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The effects of sensitisation on the activator emission in laser crystals
JOURNAL OF
LUMINESCENCE ELSEWIER
Journal
of Luminescence
72-74
(1997) 948-950
The effects of sensitisation on the activator emission in laser crystals V. Lupei”T*, A. Lupei”, G. Boulonb aInstitute of Atomic Physics, 76900 Bucharest, Romania ‘Universite Claude Bernard Lyon I, LPCML, 69622 Villeurbanne, France
Abstract
The complex effects of the sensitisation of laser crystals on the spectral and temporal behaviour of the activator emission is discussed. It is thus shown that the mutual crystal-field perturbations produced by the sensitizer S and activator A ions transforms the systems formed by these ions into inhomogeneous systems composed of homogeneous subsystems, which are further individualised by specific manifestation of the SA energy transfer processes. A suitable rate equation modelling for each of the S-A subsystems which takes into account the energy transfer between the subsystems enables a correct description of the emission properties in various laser crystals under selective or non-selective pump. Keywords:
Sensitised emission; Sensitization
Sensitisation of the weakly absorbing active ions by co-doping with another ions whose absorption matches the pump radiation better and are able to transfer non-radiatively this excitation to the emitting ion is considered currently as a possibility to improve the pump efficiency of the solid state lasers. The energy transfer modifies the evolution of populations of the excited levels both of the sensitizer (donor, D) and activator (acceptor, A). Usually, the ensembles of donor and acceptor ions are considered as homogeneous, i.e. all the members have identical spectral and temporal emission properties: for these systems the transfer modifies the donor emission after a short pulse excitation by a factor exp[ - P(t, C,)] which represents in fact the probability, averaged over the ensemble of ac-
*Corresponding @roifa.ifa.ro.
author.
Fax: (40) 1420.9391;
e-mail: dascalu
0022-2313/97/$17.00 c) 1997 Elsevier Science B.V. All rights reserved PII SOO22-2313(96)00301-S
ceptor ions (of relative concentration C,) that the donor is not de-excited at the moment of time t due to this transfer. The transfer function P(t, C,) for direct D-A transfer without preliminary migration could be calculated for specific models of acceptor distribution if the transfer rates W (rJ to each individual acceptor i, placed at the distance ri from donor are known. These rates are determined by the type of D-A interaction responsible for transfer; for multipolar interactions W (ri) = CDA t-7” where the microparameter CnA depends on the spectroscopic properties of the D and A ions (donor intrinsic de-excitation rate, integral acceptor absorption cross-section, superposition integral of donor emission and of acceptor absorption) and the exponent s equals 6, 8 or 10 for dipole-dipole (d-d), dipole-quadrupole and quadrupole-quadrupole interactions, respectively, while the short-distance superexchange interactions determine a stronger distance dependence. Thus, for the nearest D-A
V. Lupei et al. / Journal
ofLuminescencu
pairs a mixed interaction picture could hold while for distant pairs the transfer is dominated by the low-order multipolar interactions usually d-d. The most popular models of acceptor distributions in the absence of charge or dimensional correlation are the continuous uniform distribution [l] which gives P(t) = ~(s)t3/sand the discrete, random and equiprobable placement [2] when P(t) = C In (1 - CA + C,exp[
- P(CA. t)ll\,
(1)
i
where the sum extends over all the sites available to the acceptors. The strong ri dependence of the transfer rates favours active media with short D-A distances and a good packing of the acceptor ions around the donor. However, in these cases, due to the dimensional mismatch between the D or A ions and the substituted host cations, strong mutual asymmetric perturbations, which modify the symmetry and the strength of the crystal field could be produced in the near D-A pairs. These perturbations could produce a partial rise of the residual degeneracy of the energy levels, shifts (of several cm-’ to tens of cm- ‘) of the levels and modification of their relative position, alteration of the selection rules for the optical transitions and/or the modification of transition probabilities (with possible modification of the radiative lifetime) and of electron-phonon interactions. The most intense perturbation take place for the nearest D-A pairs due to the strong dependence on the D-A distance and on the direction of perturbation with respect to the local symmetry axes of the centres. Due to the discreteness of the crystalline lattice a chain of discrete perturbations can be produced, resulting in resolvable spectroscopic effects, such as the apparition of groups of satellites whose structure and intensity (and sometimes the intrinsic radiative properties) depend on the static effects discussed above, connected with the structure of the crystal. The perturbative effects for distant D-A pairs cannot be resolved but they may produce an inhomogeneous broadening of the lines. As a consequence of these perturbations the ensembles of D and A ions are transformed into inhomogeneous systems, which are however composed by homogeneous subsys-
