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Theoretical and experimental studies on laser-induced transient gratings in laser dyes
Journal of Luminescence 99 (2002) 301–309
Theoretical and experimental studies on laser-induced transient gratings in laser dyes R. Justin Rajesh, Prem B. Bisht* Department of Physics, Indian Institute of Technology Madras, Chennai 600 036, India Received 20 November 2000; received in revised form 10 April 2002; accepted 2 May 2002
Abstract Laser-induced transient grating technique has been used to measure the diffraction efficiency (Z) and calculate the third-order nonlinear susceptibility (wð3Þ ) of some laser dyes. Theoretical simulations have been carried out on Z and wð3Þ as a function of wavelength covering the spectral range corresponding to the first excited singlet state of the dyes. Theoretically simulated values have been found in agreement to those observed experimentally. The decay profiles for these dyes have been measured by using diffraction of a delayed probe laser pulse to estimate the relaxation times in the excited state. r 2002 Published by Elsevier Science B.V. PACS: 39.90; 42.62.F; 42.65.H; 42.65.A; 78.47 Keywords: Transient gratings; Kramers–Kronig relation; Third-order susceptibility; Diffraction efficiency
1. Introduction The laser-induced transient grating (LITG) technique is used to investigate the properties of optically excited materials [1–8]. LITG is produced by the interference of two intersecting time coincident beams of a laser. The interference produces a spatially periodic light intensity distribution, which changes the complex refractive index of the medium. LITG can be detected by the self-diffraction as well as the diffraction of a probe beam (derived from the same or another laser) at the grating. There are two contributions to the total diffraction efficiency of the grating: (i) due to the *Corresponding author. Fax: +44-235-2545. E-mail address: [email protected] (P.B. Bisht).
absorption of the medium (the amplitude grating) and (ii) due to refraction (the phase grating). The amplitude part of the diffraction efficiency is proportional to the square of the change in absorption coefficient (DK) while the phase part is proportional to the square of change in refractive index. The change in the refractive index (Dn) of the medium as a result of the grating formation is small (B107). These small changes in refractive index can be calculated by using a relation analogous to the Kramers–Kronig relation [9,10]. Fayer et al. have measured the decay rates of rhodamine B (RhB) by using transient grating technique in solvents of varying viscosity [2]. Weise et al. [3] have calculated wð3Þ of cresyl violet (CV) in methanol by measuring the diffraction efficiency of LITG as a function of the concentration of the
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dye. Langhans et al. [4] have measured the diffraction efficiency and the anisotropic decay profiles of decay of LITG for R6G in methanol. In the present paper, we have measured diffraction efficiency of self-diffraction and the decay profiles of LITG for R6G, RhB, CV and for N,N0 bis (2,5,-di-tert-butylphenyl)-3,4:9-10-perylenebis (dicarboximide) (DBPI). While R6G, RB and CV are well-known laser dyes, the dye DBPI is potentially useful in energy and electron transfer reactions, site-selection spectroscopy experiments with biological systems, in p2n heterojunction solar cells and also as a laser dye [11,12]. Certain photophysical characteristics of DBPI exist in literature such as fluorescence quenching, high photostability and effect of medium polarity [12– 14]. Effect of morphology-dependent resonances in fluorescence of DBPI dissolved in polymer microparticles and its microcrystals has also been reported [15,16]. DBPI is an important highly photostable probe molecule and to the best of our knowledge its nonlinear properties do not exist in literature. In addition, theoretical calculations are not available for RhB and DBPI in literature. Therefore in this paper, the diffraction efficiency of LITG has also been simulated theoretically for these laser dyes at all wavelengths corresponding to the first excited singlet state. From these calculations we have obtained the third-order susceptibility as a function of the wavelength. Theoretically calculated values have been compared with those obtained experimentally at 532 nm. The decay profiles of the LITG have been measured for the dyes by the diffraction of a third beam that is scanned in time. It is observed that the decay profiles contain a sharp peak at zero time delay. The relaxation times have been calculated by fitting the obtained decay curves.
2. Theory Two laser beams (with wave vectors k1 and k2) when superimposed in a medium produce an interference pattern. The grating vector (q) of the interference pattern is given by q ¼ k1 k2 :
ð1Þ
If the frequencies of the two beams (o1 and o2 ) are different, the interference pattern propagates like a wave with a frequency o1 o2 : However, for o1 ¼ o2 the interference pattern is stationary. The grating period (L) is given by L ¼ l=2 sinðy=2Þ;
ð2Þ
where y is the angle of intersection of the two beams. The grating is detected by diffraction of a third laser beam with a frequency of o3 and wave vector k3. For a thin grating, diffraction is obtained for a beam of any incident angle. Absorption of light pulses results in the change of the refractive index of the medium and it can be described by the complex refractive index (n) * given by n* ¼ n þ iK=k;
ð3Þ
where n is the ordinary refractive index of the medium, K is the absorption coefficient and k is the magnitude of the wave vector. For polarized Gaussian beam the diffraction efficiency (Z) of a thin grating of thickness d is given by [4] Z¼
d2 9m2 ðDK 2 þ k2 Dn2 Þ : 4 25
ð4Þ
Here m ¼ 2ðI1 I2 Þ1=2 =ðI1 þ I2 Þ is the modulation or contrast of the interference fringes, where I1 and I2 are the intensities of the interfering beams. The change of the absorption coefficient (DK) is given by DK ¼ 12 ðsa0 sa1 þ se0 Þ N1 ;
ð5Þ
where sa0 and sa1 are the absorption cross sections of the ground and first excited states, respectively. se0 is the stimulated emission cross section to the ground state. By using Eq. (4) we can also calculate Dn from experimentally measured values of DK and Z: For a thin sample the number of molecules in the excited state N1 is given by sa0 Wp N1 ¼ N0 1 exp ; ð6Þ hn where WP is the total peak energy density due to both the excitation pulses and N0 is the number of molecules in the dye solution.
