Photocaloric spectroscopy of the excited state absorption and of the fluorescence quantum efficiency in fluorescent material

Journal of Luminescence 36 (1987) 355—362 North-Holland, Amsterdam

355

PHOTOCALORIC SPECTROSCOPY OF TILE EXCITED STATE ABSORPTION AND OF THE FLUORESCENCE QUANTUM EFFICIENCY IN FLUORESCENT MATERIAL W. SEELERT and E. STRAUSS FB Physik, Universität, P.O. Box 2503, 2900 Oldenburg, Fed. Rep. Germany Received 18 August 1986 Accepted 4 November 1986 A compensation photocalorimetric technique is described to determine the excited state absorption cross section 02 of fluorescent materials at the pump wavelength and also their fluorescence quantum efficiency QF. Excitation with a continuous, moderate power laser suffices, 02 is inferred from the pump intensity dependence of the heat conversion efficiency which is analyzed for materials without fluorescence upconversion. The 02 obtained is most useful as a calibration point for pump-and-probe excited state absorption measurement, for example, for an analysis of the optical pumping efficiency of laser 3~)up to high excited state materials. The technique is successfully tested with the well-characterized ruby (A1 203 : Cr population densities.

Introduction Excited state absorption (ESA), i.e., absorption from the lowest excited electronic state to higher lying states, can severely change optical parameters of a material when exposed to intense light. This is the case in particular for an optically pumped laser medium where ESA reduces the overall efficiency [1] or even renders an otherwise promising laser material unsuitable for laser applications [2]. ESA at the laser transition reduces the optical gain below the value expected from fluorescence data. ESA in the optical pumping region lowers the pump efficiency and increases the thermal load of the material. ESA also may occupy higher lying states prone to drive unwanted photochemical reactions, for example, colour center formation in solids [3]. Therefore, the presence of ESA is harmful to the performance of an optically pumped laser medium and the spectrum of the excited state absorption cross section is a crucial parameter materials. in the evaluation of potential laser ESA measurements are generally performed using a pump-and-probe technique [2—4].An intense light pulse pumps the first excited state and the probe beam, either pulsed or continuous, mea-

sures the subsequent change in absorption (isa).

As detailed below these experiments do not determine the ESA cross section (p2) but rather the product of the excited state population density (n 2) and the absorption cross sections. Thus 02(X) can generally not be determined because n2 can only be obtained directly from ESA measurements in exceptional cases. In this paper we report a photocaloric method to determine an absolute value of the absorption cross section o2(XE) at the pump wavelength XE. The fluorescence quantum efficiency as well as the dependence of the excited state population density ~2(’) on the pump intensity I are also determined. The experiments are fairly easy to perform and straightforward to analyze. Continuous and comparably low power laser excitation suffices and no time dependence is involved. The ~2 obtamed in this way can be used to calibrate the ~sa scale of ESA spectra measured conventionally. The method testedspectra with 3 (ruby).is Itssuccessfully ESA cross-section Al 203 : Cr are well known and its long fluorescence lifetime, high fluorescence quantum efficiency [5] and good heat conductivity allow for large excited state population densities. Details about the electronic levels of ruby can be found in textbooks [6,7]. In

0022-2313/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

+

W. See/er!, E. Strauss / Photocaloric spectroscopy of excited state absorption and fluorescence quantum efficiency

356

our experiments the 4T2 band is pumped and ESA 2E state at 694 nm to the 2T 2T is from the 2/ 1 band [8].

3 >

ESA and its cross section

12 >

We consider here transition metal ions doped into crystalline or amorphous solid. However, the

I 2>

method toand tended other thesystems, data analysis for example can be organic easilydyes exin solutions. The behaviour under optical pump ing can be described by a three-level system coupled to the vibrations of the host as depicted in fig. 1. The system is optically pumped into the phonon sideband of the lowest excited state which relaxes very fast into its vibronic equilibrium 12). The state at the pump wavelength does not remain occupied so that stimulated emission by the pump beam does not occur. The transition back to the ground state is with the fluorescence lifetime T2. A significant population n2 is accumulated in the excited state 12> if the pump rate times the fluorescence lifetime ~2 is large enough. Absorption from 12) to the higher state 13> then may become appreciable at the pump wavelength (or a probe wavelength). Direct two-photon absorption is negligible compared to this process. Beer’s law of linear absorption gives I( A, 1) = Jo exp (n1o1 + 11202)1 —