72-74
(fYY7) 948-950
949
tems corresponding to the resolved D-A perturbative effects, a special subsystem being composed by the weakly perturbed ions. The modification of the spectral properties of D and A centres due to these perturbations influences, in a specific way, their energy transfer properties: the energy transfer microparameters CDA for a given interaction might have particular values for each subsystem and the distribution of acceptors around donor depends on the subsystem. Furthermore, for the most perturbed centres, which usually correspond to the nearest D-A pairs, the transfer could be dominated by the strong short-distance interactions and sometimes a multiple interaction picture might take place while for the more distant centres a given longer-distance interaction (such as d-d) could dominate. For non-correlated discrete substitution the probability of occurrence for the various D-A pairs can be calculated [3,4]; however, this distribution is explicitly reflected by the relative intensities of the spectrally satellites only when the transition probabilities for the perturbed centres are not strongly modified. By taking into account the parameters of the energy transfer for these subsystems, rate equations can be written for the temporal evolution of populations of the emitting levels of the D and A ions. Thus, for each donor subsystem 1 the transfer function can be written as
where WDIAI(~,)is the rate of transfer from donor to the perturbing acceptor companion (this term is missing in case of the weakly perturbed subsystem), P#A describes the global transfer function to all the distant acceptors regardless of the fact to which subsystem f they belong. Thus, in the case of perturbed centres, the energy transfer leads to a fast drop of emission at early times followed by a slower effect, for the unperturbed system only the last term is effective. In turn, the acceptors from each subsystems could be excited by fast transfer from the perturbing donor companion and by slow transfer from distant donors from all the
V. Lupri et al. /Journal
950
qfL.uminescence
subsystems:
dnA, -=----_ dt
nAg ZAg
dPA,a
Ag- dt
+ nDgwgg
dP$jAj + c nDj7 +nDn dP %:git),
(3)
.i
where the first terms on the right-hand side describe successively the acceptor intrinsic de-excitation, the de-excitation due to energy transfer inside the acceptor system, the fast transfer from the perturbing donor companion (this is missing for the unperturbed acceptor subsystems), the slow transfer from donors from the perturbed donor subsystems and the slow transfer from unperturbed donors. Due to these three possibilities of transfer, the temporal evolution of the acceptor emission consists of a superposition of three curves with rise and fall; for each of these the rise portion is determined by the fastest from donor de-excitation rate (intrinsic and by transfer) and acceptor intrinsic de-excitation. Although the solution for Eq. (3) could be written in a compact form, it contains integrals which cannot be solved analytically for general forms of transfer functions, except for linear dependence of time. The moment tAmaX and the value of maximal emission nAmax of the acceptors depend on the intrinsic de-excitation properties of the D and A subsystems and on the energy transfer. In the case of very fast transfer, tA maxiS very short is deterand nAmax is large and the rise-portion
72-74 (1997) YIN-950
mined by the donor de-excitation while for slow transfer tA max is long and nA max is small and sometimes the rise could be determined by the acceptor intrinsic de-excitation while the decay reflects the slow de-excitation of the donor. Due to the variety of characteristics of the D and A subsystems in a given crystal, both these situations could be observed simultaneously; thus, the global acceptor emission becomes very complex and shows marked differences from the case of non-sensitised crystals. Such effects have been clearly observed in important laser systems such as YAG : Tm3+ senstitised by Cr 3+ in octahedral positions or Fe3+ in tetrahedral sites [4], GSGG : Cr, Nd [S] YAG : Cr, Nd [6] and so on and they should be taken into account in the analysis of the properties of the sensitised solid state lasers.
References T. Forster, Ann. Phys. 2 (1948) 55; D.L. Dexter. J. Chem. Phys. 21 (1953) 836; M. Inokuti and F. Hirayama. J. Chem. Phys. 43 (1965) 1978. VI IS. Golubov and Y.V. Konobeev, Sov. Phys. Sol. State 13 (1972)2679. 131 V.V. Osika, Yu.K. Voronko and A.A. Sobol, in: Crystals, Vol. 10 (Springer, Berlin, 1984) p.37. M V. Lupei. A. Lupei and G. Boulon, Phys. Rev. B. 53 (1996) 10. [51 T.P.J. Han, M.A. Scott, F. Jaque, H.G. Gallager and B. Henderson, Chem. Phys. Lett. 208 (1993) 63. [61 V. Lupei. A. Lupei, C. Stoicescu and A. Petraru, to be published (in Rom. J. Phys.).