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The change in the refractive index due to the formation of grating for a given wavelength (l) is given by the Kramers–Kronig relation [9] Z N1 N ½sa1 ðl0 Þ se0 ðl0 Þ sa0 ðl0 Þ 0 DnðlÞ ¼ 2 dl : 2p 0 1 ðl0 =lÞ2 ð7Þ By using Eqs. (3) and (4), the square of the absolute value of the third-order nonlinear susceptibility can be calculated as [3] jwð3Þ j2 ¼ Z
100n4 t2p 9m2 z20 Wp2 d 2 k2
ð8Þ
;
where tp is the pulse width. The measured diffraction efficiency is given by Z ¼ ID =I0 ; where ID is the diffracted intensity and I 0 is the incident intensity of the laser beam. Under low energy densities, LITG can decay mainly by two processes: (i) the spontaneous emission and (ii) the relaxation in the excited states. For the case of a thick grating the efficiency of Bragg diffraction has been discussed by Kogelnik [17]. The time profiles obtained from the LITG experiments may contain several contributions such as the coherence peak, optical Kerr effect (OKE) of the solvent, density phase grating, acoustic grating and relaxation times of the molecule [6,7,18–21]. The observed decay is governed by the following equation [6,18]: Z N IðtÞ ¼ IPr ðt t00 Þ N
Z
t ð3Þ
00
0
0
w ðt t ÞIPu ðt Þ dt
0
2
dt00 ;
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where the first term accounts for the coherence spike and the second one is due to excited state relaxation of solute molecules.
3. Experimental Absorption spectra were measured in a 1 cm2 cuvette in a spectrometer (Hitachi model V3400). Fluorescence spectra were measured at right angled geometry with the help of a spetrofluorimeter (Hitachi model F4500) by excitation at 487 nm. The experimental set-up for creation and detection of the LITG is shown in Fig. 1. A modelocked frequency-doubled Nd:YAG laser (Continuum model YG601) was used in the experiments. The laser pulse (pulse width of 35 ps with energy of 0.14 mJ and beam diameter of 5 mm, unless otherwise specified) at 532 nm was split into two pulses by a 30% reflecting beam splitter (BS1). The transmitted beam was further split into two by a 50% beam splitter (BS2). The two reflected pulses from BS1 and BS2 were made to intersect in
ð9Þ
N
where t is the time delay between the pump and the probe pulses, Ipr and Ipu are the intensities of the probe and the pump pulses, respectively, and wð3Þ is the third-order nonlinear susceptibility tensor of the sample. wð3Þ depends upon the polarization of the pump and the probe pulses. At low pump energies for fitting the observed decay by Eq. (9), we take the form of wð3Þ as 2
wð3Þ ¼ AG e4ln2ðt=tG Þ þ A1 et=tor ;
ð10Þ
Fig. 1. Experimental arrangement for measurement of diffraction efficiency of transient grating: (SHG) second harmonic generator; (M) mirror; (P) prism; (BS1, BS2): beam splitter; (MC) monochromator; (PMT) photomultiplier tube; (ADC) analog-to-digital converter; (PC) personal computer.
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a liquid sample at an angle of 51 to form the grating. The intensity of one of the self-diffracted beam was measured with the help of a PIN photodiode (motorola MRD 510) for diffraction efficiency measurement. The intensity of one of the beams was measured (before the diffraction) by reducing the laser intensity by a known factor and then measuring it with the PIN photodiode. The pulse energy was calculated from the average power measured at 10 Hz by a power meter (Ophir30A-P). The sample was kept in a cell which is made as follows: thin sheets of known dimensions were kept between two glass plates. Three edges of the glass plates were sealed with an adhesive (Araldite). The thickness of the cell was taken to be the thickness of the sheet placed in between the glass plate. For measurement of decay profiles, the transmitted beam from BS1 was further split into two by a 50% beam splitter (BS2). The transmitted beam from BS2 was used as the probe for the decay measurement. The probe pulse was sent through the sample after passing through an optical delay line in a box geometry. Here the probe pulse and both the pump pulses are derived from the same laser. This configuration is also known as degenerate four-wave mixing. The delay line was connected to computer controlled step motor. The first diffracted probe pulse was made to fall on a photomultiplier tube (PMT, RCA 931A) after passing through a monochromator preset at 532 nm to avoid ambient light. The diffracted intensity of the probe was measured as a function of delay of the probe pulse with respect to the excitation pulses. The output of the PMT was sent through an analog-to-digital converter to the computer [22]. The instrument response function was measured by a similar set-up by using the autocorrelation of 1064 nm pulses at a 2 mm thick L-Argine phosphate monohydrate (LAP) crystal by sum frequency generation. The PMT output was averaged over 20 shots of the laser pulses before storing in the PC. Theoretical simulations were done by using standard numerical methods by writing computer program in C language in a UNIX machine [10]. The program was tested by reproducing the reported values of Dn and diffraction efficiency
[3,4]. Theoretical fitting of the decay profiles was done in two ways. In the first case a single exponential function was assumed for a fit with (ITG Þ1=2 vs. time for a limited region of the decay curve by neglecting both the initial time (o100 ps) and the long time (>700 ps) data points. On the other hand to fit the full decay profile only the fluorescence lifetime component (of the order of ns) was neglected and the experimental data were fitted with Eqs. (9) and (10) by a home-made program which utilizes the Levenberg–Marquardt method of least-square minimization.
