Picosecond transient spectral hole-burning studies on oxazine 750 in a silicate xerogel

Chemical Physics ELSEVIER

Chemical Physics 191 (1995) 303-319

Picosecond transient spectral hole-burning studies on oxazine 750 in a silicate xerogel P. Weidner, A. Penzkofer Naturwissenschaftliche Fakultiit H - Physik, Universitiit Regensburg, D-93040 Regenkburg, Germany Received 24 May 1994

•

Abstract

Transient spectral hole-burning is studied experimentally and theoretically. Measurements are carded out on a silicate xerogel sample doped with oxazine 750. A picosecond pump and probe technique is employed using a mode-locked ruby laser and an optical fiber light continuum generator. The temperature is varied in a range from 8 to 295 K. A vibronic transition hole-buming situation is observed (no zero-phonon transition is resolved). The population hole linewidth in the So band and the population antihole linewidth in the $1 band increase from A Ph = 22 cm - ~at 8 K to APh = 75 cm - ~at 295 K. The inhomogeneous linewidth is A~,n =700 c m - I. For the observed vibronic transition situation an analytical scheme is presented for the approximate determination of the homogeneous linewidth, and a numerical differential equation system is derived and applied for a detailed analysis.

1. Introduction

The homogeneous spectral lineshape of an inhomogeneously broadened spectrum may be resolved by spectral hole-burning experiments. In persistent spectral hole-burning experiments the spectrum is permanently changed by the laser excitation [!-41. Especially transitions with strong zero-phonon lines are studied. For transient spectral hole-burning the spectral hole disappears with recovery of the excited states to the ground state [ 5-9]. Using femtosecond laser pulses the hole-forming dynamics may be studied [9-11]. Coherence effects of the overlapping pump and probe pulses are involved [ 9-12]. The temporal development of transient spectral holes within the fluorescence lifetime is studied with picosecond pump pulses and time delayed broadband picosecond probe pulses [ 13-19 ]. Information on the solvent relaxation dynamics is extracted from temporal spectral shifts of the absorp0301-0104/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved S S D 1 0 3 0 1 - 0 1 0 4 ( 94 ) 0 0 3 6 4 - 5

tion and emission spectra [ 14,19-231. The transient recovery of spectral holes occurs on a longer time scale if the relaxation takes place via metastable states [ 3,5 ] (e.g. relaxation via triplet states on a millisecond time scale [24] ). In this paper we study the transient spectral holeburning of the organic dye oxazine 750 in a silicate xerogel by a picosecond pump and probe technique. The sample is excited with a small-band picosecond ruby laser pulse. Spectral transmission changes are probed at various delay times with a broadband picosecond pulse generated in an optical fiber [ 25 ]. Measurements are carried out at temperatures between 8 and 295 K. A configuration coordinate model [2,4,5,81 is applied to derive information on the dynamics of spectral hole-burning from the probe pulse transmission measurements.

304

P. Weidner, A. Penzkt~er / Chemicat Physics 191 (1995) 303-,.319

2. Experimental A picosecond pump and probe technique is applied in the transient spectral hole-burning experiments on oxazine 750 in a silicate xerogel. The sample preparation, the experimental setup, and the measurement procedure are described in the following.

2.1. Sample preparation The organic dye oxazine 750 [26] was purchased from Lambda Physik and was used without further purification. Its structural formula is included in Fig. 9. The silicate xerogel was prepared by a sol-gel process [ 27-29] using the hydrolysis and polycondensation of the tetramethoxysilane (TMOS) precursor. The preparation recipe follows the scheme described in Ref. [ 30]. It is listed in Fig. 1. A porous transparent monolith is formed. Its pores are filled with formamide which remains in the sample from the preparation process. The produced silicate xerogels are also called porous sol-gel glasses or porous silica. The size of our samples is 20 mm in diameter and 1.3 mm in thickness. The density is p = 1.39 g/cm 3. The average pore diameter is approximately 26 nm and the ratio of pore vol-

ume to total volume is appro,dmately 0.76 [ 31 ]. The dye concentration in the investigated sample is 3.4 X l0 -4 mol/dm 3.

2.2. Transient spectral hole-burning arrangement The experimental setup is shown schematically in Fig. 2. The pump pulses are generated in an active (acousto-optic modulator) and passive (saturable absorber DDI) mode-locked ruby laser (wavelength AL = 694.3 nm) [32]. Single pulses are selected from the pulse trains with a krytron triggered Pockeis cell shutter. The separated pulses are increased in energy in a ruby amplifier. The laser is operated in a single shot mode. The generated pulses have a duration ofAtL = 35 ps and an energy of WE----5 mJ. The ruby laser pump pulses are directed to the dyedoped xerogel sample S in a continuous-flow He cryostat CR via an optical delay line DL. The absorption bleaching of the sample is determined by transmission measurements with the photo-detectors PD1 and PD2. Part of the pump pulse (10%) is split off and coupled into a quartz glass step-index fiber FI (Newport type F-SS-20, core diameter 8 lxm, length 4 m) to generate a spectrally broad picosecond probe pulse by self-phase

Sample Preparahon [ M'L'LaserjL ...... ~ ml tetramethoxysdane I 25ml formamtde

....... t Amphfier [- ..... {~i i

25 ml methanol 4 ml n~tnc ac~O

DL

Magnetic st,rnng 10 m~nat room temperature 1, I Adding36.38 ml water__J Magnettc st~rnng10 mJnat room temperature I' I Pouring 2 ml solution ~n33 mm d~ameterpolystyrenetubes w~thcovers Entenng ~ndrying closet held at 60 'C

i

I

_t:

Fq ~IER i .,~--... /oo~ 7

' Gelhng 1 t" at .'~0 "C [ A d d i n g 2 ml methanohc dye so,ut,on 1o tubes J

[

' Aging72 h at 60"C V Tubes a,e partl; opened~ I

! .

I PD2

Drying48 n at 60 "C [ S,or,ng ,n desiccator [ Fig, !. Diagramof preparation procedure of dye doped silicate xerogel.

Fig. 2. Experimental setup. PD1, PD2, photodetectors. FI, optical fiber. R, ruby rod (length 10 era). S, sample. CR, continuous flow cryostat. SPI, SP2, grating spectrometers. DAI, DA2, intensified diode arrays. FI, F2, microscopeobjectives (magnification20, focal length 8.15 ram).

P. Weidner, A. Penzkofer/ Chemical Physics 191 (1995) 303-319

modulation, stimulated Raman scattering, and stimulated parametric four-photon interaction [25]. The fiber output is collimated and passed through a ruby rod R for attenuation of nonbroadened ruby laser light. It is then directed to the pump-pulse-excited volume of the xerogel sample in the cryostat. The spectral probe pulse transmission Tpr (A) ~-- Sout.pr (~.)/Sin,pr(/~) through the sample is measured with the grating spectrometers SPI, SP2 and the intensified diode array detector systems DA1, DA2 (EG&G PARC 1455R700-G detectors with Model 1461 controller and an AT computer). 2.3. Detection o f absorption and emission spectra At room t~rnperature the absorption cross-section spectra are determined from transmission measurements with a spectrophotometer (Beckman Type ACTA M4). At low temperatures the transmission measurements are carried out by modifying the experimental system of Fig. 2. The ruby laser is not used. A 100 W tungsten lamp is placed in the probe beam path as light source and the transmission is determined with the spectrometers SP1, SP2 and the diode array detectors DA 1, DA2. For fluorescence quantum distribution E(A), fluorescence quantum yield q~, and stimulated emission cross-section o-,~(A) determination a linearly polarized 4 mW He-Ne laser is placed at the position of photodetector PD2 (Fig. 2) and the fluorescence signal emitted in backward direction is collected with a lens and directed to the spectrometer SP2 and detector DA2. The determination of E(A), q~ and O's(A) from the measured fluorescence spectra is carried out following the procedure described in [ 33,34 ]. Rhodamine 800 in methanol [26] was used as reference dye. Its fluorescence quantum efficiency is q~ = 0.16 [ 35 ].