= I~exp (No1 fl2 (01 02))!, (1) where N = n1 + n2 is the density of absorbing centers, o~= o1(X) and 02 = o2(A) are the absorption cross sections for ground state absorption (GSA) and for excited state absorption (ESA), respectively, and I is the path length in the material. 112 is zero without optical pumping and therefore the change in absorption due to ESA is —

—

—

________

I ~ -___________

I 1 > Fig. 1. Electronic three-level system coupled to vibrations used in the analysis of the photocaloric data. n indicates the population density.

length A~.The absorption change then is ~a( A ~) = fl 2o1(A ~)where the GSA cross section 01 1~ known. This4Ais the2T case in ruby at the B-line absorption ( 2 2 at 21000 cm~’)so that n2 can be measured via the ground state depletion: n2 = N n1 [8]. This is one of the features making ruby particularly suitable as a test material for the photocaloric ESA cross section measurements. An indirect determination of n2 is possible from bleaching experiments. With pulsed excitation the pump power dependence n2(I) can be modeled as a function of o~,02, T2, ‘r3, N and fitted to the power dependence of the transmission of a probe —

—‘

—

beam [4]. Single-pass gain measurements have also been used to determine 02 in the lasing region [1,9]. Photocaloric determination of the ESA cross section

(2)

In the following we derive the equations needed to analyze the photocaloric experiments in terms

ESA bleaches the material if (01/02)> 1. The absorption cross section 02 characterizes the ESA properties of the ion while 112 depends on the actual pump intensity. The absolute spectrum of 02 can be obtained from ESA experiments only if the population density n2 is determined somehow. A direct measurement is possible only in the cxceptional case that 01 >> o~ at a certain wave-

of 02 and the fluorescence quantum efficiency QFIn the photocaloric method the information about 02 is inferred from the pump intensity dependence of the heat conversion efficiency ILH( I): ~H is given by the ratio of absorbed light power ~A and the heat power ~H deposited into the sample by light: !LH = ~H/~A• (3)

=

—

n2 (01

—

02),

W. Seelert, E. Strauss

/ Photocaloric spectroscopy ofexcited state absorption and fluorescence quantum

Without photochemistry we have also ~LF + ILH = 1 where ‘5F is the fluorescence energy conversion efficiency. In the absence of ESA these values can be simply related to the fluorescence quantum efficiency QF by spectroscopic data [10]. The heat power released in the relaxation of the electronic states Ii> and 12> to their respective vibronic equilibria is

efficiency

357

from 3), for example in a situation with fluorescence upconversion, the pump intensity dependence of p~~(I) would differ somewhat from the one derived below. An extended description would have to take into account the additional branching ratios and heat conversion efficiencies. With ESA the absorbed power ~A is split up between GSA and ESA according to the cross sections and population densities and converted to

P 1

=

PA(1

—

XE/AF).

The heat power released in the relaxation of the state 12) is P2 = PA(1

—

=

QF)AE/AF,

(P1 + ~2)/~’A

=

1

—

QFAE/AF.

olnl(I)+02n2(I)

With (4), (5) and follows ~

(I)

=

(4)

can be considerably smaller than 1 for a fluorescent sample with good QF. ~ changes in the presence of ESA, because the relaxation of the state 13> contributes additional heat (P3). The amount depends on the active relaxation channels. 13) can decay radiatively or nonradiatively to 12> or Ii). Radiative relaxation may be disregarded in the systems considered, because no additional fluorescence is observed following ESA. Hence the relaxation of 13> is completely nonradiative even though oi and 02 or rather the radiative transition rates 13> 12> and 2> Ii>, respectively, are of the same order of magnitude. Consequently i~ as well as ~ 2~Nonradiative relaxation directly to the ground state would release more heat than relaxation back to 12>. However the multiphonon decay to 12> completely overwhelmes the decay 3> Ii>, because the energy difference 3) 12> is only about half. Therefore all optical power going into ESA is converted to heat with IxH(ESA) = 1. (5) —

—

—‘

+ILH(ESA)02fl2(I)

P~H(’)— !LH(G5A)olfl(1) —

using QF = ~F’E/XF. Here AE and AF are the wavelengths of the excitation and of the center of the fluorescence band, respectively, see fig. 1. The heat conversion efficiency is then !LH(GSA)

heat with efficiencies ~LH(GSA)and ~tH(ESA),respectively:

[(1

—

113 ~Z

n1, n2, i.e. N = n1 +

~2’

QFAE/A F)

x [1 +

—1 + QFAE/XF)n2(1)/N] (°2/°1 —1) n2(I)/N] (6) -~.