4. Results and discussion 4.1. Theoretical simulations The absorption cross section in the ground state (sa0 ) and the stimulated emission cross section (se0 ) to the ground state were calculated with the help of the measured spectra of dilute solutions of the dyes. The values of sa0 were obtained with the help of optical density (OD) by using the formula sa0 ¼ OD=Nd, where N is the number of molecules in the solution. The values of se0 were calculated by using the formula [24]: se0 ðlÞ ¼
l4 EðlÞ f; 8pn2 ctF
ð11Þ
where t is the fluorescence lifetime, c is the speed of light, f is the fluorescence quantum yield and EðlÞ is the fluorescenceR intensity profile normalized by the expression EðlÞ dl ¼ 1: For all calculations the intensity of excitation beams were taken to be the same. The change of the refractive index (Dn) at a wavelength is calculated by Eq. (7). For the case of RhB, R6G and CV the values of sa0 ; sa1 and se0 used in the simulations were also taken from literature [23–26]. Fig. 2 shows simulations for the diffraction efficiency for RhB in methanol–ethylene glycol mixture (1:1) and DBPI in benzene. For DBPI we have used benzene as a solvent due to its good solubility. It is seen that the contribution of amplitude grating dominates over the phase grating. Since we are using low-energy densities (4–7 104 J/cm2 at 35 ps pulse width) the
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Fig. 2. Plot of theoretically simulated diffraction efficiency as a function of wavelegnth for: (A) RhB in methanol–ethylene glycol (1:1) and (B) DBPI in benzene. The parameters are same as indicated in Table 2.
Table 1 Photophysical parameters for laser dyes in methanol–ethylene glycol (1:1) Dye
labs a71 (nm)
lem b72 (nm)
tF c (ns)
l at Zmax d (nm)
Rangee 72 (nm)
jwð3Þ jmax f (m2/V2)
R6G RhB CV DBPIg
528 548 602 526
570 582 625 544
3.6 2.6 3.0 3.7
522.5 550.0 583.5 526.5
470–550 500–580 525–615 450–600
2.25 1018 1.04 1017 0.75 1018 5.72 1018
[23] [23] [16] [16]
a
labs is the absorption maximum for the dye. lem is the fluorescence maximum (lexc ¼ 487 nm). c tf is the fluorescence lifetime, The values in bracket indicate the reference numbers. d l is the wavelength for which diffraction efficiency is maximum. e Range of the wavelength for which there is diffraction. f Maximum value of wð3Þ : g In benzene. b
population grating is free from other effects such as acoustic grating [27]. For RhB the efficiency of diffraction is maximum at 550 nm and it vanishes below 500 nm and above 580 nm. DBPI shows a maximum at 526.5 nm and it vanishes below 450 and above 600 nm. This observation indicates that the second harmonic of YAG laser (532 nm) can be used for the self-diffraction experiments. Table 1 shows the photophysical parameters for different dyes. The wavelength of absorption and emission are found to be red shifted in polar
solvents as compared to nonpolar solvents that is consistent with the effect of solvation arising due to polarity [28,29]. Fig. 3 shows the plot of total diffraction efficiency vs. intensity of an excitation beam for RhB. It is observed that the efficiency of diffraction has quadratic dependence on lower values of pump energies (Eqs. (6) and (8)). With the values of diffraction efficiency given in Fig. 2, the third-order susceptibility was calculated by using Eq. (8). The absolute value of thirdorder nonlinear susceptibility as a function of
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experiments. This is in agreement with value reported earlier [4]. Similarly, for other dyes, experimentally observed values are in close agreement with those obtained theoretically within the experimental error. For DBPI the sa1 values are not available. Therefore, an effect of noninclusion of the excited state absorption results in small difference in the observed values. We have confirmed this fact by reproducing the values of efficiency of R6G [4] and comparing the simulations by excluding the values of sa1 : The other source of error involved is to measure the intensity of the transmitted beam by suitably reducing it with neutral density filters. Nevertheless, the error in the experimentally observed values has been estimated to be o20%. 4.3. Measurement of relaxation times
Fig. 3. Log–log plot of simulated diffraction efficiency of RhB vs. intensity of a pump beam. The parameters are concentration of RhB in methanol–ethylene glycol (1:1)=2 104 M, l ¼ 532 nm and tp ¼ 35 ps.
wavelengths is plotted in Fig. 4 for RhB and DBPI. Maximum value of the wð3Þ and the range of wavelength for which the diffraction can be observed is indicated in Table 1. 4.2. wð3Þ measurements Self-diffraction of the laser beams was observed by using the set-up as shown in Fig. 1. The intensity of one of the excitation beams was measured before and after the first-order selfdiffraction by the LITG. The ratio of the diffracted intensity to that of the pump intensity gives the value of the efficiency of the diffraction. Table 2 shows a comparison of theoretical and experimentally observed values of nonlinear optical parameters for R6G, RhB, CV and DBPI. At a wavelength of 532 nm the calculated value of |wð3Þ | for R6G is 1.85 1018 m2/V2 which is in close agreement with the value obtained by the
Fig. 5 shows the decay profiles of the grating formed by the pump beams at lower pump energy (o0.5 mJ) for the DBPI in benzene and R6G in ethylene glycol. The decay profiles have been measured with sample thickness of 0.8 mm to increase the diffracted signal. The observed decay profiles show a sharp peak at short time followed by decaying components. The decay curves are expressed by Eq. (9). The sharp peak at zero time is known as the coherence peak that occurs in LITG experiments due to the diffraction of one of the pump beams into the direction of probe diffraction by a grating formed by other pump beam and the probe beam. The coherence spike appears only when the pump and the probe beams are derived from the same laser [6,18]. A Gaussian profile with a half-width equal to that of the pump laser pulse accounts for this. In any case, the decay curves can have a varying nature depending upon the polarization of the pump and probe beams, intensity of the incoming beams and wavelength of probe beam. Myers et al. [19] have shown this dependence of the decay profiles for R6G in ethylene glycol. In the present case the polarization of the pump and probe beams is parallel. Since the decay curves are recorded only up to approximately 700 ps, we ignore the fluorescence lifetime component in the analysis that will nearly be a constant. By fitting
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307
Fig. 4. Plot of theoretically obtained values of |wð3Þ | vs. wavelength for: (A) RhB in methanol–ethylene glycol (1:1) and (B) DBPI in benzene. The parameters are same as in Table 2.
