AMPLIFIED SPONTANEOUS EMISSION IN RHODAMINE DYES: GENERATION OF PICOSECOND LIGHT PULSES AND DETERMINATION OF EXCITED STATE ABSORPTION AND RELAXATION

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1 AMPLIFIED SPONTANEOUS EMISSION IN RHODAMINE DYES: GENERATION OF PICOSECOND LIGHT PULSES AND DETERMINATION OF EXCITED STATE ABSORPTION AND RELAXATION W. FALKENSTEIN, A. PENZKOFER* nd W. KAISER Physik Deprtment der Technischen Universität München, München, Federl Republic Germny Received 12 July 1978 The following quntittive investigtions with picosecond pump pulses were mde s function of intensity: (1) fluorescence in the forwrd direction; (2) durtion of the fluorescence; (3) nd (4) spectrl pek nd width of the emission; (5) energy trnsmission of the pump pulse. Lrge energy mplifiction (fctor 300) nd drstic reduction of the durtion of the fluorescence (fctor 150) were observed. Comprison with model clcultions llows the determintion of vrious moleculr bsorption nd relxtion prmeters. During the pst decde, mplified spontneous emission of fluorescent molecules hs been studied under vriety of experimentl conditions [1]. While stimulted emission is the prerequisite for ny lser, the sme physicl process might be quite disturbing when spectroscopic prmeters (e.g. the spontneous emission lifetime) re mesured t high excittion intensities. Qulittive investigtions of mplified spontneous emission of orgnic dyes hve been reported by number of uthors using picosecond light pulses s pump source [2 6]. In this letter we present quntittive mesurements of five physicl phenomen studied s function of input intensity with moleculr concentrtion s the min prmeter. We investigted; (1) the fluorescence emission in the forwrd direction; (2) the reduced durtion of the fluorescence; (3) the wvelength shift of the pek of the emission, (4) the spectrl width of the fluorescence nd (5) the energy trnsmission of the picosecond pump pulse. The purpose of these investigtions is two-fold: First, we wnted to see to which extent the fluorescence emission chnges for high input intensities; in prticulr we were interested in the shortest possible pulse durtion of the fluorescence * Present ddress: Universität Regensburg, Germny emission. Second, we determined importnt moleculr bsorption nd relxtion prmeters by fitting model clcultions to our vrious experimentl results. Experimentlly we worked with mode-locked Ndglss lser [7]. A single pulse is selected from the beginning of the pulse trin with n electro-opticl shutter. The second hrmonic (? L = cm - 1 ) of the lser pulse is generted in KDP crystl. The durtion nd width of the green pulse is Af L ^ 4 ps nd Av «5 cm - 1, respectively. The pek intensity is determined by mesuring the energy trnsmission through two-photon bsorbing rutile crystl [8]. Rhodmine 6G nd rhodmine B dissolved in ethnol re investigted. The dye cells re tilted to void mplifiction of reflected fluorescence light. Different detection systems were pplied fter the smple depending upon the specific investigtion. The divergence of the mplified spontneous emission ws nlysed with pertures of different size. The fluorescence energy within solid ngle A 2 ws mesured with photomultiplier. The fluorescence durtion ws recorded with strek cmer (3ps resolution). The spectrl distribution of the fluorescence light, the spectrl nrrowing, nd the spectrl shift were studied with spectrometer in conjunction with n opticl multi-chnnel nlyser. (1) The normlized fluorescence energy = ^p^abs

2 versus the pek intensity 7 0 L f t n e pump pulse is shown in fig. 1. p represents the fluorescence energy emitted in forwrd direction within solid ngle A^2 e x p = 1.40 X 10~~ 3 sr.i?abs * s t n e l s e r energy bsorbed in the dye smple. The points represent experimentl dt nd the curves re clculted (see below). The open circles (curves 1) nd the tringles (curves 2) correspond to dye concentrtions of 10~ 4 M nd 2 X 10~ 4 M, respectively. The effective length of the tilted smples is 1.13 cm. The fluorescence t low intensities (ZQL < 5 X 10 8 Wcm 2 ) is determined by spontneous emission. Fig. 1 shows clerly the rpid rise of the fluorescence emission resulting from stimulted emission (7 0 L > 10 9 Wcm 2 ). At very high pump intensities the normlized emission levels or decreses s result of excited stte bsorption. At lower dye concentrtions of 4 X_10~ 5 M in cells of 0.56 cm length n increse of E F could not be observed. The number of inverted molecules is too smll for effective mplifiction. At very high concentrtions (!