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Changes in fluorescence lifetimes induced by variation of of the radiating molecules' optical environment
Volume 31, number 1
OPTICS COMMUNICATIONS
CHANGES IN FLUORESCENCE LIFETIMES INDUCED BY VARIATION OF THE RADIATING MOLECULES’ OPTICAL ENVIRONMENT
October 1979
OF
W. LUKOSZ and R.E. KUNZ Swiss Federal Institute of Technology,
Professur fiir Optik, ETH,
8093 Ziirich, Switzerland Received 27 June 1979
We report results of experiments with about 30 nm thick evaporated layers of an europium-chelate fluorescing at h = 612 nm: i.) For layers on different substrates S1 in air the lifetime decreases with increasing refractive index nl of S1. ii.) For a layer on a substrate S1 the lifetime decreases when the width d of an air gap between the layer and a second plate Sz is reduced from d > h to d = 0. Theoretically, we derived analytic expressions for the spontaneous emission rates of electric and magnetic dipole transitions taking place in an atomic system embedded in a very thin layer of refractive index no and optical thickness nodo < h/S, which is sandwiched between two dielectric loss-free media of refractive indices n t and “2. Comparison of theory and experiment allows to determine the absolute quantum efficiency of the emitting state.
1. Introduction The fluorescence lifetime of an excited dye molecule has been experimentally shown to depend on its distance z. from a metal surface or from a dielectric interface. In these experiments Drexhage, Kuhn, Schgfer, Tews et al. [l-.5] used fatty-acid spacer layers for the precise definition of the distance z. and an europium-dibenzoylmethane-complex as the dye. The experiments demand mastery of the monolayer assembly technique. Theoretical investigations of the effect are listed in refs. [4-91. In this letter we report investigations of lifetime changes by variation of the optical environment of fluorescent molecules in three different types of experiments: I) A thin layer (no) of fluorescent molecules is deposited simultaneously on a number of substrates S, with different refractive indices nl. The dependence of the lifetime on nl is measured in air. II) The ‘optical contact experiments’ work with a homogeneous layer (no) of fluorescent molecules on one substrate S, with index nl. The width d of the air gap between layer (no) on substrate S, and, a second plate S, with refractive index n2 is varied between d & X, where X is the emission wavelength, 42
and d = 0, i.e. optical contact. In experiment IIa the distance d is varied spatially, i.e. d = d(x), and the lifetime is measured as a function of coordinate x (cf. inset fig. 3). In experiment IIb the lifetime is measured at x = const. while the distance d is varied as a function of time, i.e. d = d(t). We point out an important feature of experiment IIb: The monolayer technique experiments of Drwe Drexhage, Kuhn, et al., and our experiments of type I and Ha compare lifetimes of theoretically identical but actually different systems (which are, of course, prepared to be as similar as possible). But in experiment IIb we actively vary as a function of time the optical environment of the very same system. Our experiments IIb show for the first time that the lifetime of the very same emitters can be reversibly changed by a variation of their optical environment. Our experimental results were obtained with fluorescing layers deposited in vacuum by evaporation of europium-chelate Eu(BTF)~HP~~~. The decay of the fluorescence of the Eu3+-ions near h w 612 nm and X = 592 nm after uv pulse excitation was measured.
Volume
2.
3 1, number
1979
Theory
For the analysis of our experiments we derive theoretically how the spontaneous emission rate for a fluorescent molecule embedded in a very thin layer of refractive index n0 and thickness d, depends on the refractive indices n 1 and n2 of the two adjoining loss-free dielectric half-spaces (cf. fig. 1). For very thin layers with optical thickness nOdO Q X/8 we obtain analytic expressions for the (normalized) spontaneous emission rates for electric and magnetic dipole transitions. The theory allows: i) to predict the maximum values of the (relative) lifetime changes which would occur in experiments I and II if no non-radiative transitions would compete with the radiative transitions, and ii) to determine the absolute quantum efficiency from the experimentally observed lifetime changes. The determination of the q.e. is based on the assumption that the rate of non-radiative transitions is not influenced by a variation of n1 or n2. This variation of the optical environment of the emitting molecules leaves their environment on an atomic distance scale essentially unchanged, at least for the majority of emitters in a several nm thick layer (no). Therefore, we expect the above assumption to be realistic. We consider a radiating classical electric (e) or magnetic (m) dipole located in the layer (no). The dipole is assumed to oscillate with fixed frequency V, fixed dipole moment, and fixed orientation ~3.Generalizing a method we had previously used for a dipole in front of a single interface [8,9] we have rigorously solved the electromagnetic boundary value problem. Both the wide-angle interferences of the plane waves emitted by the dipole and emission from evanescent waves in the dipole’s near field are taken into account. The normalized total power radiated by the dipole with orientation 0 is
= cos20 (4,0,2)L
+ sin21J Ol,O,2>,,,
(1)
where the indices 1 and IIdenote dipoles perpendicular (0 = 0) and parallel (0 = 90”) to the interfaces, and L
October
OPTICS COMMUNICATIONS
1
= (QQ&
is the power radiated by the dipole in an infinite medium of refractive index no. In eq. (2), CJ= 1 for
(2)
Fig. 1. Atomic system (dipole) D embedded in very thin layer of refractive index no an thickness do sandwiched between two half-spaces with refractive indices n 1 and 112, respectively. 0 angle between transition dipole moment and z-axis.