Table 2 Simulated and experimentally observed parameters for laser dyes at 532 nm Dye
R6G RhB CV DBPI
Da (mm)
0.05 0.05 0.10 0.10
C b (mM)
10 20 10 50
tor (ps)
28897200c 500790d e
176733f
Wp (J/cm2)
4 104 7 104 6 104 7 104
Theoretical
Experimental
Z
|wð3Þ | (m /V )
Z 710%
|w(3)|710% (m2/V2)
2.5 105 1.1 104 3.4 104 4.0 104
1.85 1018 4.22 1018 0.26 1018 4.70 1018
1.8 105 1.6 104 2.5 104 7.8 104
0.65 1018 5.06 1018 0.22 1018 6.56 1018
2
2
a
d is the thickness of the sample. C is the concentration of the sample. c In ethylene glycol. d In DMSO. e Not measured due to dye unstability. f In benzene. b
the limited range of the decay curve with a single exponential function a rough estimate of the orientational relaxation time (tor ) of the molecule in the solvent can be obtained. For DBPI in benzene we obtained average value of tor as 176733 ps; while RhB in DMSO shows a longer value of 500790 ps (Table 2). Decay profile of R6G in ethylene glycol is given in panel (B) of Fig. 5. The decay curve is obtained after adding 4 curves recorded in a sequence for a sample. An improved signal-to-noise ratio allows
us to fit the obtained decay curve with Eqs. (9) and (10). As can be seen from Eq. (9) the analysis requires double deconvolution of the decay curve with the pump pulse (Ipu ). The profile contains a sharp coherence spike followed by a slower decay. Due to only a few points on initial time scale the data correlation takes place in theoretical fitting of experimental data for the parameters associated with the shorter times. However, longer time scale data fit well to give a value of 2889 ps for tor which is also reported in the case of RhB in ethylene
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Fig. 5. Decay curve for: (A) DBPI in benzene: the fitted line for a single exponential decay function for a limited range is also shown. (B) R6G in ethylene glycol: a fit with the help of Eqs. (9) and (10) gives a value of tor as 2889 ps. Panel B also shows the autocorrelation of the laser pulse recorded in a separate experiment.
glycol [2]. The value of tor is in close agreement to those obtained from Debye–Stokes–Einstein [30] hydrodynamic theory (tor ¼ gV =kB T; where g is the viscosity of the solvent, V is the volume of the molecule and T is the temperature). As mentioned earlier while for DBPI due to solubility reasons the solvent used was benzene (viscosity=0.7 cP), for other dyes the solvents for decay profile measurement was chosen as either DMSO (viscosity= 2.0 cP) or ethylene glycol (viscosity=24.2 cP). We have found that the dye DBPI is an efficient and stable probe molecule at 532 nm besides RhB and R6G. Whereas for CV the signal was found to be sensitive for the large number of laser shots due to bleaching effect, which prevented us from recording its decay profile reliably.
those for similar reported values of R6G and CV for a comparison. Theoretical simulations are found to be in close agreement with the experimentally obtained values. The decay profile of the gratings of these dyes show a fast coherence peak followed by the relaxation times.
Acknowledgements We thank DST, New Delhi, for financial assistance. This work was in part supported by a grant-in-aid no. 03 (0957)/02/EMR-II from CSIR, New Delhi.
References 5. Conclusions The diffraction efficiency of LITG in organic laser dyes has been measured. The third-order nonlinear susceptibility has been calculated as a function of the wavelength. Theoretical calculations for RhB and DBPI are given here alongwith
[1] H.J. Eichler, P. Gunter, D.W. Pohl, Laser Induced Transient Grating, Springer, Berlin, 1986. [2] R.S. Moog, M.D. Ediger, S.G. Boxer, M.D. Fayer, J. Phys. Chem. 86 (1982) 4694. [3] N. Wiese, H.J. Eichler, J. Salk, IEEE J. Quantum Electron. 25 (1989) 403. [4] D. Langhans, J. Salk, N. Weise, Physica 144C (1987) 411.
R.J. Rajesh, P.B. Bisht / Journal of Luminescence 99 (2002) 301–309 [5] D.S. Larsen, K. Ohta, Q.-H. Xu, M. Cyrier, G.R. Fleming, J. Chem. Phys. 114 (2001) 8008. [6] J.-C. Gumy, O. Nicolet, E. Vauthey, J. Phys. Chem. A 103 (1999) 10737. [7] M. Terazima, Adv. Photochem. 24 (1998) 255. [8] P.B. Bisht, Rev. Chem. Intermed. 27 (2001) 539. [9] J.D. Jackson, Classical Electrodynamics, Wiley Eastern, New Delhi, 1975. [10] R.J. Rajesh, P.B. Bisht, B.M. Sivaram, International Conference on Mathematical Modeling of Nonlinear Systems, IIT, Kharagpur, 1999, p. 134. [11] M. Sandrai, G.R. Bird, Opt. Commun. 51 (1984) 62. [12] W.E. Ford, P.V. Kamat, J. Phys. Chem. 91 (1987) 6373. [13] E-Z.M. Ebeid, S.A. El-Daly, H. Langhals, J. Phys. Chem. 92 (1988) 4565. [14] S.A. El-Daly, M. Okamoto, S. Hirayama, J. Photochem. Photobiol. A: Chem. 91 (1995) 100. [15] P.B. Bisht, K. Fukuda, S. Hirayama, J. Chem. Phys. 105 (1996) 9349. [16] P.B. Bisht, K. Fukuda, S. Hirayama, J. Phys. Chem. B. 101 (1997) 8054. [17] H. Kogelnik, Bell. System Tech. J. 48 (1969) 2909. [18] F.W.D. Deeg, M.D. Fayer, J. Chem. Phys. 91 (1989) 2269.