LUMINESCENCE ELSEWIER
Journal
of Luminescence
72-74
(1997) 948-950
The effects of sensitisation on the activator emission in laser crystals V. Lupei”T*, A. Lupei”, G. Boulonb aInstitute of Atomic Physics, 76900 Bucharest, Romania ‘Universite Claude Bernard Lyon I, LPCML, 69622 Villeurbanne, France
Abstract
The complex effects of the sensitisation of laser crystals on the spectral and temporal behaviour of the activator emission is discussed. It is thus shown that the mutual crystal-field perturbations produced by the sensitizer S and activator A ions transforms the systems formed by these ions into inhomogeneous systems composed of homogeneous subsystems, which are further individualised by specific manifestation of the SA energy transfer processes. A suitable rate equation modelling for each of the S-A subsystems which takes into account the energy transfer between the subsystems enables a correct description of the emission properties in various laser crystals under selective or non-selective pump. Keywords:
Sensitised emission; Sensitization
Sensitisation of the weakly absorbing active ions by co-doping with another ions whose absorption matches the pump radiation better and are able to transfer non-radiatively this excitation to the emitting ion is considered currently as a possibility to improve the pump efficiency of the solid state lasers. The energy transfer modifies the evolution of populations of the excited levels both of the sensitizer (donor, D) and activator (acceptor, A). Usually, the ensembles of donor and acceptor ions are considered as homogeneous, i.e. all the members have identical spectral and temporal emission properties: for these systems the transfer modifies the donor emission after a short pulse excitation by a factor exp[ - P(t, C,)] which represents in fact the probability, averaged over the ensemble of ac-
*Corresponding @roifa.ifa.ro.
author.
Fax: (40) 1420.9391;
e-mail: dascalu
0022-2313/97/$17.00 c) 1997 Elsevier Science B.V. All rights reserved PII SOO22-2313(96)00301-S
ceptor ions (of relative concentration C,) that the donor is not de-excited at the moment of time t due to this transfer. The transfer function P(t, C,) for direct D-A transfer without preliminary migration could be calculated for specific models of acceptor distribution if the transfer rates W (rJ to each individual acceptor i, placed at the distance ri from donor are known. These rates are determined by the type of D-A interaction responsible for transfer; for multipolar interactions W (ri) = CDA t-7” where the microparameter CnA depends on the spectroscopic properties of the D and A ions (donor intrinsic de-excitation rate, integral acceptor absorption cross-section, superposition integral of donor emission and of acceptor absorption) and the exponent s equals 6, 8 or 10 for dipole-dipole (d-d), dipole-quadrupole and quadrupole-quadrupole interactions, respectively, while the short-distance superexchange interactions determine a stronger distance dependence. Thus, for the nearest D-A
V. Lupei et al. / Journal
ofLuminescencu
pairs a mixed interaction picture could hold while for distant pairs the transfer is dominated by the low-order multipolar interactions usually d-d. The most popular models of acceptor distributions in the absence of charge or dimensional correlation are the continuous uniform distribution [l] which gives P(t) = ~(s)t3/sand the discrete, random and equiprobable placement [2] when P(t) = C In (1 - CA + C,exp[
- P(CA. t)ll\,
(1)
i
where the sum extends over all the sites available to the acceptors. The strong ri dependence of the transfer rates favours active media with short D-A distances and a good packing of the acceptor ions around the donor. However, in these cases, due to the dimensional mismatch between the D or A ions and the substituted host cations, strong mutual asymmetric perturbations, which modify the symmetry and the strength of the crystal field could be produced in the near D-A pairs. These perturbations could produce a partial rise of the residual degeneracy of the energy levels, shifts (of several cm-’ to tens of cm- ‘) of the levels and modification of their relative position, alteration of the selection rules for the optical transitions and/or the modification of transition probabilities (with possible modification of the radiative lifetime) and of electron-phonon interactions. The most intense perturbation take place for the nearest D-A pairs due to the strong dependence on the D-A distance and on the direction of perturbation with respect to the local symmetry axes of the centres. Due to the discreteness of the crystalline lattice a chain of discrete perturbations can be produced, resulting in resolvable spectroscopic effects, such as the apparition of groups of satellites whose structure and intensity (and sometimes the intrinsic radiative properties) depend on the static effects discussed above, connected with the structure of the crystal. The perturbative effects for distant D-A pairs cannot be resolved but they may produce an inhomogeneous broadening of the lines. As a consequence of these perturbations the ensembles of D and A ions are transformed into inhomogeneous systems, which are however composed by homogeneous subsys-
