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Enhancing Intermediate State Absorption of Resonance-Mediated Multi-Photon Absorption Process Chenhui Lu, Yunhua Yao, Shuwu Xu, Tianqing Jia, Jingxin Ding, Shi-An Zhang, and Zhenrong Sun J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp502324p • Publication Date (Web): 03 Jun 2014 Downloaded from http://pubs.acs.org on June 9, 2014

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The Journal of Physical Chemistry

Enhancing Intermediate State Absorption of Resonance-Mediated Multi-Photon Absorption Process Chenhui Lu1, Yunhua Yao1, Shuwu Xu1, 2, Tianqing Jia1, Jingxin Ding1, Shian Zhang1,*), and Zhenrong Sun1,*) 1

State Key Laboratory of Precision Spectroscopy, and Department of Physics, East China Normal University, Shanghai 200062, People’s Republic of China 2

School of Science, Nantong University, Nantong 226007, People’s Republic of China

ABSTRACT: We theoretically and experimentally demonstrate the control of the intermediate state absorption in (1+2) resonance-mediated multi-photon absorption process by shaping the femosecond laser pulse. A theoretical model is proposed to investigate the

intermediate

state

absorption

of (1+2) resonance-mediated

three-photon absorption process in the molecular system and an analytical solution is obtained based on time-dependent perturbation theory. Our theoretical results show that the intermediate state absorption can be enhanced by controlling the laser spectral phase due to final state absorption reduction, and this absorption enhancement efficiency increases with the increase of the laser intensity. These theoretical results are experimentally confirmed in IR144 dye by varying the laser spectral phase with a sinusoidal modulation function. Keywords: Three-photon absorption; Single-photon fluorescence; Pulse shaping; Coherent control

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1. INTRODUCTION Single-photon or multi-photon absorption (or fluorescence) in the molecular system has attracted widespread attention because of its potential applications on fluorescence correlation spectroscopy and fluorescence imaging spectroscopy and microscopy.1,2 If the molecular absorption (or fluorescence) under the weak laser field can be effectively enhanced, its applications can be greatly extended. Recently, the coherent control strategy by making use of the femtosecond pulse shaping technique opens a new opportunity to manipulate the single-photon or multi-photon absorption (or fluorescence),3-10 and several control schemes have been proposed to experimentally realize the single-photon or multi-photon absorption (or fluorescence) enhancement.6-10 For example, Gerullo et al.6 and Bardeen et al.7 reported the single-photon fluorescence enhancement in LD690, LDS750 and IR125 dyes using a negatively chirped laser pulse. Lee et al.8 realized the two-photon fluorescence enhancement in DCM dye by an optimal control based on evolutionary algorithm. Otake et al.9 demonstrated the two-photon fluorescence enhancement in Perylene dye by an adaptive feedback control with genetic algorithm. We achieved the two-photon fluorescence enhancement in Dichlorofluorecein dye by a phase-jump modulated laser pulse.10 In these previous studies,3-10 the control of the final state absorption was primary considered. However, in actual experiments, the control of the target state was usually affected by its higher state. Recently, the intermediate state absorption control has attracted considerable interest. For example, Das et al.11 reported the single-photon 2


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fluorescence enhancement of the (1+N) multi-photon absorption process in IR125 dye by the laser polarization modulation. We demonstrated the single-photon fluorescence enhancement of the (1+2) resonance-mediated three-photon absorption process in IR125 and IR144 dyes by varying the laser polarization or spectral phase.12,13 However, the single-photon fluorescence enhancement was just quantitatively explained by the higher excited state absorption.11-13 To completely understand the physical control mechanism of the single-photon fluorescence enhancement, in this paper we establish a theoretical model to investigate the intermediate state absorption of the (1+2) resonance-mediated three-photon absorption process in the molecular system, and an analytical solution is obtained based on time-dependent perturbation theory. We theoretically show that the intermediate state absorption can be enhanced by controlling the laser spectral phase due to the final state absorption reduction, but the absorption enhancement depends on the laser intensity and the larger absorption enhancement is obtained for the higher laser intensity. We experimentally confirm these theoretical predictions in IR144 dye by a sinusoidal phase modulation.