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[19] A.B. Myers, R.M. Hochstrasser, IEEE J. Quantum Electron. 22 (1986) 1482. [20] J.R. Salcedo, A.E. Siegman, D.D. Dlott, M.D. Fayer, Phys. Rev. Lett. 41 (1978) 131. [21] H.J. Eichler, D. Langhans, F. Massman, Opt. Commun. 50 (1984) 117. [22] R.J. Rajesh, T.S. Natarajan, P.B. Bisht, Ind. J. Pure, Appl. Phys. 39 (2001) 636. [23] W. Falkenstein, A. Penzokofer, W. Kaiser, Opt. Commun. 27 (1978) 151. [24] D. Magde, S.T. Gaffney, B.F. Campbell, IEEE J. Quantum Electron. 17 (1981) 489. [25] J. Shah, R.F. Leheny, Appl. Phys. Lett. 24 (1974) 562. [26] P. Hammond, IEEE J. Quantum Electron. 15 (1979) 624. [27] D.W. Phillon, D.J. Kuizenga, A.E. Siegman, Appl. Phys. Lett. 27 (1975) 85. [28] P.B. Bisht, H.B. Tripathi, D.D. Pant, Chem. Phys. 147 (1990) 173. [29] M. Kamlet, J. Abboud, R. Taft, in: R.W. Taft (Ed.), Progress in Physical Organic Chemistry, Interscience, 1981. [30] G.R. Fleming, Chemical Applications of Ultrafast Spectroscopy, Oxford University Press, New York, 1986.
Theoretical and experimental studies on laser-induced transient gratings in laser dyes R. Justin Rajesh, Prem B. Bisht* Department of Physics, Indian Institute of Technology Madras, Chennai 600 036, India Received 20 November 2000; received in revised form 10 April 2002; accepted 2 May 2002
Abstract Laser-induced transient grating technique has been used to measure the diffraction efficiency (Z) and calculate the third-order nonlinear susceptibility (wð3Þ ) of some laser dyes. Theoretical simulations have been carried out on Z and wð3Þ as a function of wavelength covering the spectral range corresponding to the first excited singlet state of the dyes. Theoretically simulated values have been found in agreement to those observed experimentally. The decay profiles for these dyes have been measured by using diffraction of a delayed probe laser pulse to estimate the relaxation times in the excited state. r 2002 Published by Elsevier Science B.V. PACS: 39.90; 42.62.F; 42.65.H; 42.65.A; 78.47 Keywords: Transient gratings; Kramers–Kronig relation; Third-order susceptibility; Diffraction efficiency
1. Introduction The laser-induced transient grating (LITG) technique is used to investigate the properties of optically excited materials [1–8]. LITG is produced by the interference of two intersecting time coincident beams of a laser. The interference produces a spatially periodic light intensity distribution, which changes the complex refractive index of the medium. LITG can be detected by the self-diffraction as well as the diffraction of a probe beam (derived from the same or another laser) at the grating. There are two contributions to the total diffraction efficiency of the grating: (i) due to the *Corresponding author. Fax: +44-235-2545. E-mail address: [email protected] (P.B. Bisht).
absorption of the medium (the amplitude grating) and (ii) due to refraction (the phase grating). The amplitude part of the diffraction efficiency is proportional to the square of the change in absorption coefficient (DK) while the phase part is proportional to the square of change in refractive index. The change in the refractive index (Dn) of the medium as a result of the grating formation is small (B107). These small changes in refractive index can be calculated by using a relation analogous to the Kramers–Kronig relation [9,10]. Fayer et al. have measured the decay rates of rhodamine B (RhB) by using transient grating technique in solvents of varying viscosity [2]. Weise et al. [3] have calculated wð3Þ of cresyl violet (CV) in methanol by measuring the diffraction efficiency of LITG as a function of the concentration of the
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dye. Langhans et al. [4] have measured the diffraction efficiency and the anisotropic decay profiles of decay of LITG for R6G in methanol. In the present paper, we have measured diffraction efficiency of self-diffraction and the decay profiles of LITG for R6G, RhB, CV and for N,N0 bis (2,5,-di-tert-butylphenyl)-3,4:9-10-perylenebis (dicarboximide) (DBPI). While R6G, RB and CV are well-known laser dyes, the dye DBPI is potentially useful in energy and electron transfer reactions, site-selection spectroscopy experiments with biological systems, in p2n heterojunction solar cells and also as a laser dye [11,12]. Certain photophysical characteristics of DBPI exist in literature such as fluorescence quenching, high photostability and effect of medium polarity [12– 14]. Effect of morphology-dependent resonances in fluorescence of DBPI dissolved in polymer microparticles and its microcrystals has also been reported [15,16]. DBPI is an important highly photostable probe molecule and to the best of our knowledge its nonlinear properties do not exist in literature. In addition, theoretical calculations are not available for RhB and DBPI in literature. Therefore in this paper, the diffraction efficiency of LITG has also been simulated theoretically for these laser dyes at all wavelengths corresponding to the first excited singlet state. From these calculations we have obtained the third-order susceptibility as a function of the wavelength. Theoretically calculated values have been compared with those obtained experimentally at 532 nm. The decay profiles of the LITG have been measured for the dyes by the diffraction of a third beam that is scanned in time. It is observed that the decay profiles contain a sharp peak at zero time delay. The relaxation times have been calculated by fitting the obtained decay curves.
