Nonlinear dynamics of picosecond pulse trains in naphthalocyanines and phthalocyanines

Computational and Theoretical Chemistry 1104 (2017) 32–36

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Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc

Nonlinear dynamics of picosecond pulse trains in naphthalocyanines and phthalocyanines Quan Miao a,⇑, Erping Sun a, Min Liang a,b, Qixin Liu a,b, Yan Xu a,b a b

College of Electronics, Communication and Physics, Shandong University of Science and Technology, Qingdao, 266590 Shandong, People’s Republic of China College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590 Shandong, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 5 January 2017 Received in revised form 2 February 2017 Accepted 3 February 2017 Available online 6 February 2017 Keywords: Pulse trains Optical limiting Naphthalocyanine Phthalocyanine Reverse saturable absorption

a b s t r a c t We study the optical dynamics of picosecond pulse trains in naphthalocyanines and phthalocyanines. The pulse train is assumed to contain 35 ps subpulses with each subpulse width of 100 ps and with spacing between subpulses of 12 ns. In this work, we used numerical theoretical method by solving twodimensional paraxial filed equation coupled with rate equations. Molecular parameters are extracted from experiments and our results show good consistency with the experimental work. The dynamical processes in naphthalocyanines and phthalocyanines are simulated with a five-level model, where the main optical mechanism is the sequential (singlet-singlet)
(triplet-triplet) two-photon absorption. The results of this work emphasize that both naphthalocyanines and phthalocyanines are good optical limiting materials, and naphthalocyanine with lighter central metal Ga shows better optical behaviour with picosecond pulse trains. Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction Nowadays, laser technology has got extremely rapid development and it has been widely used in various fields such as medicine, communication, military and many other influential fields [1]. The widespread applications of laser gradually give rise to one important issue, which is the protection of optical devices and human eyes from the strong intensity laser. One of the most efficient method is to adopt optical limiting (OL) materials for protection [2,3]. Until now, reverse saturable absorption (RSA) is the most frequently used one among various mechanisms to achieve OL function [4–6]. The absorption cross section of excited state is larger than that of ground state, which is the main characteristic of RSA materials [7–9]. The OL dynamics are mainly determined by the duration of interaction between laser pulses and materials. For ultrashort pulses such as femtosecond pulses, the primary OL absorption process is the one-step coherent two-photon absorption (TPA). But for long laser pulses such as nanosecond pulses or laser pulse trains, two-step sequential TPA dominates the OL absorption where RSA is the main OL mechanism. In this case, the light-matter interaction requires a finite response time [10–13]. So for those materials with singlet and triplet states, the principal absorption channel is the

⇑ Corresponding author. E-mail address: [email protected] (Q. Miao). http://dx.doi.org/10.1016/j.comptc.2017.02.004 2210-271X/Ó 2017 Elsevier B.V. All rights reserved.

sequential (singlet-singlet)
(triplet-triplet) TPA [4]. The duration of laser pulses could be comparable with the effective population transfer time which is known as the transfer time from ground to triplet state. In the course of finding and synthesizing better RSA materials, naphthalocyanines (Npcs) and phthalocyanines (Pcs) attract thousands of researchers. The main advantage lies in their special structure with highly conjugated delocalized p-electron [14–22]. One recent experiment reported their OL and photophysical study of Npcs and Pcs with different central metal-coordination bond [23]. Our previous work has theoretically studied Npcs and Pcs based on the experiment with single nanosecond laser pulses [24]. In this work we focus on the nonlinear dynamics of picosecond pulse trains in Npcs and Pcs by numerically solving the paraxial field equation together with the rate equations [25].

2. Method The molecular structures of Npcs and Pcs are shown in Fig. 1(a). Considering the interaction between picosecond pulse trains and Npcs and Pcs, we simplified the system to be a five-level scheme as shown in Fig. 1(b). Since we considered long pulses, so there are two sequential TPA channels in this scheme: (S0 ! S1 Þ
ðS1 ! Sn ) and (S0 ! S1 Þ
ðT 1 ! T 2 Þ. Also we assumed the frequency of pulse trains to be in the vicinity of one-photon transitions in accordance with the experiment [23].