2. THEORETICAL METHOD Figure 1(a) shows the schematic diagram of the (1+2) resonance-mediated three-photon absorption process in the molecular system excited by the femtosecond laser pulse E ( t ) , where S0 , S1 and S2 are the ground state, intermediate state and final state, respectively. The transition from the S0 to S1 states is coupled by a single-photon absorption while the transition from the S1 to S2 states is coupled by a non-resonant two-photon absorption. Here, the S1 → S2 state coupling originates 3



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from a manifold of intermediate V states that are far from resonance. In present study, we consider the perturbative regime that the light-matter interaction can be well described by time-dependent perturbation theory. Thus, the S1 state population PS1 of the (1+2) resonance-mediated three-photon absorption process can be given by PS 1 = AS 1 − AS 2 ,

(1)

where A S1 is the absorption in the S1 state by the single-photon excitation process, and A S2 is the absorption in the S2 state by the (1+2) resonance-mediated three-photon excitation process, which is also corresponding to the absorption from the S1 to S2 states. In the molecular system with broad absorption line, the multi-photon absorption is proportional to a sum of each individual transition. Based on the theoretical model of the atom system with narrow absorption line limit,14,15 A S1 and A S2 can be written as

AS 1 =

1 h2

∫

+∞

−∞

G ( ωS 1 )

∫

+∞

−∞

2

µS 0→S 1E ( t ) exp ( iωS 1t ) dt dωS1 ,

(2)

and

AS 2 =

1 h6

×∫

+∞

−∞

∫

+∞

−∞ t1

G ( ωS 2 )

∫ ∫

t2

−∞ −∞

∫

+∞

−∞

G (ωS1 ) ∑ µ S 0→ S1µ S 1→V µV → S 2 V

E ( t1 ) E ( t2 ) E ( t3 ) exp i ( ωS 2 − ωV ) t1 

,

(3)

2

× exp i (ωV − ωS 1 ) t2  exp ( iωS 1t3 ) dt3 dt2 dt1d ωS 1 d ωS 2 where h is the Planck constant, G ( ωS1 ) and G ( ωS2 ) are the absorption line-shape functions in the S1 and S2 states, µ S0→S1 , µ S1→ V and µ V→S2 are the dipole matrix elements between a pair of states, and ωS1 , ω V and ωS2 are corresponding to the energy differences between the states S0 and S1 , S0 and V , and S0 and S2 . By transforming Eqs. (2) and (3), A S1 and A S2 can be further 4


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written as AS 1 =

1 h2

∫

+∞

−∞

2 G (ωS 1 ) µ S 0→ S 1 E0 E% (ωS 1 ) d ωS 1 ,

(4)

and AS 2 =

π 2h

×∫

6

+∞

−∞

∫

+∞

−∞

G (ωS 2 )

∫

+∞

−∞

G (ω S 1 ) µ S 0→ S 1µ S 1→ S 2 E03 E% (ωS 1 ) 2

,

(5)

E% (ω )E% (ωS 2 − ωS 1 − ω ) d ω d ωS 1 d ωS 2

where µ S1→S2 is the effective non-resonant two-photon dipole coupling between the S1 and S2 states, E 0 is the peak spectral amplitude, and E% ( ω ) is the normalized spectral field with E% ( ω ) = E ( ω ) E 0 , here E ( ω ) is given by the Fourier transform of E ( t ) with E ( ω ) =A ( ω ) exp iΦ ( ω )  , and A ( ω ) and Φ ( ω ) are the spectral amplitude and phase, respectively. Thus, the S1 state population PS1 can be further simplified as 2 E02 µ S20→ S 1  +∞ G (ωS 1 ) E% (ωS 1 ) d ωS 1 2 ∫  −∞ h 4 2 +∞ +∞ πE µ − 0 S41→ S 2 ∫ G (ωS 2 ) ∫ G (ωS 1 ) E% (ωS 1 ) . −∞ −∞ 2h 2 +∞  ×∫ E% (ω )E% (ωS 2 − ωS 1 − ω ) d ω d ωS 1 d ωS 2  −∞ 

PS 1 =

(6)

It is easy to verify that the first term in Eq. (6) (i.e., A S1 ) is independent of the laser spectral phase and therefore is uncontrollable, but the second term (i.e., A S2 ) is maximal value for the transform-limited laser pulse and can be effectively suppressed by varying the laser spectral phase. Since the three-photon absorption A S2 can be suppressed while the single-photon absorption A S1 is uncontrollable, the S1 state population PS1 (i.e., intermediate state absorption) can increase by rationally designing the laser spectral phase. The single-photon absorption A S1 is proportional 5



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to the laser intensity (i.e., E 02 ) while the three-photon absorption A S2 is proportional to the cube of the laser intensity (i.e., E 60 ), and thus the laser intensity will affect the enhancement efficiency of the intermediate state absorption and the higher laser intensity will yield the larger enhancement efficiency.