2. Theory Two laser beams (with wave vectors k1 and k2) when superimposed in a medium produce an interference pattern. The grating vector (q) of the interference pattern is given by q ¼ k1 k2 :
ð1Þ
If the frequencies of the two beams (o1 and o2 ) are different, the interference pattern propagates like a wave with a frequency o1 o2 : However, for o1 ¼ o2 the interference pattern is stationary. The grating period (L) is given by L ¼ l=2 sinðy=2Þ;
ð2Þ
where y is the angle of intersection of the two beams. The grating is detected by diffraction of a third laser beam with a frequency of o3 and wave vector k3. For a thin grating, diffraction is obtained for a beam of any incident angle. Absorption of light pulses results in the change of the refractive index of the medium and it can be described by the complex refractive index (n) * given by n* ¼ n þ iK=k;
ð3Þ
where n is the ordinary refractive index of the medium, K is the absorption coefficient and k is the magnitude of the wave vector. For polarized Gaussian beam the diffraction efficiency (Z) of a thin grating of thickness d is given by [4] Z¼
d2 9m2 ðDK 2 þ k2 Dn2 Þ : 4 25
ð4Þ
Here m ¼ 2ðI1 I2 Þ1=2 =ðI1 þ I2 Þ is the modulation or contrast of the interference fringes, where I1 and I2 are the intensities of the interfering beams. The change of the absorption coefficient (DK) is given by DK ¼ 12 ðsa0 sa1 þ se0 Þ N1 ;
ð5Þ
where sa0 and sa1 are the absorption cross sections of the ground and first excited states, respectively. se0 is the stimulated emission cross section to the ground state. By using Eq. (4) we can also calculate Dn from experimentally measured values of DK and Z: For a thin sample the number of molecules in the excited state N1 is given by sa0 Wp N1 ¼ N0 1 exp ; ð6Þ hn where WP is the total peak energy density due to both the excitation pulses and N0 is the number of molecules in the dye solution.
R.J. Rajesh, P.B. Bisht / Journal of Luminescence 99 (2002) 301–309
The change in the refractive index due to the formation of grating for a given wavelength (l) is given by the Kramers–Kronig relation [9] Z N1 N ½sa1 ðl0 Þ se0 ðl0 Þ sa0 ðl0 Þ 0 DnðlÞ ¼ 2 dl : 2p 0 1 ðl0 =lÞ2 ð7Þ By using Eqs. (3) and (4), the square of the absolute value of the third-order nonlinear susceptibility can be calculated as [3] jwð3Þ j2 ¼ Z
100n4 t2p 9m2 z20 Wp2 d 2 k2
ð8Þ
;
where tp is the pulse width. The measured diffraction efficiency is given by Z ¼ ID =I0 ; where ID is the diffracted intensity and I 0 is the incident intensity of the laser beam. Under low energy densities, LITG can decay mainly by two processes: (i) the spontaneous emission and (ii) the relaxation in the excited states. For the case of a thick grating the efficiency of Bragg diffraction has been discussed by Kogelnik [17]. The time profiles obtained from the LITG experiments may contain several contributions such as the coherence peak, optical Kerr effect (OKE) of the solvent, density phase grating, acoustic grating and relaxation times of the molecule [6,7,18–21]. The observed decay is governed by the following equation [6,18]: Z N IðtÞ ¼ IPr ðt t00 Þ N
Z
t ð3Þ
00
0
0
w ðt t ÞIPu ðt Þ dt
0
2
dt00 ;
303
where the first term accounts for the coherence spike and the second one is due to excited state relaxation of solute molecules.
3. Experimental Absorption spectra were measured in a 1 cm2 cuvette in a spectrometer (Hitachi model V3400). Fluorescence spectra were measured at right angled geometry with the help of a spetrofluorimeter (Hitachi model F4500) by excitation at 487 nm. The experimental set-up for creation and detection of the LITG is shown in Fig. 1. A modelocked frequency-doubled Nd:YAG laser (Continuum model YG601) was used in the experiments. The laser pulse (pulse width of 35 ps with energy of 0.14 mJ and beam diameter of 5 mm, unless otherwise specified) at 532 nm was split into two pulses by a 30% reflecting beam splitter (BS1). The transmitted beam was further split into two by a 50% beam splitter (BS2). The two reflected pulses from BS1 and BS2 were made to intersect in
ð9Þ
N
where t is the time delay between the pump and the probe pulses, Ipr and Ipu are the intensities of the probe and the pump pulses, respectively, and wð3Þ is the third-order nonlinear susceptibility tensor of the sample. wð3Þ depends upon the polarization of the pump and the probe pulses. At low pump energies for fitting the observed decay by Eq. (9), we take the form of wð3Þ as 2
wð3Þ ¼ AG e4ln2ðt=tG Þ þ A1 et=tor ;
ð10Þ
Fig. 1. Experimental arrangement for measurement of diffraction efficiency of transient grating: (SHG) second harmonic generator; (M) mirror; (P) prism; (BS1, BS2): beam splitter; (MC) monochromator; (PMT) photomultiplier tube; (ADC) analog-to-digital converter; (PC) personal computer.