3. Experimental results First the absorption cross-section and stimulated emission cross-section spectraofoxazine 750 in silicate xerogel are presented. Then the saturable absorption of tlie pump pulses is shown. It follows the investigation of spectral hole-burning as a function of pump pulse intensity, of sample temperature, and of temporal delay between pump and probe pulse.

305

3.1. Linear absorption and emissk, n studies Fluorescence quantum distributions E(A), fluorescence quantum yields ~k~,fluorescence lifetimes 7F, and degrees of fluorescence polarization P are determined from fluorescence spectroscopic studies [ 33-37]. The fluorescence quantum distribution spectra are used to calculate stimulated emission cross-section spectra [33,341. The degree of fluorescence polarization is defined by P = (Sll - S± ) / (Sal + S.L ), where S Hand S . are the fluorescence signals polarized parallel and perpendicular to the polarization of the excitation light. The obtained ~kF,7"F,and P results are listed in Table 1. The molecular reorientation time %r of the dye molecules may be estimated roughly from the degree of fluorescence polarization P and the fluorescence lifetime zF by the relation 1//o-1/3 P'rF , r°r= I - P / P o

(1)

with Po=0.5 (rewritten from the expression 1 / P - 1/ 3 = ( 1 / P o - !/3) ( 1 + ~'F/ror) [37] ). The fluorescence polarization values of oxazine 750 in silicate xerogel indicate molecular reorientation times of ro~(295 K) -- 1.2 ns, %r( 100 K) = 850 ps and ~'~,~(8K) = 840 ps. At room temperature real reorientation of the dye molecules in the xerogel pores contributes to %r (for a 10 -5 molar sample P=0.415 was measured, giving Z~r= 2.9 ns) [ 38]. At low temperatures ( 100 and 8 K) no real molecular reorientation is expected. The observed fluorescence depolarization is thought to be caused by reorientation of the fluorescence transition dipole moments due to F~rster type energy transfer between excited and nonexcited dye molecules [38401. The absorption cross-section and stimulated emission cross-section spectra of 3.4 × 10-4 molar oxazine 750 in silicate xerogel at room temperature, 100 and 8 K are shown by the solid curves in Figs. 3a, 3b and 3c, respectively. The dashed curves in Figs. 3a and 3c belong to 3.3× 10 -s molar oxazine 750. The dashdotted lines are the expected apparent long-wavelength absorption cross-sections due to transitions from thermally populated levels in the So band to the $1 band [41,42]. They are calculated using the relation O'abs(A ) ~---O'em(A ) ex

p(hc°(A~°~s'-A-')-) -"~B~.,~ ,

(2)

306

P. Weidner,A. Penzkofer / Chemical Physics 191 (I 995) 303-319

Table I Spectroscopic results of 3.4 × 10 4 molar oxazine 750 in ethanol and silicate xerogel Parameter

8K

100 K

295 K

Comments

No (cm -3) 4~. ~'F(ps) P ~',)~(ps) %.~ (ps) %.s, (ps) T.~.t(s) T.~.so (s) T3.s, (s) o'1 (cm) f~,,, A ~,,h (cm - ~) A)7h (cm - ~) 7", (fs)

2.04x 1017 0.245 1180 0.23 840 I I 2.8× l024 8.3 X 10"-3 8.3 X 10-'3 (3.15+0.15) × 10 -L~ 0.22 700 + 50 22 + 2 480+50

2.04X 10 =7 0.163 1060 0.245 850 I I 5 × l0 -7 1.5 X 10 -7 !.5 X 10 -7

2.04x 1017 0.094 650 0.345 1200 I I 4.9× 10 - ° 1.5 X 10 -9 1.5 X 10 -9

Eq. ( 1) assumed assumed Eq. (6) see text see text

700 + 50 46 __+6 230+40

700 _+50 75 + 5 140+ 10

numerical fit Eq. (14)

where h is the Planck constant, co the velocity of light in vacuum, Aso.s, is the electronic zero-phonon So-S~ transition wavelength for which O'ab~= O'~m,ks is the Boltzmann constant, and 0 is the temperature. The absorption of the 3.4 × 10 - 4 molar dye ( solid curves) and of the 3.3 × 10- ~molar dye (dashed curves) in the porous sol-gel glass decrease more slowly than expected from thermal populations, especially at low

10 "16

~

~rem

tr~s

1017 ~

:" co

10 "16

from

tr~s

c-

_o

1017

~o

10~8

1017

500

600

700

800

Wavelength ,\ (nm) Fig. 3. Absorption and stimulated emission cross-section spectra oxazine 750 in silicate xerogel at 295 K (a), 100 K (b), and 8 K (e). Solid curves, C = 3 . 4 x 10 -4 mol/dm3; dashed curves, C = 3.3× 10 -5 mol/dm3; and dash-dotted curves, expected apparent absorption cross-section spectra due to thermal population (Eq. 2).

temperatures. The long-wavelength absorption behaviour of the 3.3 × 10-s molar dye sample is due to homogeneous and inhomogeneous broadening. The additional broadening of the 3.4 × 10-4 molar dye sample is thought to be caused by dye aggregation [ 38]. The wavenumber positions P~.p of the So-S~ absorption peaks versus temperature are displayed by circles and the straight dashed line in Fig. 4a. It is seen that the frequency position of the absorption peak does not change with temperature. The wavenumbcr positions P~.p of the S~-So apparent stimulated emission crosssection peaks are given by triangles in Fig. 4a. The stimulated emission cross-section spectra were determined from fluorescence quantum distribution measurements using a He-Ne laser as excitation light source (A = 632.8 nm, see above). At room temperature the Stokes shift between emission peak and absorption peak is 8P.~,c= ~.,,p- ~c.P=500 cm -m. At low temperatures this Stokes shift reduces to 8P.~.~=240 c m - = The spectral shift is due to solute-solvent relaxation (dielectric relaxation) and vibronic relaxation within the fluorescence lifetime which lowers the energy levels in the S~ band [36,43,44]. At low temperatures the solute-solvent relaxation becomes frozen in leading to a reduced Stokes shift. The temperature dependence of the stimulated emission peak position Pc,P(O) may be expressed by a temperature dependent correlation function C~(O) defined by Co(O) = P .p(O) -

(3)

P. Weidner, A. Penzkofer / Chemical Physics 191 (1995)303-319

E o

15000

~ I '$,p

T%t(O ) =

E 14800 .g o CL

zF(O)

In[Ce(O)] - rF(

9)

= In[ I -exp( - 8^/a9) ] " 14600 . . . .

104

,

. . . .

t

.

.

.

.

.

.

.

,

.

.

.

.

.

.

,

. . . .

10 3

102

C

o 0

101

E b--

10°

(b)

.