3. EXPERIMENTAL RESULTS AND DISCUSSION In order to verify the intermediate state absorption enhancement in the (1+2) resonance-mediated three-photon excitation process, we perform the experiment in IR144 dye, which was purchased from Exciton Company and used without further purification. In our experiment, IR144 dye is dissolved in methanol solution and its concentrations is 5×10-5mol/L. The experimental arrangement is schematically shown in Fig. 2. A Ti-sapphire mode-locked regenerative amplifier (Spectra-physics, Spitfire) is used as the excitation source with the pulse width of about 50 fs, the central wavelength of 800 nm and the repetition rate of 1 kHz. The output laser pulse is sent into a programmable 4-f configuration zero-dispersion pulse shaper, which is compose of a pair of diffraction gratings with 1200 lines/mm, a pair of concave mirrors with focal length of 200 mm and a one-dimension liquid-crystal spatial light modulator (SLM-S320d, JENOPTIK), and the SLM is placed at the Fourier plane and utilized to control the laser spectral phase in frequency domain. The phase-shaped femtosecond laser pulse is focused into a 10-mm quartz cuvette full of IR144 dye with a lens of 500-mm focal length. The fluorescence signal is perpendicularly collected and measured by a spectrometer with charge-coupled device (CCD). Figure 1(b) shows the absorption (green solid line) and fluorescence spectra (red 6


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solid line) of IR144 dye. There are two distinct broadband absorption peaks around the wavelength of 216 and 785 nm, which are corresponding to the S1 and S2 states. The fluorescence peak position is at 837 nm, corresponding to single-photon fluorescence (SPF), which results from the S1 to S0 state transition. In our experiment, we utilize a sinusoidal phase modulation to control the single-photon fluorescence of IR144 dye, and the spectral phase modulation is shown in the inset of Fig. 2. The sinusoidal phase modulation can be defined by the function of Φ ( ω ) =Asin  T ( ω-ω 0 )  , where ω0 is the laser central frequency, and A and T

represent the modulation amplitude and modulation time, respectively. The sinusoidal phase modulation in frequency domain leads to a sequence of sub-pulses in time domain,16-18 and the modulation amplitude A and the modulation time T are used to control the number and temporal separation of these sub-pulses, respectively. We first demonstrate the single-photon fluorescence intensity control of IR144 dye by varying the laser intensity, and the experimental measurement and the theoretical calculation from Eq. 6 are presented in Fig. 3, together with the single-photon absorption in the S1 state A S1 (red dotted line) and the three-photon absorption in the S2 state A S2 (blue dashed line). With the increase of the laser intensity, the single-photon absorption A S1 is proportional to the laser intensity and therefore is a monotonous increase, while the three-photon absorption A S2 is proportional to the cube of the laser intensity and therefore is a slow and then fast increase, and thus the S1 state population PS1 or single-photon fluorescence intensity shows a fast and then slow increase. Obviously, these theoretical results are 7



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in good agreement with our experimental measurement. Figure 4 shows the normalized experimental (black squares) and theoretical (green solid line) single-photon fluorescence intensity as the function of the modulation time T for the modulation amplitude A=π with the laser intensity of 4.8×1012 W/cm2, and the single-photon absorption in the S1 state A S1 (red dashed line) and the three-photon absorption in the S2 state A S2 (blue dotted line) are also presented. All experimental data are normalized by the transform-limited laser pulse excitation, and hereafter the same method is utilized. As can be seen, by increasing the modulation time T , the single-photon absorption A S1 is constant, while the three-photon absorption A S2 can be effectively suppressed, and therefore the S1 state population PS1 or single-photon fluorescence intensity can greatly increase. This experimental observation is consistent with above theoretical prediction. To demonstrate the effect of the laser intensity on the intermediate state absorption enhancement, we present the normalized experimental (black squares) and theoretical (green solid line) single-photon fluorescence intensity as the function of the modulation time T for the modulation amplitude A=π with the laser intensity of 4.8×1011 W/cm2, and also the single-photon absorption in the S1 state A S1 (red dashed line) and the three-photon absorption in the S2 state A S2 (blue dotted line) are given together, as shown in Fig. 5. One can see that the S1 state population PS1 or single-photon fluorescence intensity almost cannot increase and therefore its enhancement efficiency is tremendously reduced. Inset shows the enlarged diagram of the three-photon absorption in the S2 state A S2 . It can be seen that the three-photon 8


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absorption A S2 can also be effectively suppressed, which is the same as that in Fig. 4 with the higher laser intensity of 4.8×1012 W/cm2, while the three-photon absorption A S2 is far smaller than the single-photon absorption A S1 , which leads to the enhancement efficiency reduction of the S1 state population PS1 or single-photon fluorescence intensity.

