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Resonance fluorescence spectra of dye-doped polymers
LUMINESCENCE JOURNAL OF
Journal of Luminescence 53 (1992) 235—238
Resonance fluorescence spectra of dye-doped polymers Yasuo Kanematsu, Jeung Sun Ahn and Takashi Kushida Department of Physics, Osaka UniiersiO’, Toyonaka, Osaka 560, Japan
Site-selected fluorescence spectra have been measured for Mg-octaethylporphyrin doped in polystyrene and PMMA films at low temperatures by a time-correlated single-photon counting method under CW mode-locked dye-laser excitation into the lowest optical absorption band. A narrow resonance line accompanied by a broad sideband has been observed by rejecting the scattered laser light using a time gate. A single-site fluorescence spectrum has been obtained by the use of saturation effect of the laser-induced fluorescence. The density of phonon states weighted by the electron—phonon coupling coefficient has been determined, for the first time for a dye—polymer system, from the analysis of the obtained spectrum. Temperature dependence of the laser-induced fluorescence spectrum is compared with the simulation based on the weighted phonon-state density.
1. Introduction Recently, much attention has been paid to the low-frequency modes of amorphous systems such as polymers and glasses. The study of optical spectra of localized centers embedded in amorphous materials is considered to give significant information on the low-frequency modes of the host. However, the quantitative analysis of the optical spectra from this point of view has not been made, because it is difficult to extract the homogeneous optical spectrum and the one-phonon sideband spectrum in amorphous systems on account of large inhomogeneous broadening. We have recently succeeded in obtaining the siteselected fluorescence spectrum including the narrow resonance line in dye-doped polymers by rejecting the scattered laser light. Furthermore, we have determined the single-site fluorescence spectrum by use of the saturation effect of the laser-induced fluorescence [1]. In the present paper, we report the first determination of the density of the low-frequency host modes weighted by the electron—phonon coupling strength in dye-doped polymers. This has been attained from the analysis of the single-site fluorescence spec-
Correspondence to: Dr. Y. Kanematsu, Department of Physics. Osaka University, Toyonaka, Osaka 560, Japan. 0022-2313/92/$05.O0 © 1992
—
trum obtained by the above-mentioned method. The temperature dependence of the laser-induced fluorescence spectrum has been found to be reproduced using thus determined weighted phonon-state density. This supports the validity of our procedure of analysis.
2. Experimental The experimental method has already been reported in detail [1]. The low-energy side of the ~ absorption band of Mg-octaethylporphyrin (MgOEP) in polystyrene and polymethyl methacrylate (PMMA) films was excited by a CW mode-locked rhodamine 6G laser. Fluorescence from the sample was analyzed by a monochromator and detected by a photomultiplier. A timecorrelated single-photon counting method was employed to obtain the time profile of the photon-detection probability. A time gate was set much later than the termination of the exciting pulse to reject the scattered laser light, and the photon detection signal within this gate was accumulated. In order to prevent the spectral holeburning effect and also to avoid the nonlinear response of the single-photon counting system due to the dead time, the stabilized laser intensity was reduced as much as possible.
Elsevier Science Publishers B.V. All rights reserved
236
}T Kane,nat.sii it aI. /Rt’soiianic /iuorc~sic’iuespectra of dee—doped polymers
3. Results and discussion Figure 1 shows the temperature dependence of the laser-induced fluorescence spectrum measured for MgOEP doped in polystyrene. A similar result was obtained for MgOEP doped in PMMA. The laser-induced fluorescence spectrum was also measured for various laser frequencies at 4 K. In fig. I, a sharp line located at the same energy as thc exciting light is accompanied by a hro~idband and the fraction of the former decreases with increasing temperature. To understand these spectra, let us write the spectral shape functions of the absorption and fiuorcscencc transitions of a dye molecule in a single site at temperature T as g (w w ) and f1 (w w ) respcctivelv Herc thc light frequency md w ts the zcro pho non line frequcncy of moleculcs in a given sitc Using the distribution function G(w’) of the number of molecules with the zero-phonon frequency at w’, the laser-induced (photon-counting) fluorescence spectrum is given as
L
)w1 ~‘-i-(wL; w Xw 1-(ca; w’) dw’,
~
1. _--~~
~
-
/ / I
w is
I -~ f(ca. w1) ~j(~(w3f
~
~
~. ~
L --
crn -
-
1-1g. 1. Temperature dependence ot the laser-induced tluorcsccncc spectrum of Mg-octaethylporphyrin in a polystyrene film. The solid lines have been calculated using the experimentally determined weighted phonon-state density and siteenergy distribution.