"-

0

50

100

150

Temperature

200

250

300

I~ (K)

Fig. 4. (a) Frequency position of maximum So-S~ absorption (circles, dashed line) and of maximum S~-Soemission (triangles, solid curve). The solid curve is a nonlinearregression fit (Ref. I461. Eqs. (3) and (4)). The fit parameters are ~.r(~)= 12646 cm -t and ~^ = 614.9 K. (b) Fluorescencelifetime~'F(clinics and spline-interpolated dashed curve) and estimated total cross-relaxationtime T.~,, (solid curve) versus temperature 0 for 3.4 x 10-4 molar oxazine 750 in silicate xerogel. in accordance to the time dependent correlation function Co(t) = [ ~e,p(t) - ~ , p ( ~ ) ] / [ ~.p(0) - ~e.p(~) ] determined in time resolved fluorescence measurements at a constant temperature [43,44]. The solid curve in Fig. 4a fits the P¢,t,(O) data by the function

C~(O) = l - e x p ( - O A / O ) ,

(4)

where Oa is the activation temperature. The fit parameters are ~ A = 6 1 4 . 9 K and P¢.p(~) = 12646 cm - I P¢.r(O=~) is considerably less than ~e,p(295 K) = 14495 cm - ~ showing that even at room temperature the dielectric relaxation does not reach a relaxed equilibrium within the fluorescence lifetime. The temperature dependent correlation function C~(O) may be applied to estimate the total spectral cross-relaxation time T3,, of complete relaxation to ~ , r ( O = c ¢ ) (total dielectric relaxation time) by the relation [22] C~(~9) = C , ( & ~-F) --- e x p ( - T--~.,), leading to

(6)

(a)

13_

E

-

307

(5)

In Fig. 4b the fluorescence lifetime~'Fand the estimated total spectral cross-relaxation time T3.tfor 3.4 X 10 -4 molar oxazine 750 in silicatexerogel are plotted versus temperature. The figure indicates that T3.t >> rF fer all applied temperatures. At 8 = 295 K a value of T3.t= 5 ns is estimated. The Stokes shift of the emission 8~,.c= P,.p- P~.p depends on the excitation wavelength at low temperatures. For excitation at 632.8 nm a value of ~ , # ( 8 K) --240 c m - ~ is obtained (Fig. 4a). This shift is thought to be due to vibronic relaxation and dielectric relaxation. The excitation excess energy seems to be responsible for the dielectric relaxation contribution. In the case of excitation at 694.3 nm (spectral hole burning studies, see below) a Stokes shift of P L P~.p(8 K) = 9 0 cm - i is deduced. This shift is thought to be caused by vibronic relaxation only (see below, Fig. 8).

3.2. Saturable absorption The saturable absorption dynamics of picosecond ruby laser pulses (pulse duration AtL = 35 ps) is studied in a silicate xerogel sample containing 3 . 4 × 10 -4 molar oxazine 750 at room temperature and at 8 K. In Fig. 5 the measured energy transmission (defined as output pulse energy to input pulse energy) versus input peak intensity is displayed. The circles belong to 295 K and the triangles to 8 K. The small-signal transmission (measured transmission corrected for reflection) increases from To=0.1 at 295 K to To=0.224 at 8 K. The reduction of the, long-wavelength absorption at low temperatures is due to diminishing of thermal population contributions to the long-wavelength absorption (see dash-dotted curves in Fig. 3). The remaining absorption at the ruby laser frequency at 8 K originates from inhomogeneous broadening and homogeneous broadening apart from aggregation contributions. At high input peak intensities the energy transmission is limited to TE(/OL'-+ ~, 19= 8 K) = 0.72 and T~(IoL "-+co, 8 = 2 9 5 K ) = 0 . 5 8 by excited-state

P. Weidner, A. Penzkofer / Chemical Physics 191 (1995) 303-319

308

l

0.7

/h

O

F--

0.6 oO

E O

~

O

E (/'} c b--

0.4

~

0.3

¢ILl

(8)

- Ns,(Z) [O'om(~)- o'~,(~)] ] dz),

0.5 O

where I is the sample length, Nso(Z, ~) is the number density of molecules in the So-band absorbing at wavenumber P with an absorption cross-section O.r-~bs(U) (without excitation it is Nso(Z, ~) O"b,(P) ---Noo'.b~(~), where No is the total number density of dye molecules). Ns~ (z) is the number density of population

A O

0.2 O

O

0.1

o

106

107

10e

109

101° ...-'"'*'"-

Input Peak tntens,ty IOL (W cm 2)

...... - .............

----"" .............

-°" ....

i .

Fig. 5. Intensity dependent energy transmission of picosecond ruby

laser pulses through 3.4 X 10- 4 molar oxazine 750 in silicate xerogel. Circles, 295 K; triangles, 8 K.

absorption from the Srband to higher lying singlet bands.

L9

i i

b

..... .-""

LL c"

(_9

3.3. Transient spectral hole burning

i "" ....... - ...........................

The spectral hole-burning in a 3.4 X 10 - 4 molar oxazine 750 silicate xerogel sample is studied with smallband picosecond ruby laser pump pulses and broadband picosecond ruby laser derived probe pulses. The pump pulse intensity dependence of the hole-burning at 8 K, the temperature dependence of the hole-burning in the range from 8 K to 295 K, and the temporal disappearance of the spectral hole-burning effects are investigated. The spectral analysis at the short-wavelength side is restricted by the limited spectral extension of the probe pulse spectrum. In Fig. 6 a gain factor or hole-burning factor G is presented which is defined by

G( ~, IOL, to) = ln(Tpr( ~' IOL' tO)) , ~,

To(P)

(7)

where To(P) is the small-signal transmission (without pump pulse excitation), and Tp,( P, lot., td) is the probe pulse transmission at time to after pump pulse excitation of peak intensity IOL.After pump pulse excitation the probe pulse transmission is given by

14000

..... .°--'"""

"'" ...... ...°""

14200

14400

Wavenumber D (cm 1) Fig. 6. Spectral hole-burning distributions G (P) of 3.4 × 10 - 4 molar

oxazine 750 in silicate xerogel. Vertical dash-dotted line indicates pump pulse wavenumber PL. (a) Intensity dependence at 8 K. Probepump pulse delay td = 0. Solid curve, 10L= 3. I X l0 s W/cm2; dashed curve, 10L=4.5 X l0 7 W/cm 2. Dotted curve presents Go/4. Smooth curves, nonlinear regression fits {46l in region 14200 c m - ~ < ~ < 14480 c m - t using Eq. (12) with G ' = 1.048; A ~ =32.5 c m -

(solid curve), and G'---0.637, Af~ =20.8 cm -~ (dashed curve). (b) Temporal delay dependence at 100 K. Solid curve, t a = 0 , !OL=2.4 X l OSW / cm2. Dashed curve, ta = 5OOps, loL = 2.4 x 10sW/ cm 2. Dotted curve, Go/5. Smooth curves, nonlinear regression fits in region 14200 c m - ~ < 14440 cm -" with G ' = 0 . 8 8 , A~, = 5 6 cm - i (solid curve) and G ' = 0.50, Af~ = 4 9 cm - m(dashed curve). (c) Temporal delay dependence at 295 K. Solid curve, t a = 0 , lOL=2.1 X IOSW/cm2.Dashedcurve, td=7OOps, lm.=2.1 x 10sW/ cm 2. Dotted curve, Go~5. Smooth curves, nonlinear regression fits in region 14200 c m - i < ~< ~ = 14403 c m - I w i t h G ' = 0 . 8 5 , A PH= 103 cm - m(solid curve ), G ' = 0.34, A VH= 89 cm - i (dashed curve).