an electric and 4 = 3 for a magnetic dipole, while L,, is the power radiated by the identical dipole in vacuum. In the limiting case of an extremely thin layer (no), i.e. for nod0
(Z1,0,2) = (~~/no)~Z@
(n = +l),
(3)
where p = 5 for (e,l), p = 1 for (e, II), p = 3 for both (m, 1) and (m, II). For the functions Z(‘)(n) analytic expressions were given in ref. [S] for both types of dipoles (e,m) and the two main orientations (I, II). Physically, Z(‘l(n = n2/nl) is the normalized total power radiated by a dipole located in medium (n 1) directly at the interface to an adjoining medium (n2). Eq. (3) expresses the power radiated by a dipole as shown in fig. 1 in terms of the power radiated by the same dipole located at the interface between the halfspaces (nl) and (n2) not separated by a layer (no). For an ensemble of randomly oriented dipoles with equal dipole moments, assumed to radiate incoherently, we obtain from eq. (1) the average power radiated per dipole (Ll,0,2)i=:(Ll,0,2)1
+3(Ll,0,2)11.
(4)
From eqs. (l)-(3) we conclude that the power L1,0,2/Lvac for magnetic dipoles of any orientation and for the parallel electric (e, 11)dipole is independent of no. In fig. 2, the powers L1,0,2/Lvac as functions of nl are shown for (e) and (m) dipoles with orientations (I, ll,i) in the special cases n2 = 1 and n2 = nl. In the latter case we have since ZCol(n= 1) = 1, (Ll,0,2)/Lvac
= (nl)qno)~-~.
(5)
The dipoles (e, II) and (m, II,1, i) radiate as if they were in an infinite medium nl . The spontaneous emission rate for a dipole transition is l/r, = L/Zzu, when in the classical expression 43
Volume 31, number 1
3. Experimental
oIir-e---
2.0
3.0
4
Fig. 2. Normalized power L1 ,~,&~c radiated by electric (e) and magnetic (m) dipoles shown in fii. 1 versus n 1, for
f12= n 1 (solid lines) and n2 = 1 (dashed lines), respectively. no = 1.57. Subscripts 1, II,i denote perpendicular, parallel, and random isotropic orientation, respectively. for the radiated power L the dipole moment is replaced by the corresponding transition moment. The rat@ of the transition rates of the same system in two different optical environments (denoted by a prime and no prime, respectively) iS equal to the inverse ratio of the powers radiated by the same classical dipole in the two situations ~JT: = L’/L, provided that the transition moment is not changed by variation of the system’s optical environment. Supposing an analogue independence of the thermal deactivation rate l/rth, we obtain with I/T = l/rr + I/T* a relation for the lifetimes T and T’ in the two situations 7/?’ = I + q(L’/L - l),
(6)
(cf. refs. [2-71). The absolute quantum efficiency 77E T/T~ depends on the environment. Therefore, the q.e. TJ, in an infinite homogeneous medium (no) is introduced which can be calculated from the known value of 17in a given environment l/7), - 1 = 44
(L/-L)(lIrl -
October 1979
OPTICS COMMUNICATIONS
0.
