Heumann, E.

Huber, G.

Pollnau, M.

Pollnau, Markus

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Short Notes K121 phys. stat. sol. (a) 130, K121 (1992) Subject classification: 78.50 Institut fur Angewandte Physik, Universitat Hamburg ') Time-Resolved Measurement of Excited-State Populations in Atomic Systems BY M. POLLNAU, E. HEUMANN, and G.  HUBER Introduction The absorption of light is the most common method for the investigation of the energy levels and transfer processes of atomic and molecular systems. The measurement of the ground-state absorption (GSA) provides information on the energy level scheme. If the density of the atoms or molecules in the stable ground state is known then the cross sections of the GSA transitions can be calculated from a Lambert-Beer law (see (2 )  of the next Section). Once the cross section of a certain transition has been determined an unknown density of atoms can be ascertained by measuring the absorption of light on this transition. The case is much more difficult if the populations of excited states and the cross sections of ESA are to be investigated because these states are unstable and decay, e.g. by the emission of light. In most cases it is impossible to obtain a defined distribution of the energy over the excited states and, therefore, the calculation of the ESA cross sections seems to fail. In this contribution we show that time-resolved ESA measurements, without the knowledge of the corresponding cross sections, provide enough information for the calculation of the excited-state populations. The ESA cross sections can then easily be calculated, and with the knowledge of the cross sections the distribution of the energy after any excitation can be derived. Measuring method A pump- and probe-beam technique is used for the time-resolved measurement of excited-state absorption. The populations n, of the excited states are achieved by pumping with a pulsed laser into one level. Subsequent relaxation populates lower lying excited states. n, n,(t), and n,(t) are the doping concentration, the time-depending population densities of the ground state and of all excited levels, respectively, n = n,(t) + n,(t) = n,(t) + Eni(t). (1) The sum in (1) generally extends over all populated excited levels. A pulsed probe beam of low intensity I,, such that the populations of the levels are unperturbed, passes through the sample of length d. The relevant processes induced by the probe beam are characterized by their cross sections oGSA (ground-state absorption) and oESA (excited-state absorption). In the unpumped case all electrons are in the ground state and the transmitting probe beam intensity is f,(d) = I ,  exp (-no,sAd), (2) ') Jungiusstr. 11, W-2000 Hamburg 36, FRG. K122 physica status solidi (a) 130 whereas in the pumped case it is From (1) to (3) we calculate To obtain the populations ni the terms on the left hand side of (4) must be determined. The cross sections oESA do not have to be known. oGSA is obtained by measuring I ,  and I, and using (2). The measurement of the transmitted probe beam without pump excitation or at adjustable delay times after pulsed laser excitation provides the quantities I ,  and I,, whilst n, can be determined from the bleaching of the GSA. At wavelength regions where GSA but no ESA occurs we obtain from (4) 1 n, = - -- In (I,/Z,). o G s A d  The populations n, of the excited states can be derived from the following considerations: The sum of the absolute populations of all excited states at a certain delay time tk after pulsed excitation is ni(tk) = n e ( t k )  ' ( 6 )  The time-dependent measurements of ESA originating from m different levels provide the quantities n j ( t k )  o E s A ( i )  ; i 1 , . . . , m ,  (7)  as demonstrated in (1) to (4). The comparison of the same ESA peak at different delay times t,, t k  yields (8) ni(tl) o E s * ( i )  - ni(tl)  . , i = l ,  ..., m ,  k = 2  ,..., m .  oESA(i) n i ( t k )  So the temporal information replaces the information of the cross sections which are eliminated from the calculation. The measurement of ESA at m different delay times leads to m equations of form (6) and m (m - 1) independent equations of form (8). In total m2 equations allow the determination of the m2 quantities (9) t : ni(tk) ; i, k = 1 , . . . , m .  Finally, the cross sections oEsA(i) are obtained from (4). Results and d i s c u s  ESA spectra of Er3+ doped yttrium-aluminum-perovskite (YA10,) were measured at several delay times. According to the temporal behaviour of the ESA peaks the initial levels of the ESA in Er3+ were identified and the populations of these levels were calculated. Results for the metastable levels in Er3+ (2.9 x 10'' cm-'): YA10, are shown in Fig. 1. ESA from other levels was not detected because, due to the short lifetimes, the populations of these levels are very small. Detailed results on ESA cross sections and ESA effects in the laser system Er3+ : YA10, will be published elsewhere /l/. Short Notes K123 ' 0.8 2 0.6 E, m T- 0.2 0 1000 2000 3000 tirne(ps1 - Fig. 1. Populations ofthe metastableexcited states in Er3+ : YAIO, after pulsed excitation Conclusions In conclusion, we have demonstrated that, with the information of time-resolved excited-state absorption spectra, the absolute populations of the excited states and the cross sections of the ESA transitions can be calculated. We wish to thank the Deutsche Forschungsgemeinschaft for their support. Reference /1/ M. POLLNAU, E. HEUMANN, and G. HUBER, Appl. Phys., to be published. (Received February 17, 1992) 

Time-resolved measurement of excited-state populations in atomic systems

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