> 4 X 10~ 4 M), on the other hnd, the input pulse is b T r r-] 1 1 r r RHODAMINE 6G J XX A sorbed t the very beginning of the smple nd the forwrd direction is not preferred in the mplifiction process. (2) The durtion of the fluorescence pulses ws determined from strek cmer trces of the forwrd emitted fluorescence light. The rise time of the fluorescence emission ws found to be pproximtely 6 ps in greement with the length of the pump pulse. Following the excittion, the fluorescence signl decys nonexponentilly due to the fst depopultion of the level by mplified spontneous emission. At lter times, when the popultion is smll, the norml spontneous emission rte is observed. In fig. 2 the durtion Ap (fwhm) of the fluorescence is presented. The dye concentrtions re 10" 4 M (circles, curves 1) nd 2 X 10~ 4 M (tringles, curves 2). Fluorescence emission s short s 20 ps ws experimentlly observed. Comprble fluorescence shortening ws observed with 4 X 10~ 4 molr solutions. The curves re clculted with the sme prmeters s used in fig. 1. (3) The bsorption nd emission bnds overlp nd the short wvelength fluorescence is rebsorbed. The observed fluorescence pek is shifted to longer wvelengths for higher dye concentrtions. With incresed pump intensity, however, the ground stte bsorption is reduced nd the fluorescence emission shifts to : V Hier 2 10< - 2 A < o A y O y 1 2 ^ : CO UJ O 10' IT 1 ^ " S 0 i i i i 1 i 10 3 INPUT PEAK RHODAMINE B. i.. I i.. I Fig. 1. Normlizedfluorescenceenergy itp versus input pek intensity for () rhodmine 6G nd (b) rhodmine B. Experimentl points: circles, C= 10" 4 M; tringles, C = 2 X 10" 4 M. The curves re clculted using the dt of tble 1. 10" < OH o PEAK Fig. 2. Durtion of mplified spontneous emission versus input pek intensity for () rhodmine 6G nd (b) rhodmine B. Dye concentrtions 10" 4 M (circles, curves 1), nd 2 X 10~ 4 M (tringles, curves 2). The curves re clculted with the sme prmeters s in fig. 2.

3 shorter wvelengths, i.e. towrds the frequency of the pek stimulted emission cross section e m (see figs. 3, 3b nd 6). (4) The spectrl width of the fluorescence decreses t high pump intensities. The mplifiction of spontneous emission depends on the spectrl distribution of the emission cross section e m (y) leding to spectrl nrrowing of the fluorescence light. For 10~ 4 M rhodmine 6G the experimentlly observed spectrl width is depicted in fig. 3c. At low intensities hlf width of ~1050 cm" 1 is observed. For high pump intensities the spectrl width reduces to ~320 cm - 1. Theoreticl studies [9] predict for inhomogeneously brodened lines t high gin: A* F )A»> F (0) = (ln{tf F )Ar F (0)[ F (0) Af F )] )r 1 2 (1) In fig. 3c the mplifiction hs vlue of E {I^)IE^{0) ^ 300 nd the pulse shortening ws mesured to be Af F (0)Af F ) «30 t high pump intensities. With these numbers we clculte frequency nrrowing of A^ F )A^ F(0) = 0.33 which is in good greement with the experimentl vlue of (5) The energy trnsmissions through rhodmine 6G nd rhodmine B re depicted in figs. 4 nd b ( = 13 cm, C= 10~ 4 M). The circles nd tringles represent experimentl dt for Af L = 4ps nd 20 ps, respectively. The dt points indicte rpid bleching of the solution. The trnsmission depends on the excited stte bsorption nd on the relxtion from higher excited sttes s nlysed below. (6) Using mixtures of rhodmine 6G nd rhodmine B the frequency of the fluorescence emission pek could be shifted continuously between the emission frequencies of the pure dye solutions, i.e. between 555 nd 580 nm. This fct llows the genertion of picosecond light pulses with tunble frequencies. In theoreticl model we described the dissolved rhodmine molecules by multi-level system contin _ RHODAMINE 6G AS A - yl \j ' l o 1(f 00 1 A I fl ~ 1 1, 1 1 I I I _ RHODAMINE B - _ ~ A r y ' 2' : i i > v 1 I I I I INPUT PEAK INTENSITY I 0LCWcm 2 ] Fig. 3. Shift of spectrl pek of fluorescence emission of rhodmine B () nd rhodmine 6G (b) nd spectrl nrrowing of rhodmine 6G (c) versus input pek intensity. The wvelength of pek fluorescence emission t low dye concentrtions is indicted by the dshed lines. Fig. 4. Energy trnsmission through rhodmine smples. = 1.13 cm, C= 10" 4 M; curves 1 nd 1', At L = 20ps (tringles); curves 2 nd 2', Atj^ = 4ps (circles), () Rhodmine 6G. Solid curves (1 nd 2), QxL = 5 X 10" 17 cm 2 nd he = i n 10 l 3 ~ * s _ 1 ' 12 2 dshed curves (1' nd 2'), ex^ = 7.5 X 10" cm nd k s 1.(b) Rhodmine B. Solid curves, ( X cm 2 nd k& = s 1 ; dshed curves, o QX^ = 6X 10" 17 cm 2 ndfc 6 = s" 1.