The pump intensity dependence is contained in the population density n2 (I). It is rewritten using the stationary rate equations appropriate for constant excitation: = 0 = ~01fl1 + n2/r2, ~2 = 0 = + ~ 112/T2 ~ + n3/i~, —

—

—

fl3 = 0 = + ~I~ti2 ~ ~l 3/T3, where ~ is the photon flux density (I = E~cP, EE = photon energy) and N = n1 + ~2 + 113. Note that pump rates are functions of ~ while thermal values depend on I. The solutions of these equations are —

~hi

( ~P)

=

n2(~3)= n = N( 1

—

(1

+

)/~},

~01T2

—*

where 20 TOT = 1 + ~o~.r1+ ~ As pointed out before, o 2’r3

This difference from the fluorescent state turns out to make the effective i~~(’) rise considerably even at low population densities n2, i.e., at modcrate pump intensities. In the presence of additional decay channels

‘~

o~i~ so that ap-

proximately ~= 1 + and n2(~)/N= ~a1’r2/(1 + ~o1T2);

113 <
(7)

W. Seelert, E. Strauss / Photocaloric spectroscopy of excited state absorption and fluorescence quantum efficiency

358

The dependence of the heat conversion efficiency on the photon flux density ~ is obtained from (6)

The integration over z is possible after expanding the quotient in a power series for a2T~~< 1. It

and (7):

gives a rapidly converging series

=

(1

+

&12T2

—

QFAE/AF)/(1 + cI~o2r2). (8)

XE F

Equation (8) is only correct for a constant photon flux density in the whole excitation volume. In the actual experiments an excitation beam with a Gaussian profile is used

______________________________

=

{

X ~ (02~~o)n_1(1)n[(1 aI~ 2al n=1 n 1 QF~ c13 0(1 al/2) + F l02T2 2 (11) —

—

—

2. ~(r)=~0exp—(r/r0) Consequently ~tH varies spatially and the experimentally determined ~aH is the average over the excitation volume: !1H~ _f1.tH(t’~

z’

°)IA(r,

~,8) dv,

where r, z, 8 are cylindrical coordinates, IA(r, z, 0) is the intensity absorbed at (r, z, 0) and the integration is over the excitation volume. This equation can be integrated for an optically thin sample (al< 1, i.e., exp(—al) 1 a!) and little bleaching (112(01 02) << a). Both conditions are met in the low pump intensity range which is analyzed below to obtain the QF and 02 values. In this case the beam profile does not change significantly inside the sample so that ~(r, z) can be separated in good approximation into a radial and an axial part: 2, ~(r,= ‘~~(1 z) = az). exp (r/r0) (9) —

—

~ —

—

—

}

Note that ~ (1 aI/2) = (~>is the photon flux density averaged along z. cP,,~decreases little for an optically thin sample and (~) is a good approximation. Replacing c~in (10) by its average <~)it can be written XE ln(1 + (12) ILH((~o))= 1 QF~T 0 —

—

F

2T2<~I30>

This result allows for the easy analysis of the photocaloric data, because the only excitation parameter is the photon flux density in the beam center. ~~(K~~))provides for the independent determination of absolute values for QF and 02 = 02(AE). QF is calculated from the intercept of i~i~(<~~)) on the ~i~i axis: QF = (1 —~(K~~ = 0))AF/XE, (13) which agrees with (4), the case without ESA. 02 can be inferred from the slope of ~~(<~~))at low excitation densities, i.e., the derivative of (11):

With (7), (8), (9) and using d~((~ 2AF d<~ 0)) 0) QF~(1—a1/2)AE (14) We point out that an expression similar to (14) can be derived for ~2 from the pump intensity

2,

02

IA(r, z)=aI0exp—(r/F~) a10 I 2,r ~ A 0 dzf0 dO Jo dr r exp ILH=

-~--J

—

(

2 —

(r/r0)

Q+ o 2 1 + o 2’r~exp (r/lb)2 2r2~~ exp (r/r0) where ~2= 1 QFXE/XF. Integration over the

dependence of the eqs. absorption in follows: cw bleaching experiments. From (2) and (7) da(~) 1 02 = 01 + ~-.o lim d~ No

beam profile simple after substituting x 2. Itis yields exp (r/!b) = 1 ~ J’dz ln(1 0 2T2~2) (10) AF o l02T2~2