(I)
where w1 is the exciting laser frequency. At low temperatures, the functions g~(w; w’) and f1-(w; w’) are considered to be composed of a narrow zero-phonon line and a broad phonon sideband in our sample. It is clear that the sharp resonance fluorescence line in fig. I results from the purely electronic zero-phonon transitions both in absorption and fluorescence. Since the resonance fluorescence line is very narrow at the lowest temperature in our experiment, we regard the zero-phonon line in this case as a ~ function. Then, we find from eq. (1) that the excitation spectrum of the resonance fluorescence line is expressed as coLG(w~).Therefore, it is possible to determine the site-energy distribution function G(w’) from our experiment. The result was found to he expressed by a skewed Gaussian in our sample. The laser-induced fluorescence intensity was not proportional to the exciting laser intensity even under weak excitations for which no persis-
tent spectral hole was observed. Furthermore, the spectral shape of the broad band in the laser-induced fluorescence varied with excitation intensity. These characteristics are considered to arise from the saturation effect. At 4 K, the peak absorption cross-section of the zero-phonon line is much larger than that of the phonon sideband in our sample. Therefore, the saturation effect is expected to be much more significant for the fluorescence excited through the zero-phonon absorption line than that through the phonon sidehand. We measured the fluorescence spectra of MgOEP at 4 K under CW dye laser excitation at 17123 cm~ with two different intensities. One was obtained under sufficiently weak excitation, while the other was for the case where the saturation effect was considered to occur in the fluorescence excited through the zero-phonon line but not through the sideband. The single-site fluorescence spectra obtained from the difference hetween the two spectra are plotted by dashed curves in fig. 2.
Y Kanematsu et al.
/ Resonance fluorescence spectra of dye-doped polymers
an ensemble of normal-mode harmonic oscillators. For simplicity, we consider only the linear electron—phonon coupling and limit ourselves to
(a) ~
-
237
~--
-
______________________________________
the first-order perturbation. Then, we can express the Stokes and anti-Stokes one-phonon sidebands as ST(fl) S~(Q)[nT(I2) + 1] + S 0( —~)~T(—11), =
(3)
0
~
50
-
100 SHIFT (CS-i
150
200
Fig. 2. Single-site fluorescence spectrum (dashed line) and weighted phonon-state density (solid line) for MgOEP in PMMA (a) and polystyrene (b).
For the excitation within a high-energy broad absorption band, the molecules in various sites are expected to be excited rather uniformly. In this case, the fluorescence spectrum is given by 3fT(w; w’) dw’. (2) F(w) cx G(w’)w The fluorescence spectrum of MgOEP-doped polystyrene at 4 K excited by the 472.7 nm line of an Ar5 laser was found to be well reproduced by eq. (2), where we used experimentally determined site-energy distribution function G(w’) and single-site fluorescence spectrum fT(w; to’), whose shape was assumed to be site-independent. The good agreement between the observed and calculated fluorescence spectra indicates that the cxperimentally determined single-site fluorescence spectrum can be regarded as the homogeneous spectrum that does not depend on the site. Thus, we write fT(W; w’) as fT(w’ w). Generally, the single-site fluorescence spectrum contains multi-phonon sidebands in addition to the one-phonon sideband. Now, let us extract the one-phonon sideband spectrum from the single-site fluorescence spectrum determined above. Using the adiabatic and the Condon approximations, we deal with optical transitions be-
f
the electron—phonon ‘~T(~) where is the isoccupation S(Q) the phonon coupling number densityof strength weighted the phonon and by with the energy hfl at temperature T. Using the dimensionless coupling coefficient ~ for the jth mode with the frequency f2~, the weighted phonon-state density S0(f2) is given as Ii) —
If we put the inverse Fourier transform of ST(Q) the Debye—Waller is expressedasasST(t), a exp[—ST(O)], while factor S~(O)corresponds to the Huang—Rhys factor. Using this inverse Fourier transform, cence spectrum is written asthe single-site fluores=
fT(~)
=
f e’11~e5~ 2~J_~
~T(~)
dt.