4 Fig. 5. Multi-level model. 1, ground stte; 2, Frnck-Condon stte in Si-bnd; 3, temporl equilibrium position in Si-bnd; 4, Frnck-Condon stte in So-bnd; 5, stte in Si-bnd reched by rebsorption; 6, S n -stte populted by excited stte bsorption; 8, triplet stte or stte of photodecomposed molecules. The solid rrows indicte bsorption nd stimulted emission processes, the dshed rrows illustrte the vrious relxtion chnnels. ing different bsorption, emission nd relxtion processes [10] (see fig. 5). Rte equtions for the energy sttes nd for the photon fluxes of the pump nd fluorescence rdition were solved on computer. The considered energy levels re: 1, ground stte; 2, pumped Frnck-Condon stte in the Sj bnd; 3, temporl equilibrium level in the Sj stte; 4, Frnck-Condon level in the ground stte S 0 ; 5, level in the bnd populted by rebsorption of fluorescence light; 6, S n -level populted by excited stte bsorption of lser (tf exl ) nd fluorescence light ( e x F ); 8, level comprising triplet nd decomposition sttes. Model clcultions llow us to estimte the excited stte bsorption cross-sections nd relxtion rtes. These dt re listed together with known prmeters in tble 1: (i) 1 2 is the verge bsorption cross-section of isotropiclly distributed dye molecules in the ground stte. The moleculr dichroismd m = (y L )(^ + x ) represents the dependence of bsorption on the orienttion of molecules. ( 1 2 = (y + 2 ± )3; y = (l + > m )(3-Z> m );c i = (l -D m )(3-D m )) [11, 12]. D m is ssumed to be equl for the ground stte nd the excited stte bsorption [12], (ii) The cross-section of stimulted emission e m is strongly wvelength dependent. The em (X)-curves re obtined from the spectrl distribution E(X) of the fluorescence light (quntum distribution; fe(k) dx = 1). The reltion between o r em(x) nd E(X) is [13] m to = tfku s (til*w 2 c 9 (2) Tble 1 Prmeter Rhodmine 6G Rhodmine B on@l = cm" 1 ) 4.17 X 10~ 16 cm 2 [11] 1.87 X 10" 16 cm 2 [11] D m 0.95 ±0.03 [12] 0.93 ±0.03 [12] r 23 (0.9±0.3)ps [11] (l.l±0.3)ps [11] T41 «1 ps «1 ps *3i (2.8 ± 0.3) X 10 7 s" 1 [17,18] (1.85 ± 0.2) X 10 8 s" 1 [19] fc 34 (2.1 ± 0.2) X 10 8 s" 1 [17,18,] (1.85 ± 0.2) X 10 8 s" 1 [19,] k X 10 5 s" 1 [20] 1.7 X 10 6 s" 1 [18] results obtined here e x L (5 ± 1)X 10" 17 cm 2 (5 ± 1) X 10~ 17 cm 2 e x F (7 ± 2) X 10" 17 cm 2 (1.0 ± 0.3) X 10" 16 cm 2 k 6 >2X s" 1 >10 13 s" 1 k 61 k ± ±0.05 ^63^ ± ± 0.05 ^68^ ± ±0.01 Vlues redetermined in this pper.