Although cw bleaching allows in principle for a convenient determination of 02, the excitation

—

—

—

—

—

1~ =

—

.

densities needed a sufficiently precise much measure of the slopetoofgetL~a(~) are generally

W. See/ert, E. Strauss / Photocaloric spectroscopy of excited state absorption and fluorescence quantum efficiency

359

Experimental method

Glass Container Heater ç~pper

Vacuum

The heat conversion efficiency

~

Laser

weak thermal link ______

______

window

~

______ ______ __________________

~t~/~

was measured by a compensation photocalorimeter [10]. In the calorimeter the sample is connected to a thermal bath via a weak thermal link. The heat flow from the sample to the bath is replenished by an electronically regulated heater which keeps the sample at a constant temperature. Thus when light is absorbed which deposits heat into the sample, less electrical heater power is required to maintain the same constant heat flow. The difference be0>)

Fig. 2. Schematic depiction of the compensation photocalorimeter head. For details see text.

tween steady state heater power when the light is on and off provides a precise measure of the amount of heat power ~A deposited by the light.

higher than required in the photocaloric expenments for the slope in i~(~~>). In the derivation of (8) we have concluded that ~H(ESA) = 1, i.e., the rates are zero for nonradiative relaxation from 13> directly to the ground state ~i) or for other competing processes. This conclusion can be confirmed from the pump intensity dependence of the fluorescence intensity F2(J~).It depends linearly on the population density n2(~) and is a direct measure of it. With 13> Ii> relaxation operative or with significant photochemistry or two-ion processes, ESA would contribute to the depopulation of 2> and ~ 2(I) would deviate from (7). In the actual experiments fluorescence is collected from a thin slice perpendicular to the propagation direction of the excitation beam and close to the incident surface. The advantage of this geometry is being the fact that F2( cli) can be analyzed without restricting assumptions to high pump intensities. The measured signal is the average over the Gaussian excitation profile

The heat conversion efficiency !LH = ~H/~A can be calculated when the absorbed light power ~A is known. Experimental details: The compensation calorimeter head was built in an evacuated radiation shield with windows. The shield was kept close to the bath temperature. Its inside was black so that all fluorescence light was absorbed. The heat flow to the bath was through a direct thermal contact and also through the low-pressure gas. A small NTC resistive temperature sensor and two miniature resistors were glued onto the sample. A PID regulator powered one of the resistors and kept the temperature constant within ±5 mK. The heater current was measured with a precision meter, recorded on a chart recorder and the heater power difference calculated. The second resistor was used as a test heater. Typically 99% of the test heat was detected by the calorimeter. The calorimeter detected heat power of less than 200 ~iWwith good precision. The precise determination of the excitation intensity I~or of the photon flux density 4li~(~= I/EphOtOfl) is crucial to the experiments. It requires a Gaussian beam shape and precise measurement of the optical power. Excitation was with a one Watt Ar~laser which was lasing in a stable TE~ mode. The beam was focused with a nearly diffraction limited lens. The 1/e radius at the beam waist was determined to be ‘b = 56 ~m from the transmission through a 30 ~m diameter circular aperture. The focal length of 500 mm was chosen so that the Rayleigh length of the focal waist was

—~

F2(cli) 0

ff 0

n2(cl~(r))r dr dO. 0

With (7) and (9) the integration yields = const X r~ln(1 + 01T2~0).

(15)

To confirm the assumption ~H(ESA) = 1, the measured F2 ( cl~)must coincide with the logarithmic increase (15) using the fluorescence lifetime r2, the cross section 01 and just one scaling constant.