P. Weidner, A. Penzkofer / Chemical Physics 191 (1995) 303-319

of the S~ level. The small signal transmission is given

by To(P) =exp[ -Noo',t,~(P)l] .

(9)

From Eqs. (8) and (9) it is seen that the spectral distribution of the hole-burning factor G is determined by a reduction of the ground-state absorption (groundstate population hole), and by the occurrence of stimulated emission and excited-s~ate absorption. In regions of o"~b~(P)--->0, and O'~m(P)
=

[Grabs(P ) -}"Greta(~) ]No/,

(lo)

which would be measured by pump-probe measurements when all molecules would be excited to the $1 state and no excited-state absorption would be present. (Note that the dotted curves are multiplied by demagnification factors to fit into the diagrams.) In Fig. 6a the effect of the pump pulse intensity on the spectral hole-burning behaviour is displayed. The sample temperature is 8 K and the time delay between pump and probe pulse is set to td = 0. The dashed curve belongs to a pump pulse input peak intensity of IOL=4.5 × 107 W/cm 2 and the solid curve belongs to lOL=3.1 × l0 s W/cm 2. The dotted curve represents Go14. No zero-phonon peak is resolved. Vibronic transitions are responsible for the observed probe pulse transmission behaviour. A power broadening [ 12] of the hole-burning curves is seen: At low pump pulse intensities the homogeneously broadened transition whose transition frequency coincides with the pump laser frequency is dominantly excited. At high pump pulse intensities this transition is saturated and adjacent homogeneous lines are excited due to their homogeneous absorption cross-sections in the wings. The peak position of the hole-burning factor G is slightly Stokes shifted compared Io the pump laser frequency (shift 8Pv -- 45 cm - i ). Its origin will be explained in the next section as the envelope c :',he overlapping So absorption hole profile centered at the pump laser frequency and the S~ emission profile centered at the vibronically relaxed frequency position P~ = PL -- 28P~ (see Fig. 8) [5 ]. The smooth fitting curves consisting of two overlapping Lorentzians will be discussed in the next section.

309

In Fig. 6b two hole burning curves at I00 K are shown for temporal pump-probe delays oftd = 0 (solid curve, loL = 2.4 × 108 W/cm 2) and ta = 500 ps (dashed curve, IoL= 2.4 × 108 W/cm2). The dotted curve represents Go~5. The gain factor G reduces with delay time according to the fluorescence lifetime (TF ~- 1.06 ns) but the spectral shapes of the curves remain unchanged. The widths of the hole-burning curves G are broadened compared to the 8 K case. The spectral linewidths of the absorption hole profile and of the stimulated emission profile are broadened compared to 8 K. A Stokes shift of the hole burning curves G is no longer observed, because of the broadening of the absorption and emission profiles. The absorption in the wings of short-wavelength adjacent homogeneous transitions within the inhomogeneous distribution shift the peak of the G-envelope towards the high frequency side. A vibronic broadening due to thermal level population is expected. The thermal frequency at 100 K is already 8 ~ = kBO/hco = 70 c m - ~. In Fig. 6c two hole-burning curves at O = 295 K are displayed The pump-probe delay times are td=O (solid curve, loL= 2.1 × 108 W/cm2), and ta =700 ps (dashed curve, loL=2.1 × 108 W/cm2). The dotted curve represents Go~5. The gain factor curves G decrease with increasing delay in accordanc~.~with the fluorescence lifetime. The spectral shapes of the two hole-burning curves are the same within the experimental accuracy. Their shapes still deviate slightly from the Go curve. The observed hole-burning profiles are determined by increased homogeneous broadening of Franck-Condon type vibronic transitions, by multilevel absorption starting from thermally populated states in the So band, and multilevel emission starting from temporary thermally populated states in the S~ band. The decrease of the spectral hole-burning signal with pump-probe delay is illustrated in Fig. 7. The frequency-integrated gain factor versus delay time td is displayed for ~ = 8 K, 100 K, 198 K, and 295 K. The straight lines are exponential least square fits of the hole-burning signal decay, i.e. ~G(P, td)dP/JG(P, O) d ~ = e x p ( - t d / ~ ) . The ~ values agree reasonably well with the temperature dependent fluorescence lifetimes ~'Fdetermined from fluorescence quantum yield measurements. In all measurements down to 8 K no permanent spectral hole-burning effects have been observed, and no

310

P. Weidner, A. Penzkofer / Chemical Physics 191 (1995) 303-319 1

-

,

'

"

'

"

'

"

'

0.7 d~ 0.6

0.5

'~., "..

"",.',,,.

'".,.".,.. ~ ,'~,.. '".".,. "',. "'-.~ o LI-\, x'x. ~ "4 ".,, - , ~

^-

_e u/4 N

..

".,

0.3

"

0

,,

z 0

i

i

200

400

".

,

600

800

,I

1000

Probe Pulse Delay T~me to (ps) Fig. 7. Temporal decay of hole-burning signal for 3.4 X 10 - 4 molar oxazine 750 in silicate xerogei, j,39oo~m-t4ss°~m-" G(~,td) d~/ j.,4s5oc,,,-,, G( g 0) d~ versus td is displayed• ] 0 L ~ 2 X 1 0 8 W/cm 2. I39OOcmCircles and solid line, O= 8 K, ¢= 1102.5 ps. Triangles and dashed line, O= 100 K, r = 1016 ps. Squares and dash-dotted line, O= 198 K, ¢=818.5 ps. Diamonds and dotted line, 0--295 K, r--717.5 ps.

dye degradation was found in the course of the studies. No zero-phonon line could be resolved in our experiments where the spectral resolution was approximately ! cm-L

axis is an energy coordinate. The So ground state and the Sm first excited singlet state are displayed. Part (a) illustrates the absorption and dielectric nonrelaxed emission dynamics, while part b sketches the partially dielectric relaxed emission dynamics. The equilibrium excited-state displacement qo is indicated. Before excitation, the $o potential curve of the molecules is energetically spread out (inhomogeneousdistfibution) because of site-to-site varying solventsolute interaction. The level energy depends on the orientational distribution and on the spatial distance distribution between solvent molecules and solute molecules. The energy is lowest for parallel orientation of the solvent and solute dipoles and close contact between solvent and solute (dashed So curve in Fig. 8a). The solid So curve in Fig. 8a belongs to larger solute-solvent spacing and some orientational dipole misalignment. In this potential curve a vibronic level structure is indicated. The inhomogeneous potential curve spreading due to solute-solvent interaction is transferred to the S~ state by laser excitation. The excitation changes the electronic distribution of the solute. The solvent molecules are incorrectly oriented and therefore not in their energetically relaxed states. As is shown by the dashed (a)

(b)

0

00o~ 0

4. Transient spectral hole-burning analysis

I \

\

/

o\, A schematic configuration coordinate model is presented [ 5 ] which is applicable to dominant zero-phonon transitions, mixed zero-phonon and multi-phonon excitation, and dominant vibronic (multi-phonon) excitation. Since no zero-phonon transition is resolved in our experiments, we apply the model to describe dominant vibronic excitation. Approximate vibronic homogeneous linewidths data are derived analytically, and a numerical description of the hole-burning dynamics is developed.

O0

/ ~

s, °

//

// // // ,,( /

~.