(4)
We separate this into the 6-function-like zerophonon line and the phonon sideband ~T(~1) as fT(~) =a6(Q) + ‘~T(~). (5) The inverse Fourier transform of PT(Q) can be described as —
e~ST6b[e5iO) 1]. (6) If we differentiate both sides of eq. (6) with respect to t and perform the Fourier transform, we obtain the following integral equation: IDT(t)
=
—
—
~~T(~2)
=
e_STOPQST(fl) +f~T([1_Q)PSI(11)
which can be rewritten, at T fl~ 0(Q) aflS0(fl)
=
dQ’, (7)
0 K, as
=
tween two electronic states of a guest dye molecule in a host polymer. We regard the lowfrequency vibrational modes of the host that interact with the electrons in the dye molecule as
12
+
f ‘I~(Q
—
Q’)fl’S11(fl’) d12’, (8)
1 /sa,ls,flslt sit it al.
235
z
Resonance fluorescence spectra of die--sloped pols’mcrs
P51(12) and 5/12) have non—zero values only for 12 > 0. It is easy to solve this equation numerically, and we can determine the one—phonon sideband spectrum at (I K, i.e., the weighted phonon-state density, from the single-site fluorescence spectrum at T 0 K [2,3]. We used ‘-~-~ 12). obtained at 4 K, instead of because
~( 12). i~hisis considered to be a good approxi— mation. because, at very low temperatures. I~(12) is expected to show weak temperature dependencc only in the vicinity of 12 = 0. Solving eq. (8) numerically and making correctton with respect to the factor n-1-( 12) + 1. we determined the weighted phonon-state density S~~( 12). The results obtained br MgOEP in PMMA and polystyrene are plotted in fig. 2. As far as we know, this is the first case that the weighted phonon—state density has been determined for a dye-—polymer system. Personov et al. obtained the weighted phononstate density for n—paraffin crystals from the phonon—wing profiles of the fluorescence spectra in n—paraffins doped with organic molecules on— ~ler mercury lamp excitation [3]. If we expand the factor expLS’ (1 )] in eq. (4) as ~m[S-1(1 )I’/n’ !, and express S (i ) by its inverse Fourier transform, P (12) is obtained in the form of the sun~of convolutions of .S’ ([2) as follows:
in eq. (9h) by performing convolution repeatedly. ihe phonon sideband in the single—site fluores—
cence spectrum should he obtained by the sum of these spectra. This was confirmed using the above-determined one-phonon sideband spectra. We also calculated the temperature dependence of the laser—induced fluorescence spectrum using experimentally determined .S1( [2) and (( w’ ). The mirror symmetry relation was as— somed to hold between the absorption and tluorescence shape functions. The obtained spectra were convoluted using a Gaussian function with the width corresponding to the resolution of the experimental equipment. The results are shown by solid lines in fig. 1. The simulated curves reproduce the observed spectra very well, which supports the validity of the obtained weighted phonon-state density. At higher temperatures, the observed resonance fluorescence line has broader width than the experimental resolution. This broadening can be explained by taking into ac— count the quadratic coupling and/or the second— order perturbation. This type of analysis and also the relation between tile above results and the data of the pilotoil cello and Raman scattering experiments will be reported elsewhere.
5)a)
(t)~(X2) (/d 551
( [2)
(I)”(12).
(
f.s
~
(12~ ) 5r
(
~
1
(I) IS. ,\hn. Y. Kancni:iisu :iiid 1. Ku’,liids, .1. luinin. 45&4U (i~)~)l) 4(0.
-(1l~) x5( 12—- 12 x d12 d12.
-—
References
I)
12 )
12,
(2) IS. Kukushkin. Sos. l~hs.’,. Solid Slate S (1964) 1551: 7 I lUH( 35.
Lit2, 5.
(~Th)
l’heretore, once the one—phonon sideband spectrum is obtained, we can calculate each terill
[3] l~.l. t’ersonov. IS. ()sasl’ko. E:.D. (ioslyaes and El. ,-\lstiits, Soy. Phys. Sol~iStale 3 (11)72) 2224: IS. O~adko. [.1 .shits and R. I. l’cr,,onov. Soy. Phy~. Solid State 16 ( 975) 125o.