4. CONCLUSIONS In conclusion, we have presented a theoretical model to investigate the intermediate state absorption of the (1+2) resonance-mediated three-photon absorption process in the molecular system and obtained an analytical solution based on time-dependent perturbation theory. Our theoretical results showed that, by controlling the laser spectral phase, the intermediate state absorption can be enhanced due to the final state absorption reduction, but the laser intensity will affect the absorption enhancement and the higher laser intensity can yield the larger absorption enhancement. We experimentally validated the intermediate absorption enhancement in IR144 dye by a sinusoidal phase modulation and the effect of the laser intensity on the absorption enhancement. Our theoretical and experimental results can be further extended to understand and control the intermediate absorption enhancement of various resonance-mediated multi-photon absorption processes, and have significant applications on molecular fluorescence spectroscopy and imaging.

AUTHOR INFORMATION Corresponding Author *Email: [email protected]; [email protected]. 9



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Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This work was partly supported by National Natural Science Fund (NO. 11004060, NO. 11027403 and NO. 51132004) and Shanghai Rising-Star Program (NO. 12QA1400900).

REFERENCES (1) Krichevsky, O.; Bonnet, G. Fluorescence Correlation Spectroscopy: the Technique and its Applications. Rep. Prog. Phys. 2002, 65, 251-297. (2) Dedov, V. N.; Cox, G. C.; Roufogalis, B. D. Visualisation of Mitochondria in Living Neurons with Single- and Two-Photon Fluorescence Laser Microscopy. Micron. 2001, 32, 653-60. (3) Walowicz, K. A.; Pastirk, I.; Lozovoy, V. V.; Dantus, M. Multiphoton Intrapulse Interference 1: Control of Multiphoton Processes in Condensed Phases. J. Phys. Chem. A 2002, 106, 9369-9373. (4) Cruz, J. M. D.; Pastirk, I.; Lozovoy, V. V.; Walowicz, K. A.; Dantus, M. Multiphoton Intrapulse Interference 3: Probing Microscopic Chemical Environments. J. Phys. Chem. A 2004, 108, 53-58. (5) Silva, D. L.; Misoguti, L.; Mendonca, C. R. Control of Two-Photon Absorption in Organic Compounds by Pulse Shaping: Spectral Dependence. J. Phys. Chem. A 2009, 113, 5594-7. (6) Cerullo, G.; Bardeen, C. J.; Wang, Q.; Shank, C. V. High Power Chirped Pulse 10


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Excitation of Molecules in Solution. Chem. Phys. Lett. 1996, 262, 362-368. (7) Bardeen, C. J.; Yakovlev, V. V.; Wilson, K. R.; Carpenter, S. D.; Weber, P. M.; Warren, W. S. Feedback Quantum Control of Molecular Electronic Population Transfer. Chem. Phys. Lett. 1997, 280, 151-158. (8) Lee, S. H.; Jung, K. H.; Sung, J. H.; Hong, K. H.; Nam, C. H. Adaptive Quantum Control of DCM Fluorescence in the Liquid Phase. J. Chem. Phys. 2002, 117, 9858-9861. (9) Otake, I.; Kano, S. S.; Wada, A. Pulse Shaping Effect on Two-Photon Excitation Efficiency of Alpha-Perylene Crystals and Perylene in Chloroform Solution. J. Chem. Phys. 2006, 124, 014501. (10) Zhang, S.; Zhang, H.; Yang, Y.; Jia, T.; Wang, Z.; Sun, Z. Coherent Enhancement in Two-Photon Fluorescence in Molecular System Induced by Phase-Jump Modulated Pulse. J. Chem. Phys. 2010, 132, 094503. (11) Das, D. K.; Makhal, K.; Singhal, S.; Goswami, D. Polarization Induced Control of Multiple Fluorescence from a Molecule. Chem. Phys. Lett. 2013, 579, 45-50. (12) Zhang, H.; Zhang, S.; Lu, C.; Jia, T.; Wang, Z.; Sun, Z. Single-Photon Fluorescence Enhancement in IR144 by Phase-Modulated Femtosecond Pulses. Chem. Phys. Lett. 2011, 503, 176-179. (13) Zhang, S.; Zhang, H.; Lu, C.; Jia, T.; Wang, Z.; Sun, Z. Mechanism of Polarization-Induced Single-Photon Fluorescence Enhancement. J. Chem. Phys. 2010, 133, 214504. (14) Meshulach, D.; Silberberg, Y. Coherent Quantum Control of Multiphoton 11