Z

0

ooo\

oOo o

I

//

So

/

0

rr I I /I - fI/.,"

\

~', ,,,,\ --

o

"--'--6

/

I

i

0

qo

p_

0 o

o

o

q

Displacement

/ "-

I~/

,,~

// //

0

8 °

/

/ ~ "

o

O0 0 0

4.1. Configuration coordinate model

0

/

,/ i 0

i qo

=_ q

Displacement

A schematic configuration coordinate system [2,4,5,8] of an organic dye molecule in a solvent is shown in Fig. 8. The horizontal axis of parts a and b represents a displacement coordinate q. The vertical

Fig. 8. Configuration coordinate model with schematic indication of solute-solvent arrangement. (a) Absorption and emission dynamics without dielectric relaxation at low temperatures. (a and b) Absorption and emission dynamics including solute-solvent relaxation at elevated temperatures.

P. Weidner, A. Penzkofer / Chemical Physics 191 (1995) 303-319

curves in Fig. 8a the lowest energetic potential curve of closely spaced solute-solvent molecules of optimum orientation in the So state becomes the energetically highest potential curve in the Sz state because of wrong solvent-solute orientation and strong interaction due to closely spacing. In the case of long wavelength excitation the energetically high lying molecules in the So state are selectively excited to the corresponding energetically low lying molecules in the S~ state as is indicated by the solid arrow VL between the solid potential curves in Fig. 8a. A spectral hole is burned into the inhomogeneous So level distribution and a spectral population (antihole) is built up in the S~ band. The configuration coordinate minima of the potential energy curves in the So and $1 states do not coincide because of modification of the electronic charge distribution by the excitation process [5]. Therefore in the excitation process and in the emission process some vibronic excitation is involved which relaxes quickly to a thermal equilibrium [8,19] (Stokes shift [5] ). Since the Franck--Condon transitions extend over a certain displacement region, (extension of wave function) more than one vibronic level (multi-phonon level) might be excited. Zero-phonon transitions have very small linewidths at low temperatures, because their linewidths become determined by the S~-state lifetime. With increasing excited-state equilibrium displacement zero-phonon excitation looses importance [5]. The homogeneous linewidth of a vibronic transition is likely to be broad even at low temperature because of fast relaxation to thermally relaxed zerophonon positions. In our analysis we assume one dominant homogeneously broadened vibronic FranckCondon transition and neglect zero-phonon contributions, since no zero-phonon line was observed. The observed Lorentzian lineshapes support the restriction to one homogeneously broadened vibronic transition. At low temperatures the geometrical solute-solvent arrangements are frozen in. There occurs no rearrangement hole filling in the So band (T3.so> cF) and no rearrangement antihole spreading in the S~ band (Txs, > rF) within the fluorescence lifetime cF. At elevated temperatures the disturbed So-level population and S~-level population tend to relax to equilibrium distributions by solvent-solute rearrangement. The $1 potential energy curves of Fig. 8a relax to the S~ potential energy curves of Fig. 8b by solvent dipole

311

reorientation and spatial solvent-solute changes. From the populated Sz states of Fig. 8b stimulated emission, spontaneous emission and nonradiative decay bring the molecules down to energetically excited levels of the So band (no equilibrium orientational and spatial solute-solvent arrangement) as indicated in Fig. 8b. From there the molecules relax back to the equilibrium So level distribution of Fig. 8a. The overall So-S1 absorption and St-So emission bands as presented in Fig. 3 are a convolution of homogeneously broadened multi-level transitions between vibronic states and zero-phonon states which are inhomogeneously broadened by site to site varying orientational and spatial solvent-solute interaction. Homogeneous broadening is characterized by the fact that there exists no physical method to resolve a finer structure of the profile [ 12]. Our picosecond excitation and our spectrometer restrict the spectral resolution to about I cm- ~. This spectral resolution is sufficient to resolve the homogeneous linewidth of vibronic transitions, but no zero-phonon line contribution could be resolved. A sharp zero-phonon line structure might be observable under narrow-band cw laser excitation even in the case of low zero-phonon contribution to the absorption spectrum (low Debye-Waller factor [5] ). Inhomogeneous broadening is due to different frequency spacings of the same transition of different molecules because of site specific interaction (here solutesolvent interaction). At elevated temperatures a thermal population of the vibronic states occurs.

4.2. Approximate analytical extraction of vibronic homogeneous linewidths In our experiments spectral cross-relaxation may be neglected (see Fig. 4). At low temperatures the homogeneous broadening is small compared to the inhomogeneous broadening, so that at moderate excitation intensities a constant inhomogeneous distribution may be assumed around the laser excitation frequency (inhomogeneous broadening limit [ 12 ] ). We consider a dominant vibronic Franck--Condon transition. The hole-burning factor G(~) (Eq. (7)) is composed of a power-broadened Lorentzian describing the absorption process centered at ~L and of a power-broadened Lorentzian of the same halfwidth describing the stimulate~i emission process centered at ~e. It becomes [ 12]

P. Weidner. A. Penzkofer / Chemical Physics 191 (1995)303-319

312

A~h2oA(l "4-IOL/I~) G(P) = G A ( P - #L) 2 + Ap2.A( 1 +IoL/I's) AP2E( 1 +IoL/I's) (11)

+ G E (K,_~.,E)2+ A~,2h,E(I +IoL/I~j) ,

where GA and G~ are gain contribution factors, and A#h,A and A~,ts are the homogeneous linewidths (FWHM) of absorption and emission, respectively. They are the linewidth of the So-state population hole ( A Uh.A), and of the S t-state population peak (antihole) (A~h,E) caused by absorption of weak excitation pulses. The linewidth of the G(P) probe pulse gain profile is twice as broad as the level population hole width. IOL is the pump pulse peak intensity, and I[ is an effective saturation intensity for which the pump pulse energy transmission is reduced to TE(PL, I~)=[To(f'L)TE(K'L, IOL~O°)] n/2. At low temperatures the fluorescence Stokes shift is small and it is reasonable to assume O'.bs(PL)=tr~m(~) and A1)h.A= A~u,E = A ~ . Under these assumptions it is GA=GE=G ', and PE= PL--28~v where ~P, is the Stokes shift of the center frequency of the hole-burning profile relative to the pump laser frequency (see Fig. 6a). Eq. ( 11 ) reduces to

Is ]

The transient spectral hole-burning in the vibronic transition limit caused by narrow-band picosecond laser pulse excitation is described by the following differential equation system ( v= ~Co) exploiting the configuration coordinate model of Fig. 8:

0Nso(v') Ot' hVL

(

+ Ns,.~(v') + Nso.~(v')

(~__ ~L)2 .~ AK,2(I+IoL/ItS )

+ (O_~L+2~,O2+~(l+toL/rs)

4.3. Numerical simulations

/L m erA( PL-- V'-- Vv.S,)[Nso(V') - N s , A v') ]

G(~) = G'A~h2 (1 + ~-~1

X

parameters G' and A~, [46]. The fit parameters are listed in the figure captions. Homogeneous linewidths of A~h(8 K ) = 2 8 + 5 cm -I (T2--380+60 fs), A ~ ( 1 0 0 K ) = 5 3 + 5 cm -I (T2=200+20 fs), and A#h(295 K ) = 9 3 ± 6 cm -I ( T 2 = l l 5 + 1 0 fs) arc obtained. The deviations of the fit-curves from the experimental curves at the high frequency side in Figs. 6b and 6c are due to the fact that the spectral hole is burned in the long-wavelength wing of the inhomogeneous distribution (violation of inhomogencous broadening limit [ 12 ] ). The slight deviations of the fit curves from the experimental curves at the low frequency side of Fig. 6b and 6c are thought to he caused by vibronic contributions from thermally populated levels.