360

W. Seelert, E. Strauss / Photocaloric spectroscopv of excited state absorption and fluorescence quantum efficiency

somewhat longer than the thickness of the sample. The photon flux density c1~at the beam center was calculated from these parameters. ~ was varied by neutral density filters and by using lenses with longer focal lengths. Note that thermal lensing (11) may expand the beam inside the sample thus considerably reducing the actual Rayleigh length. This would lower the effective intensity averaged over the sample length. Thermal lensing can be sensitively visualized by the “blooming” of the transmitted beam at large distances. Thermal lensing turns out to be insignificant in ruby below the excitation intensities used in these experiments. This is mainly due to the fact that ruby has a comparably good heat conductivity and that its long fluorescence lifetime (~2 = 3 ms) provides for the accumulation of fairly large excited state population densities at moderate focus and power. The laser power was measured with a thermopile-type power meter. It was calibrated utilizing the compensation calorimeter. The absorbed power was calculated from thewere incident power corand transmitted power which very carefully rected for reflections at the various surfaces. The 2E fluorescence intensity F 2(I) atwas by 2E emission 694measured nm through imaging part of the a monochromator on a detector. 3~)was of good The quality ruby sample (A1203: Cr The chromium optical and well polished. concentration was determined photometrically to be 0.06 mol%, i.e. 3 x 1019 Cr/cm3 [12]. The sample was 2.5 mm thick with the beam propagating parallel to the crystal axis. Excitation was with the 514 nm line in the 4T 2 band or with the 458 nm 4T line in the 1 band. No evidence of colour center formation was found. All experiments were performed with samplebath. close to room temperature and a dry icethe thermal Results The experimental results are summarized in figs. 3 to 5. The data are plotted as functions of the generally more familiar intensity ~ (in the center of the Gaussian excitation beam) even though the photon flux density ~ = IO/EPhOtOfl is

—

07-

~

0.5

2 <~ E IW/mm Fig. 3. Measured heat conversion efficiency ~i~of ruby (0) at low excitation intensity (Is) = (~o) E~h 0tOfl with a Gaussian beam. The straight line is the best fit to the very low intensity data. It is used to calculate QF and °2 (514 mn). The curved line is calculated with these values from eq. (12).

the essential parameter in the analysis. The scaling constant (I,~/cl~) for our experiments is the energy of the 514 nm photons, i.e. 3.8 X 8PH/~H 1019 J. The is relative due error ~H/I~H SPA/PA + mainly to the error in= the ~A measurement. It is smaller than 5%. Figure 3 depicts the heat conversion efficiency ~~~(<‘ 0)) of pink ruby at low excitation densities (n 2/N < 10-1). ~~((pump I~)i)increases 0.47 to 0.54 already at this intensity. from As expected the data fit a straight line very well. The fluorescence quantum efficiency of pink ruby at room temperature is calculated according to (13) from the intercept of the line at ,.t~ = 0.46 and with XE = 514 nm, XF = 694 nm to be QF = ±3%. ‘~

The slope is used to determine the excited state absorption cross section according to eq. (14). cc! = 0.67 for the sample used and i~2.= 3 ms. The result is 02(514 nm)~/1~>) = 4.9 x 10—20 cm Figure 4 dipicts up to high excitation densities. At these pump intensities a large fraction of the Cr3 + ions are pumped in the excited state. The full line is calculated according to (12) using the QF and 02 obtained from the low-intensity data. It fits the data fairly well even though the assumptions adopted in (12) are not met at the higher intensities. The pump intensity dependence of the fluorescence intensity F 2(10) is plotted in fig. 5. The

W. Seelert, E. Strauss

/

Photocaloric spectroscopy ofexcited state absorption and fluorescence quantum efficiency

361

Discussion 07

The test performed with ruby confirms that photocalorimetry is a simple and suitable technique to determine absolutely the ESA cross section ~2 of most fluorescent material at specific pump wavelengths. In addition the fluorescence

06~

05

I

20

CO

I

I

60

80

100 2I

<~i,>E (W/mm

Fig. 4. Heat conversion efficiency ~ of ruby at high excitation intensities. Circles are experimental points. The full line is calculated from eq. (12) using the experimental parameters.

fluorescence was collected from within a 100 jsm slice close to the incidence surface. The full line is calculated from (15) using the 02 obtained above and the fluorescence lifetime T2. Just one scaling constant is used which accounts for geometric factors and the detection sensitivity. The agreement is excellent. The dotted line is the intensity dependence according to (7), i.e., without proper averaging over the beam,

—

—

—

—

—

—

/

=

—

1.0

Os

//

20I

40

60

80

100 2)

Fig. 5. Fluorescence intensity F

~,E

lW/mm

2 and calculated excited state population density n2 averaged over the Gaussian beam (full line, eq. 15). Just one scaling constant is used. The dotted line is the intensity dependence of n2 in the beam center according to eq. (7).