5 where r? is the refrctive index t wvelength X nd c the light velocity. In our mesurements we determined E(X) with spectrogrph nd n opticl multichnnel nlyser t dye concentrtion of 2 X 10~ 6 M. The em (X)-curves re depicted in fig. 6. (Erlier reports on e m (X) used unccurte -vlues leding to somewht different results). (iii) The relxtion r 2 3 within the S± -stte ws mesured to pproximtely lps [11]. The corresponding relxtion time r 4 1 in the S 0 -stte is ssumed to be similr [14]. (iv) The trnsition rtes # 31, nd re determined by mesuring the low-intensity fluorescence decy time f F = l(c Ä33) = lc 3, the fluorescence quntum yield # F = 34^3 nd the intersystem crossing efficiency g I S C = #33^3. We remesured the fluorescence decy times t C = 2 X 10~ 6 M with fst photomultipliers nd found r F = (4.2 ± 0.3) ns nd (2.7 ± 0.3) ns for rhodmine 6G nd rhodmine B, respectively. We recll tht the rdition energy # F ws mesured through constnt perture. The mplified fluorescence emission however occurs within lrger solid ngle given by [10] T I I I 1 I I I I 1 I I I I 1 r A AO k mk-lnln{[exp(k) + l]2} " l 2 " 2 In 2 ' V> ^eff where d L» 0.5 mm is the dimeter of the pump bem, 7 eff is the penetrtion depth of the lser light nd k = ln{[^f(l)ar F )] [tf F (0)A F (0)]} represents the nrrowing t high intensities. ASl^ depends strongly on the dye concentrtion nd the pump intensity. The clculted solid ngles gree with experimentl observtions. The verge rebsorption cross section 1 5 is pproximtely equl to the ground stte bsorption crosssection t the emitting wvelength 1 2 (X F m x ). The 12 (X) curves re included in fig. 6 nd X F m x is depicted in fig. 3 nd b. At low pump intensities the fluorescence emission is quite brod nd the bsorption cross section vries substntilly over the fluorescence bnd width. By compring the experimentl fluorescence signls (t 7 0 L «10 8 Wcm 2 ) with clcultion we find effective 15 -vlues of (2 ± 0.2) X 10~~ 17 cm 2 nd (1 ± 0.2) X 10~ 1 7 cm 2, respectively, for 10~ 4 M nd 2 X 10~ 4 M solutions of rhodmine 6G nd rhodmine B. We now wish to compre our experimentl dt with clculted results nd determine vrious moleculr prmeters. In prticulr we re interested in the excited stte bsorption cross-sections e x L nd e x F nd the relxtion rtes # 61, nd k^. (1) The energy trnsmission T E t high pump intensities is used to determine e x L nd k. T E depends on the known prmeters 1 2 nd r 2 3 [11,12] nd on exl n ( * ^6 The effect of k 6 on T E results from the fct tht for k 6 ^ Af^1 the molecules ccumulte in level 6 nd reduce the excited stte bsorption, while for k$ > AL 1 the molecules return to the initil sttes nd increse the bsorption. A mesurement of r E for two different pulse durtions (different rtios of WAVELENGTH X CnmD Fig. 6. Absorption nd emission spectr for rhodmine 6G (curves 1 nd 1') nd rhodmine B (curves 2 nd 2'). k^at^1) llows the seprte determintion of e x L nd k 6. In fig. 4 nd b the experimentl results re presented together with clculted curves. Curves 1 nd 1' belong to At L = 20 ps (tringles) while curves 2 nd 2' respond to Ar L = 4ps (circles). The solid curves 1 nd 2, clculted with the sme e x L nd k vlues, gree with the experimentl points t both durtions. For other sets of e x L nd & 6 simultneous fit t At L = 4 ps nd 20 ps is not possible s the dshed curves indicte.