~F

.

(12)

"rv,so

Nso(v') -Nso( v'+ ~v')

The power-broadened vibronic homogeneous linewidth is (13)

Assuming a single vibronic Franck-Condon transition, the dephasing time/'2 of the transition may be estimated from the vibronic homogeneous linewidth by use of the relation [ 12,45 ] 1

T2= ~Co A~, "

(14)

Eq. (12) is fitted to the hole-burning curves in Fig. 6. Nonlinear regression is applied to determine the fit

g i ( v ' + ~V'-- VOA)

T%So~ v'lVi.h

Nso(V') - Nso( V' - 8 v') A~,[~= A ~ 1 + Is--;-] "

gi( V'-- POA)

gi( v ' - vOA) gi( V' -- 8 V' -- P0A)

T3,So~ v'/vin. (15)

ONs,.,,( v') Ot'

/L CrA(VL- v ' - Vv.s,)[Aso(V') - N s , . . . ( v ' ) ] hVL

Ns,.~(v')

Ns,A v')

"rF

"rv,s~

(16)

P. Weidner. A. Penzkofer I Chemical Physics 191 (! 995) 303-319

ONs,(9') Ot'

Ns,,v( 9')

k h~

-- --

O'A( PL --

Nst (v')

p t + Pv,S0) [NSI (lfl') --Nso.v (9") ] gi( P'-- POE)

Ns,(p') -Ns,( p' + bv')

gi( v ' + ~P'-- P0E) T3,S! ~ P'/Pinh gi( P'-- POE) gi( V' -- ~ V' -- POE)

Ns ( V') -Ns,( V'-

T3.s, ~ P'/ Pi,h (17) 0Nso. (p') 0t'

hie +

OrA( PL -- 9'-I- Pv.S0) [NsI(pF) _Nso.v (p,,) ]

Ns,(V')

Nso. (P')

~'F

%.So

f

Off

(18)

erA( PL- P'-- P~.S,)

(1 -f x) l d r '

x [Ns,,(p') ~c

+ f CrA(PL-- P'+ P~.So) --oo

X [Ns,(p') (1 - f J

-Ns~v(v') ] d p ' ) ,

(19)

with the initial conditions Nso( v', t ' = - oo) =Nogi( v ' - POA) ,

(20)

Nso.~(v', t'= - ~ ) =Ns,(V', t ' = -o~) t'=

(21)

=0,

/L(Z'----0, t', r) =10L exp

t't°22

rr.~)o ,

(22)

(23)

313

The moving frame transformation t'=t-nz/co and z' = z is used, where t is the time, n the refractive index, z the propagation coordinate, and co the vacuum light velocity. The spectral width of the pump pulse of peak intensity IOL is neglected. The orientational anisotropy of the absorption cross-section trA(V, 0) = 30"A(V) cos20 [47 ] of the electric dipole interaction is not taken into account for the sake of simplicity ( 0 is the angle between the electric field strength and the transition dipole moment). A successive relaxation of the nonequilibrium population distributions Nso (v'), Nsl (v') to neighboring inhomogeneous distribution energy states Nso ( P' +--~ v'), Nsl ( v' +_8 v') is assumed ( cascading relaxation to equilibrium). Eq. (15) describes the temporal change of the So population distribution Nso (v') due to laser excitation. The first term gives the S o ( v ' ) ~ S l ( v ' ) subband absorption. Ns,.v (v') is the population density of the vibronic Franck-Condon state in the St subband of frequency v'. The vibronic Franck--Condon excitation frequency in the SI state is Pv.s,. The second term is responsible for spontaneous and nonradiative emission from level Si.v(V') to So(v'), and the third term is responsible for the relaxation of the So.,.(v') FranckCondon level towards So(v'). The fourth and fifth terms consider spectral cross-relaxation to a higher lying and a lower lying neighboring state in the inhomogeneous distribution, respectively (frequency separation 8 v'). gi(P'-- POA)is the inhomogeneous level distribution function of the ground state, where v' is the S~-So frequency spacing of the considered subset and P0A is the S~-So center absorption frequency. The relaxation time from v' to v ' + 8 v' is set to rSo,~,, = T3.so8 v'/~,h, where Pinhis half the 1/e width of the inhomogeneous spectral distribution of the transition. ~.so is set to 7"3.t A Pinh/[ Va,P -- Ve,P(~o) ] ( see Fig. 4). Eq. (16) describes the population dynamics of the Franck-Condon state SLy(v') in the v' subband. The first term gives the laser excitation, the second term gives the fluorescence decay, and the third term gives the vibronic relaxation to the band minimum Sj (v'). Eq. (17) handles the population dynamics of the subband state S~ (v'). The first term describes the filling from the Franck-Condon state SLy(v') while the second term describes the Sl(V') level depopulation by spontaneous emission and nonradiative decay. The third term considers the stimulated emission from S l(v') to So.,,(v'). The vibronic excitation frequency

314

P. Weidner, A. Penzkofer / Chemical Physics 191 (1995) 303-319

in the So state is Vv.so. It is lYv,so+ P~.s,= rE-- V~= 28 v~ (see above). The fourth and fifth terms consider spectral cross-relaxation (dielectric relaxation) to a higher lying and a lower lying neighboring state in the inhomogeneous level distribution, respectively, gi( ly'- roE) is the inhomogeneous level distribution function of the St state, where v' is the St-So frequency spacing of the considered subset and lyoEis the St-So center frequency of stimulated emission. The relaxation time from v' to i:' + 8 v' is chosen to be "i's,.~v,=T3.st~l/'/Vinh with T3.st=T3.tAVinh/[Va, p ~c,p(oo) ]. This relaxation concept is in agreement with dielectric relaxation studies in the S, state [22,43,44,48-55] where time-resolved measurements of fluorescence spectra at room temperature indicate an initial femtosecond shift of the emission maximum which changes over to a picosecond time range in approaching the equilibrium (time resolved correlation function C¢(t) studies I22,44] ). Eq. (18) describes the population dynamics of the Franek--Condon state So.,,(v') in the So subband. The first term gives the population by stimulated emission and the second term gives the population by spontaneous emission and nonradiative decay of level St (v'). The last term considers the depopulation by vibronic relaxation to the So(v') state. The pump pulse propagation is described by Eq. (19). Excited-state absorption is included by the term f~x which is set to be f~=ln[TE(F,L, loL-¢Oo)]/ In[To(~L)]. The first term considers the So(v') ~ St,~(ly') absorption and excited-state absorption from level SLy. The second term considers the St (ly') ~ So.v(v') stimulated emission and excitedstate absorption from level St. In Eqs. ( 16b, (17) and (18) an instantaneous relaxation from higher lying singlet states populated by excited state absorption back to the first excited singlet St system is assumed. The transmission behaviour of a probe pulse continuum at frequency v and delay time to is governed by

0/Pr(P'IgZ'td) ~--'/pr(ly, td)(--

f OrA(P--V'-- Vv.S,)

X [Nso(V') -Ns,.v(v') ( 1 -fex) l d r '

+

f

O'A(ly-- lYe"1" lYv,So)

--O0

X

(24)

[Ns,(V') (1 -f~x) -Nso.v(v') ] d r ' ) .