Q. Miao et al. / Computational and Theoretical Chemistry 1104 (2017) 32–36

33

Fig. 1. (a) Structures of the naphthalocyanines and phthalocyanines in Ref. [23] and (b) the Jablonski diagram of a generalized five-level system.

The incident laser pulse train is supposed as

IðtÞ ¼

X

In ðtÞ;

n ¼ 0; 1; . . . ; ntot  1;

ð1Þ

n¼0

where n is the subpulse number starting from 0, ntot is the total subpulses number. For each subpulse, the paraxial equation can be described in the following form [26]



 X @ 1 @ In ðtÞ ¼ N rij ðqi  qj ÞIn ðtÞ;  @z c @t j>i

ð2Þ

where N is molecular concentration, rij is absorption cross-section via transition from state i to state j. Here c is the speed of light in vacuum, z is the propagation distance and qk is the population of state k. Under the interaction of laser pulses, the dynamical populations of the five states can be described by the rate equations [27],

@ qS0 ¼ cðtÞðqS0  qS1 Þ þ CS1 qS1 þ CT 1 qT 1 ; @t   @ þ CS1 þ cc qS1 ¼ CSn qSn  cS ðtÞðqS1  qSn Þ þ cðtÞðqS0  qS1 Þ; @t   @ þ CSn qSn ¼ cS ðtÞðqS1  qSn Þ; ð3Þ @t   X @ þ CT 2 qT 2 ¼ cT ðtÞðqT 1  qT 2 Þ; qk ¼ 1; @t k where cc is the rate of intersystem crossing (ISC) transition S1 ! T 1 .

CS1 ; CSn ; CT 1 and CT 2 are the decay rates of the states S1 ; Sn ; T 1 and T 2 ,

respectively. cðtÞ; cS ðtÞ and cT ðtÞ are the populated rates to higher states via one-photon transitions S0 ! S1 ; S1 ! Sn and T 1 ! T 2 respectively, which can be written as

r IðtÞ cij ðtÞ ¼ ij ; hx

ð4Þ

where x is the laser frequency. Here  h ¼ h=ð2pÞ; h ¼ 6:626
1034 is Planck constant. In our work, we supposed the pulse train has 35 subpulses with each subpulse width of 100 ps and with spacing between subpulses of 12 ns. Also we assumed the temporal shape of the initial subpulse has rectangular form, which could characterize the shape of subpulses more accurately [26,28].

"  # "   # 2 2 nD  t 0 r In ðrÞ ¼ I0 exp  ln 2 exp  ln 2 ; r0 se

ð5Þ

where t 0 ¼ ½ðntot  1ÞD þ s=2; se ¼ 10D=3 is the half width at halfmaximum (HWHM) of the envelope, r0 ¼ 2 mm is the beam width.

The pulse trains used in experiments are usually picosecond pulses separated by nanosecond separation [9,29,30]. In experiment [23], the single pulse duration is 3:5 ns (HWHM). In our simulation, we assumed D ¼ 12 ns; s ¼ 100 ps, and ntot ¼ 35, so the total duration of all laser subpulses is also 35
100 ps ¼ 3:5 ns. To better study the OL process, we also calculated the energy transmittance,

T ðLÞ ¼

Jðz0 þ LÞ ; Jðz0 Þ

ð6Þ

where z0 ¼ 0 is the entry position of the pulse train, L is the thickness of materials. Jðz0 Þ and Jðz0 þ LÞ are the total pulse energy at z0 and at z0 þ L respectively. And the total pulse energy is written as

JðzÞ ¼ 2p

Z

R

Z

1

Iðt; r; zÞrdrdt; 0

ð7Þ

0

where Iðt; r; zÞ is the instantaneous intensity. 3. Results and discussion In order to ensure high reliability of our numerical results, we performed the simulations using photophysical parameters from the experiment [23], which are listed in Table 1. All samples in the experiment [23] were placed in a 1:0 cm path length quartz cell with concentration of 3:01
1022 m3 . According to the scaling relation Ltheo N theo ¼ Lexp N exp , we reduced the length to Ltheo ¼ 1:0 mm and increased the concentration to N theo ¼ 3:01
1023 m3 , which can highly save the computational expense. And we assumed 21 1 C1 m2 in simulations. Sn ¼ CT 2 ¼ 1 ps; CS1 þ cc  cc and rS1 Sn ¼ 10