Journal of Luminescence 53 (1992) 235—238
Resonance fluorescence spectra of dye-doped polymers Yasuo Kanematsu, Jeung Sun Ahn and Takashi Kushida Department of Physics, Osaka UniiersiO’, Toyonaka, Osaka 560, Japan
Site-selected fluorescence spectra have been measured for Mg-octaethylporphyrin doped in polystyrene and PMMA films at low temperatures by a time-correlated single-photon counting method under CW mode-locked dye-laser excitation into the lowest optical absorption band. A narrow resonance line accompanied by a broad sideband has been observed by rejecting the scattered laser light using a time gate. A single-site fluorescence spectrum has been obtained by the use of saturation effect of the laser-induced fluorescence. The density of phonon states weighted by the electron—phonon coupling coefficient has been determined, for the first time for a dye—polymer system, from the analysis of the obtained spectrum. Temperature dependence of the laser-induced fluorescence spectrum is compared with the simulation based on the weighted phonon-state density.
1. Introduction Recently, much attention has been paid to the low-frequency modes of amorphous systems such as polymers and glasses. The study of optical spectra of localized centers embedded in amorphous materials is considered to give significant information on the low-frequency modes of the host. However, the quantitative analysis of the optical spectra from this point of view has not been made, because it is difficult to extract the homogeneous optical spectrum and the one-phonon sideband spectrum in amorphous systems on account of large inhomogeneous broadening. We have recently succeeded in obtaining the siteselected fluorescence spectrum including the narrow resonance line in dye-doped polymers by rejecting the scattered laser light. Furthermore, we have determined the single-site fluorescence spectrum by use of the saturation effect of the laser-induced fluorescence [1]. In the present paper, we report the first determination of the density of the low-frequency host modes weighted by the electron—phonon coupling strength in dye-doped polymers. This has been attained from the analysis of the single-site fluorescence spec-
Correspondence to: Dr. Y. Kanematsu, Department of Physics. Osaka University, Toyonaka, Osaka 560, Japan. 0022-2313/92/$05.O0 © 1992
—
trum obtained by the above-mentioned method. The temperature dependence of the laser-induced fluorescence spectrum has been found to be reproduced using thus determined weighted phonon-state density. This supports the validity of our procedure of analysis.
2. Experimental The experimental method has already been reported in detail [1]. The low-energy side of the ~ absorption band of Mg-octaethylporphyrin (MgOEP) in polystyrene and polymethyl methacrylate (PMMA) films was excited by a CW mode-locked rhodamine 6G laser. Fluorescence from the sample was analyzed by a monochromator and detected by a photomultiplier. A timecorrelated single-photon counting method was employed to obtain the time profile of the photon-detection probability. A time gate was set much later than the termination of the exciting pulse to reject the scattered laser light, and the photon detection signal within this gate was accumulated. In order to prevent the spectral holeburning effect and also to avoid the nonlinear response of the single-photon counting system due to the dead time, the stabilized laser intensity was reduced as much as possible.
Elsevier Science Publishers B.V. All rights reserved
236
}T Kane,nat.sii it aI. /Rt’soiianic /iuorc~sic’iuespectra of dee—doped polymers
3. Results and discussion Figure 1 shows the temperature dependence of the laser-induced fluorescence spectrum measured for MgOEP doped in polystyrene. A similar result was obtained for MgOEP doped in PMMA. The laser-induced fluorescence spectrum was also measured for various laser frequencies at 4 K. In fig. I, a sharp line located at the same energy as thc exciting light is accompanied by a hro~idband and the fraction of the former decreases with increasing temperature. To understand these spectra, let us write the spectral shape functions of the absorption and fiuorcscencc transitions of a dye molecule in a single site at temperature T as g (w w ) and f1 (w w ) respcctivelv Herc thc light frequency md w ts the zcro pho non line frequcncy of moleculcs in a given sitc Using the distribution function G(w’) of the number of molecules with the zero-phonon frequency at w’, the laser-induced (photon-counting) fluorescence spectrum is given as
L
)w1 ~‘-i-(wL; w Xw 1-(ca; w’) dw’,
~
1. _--~~
~
-
/ / I
w is
I -~ f(ca. w1) ~j(~(w3f
~
~
~. ~
L --
crn -
-
1-1g. 1. Temperature dependence ot the laser-induced tluorcsccncc spectrum of Mg-octaethylporphyrin in a polystyrene film. The solid lines have been calculated using the experimentally determined weighted phonon-state density and siteenergy distribution.