(7)
results
In our experiments substrates were coated with thin fluorescing layers by evaporation of small (-0.2 mm) crystals of Eu(BTF)~HP~~~ (BTF: benzoyltrifluoroacetone, Pyrr: pyrrolidine). The fluorescence of these crystals decays exponentially with a lifetime 7 = 1.26 ms. The fluorescence decay of the evaporated layers is not strictly a single exponential decay. Comparing the fluorescence decay of layers in different optical environments, we have found that the shape of the decay curves remains essentially unchanged. Therefore, we only report the decay time t,, defined as the time during which the fluorescent intensity falls to I/e of its initial value after excitation with a uv pulse (A’= 366 nm, duration 850 /AS). We have determined the refractive index and the thickness of the layers (no = 1.57 at X = 612 nm, typically d, = 30 nm) from measurements of the angular intensity distribution and polarization of the fluorescence of layers deposited on glass hemicylinders by comparison with theoretical calculations based on a generalization of the theory developed in ref. [9]. This comparison also shows that the fluorescence at X = 612 nm corresponds to an electric dipole transition with isotropic distribution (e, i) of the dipole moments. This can be explained by random orientation either i) of the dipole moments of the different Eu3+-ions in the layer (each ion having a dipole moment with fixed orientation) or ii) of the dipole moment of an individual Eu3+-ion during the decay time t,. Only the latter possibility ii) is compatible with our experimental result that the measured decay time te is essentially independent of the direction of observation and of polarization. In the following we compire the experimentally observed changes of the decay time with the theory for (e, i). Our experiments I confirm the theoretical prediction (following from eq. (6) and dashed curves in fig. 2) that the lifetime on substrate S, in air (n2 = 1) decreases with increasing refractive index nl . We compare the decay times te and tk on two substrates S, and S;(n;) coated simultaneously. Choosing microscope glass slides (n 1 = 1.5 14) as reference substrate S, we obtained: on SF6 glass substrates S;(n; = 1.802), felt; = 1.lS, and from (L’/L)e,i = 1.219, and (L/L_)e,i = 0.677, the q.e. Q, = 0.76 + 0.05, and on SrTi03 crystal substrates S; (Hi = 2.399), t,/tL =
OPTICS COMMUNICATIONS
Volume 31, number 1
1.38, and from (L’/L)e i = 1.678, and (L/L,)e,i = 0.677, the q.e. 77, = 0.65 + 0.02. We calculated n, from eqs. (6) and (7) by inserting felt: instead of T/T’. Values 77, given were obtained from five coating runs. The decay time t, on S, of typically 595 gs varied by ?5% between different coating runs. In experiments II both plates S, and S, are optical flats separated by spacers at both ends, where d 3 X. The plates are pressed together in the middle until optical contact d = 0 is obtained. In experiment IIa with a spatially varying air gap d(x) (cf. fig. 3) the layer is scanned in x-direction by a small spot of uv light. During this scan both decay time t, and intensity of the fluorescence (near normal emission) are measured. These quantities were also measured in experiments IIb at a fixed position x = const while the width d(t) of the air gap was varied as a function of time between d S h and optical contact d = 0. This variation of d(t) can be repeated many times with reproducible results for the decay times. Our theory predicts that in optical contact experi-
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October 1979
ments with arbitrary plates S, and S2 the lifetime decreases when d is reduced from d 9 X to d = 0, i.e. tk(d = 0) < t,(d S A). This holds for (e, i) transitions and magnetic dipole transitions with arbitrary orientation 0 of the transition moment. For the special case where S, and S2 are identical, i.e. n2 = nl, fig. 2 shows that only for (e, Il) transitions practically no effect will occur. In our experiments we measured, for example, with BK7 plates S, and S,, t, = 605 PS when d %-X and tk = 525 ps when d = 0. For comparison with the theory we put 122= 1 (air) for d > h. With (L’/L)e,l = 1.362 and (~/~,)e.i = 0.678, we obtain 0, = 0.52. In an experiment with two different plates S, and S,, viz. fused silica (n 1 = 1.458) and SrTiO,, the decay time tropped from t, = 620 /*s to fk = 415 ys. With (~‘/~)e,i = 2.404 and (L/L,)e,i = 0.649 we obtain q, = 0.46. In all experiments we found that the fluorescence at X = 6 12 nm and the very much weaker fluorescence of the layers near X = 592 nm have the same decay time. A significant feature of the optical contact experiments is that the measurement of the intensity not only allows to monitor the width d of the air gap, but also to distinguish between (e) and (m) dipole transitions. The intensity variations with d are wideangle interferences. Minima at d = 0, X/2, .. and maxima at d = X/4,3h/4, .. (as in fig. 3) indicate an (e) transition, interchanged extrema an (m) transition.