The energy transmittances of the pulse train are quite important to analyze the OL dynamics of Npcs and Pcs which are shown in Figs. 2 and 3. In our simulations, the maximum peak of the incident pulse trains is set to be I0 ¼ 1
1013 W=m2 which can avoid S0 ! S1 saturation absorption. In Fig. 2 with I0 ¼ 1
1013 W=m2 , one can see that both Npcs and Pcs display remarkable OL behaviours. The primary reason is the molecular structure with highly conjugated delocalized p-electron which is enhanced by the central metals. Also one can notice that Npcs show much better OL performance than Pcs along with the distance increasing. This is because Npcs with bulky substituents have one order of magnitude faster ISC rate cc than that of Pcs. So the sequential (singletsinglet)
(triplet-triplet) TPA in Npcs is stronger than that in Pcs. With the increase of propagation distance, Npcs reach their saturation values of energy transmittances at about L ¼ 1:0 mm which is much shorter than that for Pcs at L ¼ 2:0 mm. According to the

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Q. Miao et al. / Computational and Theoretical Chemistry 1104 (2017) 32–36

Table 1 Photophysical parameters of Npcs 1,2 and Pcs 1,2 [23]. Compounds

ES0 S1 (eV)

ET 1 T 2 (eV)

sT 1 ðlsÞ

cc ðs1 Þ

Npc 1

1.5549

2.0367

4:2
10

9

Npc 2

1.5491

2.0039

2:1
10

10

Pc 1

1.7400

2.1420

3:5
108

Pc 2

1.7208

2.1057

9

2:7
10

71.4 8.3 114.2

rS0 S1 ðm2 Þ

24.1

rT 1 T 2 ðm2 Þ

1:146
10

21

5:004
1020

9:932
10

22

4:912
1020

4:584
1022

2:491
1020

22

2:774
1020

2:330
10

1.0 13

I0=1X10 W/m

2

0.8

Npc1 Npc2 T(z)

0.6

Pc1 Pc2

0.4

0.2

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

L(mm) Fig. 2. Energy transmittance T ðLÞ (Eq. (6)) as a function of the propagation distance L with I0 ¼ 1:0
1013 W=m2 .

1.0

L=1mm 0.8

Npc1 Npc2

T(L)

0.6

Pc1 Pc2

0.4

0.2

0.0

0.1

1

10

2

100

1000

I0(MW/cm ) Fig. 3. Energy transmittance T ðLÞ (Eq. (6)) as a function of the peak intensity of the incident laser pulse trains at L ¼ 1 mm.

data of Fig. 2, the energy transmittances TðLÞ of four materials at L ¼ 3:0 mm are 0.00772 (Npc1), 0.0092 (Npc2), 0.04301 (Pc1), 0.0692 (Pc2) respectively. Concerning the different peripheral substituents, one can notice that Npc1 and Pc1 have better OL per-

formances than Npc2 and Pc2 respectively. Unfortunately, the authors in experiment [23] only gave conclusion that Npcs are better OL materials than PCs. Our computational results indicate that OL properties are sensitive to the molecular structures, and not

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Q. Miao et al. / Computational and Theoretical Chemistry 1104 (2017) 32–36

5

10

13

I0=1X10 W/m Npc1 Npc2

4

10

τST(ns)

2

Pc1 Pc2

3

10

2

10

1

10

0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32 34

n (pulse number) Fig. 4. Effective time

sST of population transfer S0 ! T 1 with I0 ¼ 1
1013 W=m2 at L ¼ 0 and r ¼ 0.