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a liquid sample at an angle of 51 to form the grating. The intensity of one of the self-diffracted beam was measured with the help of a PIN photodiode (motorola MRD 510) for diffraction efficiency measurement. The intensity of one of the beams was measured (before the diffraction) by reducing the laser intensity by a known factor and then measuring it with the PIN photodiode. The pulse energy was calculated from the average power measured at 10 Hz by a power meter (Ophir30A-P). The sample was kept in a cell which is made as follows: thin sheets of known dimensions were kept between two glass plates. Three edges of the glass plates were sealed with an adhesive (Araldite). The thickness of the cell was taken to be the thickness of the sheet placed in between the glass plate. For measurement of decay profiles, the transmitted beam from BS1 was further split into two by a 50% beam splitter (BS2). The transmitted beam from BS2 was used as the probe for the decay measurement. The probe pulse was sent through the sample after passing through an optical delay line in a box geometry. Here the probe pulse and both the pump pulses are derived from the same laser. This configuration is also known as degenerate four-wave mixing. The delay line was connected to computer controlled step motor. The first diffracted probe pulse was made to fall on a photomultiplier tube (PMT, RCA 931A) after passing through a monochromator preset at 532 nm to avoid ambient light. The diffracted intensity of the probe was measured as a function of delay of the probe pulse with respect to the excitation pulses. The output of the PMT was sent through an analog-to-digital converter to the computer [22]. The instrument response function was measured by a similar set-up by using the autocorrelation of 1064 nm pulses at a 2 mm thick L-Argine phosphate monohydrate (LAP) crystal by sum frequency generation. The PMT output was averaged over 20 shots of the laser pulses before storing in the PC. Theoretical simulations were done by using standard numerical methods by writing computer program in C language in a UNIX machine [10]. The program was tested by reproducing the reported values of Dn and diffraction efficiency
[3,4]. Theoretical fitting of the decay profiles was done in two ways. In the first case a single exponential function was assumed for a fit with (ITG Þ1=2 vs. time for a limited region of the decay curve by neglecting both the initial time (o100 ps) and the long time (>700 ps) data points. On the other hand to fit the full decay profile only the fluorescence lifetime component (of the order of ns) was neglected and the experimental data were fitted with Eqs. (9) and (10) by a home-made program which utilizes the Levenberg–Marquardt method of least-square minimization.
4. Results and discussion 4.1. Theoretical simulations The absorption cross section in the ground state (sa0 ) and the stimulated emission cross section (se0 ) to the ground state were calculated with the help of the measured spectra of dilute solutions of the dyes. The values of sa0 were obtained with the help of optical density (OD) by using the formula sa0 ¼ OD=Nd, where N is the number of molecules in the solution. The values of se0 were calculated by using the formula [24]: se0 ðlÞ ¼
l4 EðlÞ f; 8pn2 ctF
ð11Þ
where t is the fluorescence lifetime, c is the speed of light, f is the fluorescence quantum yield and EðlÞ is the fluorescenceR intensity profile normalized by the expression EðlÞ dl ¼ 1: For all calculations the intensity of excitation beams were taken to be the same. The change of the refractive index (Dn) at a wavelength is calculated by Eq. (7). For the case of RhB, R6G and CV the values of sa0 ; sa1 and se0 used in the simulations were also taken from literature [23–26]. Fig. 2 shows simulations for the diffraction efficiency for RhB in methanol–ethylene glycol mixture (1:1) and DBPI in benzene. For DBPI we have used benzene as a solvent due to its good solubility. It is seen that the contribution of amplitude grating dominates over the phase grating. Since we are using low-energy densities (4–7 104 J/cm2 at 35 ps pulse width) the
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305
Fig. 2. Plot of theoretically simulated diffraction efficiency as a function of wavelegnth for: (A) RhB in methanol–ethylene glycol (1:1) and (B) DBPI in benzene. The parameters are same as indicated in Table 2.
Table 1 Photophysical parameters for laser dyes in methanol–ethylene glycol (1:1) Dye
labs a71 (nm)
lem b72 (nm)
tF c (ns)
l at Zmax d (nm)
Rangee 72 (nm)
jwð3Þ jmax f (m2/V2)
R6G RhB CV DBPIg
528 548 602 526
570 582 625 544
3.6 2.6 3.0 3.7
522.5 550.0 583.5 526.5
470–550 500–580 525–615 450–600
2.25 1018 1.04 1017 0.75 1018 5.72 1018
[23] [23] [16] [16]
a
labs is the absorption maximum for the dye. lem is the fluorescence maximum (lexc ¼ 487 nm). c tf is the fluorescence lifetime, The values in bracket indicate the reference numbers. d l is the wavelength for which diffraction efficiency is maximum. e Range of the wavelength for which there is diffraction. f Maximum value of wð3Þ : g In benzene. b
population grating is free from other effects such as acoustic grating [27]. For RhB the efficiency of diffraction is maximum at 550 nm and it vanishes below 500 nm and above 580 nm. DBPI shows a maximum at 526.5 nm and it vanishes below 450 and above 600 nm. This observation indicates that the second harmonic of YAG laser (532 nm) can be used for the self-diffraction experiments. Table 1 shows the photophysical parameters for different dyes. The wavelength of absorption and emission are found to be red shifted in polar
solvents as compared to nonpolar solvents that is consistent with the effect of solvation arising due to polarity [28,29]. Fig. 3 shows the plot of total diffraction efficiency vs. intensity of an excitation beam for RhB. It is observed that the efficiency of diffraction has quadratic dependence on lower values of pump energies (Eqs. (6) and (8)). With the values of diffraction efficiency given in Fig. 2, the third-order susceptibility was calculated by using Eq. (8). The absolute value of thirdorder nonlinear susceptibility as a function of
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experiments. This is in agreement with value reported earlier [4]. Similarly, for other dyes, experimentally observed values are in close agreement with those obtained theoretically within the experimental error. For DBPI the sa1 values are not available. Therefore, an effect of noninclusion of the excited state absorption results in small difference in the observed values. We have confirmed this fact by reproducing the values of efficiency of R6G [4] and comparing the simulations by excluding the values of sa1 : The other source of error involved is to measure the intensity of the transmitted beam by suitably reducing it with neutral density filters. Nevertheless, the error in the experimentally observed values has been estimated to be o20%. 4.3. Measurement of relaxation times
Fig. 3. Log–log plot of simulated diffraction efficiency of RhB vs. intensity of a pump beam. The parameters are concentration of RhB in methanol–ethylene glycol (1:1)=2 104 M, l ¼ 532 nm and tp ¼ 35 ps.