4. Discussion
-2
I
I
2
3
4
I
I
5
6
-0
x (cm)
Fig. 3. Intensity and decay time te of fluorescence at h = 6 12 nm versus coordinate x in experiment with spatially varying air gap 0 < d(x) < 12 I.rm between fluorescent layer (no = 1.57, do = 30 nm) deposited on substrate St and plate Sz. Inset shows schematic of experiment. Both S1 and Sz optical flats 26 X 76 X 4 mm of BK7 glass (nl = n2 = 1.516).
In the theory with which we above have analysed our experiments, the radiated power L/L, and thus the lifetime T of the fluorescing ion is independent of its position in the layer (no). The analytic expressions (3) and (5) are approximations valid for very thin layers, i.e. for nod0 Q X/8. If this condition is not satisfied, radiated power L(zo)/L, and lifetime r(zo) depend on the coordinate zo. Then energy migration in the Eu3+ion system would have interesting consequences, exemplified by the t.wo extreme cases: i) There is no energy migration. Excited Eu3+-ions in the layer radiate independently. The time decay of the fluorescence is non-exponential, being a sum of exponential decays exp{-r/r(zO)}. The form of the time decay depends through ~(2~) on the optical 45
Volume 31. number 1
OPTICS COMMUNICATIONS
environment. ii) Energy migration is rapid. The excitation energy belongs to the whole system of Eu3+ions. The time decay is exponential, the lifetime being determined by L(z,,)/L,, the radiated power spatially averaged over the layer thickness. In our experiments do = 30 nm and nOdO = 0.08 h. We consider the experiment II with two BK7 substrates S, and S,. Since the refractive indices of layer and substrate are nearly equal (no = nl = 1S), we can make the following estimations based on our results [9] for L(zo)/L, in the one interface problem. Ford Z+ h, (L(zo)/L,), i rises from its lowest value at the layer-air interface to an about 17% higher value at the layer-substrate S, interface. For d = 0, (L’(zu)lLco)e,i is approximately constant in the layer. With a value L/L’for an ion in the middle of the layer, estimated to be 9% higher than that derived from the analytic formulas (3) and (5) we find n, = 0.68. This value for the q.e. agrees better with those obtained from experiment I. We conclude that to improve the accuracy of the q.e.s. determined with the analytic approximations thinner layers have to be used in the experiments, especially in those of type II. To obtain q.e.s. and, possibly, information about energy migration from measurements with thicker layers, rigorous (computer) calculations of L(zo)/L, and of the resulting decay curves are required. In our experiments the form of the decay curves was found to be practically independent of the optical environment. Therefore, we exclude the spatial averaging over different lifetimes r(zu) as the main cause of the deviations from a single exponential decay. We presume that it caused by Eu3+ions on different sites
46
October 1979
j = 1,2, ... (i.e. having different surroundings on an atomic distance scale) which have different transition moments and, therefore, different radiative lifetimes T~,~,and possibly different non-radiative deactivation rates. (We note that the ratio of the radiative lifetimes in the primed and unprimed optical environment rr i/rii = L’/L is independent of j since the transition moment drops out of this ratio.) We stress the most important result. It has been demonstrated experimentally that the spontaneous emission rate of one and the same atomic system (an Eu3+-ion) can be reversibly changed by a variation of its optical environment.
References [l] K.H. Drexhage, M. Fleck, H. Kuhn, F.P. Schafer and W. Sperling, Ber. Bunsenges. Phys. Chem. 70 (1966) 1179; K.H. Drexhage, H. Kuhn and F.P. Schafer, Ber. Bunsenges. Phys. Chem. 70 (1968) 329. [2] K.H. Drexhage, Habilitationsschrift (Universitat Marburg, 1966). [3] K.H. Drexhage, J. Luminescence 1,2 (1970) 693. [4] K.H. Drexhage, Progress in optics, Vol. XII, ed. E. Wolf, (North-Holland Publishing Co., Amsterdam, 1974) p. 165. [5] K.H. Tews, Ann. Physik (Leipzig) 29 (1973) 97; and Ph.D. Thesis (Marburg, 1973). [6] K.H. Tews, J. Luminescence 9 (1974) 223. [7] R.R. Chance, A. Prock and R. Silbey, Adv. Chem. Phys., eds. I. Progogine and S.A. Rice, Vol. XXXVII (Wiley, New York, 1978), p. 1. [8] W. Lukosz and R.E. Kunz, Opt. Commun. 20 (1977) 195. [9] W. Lukosz and R.E. Kunz, J. Opt. Sot. Am. 67 (1977) 1607,161s.