2

(a)

I (W/m )

7

0.0

6

2.7E+08

5

5.4E+08

8.0x10

8

6.0x10

8

4.0x10

8

2.0x10

8

0

1.1E+09

1.5x10

9

1.0x10

9

5.0x10

8

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32 34

(c)

r=2.5mm

2

I (W/m )

r(mm)

r=5.0mm

0.0

8.0E+08

4

(b)

1.3E+09

3

1.6E+09

0.0

1.9E+09

2

0

2

I (W/m )

2.1E+09

1

0 0

2

4

6

2.0x10

9

1.5x10

9

1.0x10

9

5.0x10

8

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32 34

(d)

r=0.0mm

0.0

8 10 12 14 16 18 20 22 24 26 28 30 32 34

0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32 34

n (pulse number)

n (pulse number) 2

Fig. 5. (a) 2D map of the laser intensity after absorbing of Npc1 with I0 ¼ 1
1013 W=m at L ¼ 1 cm. Laser intensity at (b) r ¼ 5:0 mm, (c) r ¼ 2:5 mm and (d) r ¼ 0.

only the central metals but also the peripheral substituents could dramatically affect the OL behaviours. In Fig. 3 we give the dependence of energy transmittances on the peak intensity of the incident pulse trains at L ¼ 1 mm. According to the data of Fig. 3, the energy transmittances TðLÞ of four materials at L ¼ 1:0 mm with I0 ¼ 1:0
1013 W=m2 are 0.00799 (Npc1), 0.00996 (Npc2), 0.0436 (Pc1), 0.07348 (Pc2) respectively. It further validates that Npcs have better OL characteristics than Pcs with increase of laser intensity. Our computational results are in accordance with the experimental conclusion. The tendency of the dependence can be written as



T ¼

expðNrS0 S1 LÞ;

I0 ! 0;

expðNrT 1 T 2 LÞ; I0 ! 1:

ð8Þ

In the weak intensity region, the energy transmittances mainly depend upon one-photo absorption cross section rS0 S1 . In the strong intensity region, the energy transmittances are determined almost by rT 1 T 2 . Both rS0 S1 and rT 1 T 2 of Npcs are larger than those of Pcs (Table 1). So in the course of increasing intensity, the energy transmittances of Npcs are always lower than that of Pcs. The two steps of the sequential TPA, namely S0 ! S1 and T 1 ! T 2 , is strongly affected by the population transfer between singlet and triplet states. For the studied five-level system, we characterized the population transfer process S0 ! T 1 with effective time sST , which is shown in Fig. 4. One can see that transfer time sST of Npcs is faster than that of Pcs at the central peak of the pulse trains. The main reason is the ISC rate cc of Npcs is about one order of magnitude faster than that of Pcs (Table 1), which is

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Q. Miao et al. / Computational and Theoretical Chemistry 1104 (2017) 32–36

mainly determined by the central metals. As for the two wings with weak intensity, Npc2 and Pc2 have faster population transfer time sST than that of Npc1 and Pc1. In fact the process S0 ! T 1 depends on the competition between the transfer time sST and the state lifetime sT 1 . Npc2 and Pc2 have shorter lifetime sT 1 , so their population transfer processes become faster. Also one can notice that Npc1 and Pc1 have faster time sST than Npc2 and Pc2 respectively at the central part, which is opposite with the result with our work with single nanosecond pulses [24]. The main factor here is that the width of the picosecond subpulse is much shorter than that of the single nanosecond pulse. So at the large interval D without laser, the pumped populations have enough time to decay. In this case, the one-photo absorption cross section rS0 S1 shows its importance. So when we used picosecond pulse train at the central high intensity region, Npc1 and Pc1 with larger rS0 S1 will transfer population faster than Npc2 and Pc2 respectively. According to above discussions, we selected Npc1 with best OL performance to investigate the propagation dynamics of the pulse train. Considering the radial distribution of the pulse train, a 2D map of field intensity is shown in Fig. 5. For better exhibition of the appearance, we simulated with a long propagation distance L ¼ 1 cm. Due to the strong excited state absorption T 1 ! T 2 , one can see that the field intensity decreases drastically. The field intensity shows obvious inhomogeneous in the transverse direction in Fig. 5(a). We plotted the intensity distribution at different radial distance r in Fig. 5(b)-(d). At the axis r ¼ 0 with high intensity, there is an early and strong sequential TPA. As the radial distance r increases, the intensity decreases and therefore the absorption becomes late and slow. At r ¼ 5 mm with rather weak intensity, the population accumulation on state T 1 needs more time for start-up of the absorption process T 1 ! T 2 . Due to this, there is a wider width and a long tail of the intensity in Fig. 5(b). So one can see clearly the bending and time delay in Fig. 5(a). 4. Conclusions By employing a five-level scheme, we have numerically studied the nonlinear absorption and propagation of picosecond pulse trains for naphthalocyanines and phthalocyanines. According to theoretical analysis, both Npcs and Pcs are excellent optical limiting competitors due to the fast rate of intersystem crossing transition S1 ! T 1 , which is owing to the large p electron conjugation system. The central metals and the peripheral substituents can strongly influence the OL performance during the laser propagation. Our results indicate that naphthalocyanine with lighter central metal Ga shows better OL characteristics with picosecond pulse trains, which is quite different with the case with single nanosecond pulse. In the different region of weak or strong field intensity, the photophysical parameters such as one-photo absorption cross sections rS0 S1 ; rT 1 T 2 and state lifetime sT 1 play quite different roles in propagation dynamics. So we can observe the fine distinctions in numerically results. Acknowledgments Financial supports from the National Natural Science Foundation of China (Grant Nos. 11604181, 11547037 and 61675118), Shandong Provincial Natural Science Foundation, China (Grant No. 2016ZRB01A38), and Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (Grant No. 2015RCJJ015) are gratefully acknowledged. References [1] G. Mourou, T. Tajima, More intense, shorter pulses, Science 331 (2011) 41–42.