72-74
(fYY7) 948-950
949
tems corresponding to the resolved D-A perturbative effects, a special subsystem being composed by the weakly perturbed ions. The modification of the spectral properties of D and A centres due to these perturbations influences, in a specific way, their energy transfer properties: the energy transfer microparameters CDA for a given interaction might have particular values for each subsystem and the distribution of acceptors around donor depends on the subsystem. Furthermore, for the most perturbed centres, which usually correspond to the nearest D-A pairs, the transfer could be dominated by the strong short-distance interactions and sometimes a multiple interaction picture might take place while for the more distant centres a given longer-distance interaction (such as d-d) could dominate. For non-correlated discrete substitution the probability of occurrence for the various D-A pairs can be calculated [3,4]; however, this distribution is explicitly reflected by the relative intensities of the spectrally satellites only when the transition probabilities for the perturbed centres are not strongly modified. By taking into account the parameters of the energy transfer for these subsystems, rate equations can be written for the temporal evolution of populations of the emitting levels of the D and A ions. Thus, for each donor subsystem 1 the transfer function can be written as
where WDIAI(~,)is the rate of transfer from donor to the perturbing acceptor companion (this term is missing in case of the weakly perturbed subsystem), P#A describes the global transfer function to all the distant acceptors regardless of the fact to which subsystem f they belong. Thus, in the case of perturbed centres, the energy transfer leads to a fast drop of emission at early times followed by a slower effect, for the unperturbed system only the last term is effective. In turn, the acceptors from each subsystems could be excited by fast transfer from the perturbing donor companion and by slow transfer from distant donors from all the
V. Lupri et al. /Journal
950
qfL.uminescence
subsystems:
dnA, -=----_ dt
nAg ZAg
dPA,a
Ag- dt
+ nDgwgg
dP$jAj + c nDj7 +nDn dP %:git),
(3)
.i
where the first terms on the right-hand side describe successively the acceptor intrinsic de-excitation, the de-excitation due to energy transfer inside the acceptor system, the fast transfer from the perturbing donor companion (this is missing for the unperturbed acceptor subsystems), the slow transfer from donors from the perturbed donor subsystems and the slow transfer from unperturbed donors. Due to these three possibilities of transfer, the temporal evolution of the acceptor emission consists of a superposition of three curves with rise and fall; for each of these the rise portion is determined by the fastest from donor de-excitation rate (intrinsic and by transfer) and acceptor intrinsic de-excitation. Although the solution for Eq. (3) could be written in a compact form, it contains integrals which cannot be solved analytically for general forms of transfer functions, except for linear dependence of time. The moment tAmaX and the value of maximal emission nAmax of the acceptors depend on the intrinsic de-excitation properties of the D and A subsystems and on the energy transfer. In the case of very fast transfer, tA maxiS very short is deterand nAmax is large and the rise-portion
72-74 (1997) YIN-950
mined by the donor de-excitation while for slow transfer tA max is long and nA max is small and sometimes the rise could be determined by the acceptor intrinsic de-excitation while the decay reflects the slow de-excitation of the donor. Due to the variety of characteristics of the D and A subsystems in a given crystal, both these situations could be observed simultaneously; thus, the global acceptor emission becomes very complex and shows marked differences from the case of non-sensitised crystals. Such effects have been clearly observed in important laser systems such as YAG : Tm3+ senstitised by Cr 3+ in octahedral positions or Fe3+ in tetrahedral sites [4], GSGG : Cr, Nd [S] YAG : Cr, Nd [6] and so on and they should be taken into account in the analysis of the properties of the sensitised solid state lasers.
References T. Forster, Ann. Phys. 2 (1948) 55; D.L. Dexter. J. Chem. Phys. 21 (1953) 836; M. Inokuti and F. Hirayama. J. Chem. Phys. 43 (1965) 1978. VI IS. Golubov and Y.V. Konobeev, Sov. Phys. Sol. State 13 (1972)2679. 131 V.V. Osika, Yu.K. Voronko and A.A. Sobol, in: Crystals, Vol. 10 (Springer, Berlin, 1984) p.37. M V. Lupei. A. Lupei and G. Boulon, Phys. Rev. B. 53 (1996) 10. [51 T.P.J. Han, M.A. Scott, F. Jaque, H.G. Gallager and B. Henderson, Chem. Phys. Lett. 208 (1993) 63. [61 V. Lupei. A. Lupei, C. Stoicescu and A. Petraru, to be published (in Rom. J. Phys.).