The first term gives the So-St absorption and the St.v excited-state absorption. The second term gives the S tSo stimulated emission and the St excited-state absorption. The probe pulse transmission is given by

[pr(P, t d, l)

(25)

Tpr(v' td) = /pr( V, td, 0 ) '

where I is the sample length. The gain factor or holeburning factor is obtained from Eq. (25) by use of Eq. (7). The vibronic homogeneous absorption cross-section spectrum is described by a Lorentzian [5] trg( v - v') = trtgh( v - v')

1

(A Vh/2 )

=crt "tr ( v-- V') 2 + ( A v h / 2 ) 2'

(26)

where crLis the total frequency-integrated homogeneous absorption cross section, i.e. o't = S~-o~or^( v - v') d v'. A vh is the spectral halfwidth of the homogeneous line (FWHM). The inhomogeneous level distribution gi(/"'-- PO) due to site specific solute-solvent interaction is assumed to be Gaussian, i.e. 1 exp( gi(v'-- Vo)---- ,./l.l/2pinh

VZh

1'

(27)

where Vi,h is half the 1/e spectral width of the inhomogeneous distribution. It is related to the inhomogeneous full width at half maximum (FWHM) by A Vl.h= 2 [ In (2) ] t/2 V~nh.The distribution gi ( V' -- Vo) is normalized according to I'~_~gi( v ' - vo) d v' = 1. The total inhomogeneously broadened small-signal ground-state absorption spectrum is given by

P. Weidner, A. Penzkofer/ Chemical Physics 191 (1995) 303-319

trabs(V) = O ' t /

gh(V-- V'-- Vv.s,)gi(v'-- VOA) d r ' ,

(28) and the total inhomogeneously broadened small-signal Srstate stimulated emission cross-section is given by

(29) In our calculations we set VoA= v,.p (Fig. 4a) and Vo.E= V~.p(O) (Fig. 4a). Including multilevel transitions to higher lying vibrational levels in the S~ state (absorption) and in the So state (emission) the Eqs. (28) and (29) change to

.,.., f gh, v- v:,, -

=

/g¢

2"1016 E 1-1016

&x.~

/,/,,

Z" I:"

03

"

_o 2,10.1z / O'em(P)----'O't / g h ( V - - /"'Jr Vv'S°) g i ( / ' d - - rOE) d r ' .

315

1/

/ "

co 0

2,10-is 14000

14500

15000

15500

Wavenumber b (cm 7) Fig. 9. Experimental absorption cross-section spectrum (solid curve) and theoretical Voigt absorption cross-section profiles (Eqs. (26)(28)). The inhomogeneous linewidth is set to A ~inh = 700 cm-~. The homogeneous linewidths are A ~ = l 0 cm - ~ ( 1 ), 60 c m - t ( 2 ), and 200 cm - I (3). The structural formula of oxazine 750 is inserted.

nl

X g i ( V~, -- I-'0A) d v ' ,

(30)

and drem (V) = E nl

O't....

f

Xgi( v~,, - voF)d v',

gh( l ' - - Vm Jr 1,'v.So)

(31)

where m is the index of the vibrational levels. Here only a small frequency region around the Franck-Condon So-S~ transition is considered and Eqs. (28) and (29) are used. Numerical simulations of the transient spectral holeburning experiments are presented in the following in order to get insight into the intensity dependence and the homogeneous l inewidth dependence of the spectral probe pulse transmission (gain factor G) and on the level populations in the ground state and excited state. The applied sample parameters apply to O = 8 K. They are listed in Table ! and in the figure captions. The real absorption cross-section spectrum (Fig. 3c and solid curve in Fig. 9) is approximated by Voigt profiles according to Eqs. (26)-(28) (convolution of Lorentzian and Gaussian profiles [56] ). These absorption cross-section distributions are displayed in Fig. 9.

For the sake of saving computer time in solving the equation system ( 15)-(19), integration over the sample length and over the radial intensity distribution is avoided by setting G(v, fOE, l ) = G ( v , Im, Al)l/A1 where/.1 is approximately given by Im =f, fflOL----0"5 [ ( 1 JrTE)/2]IOL. T E is the energy transmission of the pump pulse. In Fig. 10 the dependence of the hole-burning factor G(P) on the input pump pulse peak intensity is displayed. The vibronie homogeneous linewidth is kept constant at APh = 30 cm - ~. At low pump pulse intensities a well behaved double-peaked gain factor distribution G(P) is obtained. The double peak is due to absorption bleaching at PL and light amplification by stimulated emission at VL- 2B~v = ~L -- ~v.S,,- ~v.S,• With rising pump pulse intensity the gain factor distribution G(P) becomes asymmetric and the high frequency side dominates. The gain factor shape approaches the shape of the initial inhomogeneous level distribution since finally all molecules become excited due to absorption in the homogeneous absorption distribution wings. In Fig. 11 G(P) curves at IOL=2× 108 W/em 2 (Im=7 X 107 W/era 2, TE= 0.4) are presented for various homogeneous linewidths A Ph" With rising homogeneous linewidth the initially double-peaked

P. Weidner. A. Penzkofer / Chemical Physics 191 (1995) 303-319

316

-

,

-

.

,

.

,

• v

-

il

,

•

/ "'/"'~-''~''~ .x

/

iI

(.9

/' " '" , /'./ • , /'"

I i

1.5

1.5

i

b i.'.', 5 /

I1 t'-

\

/,'"

/

,,' , "

b

~

,."

/ \

...

•

II

......

"

c-

//~'"

CO

,h' 0.5

.- .............

........

,

t

i ". ,

14200

I

i

14600

,

i

14800

V . ' - ........

-..~

-

0.5

""

.'..

..,..;.-"/.?.?

.........

14400

Wavenumber

//'" ~

(5

/~:'i:,.: .. ~: !'.!,, ',-~'---. - . . . . //../

//./:./14000

i ~ ", 4

! ~'.,.."

...."

:...;

- ~ ~ "

0

,

,

16000

14000

i

/', (cm 4)

Fig. 10. Calculated spectral hole-burning distribution G(P) (Eq. (7)) for various input pump pulse peak intensities lot.. Homogeneous linewidth A ~ = 3 0 ~.m - t . The fixed parameters are ~7oA= 15000 cm - t (Fig. 5), Pot:.= 14760 cm - t (Fig. 5). A~i., = 7 0 0 cm - t , trt=3.15 × 10 -t~ cm (Fig, 15 and Eq. ( 2 8 ) ) , f ~ = 0 . 2 2 , ~'v= 1.18 ns, %.~, = r,..so = 1 ps, P,,.so = ~.s, = B~,,=45 cm - t , T x t = l s. The curves belong to ( i ) IoL = 1.1 X i 0 {' W / cm 2 (ira = 4 × I 0 ~ W / cm 2), ( 2 ) lot. = 1.1 × 107 W / c m ~ ( ! , , = 4 × 10 {' W / c m 2 ) , ( 3 ) lot. = I.I X 10s W / c m -~ ( I , ~ = 4 X 107 W/cm'-), (4) /ot.=2.9X 10a W/cm-" (Ira= 10aW/cm-'), (5) IoL= 5.7 X 108W/cm 2 (Ira= 2X 10a W/cm-~), and (6) IoL = I.I × 10'~ W / c m -~ ( / m = 4 x 10a W/cm2). Dash-dotted vertical line indicates pump laser wavenumber position

,

14200

i

14400

,

14600

i

,

14800

:5000

Wavenumber ~', (cm1) Fig. ! I. Calculated spectral hole-burning distribution G ( ~ ) (Eq. ( 7 ) ) for various homogeneous linewidths A &. Input peak intensity iOL=2X l0 s W / c m 2 ( l m = 7 X 107 W/cm2). "['he curves belong to APh = 10 cm - t (1), 2 0 c m - t (2), 3 0 c m -t ( 3 ) , 4 0 cm - t (4), 60 em - t (5), 100 c m - ' (6), 200 em - t (7), and 300 cm - t (8). The same fixed parameters are used as in Fig. 10. Vertical line, ~..

