 = 15ns.τ 2 and τ 3 are set as 47ps and 100 f s respectively according to Ref. [23].Herein, we firstly choose them as reference values.Next, according to our experimental results, we subtly adjust the parameters to largely well reproduce and elucidate the experiment phenomena.The simulation results are given in Fig. 5, which illustrates the curves of populations n 0 , n 1 , n 2 and n 3 versus the time during a single light pulse under four different excitation intensities.It should be noted that all the molecules will return to the ground state after a sufficiently long time after the pulse.From Fig. 5(a) we can see that when the excitation intensity is at I = 2.83 × 10 12 W /cm 2 , most molecules are populated in the ground state S 0 .In this case, the contribution of the ground state to NLA is dominated so that SA should be observed.From Fig. 5(b) we can see that when the excitation intensity is at I = 10.6 × 10 12 W /cm 2 , many molecules are excited to the second excited singlet state S 2 from the ground state S 0 , and a critical part of molecules are excited to the higher excited singlet state S n .In this case, n 0 = n 2 = n 3 , which can be regarded as a critical population at the critical excitation intensity.It corresponds to the beginning of the transition from SA to meaning that the fifth-order effect occurs.From Fig. 5(c) we see that when the excitation intensity increases to be I = 13.4 × 10 12 W /cm 2 , more molecules are excited to the higher excited singlet state S n from the second excited singlet state S 2 .In this case, the contribution of the higher excited singlet state S n to NLA is becoming predominated, so that the fifth-order effect is becoming predominated due to which a RSA response should be observed.From Fig. 5(d) we can see that when the excitation intensity increases to be I = 19.8× 10 12 W /cm 2 , most molecules have been further excited to the higher excited singlet state S n from the second excited singlet state S 2 .In this case, the contribution of the higher excited singlet state S n to NLA is completely predominated, a stronger RSA response can be observed.From the simulation of the intensity dependence of the level populations, it can be concluded that TPA is dominant until a sufficient S 2 population is reached, such that another incident photon can be absorbed and excite the molecule from S 2 to a higher excited singlet state S n .The critical value of the intensity signifies that a critical population must be excited to the higher excited singlet state S n by a TPA-induced ESA process, and then the fifth-order effect becomes significant so that RSA occurs.
In order to interpret the observed transition more clearly from SA to RSA, we simulate the transient transmission T (t) = I(t, L)/I(t, 0) versus time during a light pulse based on the above rate equations.In the calculation, the pulse duration is set as 50 fs and six excitation intensities are adopted according to our experiments.The results are given in Fig. 6, which shows two distinct NLA phenomena.When the input intensity is at (a) I = 2.83 × 10 12 W/cm 2 , (b) I = 5.66 × 10 12 W/cm 2 , (c) I = 10.6 × 10 12 W/cm 2 , the transmission increase with the excitation intensity increasing and decrease with the excitation intensity decreasing during the laser pulse.
It is an obvious SA phenomenon.However, when the excitation intensity is at (d) I = 13.4 × 10 12 W/cm 2 , (e) I = 17.0 × 10 12 W/cm 2 , (f) I = 19.8× 10 12 W/cm 2 , the transmission decrease with the excitation intensity increasing and increase with the excitation intensity decreasing during the laser pulse.It is an obvious RSA phenomenon.Moreover, the RSA effect becomes stronger with increase of the excitation intensity.Therefore, the theoretical simulation can well elucidate our experimental results.
In addition, we have studied the femtosecond optical-limiting characteristic of CuPc-doped PMMA thin film.The sample is prepared according to the above mentioned procedure.The laser used is 50 fs pulse duration and 1 kHz repetition rate with 800 nm wavelength.Figure 7 shows the optical-limiting response of the CuPc-doped PMMA thin film by increasing and decreasing the intensity, keeping the same position on the sample.At very low input intensity, the transmission obeys Beer-Lambert law.At high input intensity, the output intensity decreases with an increase in input intensity.When the maximum input intensity is 19.8 × 10 12 W/cm 2 , this process is reversible by decreasing the input intensity.It shows a good optical-limiting property.As the above analysis reveals RSA due to ESA induced by TPA is the main mechanism for  CuPc molecules to produce an optical-limiting effect.We have also measured the laser damage thresholds for the CuPc-doped PMMA thin film.The laser damage threshold is defined here to be the intensity necessary to cause a permanent measurable change in the sample transmission measurements.It is found that the damage threshold of the sample ranged between 25.0 × 10 12 W/cm 2 (1.25 J/cm 2 ) and 30.0 × 10 12 W/cm 2 (1.50 J/cm 2 ).It's a little lower than that reported in other metallophthalocyanine-doped copolymer matrix with nanosecond excitation, which is between 1.80 J/cm 2 to 2.00 J/cm 2 [32].

Conclusion
In summary, the NLA properties of CuPc-doped PMMA thin film in the femtosecond regime is investigated both experimentally and theoretically.A transition from SA to RSA is observed by increasing the intensity, and an efficient four-level model for the organic system in the femtosecond regime is developed.The rate equation analysis based on this model greatly enhances the understanding of the complex dynamics of the level populations and reveals the source of NLA, providing a clear interpretation of the experimental results, that is, the transition from SA to RSA is ascribed to the fifth-order effect.Moreover, the CuPc-doped PMMA thin film possesses a large fifth-order coefficient and good femtosecond optical-limiting properties, Hence it has great potential applications for protection of eyes and sensors from intense laser pulses.Most importantly, this study is helpful to control the NLA of organic molecular system by the laser excitation intensity in the femtosecond regime.

Fig. 1 .
Fig. 1.The linear absorption spectra for (a) the mixed solution and (b) the CuPc-doped PMMA thin film.

Fig. 3 .
Fig.3.OA z-scan experimental curves (a) to (j) orderly correspond to the curve when increasing and decreasing the intensity.Scattered data are experimental results and solid red lines are theoretical fittings.