OPTICS COMMUNICATIONS
CHANGES IN FLUORESCENCE LIFETIMES INDUCED BY VARIATION OF THE RADIATING MOLECULES’ OPTICAL ENVIRONMENT
October 1979
OF
W. LUKOSZ and R.E. KUNZ Swiss Federal Institute of Technology,
Professur fiir Optik, ETH,
8093 Ziirich, Switzerland Received 27 June 1979
We report results of experiments with about 30 nm thick evaporated layers of an europium-chelate fluorescing at h = 612 nm: i.) For layers on different substrates S1 in air the lifetime decreases with increasing refractive index nl of S1. ii.) For a layer on a substrate S1 the lifetime decreases when the width d of an air gap between the layer and a second plate Sz is reduced from d > h to d = 0. Theoretically, we derived analytic expressions for the spontaneous emission rates of electric and magnetic dipole transitions taking place in an atomic system embedded in a very thin layer of refractive index no and optical thickness nodo < h/S, which is sandwiched between two dielectric loss-free media of refractive indices n t and “2. Comparison of theory and experiment allows to determine the absolute quantum efficiency of the emitting state.
1. Introduction The fluorescence lifetime of an excited dye molecule has been experimentally shown to depend on its distance z. from a metal surface or from a dielectric interface. In these experiments Drexhage, Kuhn, Schgfer, Tews et al. [l-.5] used fatty-acid spacer layers for the precise definition of the distance z. and an europium-dibenzoylmethane-complex as the dye. The experiments demand mastery of the monolayer assembly technique. Theoretical investigations of the effect are listed in refs. [4-91. In this letter we report investigations of lifetime changes by variation of the optical environment of fluorescent molecules in three different types of experiments: I) A thin layer (no) of fluorescent molecules is deposited simultaneously on a number of substrates S, with different refractive indices nl. The dependence of the lifetime on nl is measured in air. II) The ‘optical contact experiments’ work with a homogeneous layer (no) of fluorescent molecules on one substrate S, with index nl. The width d of the air gap between layer (no) on substrate S, and, a second plate S, with refractive index n2 is varied between d & X, where X is the emission wavelength, 42
and d = 0, i.e. optical contact. In experiment IIa the distance d is varied spatially, i.e. d = d(x), and the lifetime is measured as a function of coordinate x (cf. inset fig. 3). In experiment IIb the lifetime is measured at x = const. while the distance d is varied as a function of time, i.e. d = d(t). We point out an important feature of experiment IIb: The monolayer technique experiments of Drwe Drexhage, Kuhn, et al., and our experiments of type I and Ha compare lifetimes of theoretically identical but actually different systems (which are, of course, prepared to be as similar as possible). But in experiment IIb we actively vary as a function of time the optical environment of the very same system. Our experiments IIb show for the first time that the lifetime of the very same emitters can be reversibly changed by a variation of their optical environment. Our experimental results were obtained with fluorescing layers deposited in vacuum by evaporation of europium-chelate Eu(BTF)~HP~~~. The decay of the fluorescence of the Eu3+-ions near h w 612 nm and X = 592 nm after uv pulse excitation was measured.
Volume
2.
3 1, number
1979
Theory
For the analysis of our experiments we derive theoretically how the spontaneous emission rate for a fluorescent molecule embedded in a very thin layer of refractive index n0 and thickness d, depends on the refractive indices n 1 and n2 of the two adjoining loss-free dielectric half-spaces (cf. fig. 1). For very thin layers with optical thickness nOdO Q X/8 we obtain analytic expressions for the (normalized) spontaneous emission rates for electric and magnetic dipole transitions. The theory allows: i) to predict the maximum values of the (relative) lifetime changes which would occur in experiments I and II if no non-radiative transitions would compete with the radiative transitions, and ii) to determine the absolute quantum efficiency from the experimentally observed lifetime changes. The determination of the q.e. is based on the assumption that the rate of non-radiative transitions is not influenced by a variation of n1 or n2. This variation of the optical environment of the emitting molecules leaves their environment on an atomic distance scale essentially unchanged, at least for the majority of emitters in a several nm thick layer (no). Therefore, we expect the above assumption to be realistic. We consider a radiating classical electric (e) or magnetic (m) dipole located in the layer (no). The dipole is assumed to oscillate with fixed frequency V, fixed dipole moment, and fixed orientation ~3.Generalizing a method we had previously used for a dipole in front of a single interface [8,9] we have rigorously solved the electromagnetic boundary value problem. Both the wide-angle interferences of the plane waves emitted by the dipole and emission from evanescent waves in the dipole’s near field are taken into account. The normalized total power radiated by the dipole with orientation 0 is
= cos20 (4,0,2)L
+ sin21J Ol,O,2>,,,
(1)
where the indices 1 and IIdenote dipoles perpendicular (0 = 0) and parallel (0 = 90”) to the interfaces, and L
October
OPTICS COMMUNICATIONS
1
= (QQ&
is the power radiated by the dipole in an infinite medium of refractive index no. In eq. (2), CJ= 1 for
(2)
Fig. 1. Atomic system (dipole) D embedded in very thin layer of refractive index no an thickness do sandwiched between two half-spaces with refractive indices n 1 and 112, respectively. 0 angle between transition dipole moment and z-axis.