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Transitions by Shaped Ultrashort Optical Pulses. Phys. Rev. A 1999, 60, 1287-1292. (15) Gandman, A.; Chuntonov, L.; Rybak, L.; Amitay, Z. Coherent Phase Control of Resonance-Mediated (2+1) Three-Photon Absorption. Phys. Rev. A 2007, 75, 031401(R). (16) Meshulach, D.; Silberberg, Y. Coherent Quantum Control of Two-Photon Transitions by a Femtosecond Laser Pulse. Nature 1998, 396, 239-242. (17) Herek, J. L.; Wohlleben, W.; Cogdell, R.; Zeidler, D.; Motzkus, M. Quantum Control of Energy Flow in Light Harvesting. Nature 2002, 417, 533-535. (18) Wollenhaupt, M.; Präkelt, A.; Sarpe-Tudoran, C.; Liese, D.; Bayer, T.; Baumert, T. Femtosecond Strong-Field Quantum Control with Sinusoidally Phase-Modulated Pulses. Phys. Rev. A 2006, 73, 063409.

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1.5

1.0

1.4

0.8

1.3

0.6

High Laser Intensity

1.2 1.1

0.4 0.2

1.0

0.0 0

500

1000

1500

2000

2500

3000

3500

4000

A S1 and A S2 (arb. units)

Table of Contents (TOC) Graphic

SPF intensity (arb. units)

4500

1.0

1.0

0.8 0.6 0.4 0.2

0.8

0.006 0.005

Lowlaser intensity

0.004 0.003 0.002

0.6 0.4

0.001 0.000 0

1000

2000

3000

Modulation time Τ (fs)

0.2

4000

0.0

0.0 0

500

1000

1500

2000

2500

3000

3500

4000

AS1 and A S2 (arb. units)


AS2 (arb. units)

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4500


13


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S2

(a) E(t)

S1

E(t)

S0

Relative intensity (arb. units)


1.0 0.8

(b) Fluorescence

0.6 0.4 0.2

Absorption

0.0 200 300 400 500 600 700 800 9001000

Wavelength (nm)

Figure 1. (a) Schematic diagram of the (1+2) resonance-mediated three-photon absorption process in the molecular system. (b) The absorption (green line) and fluorescence spectra (red line) of IR144 dye.

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SLM

C1

C2

fs laser@ 800 nm L1 Cell 1.0

G1

3

0.8 2

0.6 0.4

1

0.2

Phase (rad)

Intensity (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


L2 L3 PC

0

0.0

G2

740 760 780 800 820 840 860

CCD

Wavelength (nm)

Figure 2. (a) Schematic diagram of the experimental arrangement. The output femtosecond laser pulse is shaped by a 4f-configuration pulse shaping system combined with a one-dimension liquid-crystal spatial light modulator (SLM-S320d, JENOPTIK). Inset shows the laser spectrum modulated by a sinusoidal phase modulation.

15



140


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130 120 110 100 90 80 70 60 50 10

20

30

40 11

50

60

2

Laser power (10 W/cm )

Figure 3. The experimental (black squares) and theoretical (green solid line) single-photon fluorescence intensity by varying the laser intensity. The single-photon absorption A S1 (red dashed line) and the three-photon absorption A S2 (blue dotted line) are also presented.

16


1.5

1.0

1.4

0.8

1.3

0.6

1.2

0.4

1.1

0.2

1.0

0.0 0

AS1 and AS2 (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



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500 1000 1500 2000 2500 3000 3500 4000 4500


Figure 4. The normalized experimental (black squares) and theoretical (green solid line) single-photon fluorescence intensity as the function of the modulation time T for the modulation amplitude A=π with the laser intensity of 4.8×1012 W/cm2, together with the single-photon absorption A S1 (red dashed line) and the three-photon absorption A S2 (blue dotted line).

17



1.0

0.8

0.8

AS2 (arb. units)

0.006

0.6 0.4

0.005 0.004

0.6

0.003 0.002

0.4

0.001 0.000

0.2

0

1000

2000

3000

4000

0.2

Modulation time Τ (fs) 0.0

AS1 and AS2 (arb. units)

1.0


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0.0 0

500 1000 1500 2000 2500 3000 3500 4000 4500


Figure 5. The normalized experimental (black squares) and theoretical (green solid line) single-photon fluorescence intensity as the function of the modulation time T for the modulation amplitude A=π with the laser intensity of 4.8×1011 W/cm2, and also the single-photon absorption A S1 (red dashed line) and the three-photon absorption A S2 (blue dotted line) are given. Inset shows the enlarged diagram of the three-photon absorption A S2 .

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