(I)
where w1 is the exciting laser frequency. At low temperatures, the functions g~(w; w’) and f1-(w; w’) are considered to be composed of a narrow zero-phonon line and a broad phonon sideband in our sample. It is clear that the sharp resonance fluorescence line in fig. I results from the purely electronic zero-phonon transitions both in absorption and fluorescence. Since the resonance fluorescence line is very narrow at the lowest temperature in our experiment, we regard the zero-phonon line in this case as a ~ function. Then, we find from eq. (1) that the excitation spectrum of the resonance fluorescence line is expressed as coLG(w~).Therefore, it is possible to determine the site-energy distribution function G(w’) from our experiment. The result was found to he expressed by a skewed Gaussian in our sample. The laser-induced fluorescence intensity was not proportional to the exciting laser intensity even under weak excitations for which no persis-
tent spectral hole was observed. Furthermore, the spectral shape of the broad band in the laser-induced fluorescence varied with excitation intensity. These characteristics are considered to arise from the saturation effect. At 4 K, the peak absorption cross-section of the zero-phonon line is much larger than that of the phonon sideband in our sample. Therefore, the saturation effect is expected to be much more significant for the fluorescence excited through the zero-phonon absorption line than that through the phonon sidehand. We measured the fluorescence spectra of MgOEP at 4 K under CW dye laser excitation at 17123 cm~ with two different intensities. One was obtained under sufficiently weak excitation, while the other was for the case where the saturation effect was considered to occur in the fluorescence excited through the zero-phonon line but not through the sideband. The single-site fluorescence spectra obtained from the difference hetween the two spectra are plotted by dashed curves in fig. 2.
Y Kanematsu et al.
/ Resonance fluorescence spectra of dye-doped polymers
an ensemble of normal-mode harmonic oscillators. For simplicity, we consider only the linear electron—phonon coupling and limit ourselves to
(a) ~
-
237
~--
-
______________________________________
the first-order perturbation. Then, we can express the Stokes and anti-Stokes one-phonon sidebands as ST(fl) S~(Q)[nT(I2) + 1] + S 0( —~)~T(—11), =
(3)
0
~
50
-
100 SHIFT (CS-i
150
200
Fig. 2. Single-site fluorescence spectrum (dashed line) and weighted phonon-state density (solid line) for MgOEP in PMMA (a) and polystyrene (b).
For the excitation within a high-energy broad absorption band, the molecules in various sites are expected to be excited rather uniformly. In this case, the fluorescence spectrum is given by 3fT(w; w’) dw’. (2) F(w) cx G(w’)w The fluorescence spectrum of MgOEP-doped polystyrene at 4 K excited by the 472.7 nm line of an Ar5 laser was found to be well reproduced by eq. (2), where we used experimentally determined site-energy distribution function G(w’) and single-site fluorescence spectrum fT(w; to’), whose shape was assumed to be site-independent. The good agreement between the observed and calculated fluorescence spectra indicates that the cxperimentally determined single-site fluorescence spectrum can be regarded as the homogeneous spectrum that does not depend on the site. Thus, we write fT(W; w’) as fT(w’ w). Generally, the single-site fluorescence spectrum contains multi-phonon sidebands in addition to the one-phonon sideband. Now, let us extract the one-phonon sideband spectrum from the single-site fluorescence spectrum determined above. Using the adiabatic and the Condon approximations, we deal with optical transitions be-
f
the electron—phonon ‘~T(~) where is the isoccupation S(Q) the phonon coupling number densityof strength weighted the phonon and by with the energy hfl at temperature T. Using the dimensionless coupling coefficient ~ for the jth mode with the frequency f2~, the weighted phonon-state density S0(f2) is given as Ii) —
If we put the inverse Fourier transform of ST(Q) the Debye—Waller is expressedasasST(t), a exp[—ST(O)], while factor S~(O)corresponds to the Huang—Rhys factor. Using this inverse Fourier transform, cence spectrum is written asthe single-site fluores=
fT(~)
=
f e’11~e5~ 2~J_~
~T(~)
dt.