an electric and 4 = 3 for a magnetic dipole, while L,, is the power radiated by the identical dipole in vacuum. In the limiting case of an extremely thin layer (no), i.e. for nod0
(Z1,0,2) = (~~/no)~Z@
(n = +l),
(3)
where p = 5 for (e,l), p = 1 for (e, II), p = 3 for both (m, 1) and (m, II). For the functions Z(‘)(n) analytic expressions were given in ref. [S] for both types of dipoles (e,m) and the two main orientations (I, II). Physically, Z(‘l(n = n2/nl) is the normalized total power radiated by a dipole located in medium (n 1) directly at the interface to an adjoining medium (n2). Eq. (3) expresses the power radiated by a dipole as shown in fig. 1 in terms of the power radiated by the same dipole located at the interface between the halfspaces (nl) and (n2) not separated by a layer (no). For an ensemble of randomly oriented dipoles with equal dipole moments, assumed to radiate incoherently, we obtain from eq. (1) the average power radiated per dipole (Ll,0,2)i=:(Ll,0,2)1
+3(Ll,0,2)11.
(4)
From eqs. (l)-(3) we conclude that the power L1,0,2/Lvac for magnetic dipoles of any orientation and for the parallel electric (e, 11)dipole is independent of no. In fig. 2, the powers L1,0,2/Lvac as functions of nl are shown for (e) and (m) dipoles with orientations (I, ll,i) in the special cases n2 = 1 and n2 = nl. In the latter case we have since ZCol(n= 1) = 1, (Ll,0,2)/Lvac
= (nl)qno)~-~.
(5)
The dipoles (e, II) and (m, II,1, i) radiate as if they were in an infinite medium nl . The spontaneous emission rate for a dipole transition is l/r, = L/Zzu, when in the classical expression 43
Volume 31, number 1
3. Experimental
oIir-e---
2.0
3.0
4
Fig. 2. Normalized power L1 ,~,&~c radiated by electric (e) and magnetic (m) dipoles shown in fii. 1 versus n 1, for
f12= n 1 (solid lines) and n2 = 1 (dashed lines), respectively. no = 1.57. Subscripts 1, II,i denote perpendicular, parallel, and random isotropic orientation, respectively. for the radiated power L the dipole moment is replaced by the corresponding transition moment. The rat@ of the transition rates of the same system in two different optical environments (denoted by a prime and no prime, respectively) iS equal to the inverse ratio of the powers radiated by the same classical dipole in the two situations ~JT: = L’/L, provided that the transition moment is not changed by variation of the system’s optical environment. Supposing an analogue independence of the thermal deactivation rate l/rth, we obtain with I/T = l/rr + I/T* a relation for the lifetimes T and T’ in the two situations 7/?’ = I + q(L’/L - l),
(6)
(cf. refs. [2-71). The absolute quantum efficiency 77E T/T~ depends on the environment. Therefore, the q.e. TJ, in an infinite homogeneous medium (no) is introduced which can be calculated from the known value of 17in a given environment l/7), - 1 = 44
(L/-L)(lIrl -
October 1979
OPTICS COMMUNICATIONS
0.