[2] S. Hughes, B.S. Wherrett, Multilevel rate-equation analysis to explain the recent observations of limitations to optical limiting dyes, Phys. Rev. A 54 (1996) 3546–3552. [3] G.S. He, P.P. Markowicz, T. Lin, P.N. Prasad, Observation of stimulated emission by direct three-photon excitation, Nature 415 (2002) 767–770. [4] S. Gavrilyuk, S. Polyutov, P.C. Jha, Z. Rinkevicius, H. Ågren, F. Gel’mukhanov, Many-photon dynamics of photobleaching, J. Phys. Chem. A 111 (2007) 11961–11975. [5] A. Eriksson, K. Bertlisson, M. Lindgren, Simulation of beam propagation with time-dependent nonlinear processes in optical limiting applications, Synth. Met. 127 (2002) 147–150. [6] I. Polyzos, G. Tsigaridas, M. Fakis, V. Giannetas, P. Persephonis, J. Mikroyannidis, Two-photon absorption properties of novel organic materials for three-dimensional optical memories, Chem. Phys. Lett. 369 (2003) 264– 268. [7] W. Blau, H. Byrne, W.M. Dennis, J.M. Dennis, J.M. Kelly, Reverse saturable absorption in tetraphenylporphyrins, Opt. Commun. 56 (1985) 25–29. [8] D. Dini, M. Hanack, M. Meneghetti, Nonlinear optical properties of tetrapyrazinoporphyrazinato indium chloride complexes due to excited-state absorption processes, J. Phys. Chem. B 109 (2005) 12691–12696. [9] L. De Boni, D.C.J. Rezende, C.R. Mendonca, Reverse saturable absorption dynamics in indocyanine green, J. Photochem. Photobiol. A: Chem. 190 (2007) 41–44. [10] P. Prasad, Introduction to Biophotonics, Wiley, Hoboken, NJ, 2003. [11] F. Gel’mukhanov, A. Baev, P. Macak, Y. Luo, H. Ågren, Dynamics of two-photon absorption by molecules and solutions, J. Opt. Soc. Am. B 19 (2002) 937–945. [12] S. Polyutov, I. Minkov, F. Gel’mukhanov, H. Ågren, Interplay of one- and twostep channels in electrovibrational two-photon absorption, J. Phys. Chem. A 109 (2005) 9507–9513. [13] R. Signorini, C. Ferrante, D. Pedron, M. Zerbetto, E. Cecchetto, M. Slaviero, I. Fortunati, E. Collini, R. Bozio, A. Abbotto, L. Beverina, G.A. Pagani, Effective twophoton absorption cross section of heteroaromatic quadrupolar dyes: dependence on measurement technique and laser pulse characteristics, J. Phys. Chem. A 112 (2008) 4224–4234. [14] D. Dini, M. Meneghetti, M.J.F. Calvete, T. Arndt, C. Liddiard, M. Hanack, Tetrabrominated lead naphthalocyanine for optical power limiting, Chem. Eur. J. 16 (2010) 1212–1220. [15] D. Dini, M.J.F. Calvete, M. Hanack, R.G.S. Pong, S.R. Flom, J.S. Shirk, Nonlinear transmission of a tetrabrominated naphthalocyaninato indium chloride, J. Phys. Chem. B 110 (2006) 12230–12239. [16] M.T.M. Choi, P.P.S. Li, D.K.P. Ng, A direct comparison of the aggregation behaviour of phthalocyanines and 2,3-naphthalocyanines, Tetrahedron 56 (2000) 3881–3887. [17] W.F. Sun, G. Wang, Y.J. Li, M.J.F. Calvete, D. Dini, M.J. Hanack, Axial halogen ligand effect on photophysics and optical power limiting of some indium naphthalocyanines, J. Phys. Chem. A 111 (2007) 3263–3270. [18] D. Dini, M. Calvete, S. Vagin, M. Hanack, A. Eriksson, C. Lopes, Analysis of the nonlinear transmission properties of some naphthalocyanines, J. Porphyr. Phthalocya. 