(4)
We separate this into the 6-function-like zerophonon line and the phonon sideband ~T(~1) as fT(~) =a6(Q) + ‘~T(~). (5) The inverse Fourier transform of PT(Q) can be described as —
e~ST6b[e5iO) 1]. (6) If we differentiate both sides of eq. (6) with respect to t and perform the Fourier transform, we obtain the following integral equation: IDT(t)
=
—
—
~~T(~2)
=
e_STOPQST(fl) +f~T([1_Q)PSI(11)
which can be rewritten, at T fl~ 0(Q) aflS0(fl)
=
dQ’, (7)
0 K, as
=
tween two electronic states of a guest dye molecule in a host polymer. We regard the lowfrequency vibrational modes of the host that interact with the electrons in the dye molecule as
12
+
f ‘I~(Q
—
Q’)fl’S11(fl’) d12’, (8)
1 /sa,ls,flslt sit it al.
235
z
Resonance fluorescence spectra of die--sloped pols’mcrs
P51(12) and 5/12) have non—zero values only for 12 > 0. It is easy to solve this equation numerically, and we can determine the one—phonon sideband spectrum at (I K, i.e., the weighted phonon-state density, from the single-site fluorescence spectrum at T 0 K [2,3]. We used ‘-~-~ 12). obtained at 4 K, instead of because
~( 12). i~hisis considered to be a good approxi— mation. because, at very low temperatures. I~(12) is expected to show weak temperature dependencc only in the vicinity of 12 = 0. Solving eq. (8) numerically and making correctton with respect to the factor n-1-( 12) + 1. we determined the weighted phonon-state density S~~( 12). The results obtained br MgOEP in PMMA and polystyrene are plotted in fig. 2. As far as we know, this is the first case that the weighted phonon—state density has been determined for a dye-—polymer system. Personov et al. obtained the weighted phononstate density for n—paraffin crystals from the phonon—wing profiles of the fluorescence spectra in n—paraffins doped with organic molecules on— ~ler mercury lamp excitation [3]. If we expand the factor expLS’ (1 )] in eq. (4) as ~m[S-1(1 )I’/n’ !, and express S (i ) by its inverse Fourier transform, P (12) is obtained in the form of the sun~of convolutions of .S’ ([2) as follows:
in eq. (9h) by performing convolution repeatedly. ihe phonon sideband in the single—site fluores—
cence spectrum should he obtained by the sum of these spectra. This was confirmed using the above-determined one-phonon sideband spectra. We also calculated the temperature dependence of the laser—induced fluorescence spectrum using experimentally determined .S1( [2) and (( w’ ). The mirror symmetry relation was as— somed to hold between the absorption and tluorescence shape functions. The obtained spectra were convoluted using a Gaussian function with the width corresponding to the resolution of the experimental equipment. The results are shown by solid lines in fig. 1. The simulated curves reproduce the observed spectra very well, which supports the validity of the obtained weighted phonon-state density. At higher temperatures, the observed resonance fluorescence line has broader width than the experimental resolution. This broadening can be explained by taking into ac— count the quadratic coupling and/or the second— order perturbation. This type of analysis and also the relation between tile above results and the data of the pilotoil cello and Raman scattering experiments will be reported elsewhere.
5)a)
(t)~(X2) (/d 551
( [2)
(I)”(12).
(
f.s
~
(12~ ) 5r
(
~
1
(I) IS. ,\hn. Y. Kancni:iisu :iiid 1. Ku’,liids, .1. luinin. 45&4U (i~)~)l) 4(0.
-(1l~) x5( 12—- 12 x d12 d12.
-—
References
I)
12 )
12,
(2) IS. Kukushkin. Sos. l~hs.’,. Solid Slate S (1964) 1551: 7 I lUH( 35.
Lit2, 5.
(~Th)
l’heretore, once the one—phonon sideband spectrum is obtained, we can calculate each terill
[3] l~.l. t’ersonov. IS. ()sasl’ko. E:.D. (ioslyaes and El. ,-\lstiits, Soy. Phys. Sol~iStale 3 (11)72) 2224: IS. O~adko. [.1 .shits and R. I. l’cr,,onov. Soy. Phy~. Solid State 16 ( 975) 125o.