(7)
results
In our experiments substrates were coated with thin fluorescing layers by evaporation of small (-0.2 mm) crystals of Eu(BTF)~HP~~~ (BTF: benzoyltrifluoroacetone, Pyrr: pyrrolidine). The fluorescence of these crystals decays exponentially with a lifetime 7 = 1.26 ms. The fluorescence decay of the evaporated layers is not strictly a single exponential decay. Comparing the fluorescence decay of layers in different optical environments, we have found that the shape of the decay curves remains essentially unchanged. Therefore, we only report the decay time t,, defined as the time during which the fluorescent intensity falls to I/e of its initial value after excitation with a uv pulse (A’= 366 nm, duration 850 /AS). We have determined the refractive index and the thickness of the layers (no = 1.57 at X = 612 nm, typically d, = 30 nm) from measurements of the angular intensity distribution and polarization of the fluorescence of layers deposited on glass hemicylinders by comparison with theoretical calculations based on a generalization of the theory developed in ref. [9]. This comparison also shows that the fluorescence at X = 612 nm corresponds to an electric dipole transition with isotropic distribution (e, i) of the dipole moments. This can be explained by random orientation either i) of the dipole moments of the different Eu3+-ions in the layer (each ion having a dipole moment with fixed orientation) or ii) of the dipole moment of an individual Eu3+-ion during the decay time t,. Only the latter possibility ii) is compatible with our experimental result that the measured decay time te is essentially independent of the direction of observation and of polarization. In the following we compire the experimentally observed changes of the decay time with the theory for (e, i). Our experiments I confirm the theoretical prediction (following from eq. (6) and dashed curves in fig. 2) that the lifetime on substrate S, in air (n2 = 1) decreases with increasing refractive index nl . We compare the decay times te and tk on two substrates S, and S;(n;) coated simultaneously. Choosing microscope glass slides (n 1 = 1.5 14) as reference substrate S, we obtained: on SF6 glass substrates S;(n; = 1.802), felt; = 1.lS, and from (L’/L)e,i = 1.219, and (L/L_)e,i = 0.677, the q.e. Q, = 0.76 + 0.05, and on SrTi03 crystal substrates S; (Hi = 2.399), t,/tL =
OPTICS COMMUNICATIONS
Volume 31, number 1
1.38, and from (L’/L)e i = 1.678, and (L/L,)e,i = 0.677, the q.e. 77, = 0.65 + 0.02. We calculated n, from eqs. (6) and (7) by inserting felt: instead of T/T’. Values 77, given were obtained from five coating runs. The decay time t, on S, of typically 595 gs varied by ?5% between different coating runs. In experiments II both plates S, and S, are optical flats separated by spacers at both ends, where d 3 X. The plates are pressed together in the middle until optical contact d = 0 is obtained. In experiment IIa with a spatially varying air gap d(x) (cf. fig. 3) the layer is scanned in x-direction by a small spot of uv light. During this scan both decay time t, and intensity of the fluorescence (near normal emission) are measured. These quantities were also measured in experiments IIb at a fixed position x = const while the width d(t) of the air gap was varied as a function of time between d S h and optical contact d = 0. This variation of d(t) can be repeated many times with reproducible results for the decay times. Our theory predicts that in optical contact experi-
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October 1979
ments with arbitrary plates S, and S2 the lifetime decreases when d is reduced from d 9 X to d = 0, i.e. tk(d = 0) < t,(d S A). This holds for (e, i) transitions and magnetic dipole transitions with arbitrary orientation 0 of the transition moment. For the special case where S, and S2 are identical, i.e. n2 = nl, fig. 2 shows that only for (e, Il) transitions practically no effect will occur. In our experiments we measured, for example, with BK7 plates S, and S,, t, = 605 PS when d %-X and tk = 525 ps when d = 0. For comparison with the theory we put 122= 1 (air) for d > h. With (L’/L)e,l = 1.362 and (~/~,)e.i = 0.678, we obtain 0, = 0.52. In an experiment with two different plates S, and S,, viz. fused silica (n 1 = 1.458) and SrTiO,, the decay time tropped from t, = 620 /*s to fk = 415 ys. With (~‘/~)e,i = 2.404 and (L/L,)e,i = 0.649 we obtain q, = 0.46. In all experiments we found that the fluorescence at X = 6 12 nm and the very much weaker fluorescence of the layers near X = 592 nm have the same decay time. A significant feature of the optical contact experiments is that the measurement of the intensity not only allows to monitor the width d of the air gap, but also to distinguish between (e) and (m) dipole transitions. The intensity variations with d are wideangle interferences. Minima at d = 0, X/2, .. and maxima at d = X/4,3h/4, .. (as in fig. 3) indicate an (e) transition, interchanged extrema an (m) transition.