10 (2006) 1165–1171. [19] P. Tau, A.O. Ogunsipe, S. Maree, M.D. Maree, T. Nyokong, Influence of cyclodextrins on the fluorescence, photostability and singlet oxygen quantum yields of zinc phthalocyanine and naphthalocyanine complexes, J. Porphyr. Phthalocya. 7 (2003) 439–446. [20] A. Ogunsipe, J.Y. Chen, T. Nyokong, Photophysical and photochemical studies of zinc(II) phthalocyanine derivatives-effects of substituents and solvents, New J. Chem. 28 (2004) 822–827. [21] T. Nyokong, Effects of substituents on the photochemical and photophysical properties of main group metal phthalocyanines, Coord. Chem. Rev. 251 (2007) 1707–1722. [22] T.V. Dubinina, S.A. Trashin, N.E. Borisova, I.A. Boginskaya, L.G. Tomilova, N.S. Zefirov, Phenyl-substituted planar binuclear phthalo- and naphthalocyanines: synthesis and investigation of physicochemical properties, Dyes Pigments 93 (2012) 1471–1480. [23] J. Xu, J. Chen, L. Chen, R. Hu, S.Q. Wang, S.Y. Li, J.S. Ma, Enhanced optical limiting performance of substituted metallonaphthalocyanines with wide optical limiting window, Dyes Pigments 109 (2014) 144–150. [24] Q. Miao, Q. Liu, E. Sun, T. Ren, Nonlinear dynamics and optical power limiting of nanoseconds pulses in naphthalocyanines and phthalocyanines with central metals gallium and indium, J. Photoch. Photobio. A 316 (2016) 19–23. [25] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, 2007. [26] Y.-P. Sun, S. Gavrilyuk, J.-C. Liu, C.-K. Wang, H. Ågren, F. Gel’mukhanov, Optical limiting and pulse reshaping of picosecond pulse trains by fullerene C60, J. Electron. Spectrosc. Relat. Phenom 174 (2009) 125–130. [27] S. Gavrilyuk, J.C. Liu, K. Kamada, H. Ågren, F. Gel’mukhanov, Optical limiting for microsecond pulses, J. Chem. Phys. 130 (2009) 054114. [28] F. Gel’mukhanov, H. Ågren, Resonant X-ray Raman scattering, Phys. Rep. 312 (1999) 87–330. [29] T.H. Wei, T.H. Huang, J.K. Hu, Electronic energy dissipation in chloroaluminum phthalocyanine/methanol system following nonlinear interaction with a train of picosecond pulses, J. Chem. Phys. 116 (2002) 2536–2541. [30] P.J. Goncalves, L. De Boni, N.M.B. Neto, J.J. Rodrigues Jr., S.C. Zilio, I.E. Borissevitch, Effect of protonation on the photophysical properties of mesotetra(sulfonatophenyl) porphyrin, Chem. Phys. Lett. 407 (2005) 236–241.