/_.-----

10 3 104

VI..

_~ 105

symmetric G(P) distribution becomes more and more asymmetric with high frequency dominance. The broader the homogeneous distribution the easier it is to excite molecules over the whole inhomogeneous distribution. Comparison of the calculated curves in Fig. i I with the experimental curves in the Fig. 6 gives APh (8 K) = 2 2 4 - 2 cm -~, AP, (100 K) = 4 6 + 6 c m - t , and AVh (295 K) = 75 _+5 cm - '. These numbers have been obtained by fitting the experimental and theoretical curves at PL and 14540 cm - t. These results are slightly smaller than the approximate analytical nonlinear regression fits of Eq. (12). Three examples of So and St level population distributions at the sample entrance z--0, at time t ' = 35 ps and at radial position r = 0 are presented in Fig. 12 for APh = 30 cm - t. The pump pulse peak intensities are IOL= 4 X 10 s W / c m 2 (Fig. 12a), 4 X I 0 6 W / c m 2 (Fig. 12b), and I X l0 s W / c m ? (Fig, 12c). Normalized

,""i,

J

"~ lO 6

,

,f

10"3 ~

i

o Z

"

'

104

-~ 10 ~ ~ N

I"-__,

/

~ib-

....

10 6

lO.,[ 10 .4 |

10 .6 14000

(z)

i

.°..

......................... ......

" ....

.. ~ : ~ . . . _ - - - - - - - .~... " ~ // ...:;'> i -~ /

14200

14400

14600

-

14800

1

/ 15000

W a v e n u m b e r ?,' ( c m 1)

Fig. 12. Calculated population density distributions in the So state (solid curves) and the S~ state (dashed curves) at time t'= 35 ps, sample entrance z' = 0, and radial position r = 0 (ira = lot. ), A ~ = 30 cm - I, A Pi,h = 700 cm - t. Temperature O = 8 K. Dotted curves indicate the initial inhomogeneous So state level distribution gi( ~'-Po^ ) (Eq. (27)). Vertical line, f'L. (a) Pump pulse peak intensity IOL=4X 105 W / c m 2. (b) lot=4X l0 ° W / c m 2. ( c ) loL= lOs W / c m 2.

P. Weidner. A. Penzkofer/ Chemical Physics 191 (1995) 303-319

number density distributions N%(P')/No, Ns,(~')/No and the initial inhomogeneous distribution gi( P ' - POA) are displayed. No is the total number density of dye molecules. The So--' $1.,, absorption of the pump laser burns a hole into the Nso (6') population distribution at P ' = VL-- P,,.S~ ( P,,.S~= P,,.So= BY,, used in calculations). Accordingly the S~-state level population Ns~ (v') is large at PL - v,,.s, ( S m-state population antihole). The S~ ~ So.,,amplification of the pump laser burns a hole into the Ns, (v') population distribution at ~' = ~L + P,,.So-With increasing pump pulse intensity the level excitation spreads out more and more over the whole inhomogeneous distribution.

5. Discussion Our picosecond transient spectral hole-burning studies in 3.4 × l0 -4 molar oxazine 750 in silicate xerogei with a spectral resolution of approximately l c m gave a homogeneous linewidth of A~h = 22 _ 2 cm - ' at 8 K. In the case of narrow-band cw laser excitation generally narrow zero-phonon lines of spectral width A~p~ together with weak real and pseudo-phonon sidebands are observed [ 1-5 ]. As an example a zero-phonon homogeneous linewidth of A~h = 0.12 c m - ~ was observed for the symmetric molecule oxazine-4-perchlorate in amorphous silica at 5.7 K using a singlemode dye laser (3.3 × 10 -5 c m - mspectral width) and a holographic technique for burning and detecting permanent optical holes [57]. Only in cases of large equilibrium excited-state displacement qo a strong electronphonon coupling occurs [ 58] and the zero-phonon line excitation becomes weak and undetectable (small Debye-Waller factor a which is the ratio of zero-phonon absorption cross-section integral to total absorption cross-section integral). Then multiple phonon excitation in the S,-state takes place. The phonon excitation number increases approximately quadratically with the S~-state displacement [ 5,58 ]. Very broad holes of 100 to 500 cm-m have been reported fc; bacterial [59,60] and green plant [ 13] reaction centers. Spectral hole widths of about 100 c m - ' at 12 K have been observed for dimethyi-s-tetrazene (DMST) in glycerol from permanent hole-burning studies [ 61 ]. In the case of picosecond pulse excitation the spectral resolution is limited to the spectral width AP,o of the excitation pulse (0.5 to I cm -~ corresponding to 15 to

317

30 GHz for pulses of 35 ps as in our case). Additionally the high electric field strength of the applied picosecond pulses may cause a Stark broadening A Ust [9] which smears out the zero-phonon line. The peak electric field strength of the picosecond pulses is given by [ EOLI = (21oL/nCoeo)I/2, where Eois the permittivity of vacuum (lEo, I ---300 kV/cm for IOL----2X 108 W / cm2). The Stark broadening is approximately given by [5,62] A~,st= [(n2+2)/3]Ap.EoL/h, where h is the Planck constant and A/~ is the change of the dipole moment due to molecule excitation. In our experiments no zero-phonon line was resolved indicating a small Debye-Waller factor due to excitedstate displacement (~iPv = 45 cm-~). The determined homogeneous linewidth of A~h = 2 2 + 2 cm - ' at 8 K is thought to be mainly due to fast vibronic relaxation to zero-phonon equilibrium states. Franck--Condon multilevel absorption and emission (extended wave functions) might contribute to the spectral width. The broadening of the homogeneous linewidth with rising temperature may be due to increased speed of vibronic thermalization and dephasing [ 5] with ri~ing temperature.

6. Conclusions

The transient spectral hole burning in a silicate xerogel sample doped with oxazine 750 has been studied in the temperature range from 8 to 295 K. A small-band picosecond pump pulse and broad-band picosecond probe pulse measurement technique has been applied. A Stokes shift between the absorption and emission maxima of 2SPy = 9 0 c m - ~ was measured. No zerophonon line was resolved (spectral resolution limit 1 c m - ~). Vibronic homogeneo,~s linewidths of APh -- 22 cm - ~at 8 K and APh -- 75 cm - mat 295 K were found. The inhomogeneous linewidth was determined to be approximately 700 cm-~. Spectral cross-relaxation times have been estimated from temperature dependent spectral fluorescence peak shifts. An analytical method has been presented which delivers approximate vibronic homogeneous linewidths, and a numerical model has been developed which allows numerical simulations of hole-burning experiments.

318

P. Weidne r, A. Penzkofer / Chemical Physics 191 (1995) 303-319

Acknowledgement The authors thank F. Ammer, H. Gratz, and M. Kriiger for their help in preparation and analysis of the dye doped silicate xerogel samples. They thank the Deutsche Forschungsgemeinschaft for financial support and the Rechenzentrum of the University for disposal of computer time.

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