4. Discussion
-2
I
I
2
3
4
I
I
5
6
-0
x (cm)
Fig. 3. Intensity and decay time te of fluorescence at h = 6 12 nm versus coordinate x in experiment with spatially varying air gap 0 < d(x) < 12 I.rm between fluorescent layer (no = 1.57, do = 30 nm) deposited on substrate St and plate Sz. Inset shows schematic of experiment. Both S1 and Sz optical flats 26 X 76 X 4 mm of BK7 glass (nl = n2 = 1.516).
In the theory with which we above have analysed our experiments, the radiated power L/L, and thus the lifetime T of the fluorescing ion is independent of its position in the layer (no). The analytic expressions (3) and (5) are approximations valid for very thin layers, i.e. for nod0 Q X/8. If this condition is not satisfied, radiated power L(zo)/L, and lifetime r(zo) depend on the coordinate zo. Then energy migration in the Eu3+ion system would have interesting consequences, exemplified by the t.wo extreme cases: i) There is no energy migration. Excited Eu3+-ions in the layer radiate independently. The time decay of the fluorescence is non-exponential, being a sum of exponential decays exp{-r/r(zO)}. The form of the time decay depends through ~(2~) on the optical 45
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environment. ii) Energy migration is rapid. The excitation energy belongs to the whole system of Eu3+ions. The time decay is exponential, the lifetime being determined by L(z,,)/L,, the radiated power spatially averaged over the layer thickness. In our experiments do = 30 nm and nOdO = 0.08 h. We consider the experiment II with two BK7 substrates S, and S,. Since the refractive indices of layer and substrate are nearly equal (no = nl = 1S), we can make the following estimations based on our results [9] for L(zo)/L, in the one interface problem. Ford Z+ h, (L(zo)/L,), i rises from its lowest value at the layer-air interface to an about 17% higher value at the layer-substrate S, interface. For d = 0, (L’(zu)lLco)e,i is approximately constant in the layer. With a value L/L’for an ion in the middle of the layer, estimated to be 9% higher than that derived from the analytic formulas (3) and (5) we find n, = 0.68. This value for the q.e. agrees better with those obtained from experiment I. We conclude that to improve the accuracy of the q.e.s. determined with the analytic approximations thinner layers have to be used in the experiments, especially in those of type II. To obtain q.e.s. and, possibly, information about energy migration from measurements with thicker layers, rigorous (computer) calculations of L(zo)/L, and of the resulting decay curves are required. In our experiments the form of the decay curves was found to be practically independent of the optical environment. Therefore, we exclude the spatial averaging over different lifetimes r(zu) as the main cause of the deviations from a single exponential decay. We presume that it caused by Eu3+ions on different sites
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j = 1,2, ... (i.e. having different surroundings on an atomic distance scale) which have different transition moments and, therefore, different radiative lifetimes T~,~,and possibly different non-radiative deactivation rates. (We note that the ratio of the radiative lifetimes in the primed and unprimed optical environment rr i/rii = L’/L is independent of j since the transition moment drops out of this ratio.) We stress the most important result. It has been demonstrated experimentally that the spontaneous emission rate of one and the same atomic system (an Eu3+-ion) can be reversibly changed by a variation of its optical environment.
References [l] K.H. Drexhage, M. Fleck, H. Kuhn, F.P. Schafer and W. Sperling, Ber. Bunsenges. Phys. Chem. 70 (1966) 1179; K.H. Drexhage, H. Kuhn and F.P. Schafer, Ber. Bunsenges. Phys. Chem. 70 (1968) 329. [2] K.H. Drexhage, Habilitationsschrift (Universitat Marburg, 1966). [3] K.H. Drexhage, J. Luminescence 1,2 (1970) 693. [4] K.H. Drexhage, Progress in optics, Vol. XII, ed. E. Wolf, (North-Holland Publishing Co., Amsterdam, 1974) p. 165. [5] K.H. Tews, Ann. Physik (Leipzig) 29 (1973) 97; and Ph.D. Thesis (Marburg, 1973). [6] K.H. Tews, J. Luminescence 9 (1974) 223. [7] R.R. Chance, A. Prock and R. Silbey, Adv. Chem. Phys., eds. I. Progogine and S.A. Rice, Vol. XXXVII (Wiley, New York, 1978), p. 1. [8] W. Lukosz and R.E. Kunz, Opt. Commun. 20 (1977) 195. [9] W. Lukosz and R.E. Kunz, J. Opt. Sot. Am. 67 (1977) 1607,161s.