6 The e x L nd k vlues estimted from fig. 4 re listed in tble 1. (2) The brnching rtio k^k^ w s determined by compring the quntum yields of the S^SQ fluorescence fter excittion with light t X = 265 nm nd t X = 530 nm. Equl quntum yields would indicte tht ll highly excited molecules in level 6 return to level 3, i.e. = 6. In the mesurements we compre two fluorescence signls tking into ccount the bsorbed photon energy. The fluorescence life time r F ws found to be the sme for both excittion wvelengths. The observed SJ-SQ quntum yields give k^kf. = 0.95 ± 0.05 nd 0.7 ± 0.05 for rhodmine 6G nd rhodmine B, respectively (C = 2 X 10~ 6 M). The relxtion rte of rhodmine molecules from X e x c ^ nm to S± ws studied in [16] nd found to be>5x s- 1. (3) The trnsition rte leds to loss of fluorescing molecules; it reduces the mplifiction nd the pulse shortening of fluorescence light t high pump intensities. In our experiments, the k^jk^ rtio ws determined by djusting the clculted curves 1 of fig. l nd b t 7 0 L > 3 X Wcm 2 to the decresing experimentl Zip-vlues. The obtined results of k 6 %k 6 = 0.01 ± 0.01 for rhodmine 6G nd 0.02 ± 0.01 for rhodmine B indicte tht the loss of molecules from the singlet system is smll. (4) The rtio k 6l k$ of molecules returning directly to the ground stte is found by the reltion k^k^ = * ~~ ^63^6 ~~ ^68^6- T n e obtined vlues for rhodmine 6G nd rhodmine B re 0.05 ± 0.05 nd 0.3 ± 0.05, respectively. (5) The excited stte bsorption of the pump lser exl n c * t n e fluorescence light e x F reduces the mplifiction of spontneous emission. Hving determined exl ( s e e b v e ) w e estimted e x F by fitting curves 1 of fig. l nd b to the experimentl points in the rnge between 5 X 10 9 nd 2 X Wcm 2. The obtined exf -vlues re somewht lrger thn e x L (see tble 1). In our clcultions bsorption from level 6 to high sttes is included by ssuming the sme bsorption coefficients s for the -level. In this pper we demonstrted the genertion of picosecond light pulses t new frequencies by mplified spontneous emission. With the help of model clcultions we determined severl excited stte prmeters of the rhodmines. The uthors thnk Professors A. Lubereu nd M. Mier for helpful discussions. References [1] U. Gniel, A. Hrdy, G. Neumnn nd D. Treves, IEEE J. Qunt. Electron. QE-11 (1975) 881. [2] M.E. Mck, Appl. Phys. Letters 15 (1969) 166. [3] M.M. Mlley nd P.M. Rentzepis, Chem. Phys. Letters 7 (1970) 57. [4] C. Lin, T.K. Gustfson nd A. Dienes, Opt. Comm. 8 (1973) 210. [5] A.N. Rubinov, M.C. Richrdson, K. Sl nd A.J. Alcock, Appl. Phys. Letters 27 (1975) 358. [6] G.R. Fleming, A.E.W. Knight, J.M. Morris, R.J. Robbins nd G.W. Robinson, Chem. Phys. 23 (1977) 61. [7] A. Lubereu nd W. Kiser, Opto-Electr. 6 (1974) 1. [8] A. Penzkofer nd W. Flkenstein, Opt. Comm. 17 (1976) 1. [9] L.W. Csperson nd A. Yriv, IEEE J. Qunt. Electr. QE-8 (1972) 80. [10] A. Penzkofer nd W. Flkenstein, Opt. Qunt. Electr. 10 (1978). [11] A. Penzkofer, W. Flkenstein nd W. Kiser, Chem. Phys. Letters 44 (1976) 82. [12] A. Penzkofer nd W. Flkenstein, Chem. Phys. Letters 44 (1976) 547. [13] O.G. Peterson, J.P. Webb, W.C. McColgin nd J.H. Eberly, J. Appl. Phys. 42 (1971) [14] D. Ricrd nd J. Ducuing, J. Chem. Phys. 62 (1975) [15] H.B. Lin nd M.R. Topp, Chem. Phys. Letters 47 (1977) 442. [16] C.V. Shnk, E.P. Ippen nd O. Teschke, Chem. Phys. Letters 39 (1976) 320. [17] D.W. Phillion, Appl. Phys. Letters 27 (1975) 85. [18] B.G. Huth, G.I. Frmer nd M.R. Kgen, J. Appl. Phys. 40(1969) [19] A.V. Aristov nd Yu. S. Mslyukov, Opt. nd Spectrosc. 41 (1976) 141. [20] D.N. Dempster, J. Photochem. 2 (1973) 343.

interatomic distance

interatomic distance Dissocition energy of Iodine molecule using constnt devition spectrometer Tbish Qureshi September 2003 Aim: To verify the Hrtmnn Dispersion Formul nd to determine the dissocition energy of I 2 molecule