wavelengths is plotted in Fig. 4 for RhB and DBPI. Maximum value of the wð3Þ and the range of wavelength for which the diffraction can be observed is indicated in Table 1. 4.2. wð3Þ measurements Self-diffraction of the laser beams was observed by using the set-up as shown in Fig. 1. The intensity of one of the excitation beams was measured before and after the first-order selfdiffraction by the LITG. The ratio of the diffracted intensity to that of the pump intensity gives the value of the efficiency of the diffraction. Table 2 shows a comparison of theoretical and experimentally observed values of nonlinear optical parameters for R6G, RhB, CV and DBPI. At a wavelength of 532 nm the calculated value of |wð3Þ | for R6G is 1.85 1018 m2/V2 which is in close agreement with the value obtained by the
Fig. 5 shows the decay profiles of the grating formed by the pump beams at lower pump energy (o0.5 mJ) for the DBPI in benzene and R6G in ethylene glycol. The decay profiles have been measured with sample thickness of 0.8 mm to increase the diffracted signal. The observed decay profiles show a sharp peak at short time followed by decaying components. The decay curves are expressed by Eq. (9). The sharp peak at zero time is known as the coherence peak that occurs in LITG experiments due to the diffraction of one of the pump beams into the direction of probe diffraction by a grating formed by other pump beam and the probe beam. The coherence spike appears only when the pump and the probe beams are derived from the same laser [6,18]. A Gaussian profile with a half-width equal to that of the pump laser pulse accounts for this. In any case, the decay curves can have a varying nature depending upon the polarization of the pump and probe beams, intensity of the incoming beams and wavelength of probe beam. Myers et al. [19] have shown this dependence of the decay profiles for R6G in ethylene glycol. In the present case the polarization of the pump and probe beams is parallel. Since the decay curves are recorded only up to approximately 700 ps, we ignore the fluorescence lifetime component in the analysis that will nearly be a constant. By fitting
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307
Fig. 4. Plot of theoretically obtained values of |wð3Þ | vs. wavelength for: (A) RhB in methanol–ethylene glycol (1:1) and (B) DBPI in benzene. The parameters are same as in Table 2.
Table 2 Simulated and experimentally observed parameters for laser dyes at 532 nm Dye
R6G RhB CV DBPI
Da (mm)
0.05 0.05 0.10 0.10
C b (mM)
10 20 10 50
tor (ps)
28897200c 500790d e
176733f
Wp (J/cm2)
4 104 7 104 6 104 7 104
Theoretical
Experimental
Z
|wð3Þ | (m /V )
Z 710%
|w(3)|710% (m2/V2)
2.5 105 1.1 104 3.4 104 4.0 104
1.85 1018 4.22 1018 0.26 1018 4.70 1018
1.8 105 1.6 104 2.5 104 7.8 104
0.65 1018 5.06 1018 0.22 1018 6.56 1018
2
2
a
d is the thickness of the sample. C is the concentration of the sample. c In ethylene glycol. d In DMSO. e Not measured due to dye unstability. f In benzene. b
the limited range of the decay curve with a single exponential function a rough estimate of the orientational relaxation time (tor ) of the molecule in the solvent can be obtained. For DBPI in benzene we obtained average value of tor as 176733 ps; while RhB in DMSO shows a longer value of 500790 ps (Table 2). Decay profile of R6G in ethylene glycol is given in panel (B) of Fig. 5. The decay curve is obtained after adding 4 curves recorded in a sequence for a sample. An improved signal-to-noise ratio allows
us to fit the obtained decay curve with Eqs. (9) and (10). As can be seen from Eq. (9) the analysis requires double deconvolution of the decay curve with the pump pulse (Ipu ). The profile contains a sharp coherence spike followed by a slower decay. Due to only a few points on initial time scale the data correlation takes place in theoretical fitting of experimental data for the parameters associated with the shorter times. However, longer time scale data fit well to give a value of 2889 ps for tor which is also reported in the case of RhB in ethylene
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Fig. 5. Decay curve for: (A) DBPI in benzene: the fitted line for a single exponential decay function for a limited range is also shown. (B) R6G in ethylene glycol: a fit with the help of Eqs. (9) and (10) gives a value of tor as 2889 ps. Panel B also shows the autocorrelation of the laser pulse recorded in a separate experiment.
glycol [2]. The value of tor is in close agreement to those obtained from Debye–Stokes–Einstein [30] hydrodynamic theory (tor ¼ gV =kB T; where g is the viscosity of the solvent, V is the volume of the molecule and T is the temperature). As mentioned earlier while for DBPI due to solubility reasons the solvent used was benzene (viscosity=0.7 cP), for other dyes the solvents for decay profile measurement was chosen as either DMSO (viscosity= 2.0 cP) or ethylene glycol (viscosity=24.2 cP). We have found that the dye DBPI is an efficient and stable probe molecule at 532 nm besides RhB and R6G. Whereas for CV the signal was found to be sensitive for the large number of laser shots due to bleaching effect, which prevented us from recording its decay profile reliably.
those for similar reported values of R6G and CV for a comparison. Theoretical simulations are found to be in close agreement with the experimentally obtained values. The decay profile of the gratings of these dyes show a fast coherence peak followed by the relaxation times.
Acknowledgements We thank DST, New Delhi, for financial assistance. This work was in part supported by a grant-in-aid no. 03 (0957)/02/EMR-II from CSIR, New Delhi.
References 5. Conclusions The diffraction efficiency of LITG in organic laser dyes has been measured. The third-order nonlinear susceptibility has been calculated as a function of the wavelength. Theoretical calculations for RhB and DBPI are given here alongwith
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