quantum efficiency QF is determined free of ESA. 02 and QF are obtained from the heat conversion efficiency ILH(. Deviations from ~t(ESA) = 1 would show clearly in ~i~(‘~)at high intensity. However, bleaching cannot be ignored there and (12) is not strictly correct. The excited state absorption cross section ~2 2 determined from the low-intensity of ~i~(/~ (514 nm) = 4.9slope x 1020 cm 0)) agrees well with the value 02 = 5 x 10—20 cm2 calculated from the data of Fairbank et al. [8]. The GSA and ESA spectra depicted in fig. 2 of ref. [8] were used to calculate 02/al = 0.53 at 514 nm. 02 follows 2.using We the measured 01 (514 nm) = 9.2 x 10—20 cm

362

W. Seelert, E. Strauss

/ Photocaloric spectroscopv of excited state absorption

point out again that the photocaloric method is independent of any actual knowledge of n2. The only experimental parameter used in the analysis is the intensity I~,in the center of the Gaussian pump beam which is used to calculate the effective average pump intensity (‘a) = I~(1— a//2), see (11). The obvious use of this photocaloric technique is to obtain a calibration point 02 (XE) for the L~ameasurements in pump-and-probe experiments of other fluorescent material of interest, This then makes it possible to utilize ESA measurements as a spectroscopic tool for various purposes, for example, the quantitative analysis of the optical pump efficiency of laser materials. The fluorescence quantum efficiency QF calculated from the ii~(/I0))data is independent of the intensity scale. The error in QF is smaller than for a single measurement at low intensity. The value 2E fluorescence QF = 73 via pumped ±3%4T obtained is for 2 and without ESA. It differs from some of the values reported before, for a summary see [5]. We found that QF is the same for excita4T 4T tion in the 2 band at 514 nm and in the 1 band at 458 nm. With ESA the ~i~((I0)) increases and QF decreases, i.e., less fluorescence photons are emitted per photon absorbed. This effect is stronger with 458 nm excitation, because 02/al is larger at 458 nm than 4T at 514 nm [8] so that the apparent QF under 1 excitation is smaller even without any focusing of the laser beam. This led 4 4 us to false 4A conclusion in [10] that T1 —~ A2 and 2 relaxation is operative and different. Presently we can not check, 2E for excitation technical reasons, we also the higher QF under direct observed, —*

Conclusion We demonstrated that photocalorimetry is a suitable method to conveniently determine the cross section ~2 for ESA in fluorescent materials especially for potential laser media. The method

and fluorescence quantum efficiency

requires only continuous and moderate power excitation with a TE~mode laser available in most laboratories. 02 is inferred from the pump intensity dependence of the heat conversion efficiency ~(< ‘~)).The assumptions adopted in the description of !~H((Io>) are well met by the materials under consideration. The photocaloric method and the analysis are successfully tested with the specially selected material ruby, where 02 is known from purely optical measurements.

Acknowledgements We are grateful to Dr. L.J. Andrews for a preprint of his paper. We thank Prof. G.F. Imbusch, Prof. K.H. Maier-Schwartz and Dr. W. Tuszynski for comments and D. Otteken for technical assistance.

References [1] ML. Shand and H.P Jenssen, IEEE J. Quaint. Elect. QE-19 (1983) 480. [2] D.S. Hamilton, in: Tunable Solid State Lasers, Springer . . . Senes in Optical Science, Vol. 47 (Spnnger Verlag, Berlin 1985) p. 80. [3] W.J. Miniscalco, J.M. Pellegrino and W.M. Yen, App!. Phys. 49 (1978) 6109. [4] L.J. Andrews, S.M. Hitelman, M.K. Kokta and D. Gabbe, J. Chem. Phys. 84 (1986) 5229. [5] R. Quimby and W.M. Yen, J. AppI. Phys. 51 (1980) 1780. [61 K.H. Hellwege, Einfuhrung in die Festkörperphysik (Springer Verlag, 1981) p. 192. [7] G.F. Imbusch andBerlin, R. Kope!man, in: Laser Spectroscopy of Solids, ed. W.M. Yen, Springer Topics in Applied Physics, Vol. 49 (Springer Verlag, Berlin, 1981). [8] W.M. Fairbank, G.K. Klauminzer and A.L. Schawlow, Phys. Rev. B 11 (1975) 60. [9] M.L. QE-18 Shand (1982) and 1152.J.C. Walling, IEEE J. Quaint. Elect. [10] E. Strauss and W. Seelert, J. Lumin. 31/32 (1984) 191. [11] H.L. Fang and R.L. Swoford, in: Ultrasensitive Laser Spectroscopy, ed. D.S. Kliger (Academic Press, New York, [12] DM. Dodd, DL. Wood and R.L. Barns J. AppI. Phys. 35 (1964) 1183.