Chemical Physics 88 (1984) 309-313
North-Holland,
Amsterdam
M E A S U R E M E N T OF ABSORPTION CROSS SECTIONS
IN T H E L O N G - W A V E L E N G T H REGION OF T H E S - S , ABSORPTION BAND OF DYES
0
A . P E N Z K O F E R and P. S P E R B E R
Naturwissenschaftliche Fakult'at II - Physik, Universitat Regensburg, 8400 Regensburg, FRG
Received 20 February 1984
In the long-wavelength region of the S - S ! absorption band of dyes only a fraction of molecules takes part in the absorption
0
process. T h e absorption cross section of the molecules involved is deduced from non-linear transmission measurements with
picosecond light pulses. T h e absorption cross sections o (v )
A
L
(v
L
is the ruby-laser frequency) of l,l'-diethyl-2,4'-carbocyanine
iodide in methanol and oxazine 1 perchlorate i n ethanol are determined.
1. Introduction
technique are c o m p a r e d w i t h the results o f the
fluorescence technique.
A l l dye molecules contribute to the S - S
0
1
T h e n o n - l i n e a r transmission technique w i t h p i -
ab-
s o r p t i o n spectrum a r o u n d the a b s o r p t i o n peak a n d
cosecond pulses as it is described i n the f o l l o w i n g
at the short-wavelength side. T h e a b s o r p t i o n cross
is l i m i t e d to dyes w i t h negligible s i n g l e t - t r i p l e t
section a is easily derived f r o m transmission mea-
a b s o r p t i o n cross sections
surements w i t h a spectrophotometer ( a = a / 7 V ,
crossing rates s m a l l c o m p a r e d to the inverse p i c o -
ot = — l n ( X ) / / , where a
second
A
A
A
0
A
0
is the a b s o r p t i o n coeffi-
A
cient, N the total n u m b e r density o f dye m o l e 0
pulse
and with
intersystem-
duration. Furthermore
the dyes
s h o u l d completely dissolve to m o n o m e r s .
cules, T the s m a l l signal transmission a n d / the
0
sample length). I n the long-wavelength region o f
the S -S
0
l
absorption band only a fraction of mole-
cules takes part i n the a b s o r p t i o n process
mally
excited
molecules
2. Theory
(ther-
a n d inhomogeneously
shifted molecules) a n d the a b s o r p t i o n cross section
F i g . l a shows a singlet potential-energy
of the molecules i n v o l v e d c a n n o longer be d e -
S Q - S , a b s o r p t i o n at *> , o f peak S^-S
t e r m i n e d w i t h a spectrophotometer.
at *>
T h e a b s o r p t i o n cross section i n this long-wave-
dia-
g r a m o f a d y e molecule. T h e transitions o f peak
Am
Fm
0
emission
a n d the most p r o b a b l e transition o f laser
light at P (v < v )
l
L
are i n d i c a t e d . T h e r o v i b r a -
Fm
is the frequency o f
t i o n a l levels o f the g r o u n d state are t h e r m a l l y
peak fluorescence emission) is generally derived
p o p u l a t e d . T h e S - S frequency spacing is i n h o -
from
mogeneously b r o a d e n e d . A m u l t i t u d e o f transi-
length region
(p<P
fluorescence
F
m
',
P
F
m
measurements
[1-3]. H e r e a
0
1
n o n - l i n e a r transmission technique w i t h picosecond
tions between S
light pulses is described f o r the measurement of
possible at a f i x e d laser frequency.
the a b s o r p t i o n cross sections. T h e technique is
a p p l i e d to measure the a b s o r p t i o n cross
°A( L)
P
°f
t
w
o
section
dyes, d i c y a n i n e ( l , l ' - d i e t h y l - 2 , 4 ' -
0
and
r o v i b r a t i o n a l levels are
F i g . l b indicates the a b s o r p t i o n a n d emission
cross sections. T h e apparent a b s o r p t i o n cross sect i o n d (p) — a (p)/N
A
A
0
a n d apparent emission cross
c a r b o c y a n i n e i o d i d e , D O ' ) [4-6] i n m e t h a n o l a n d
section o (p) = OC (P)/N
oxazine 1 perchlorate [7,8] i n ethanol, at the r u b y -
e m i s s i o n coefficient) are given b y the solid curves
laser frequency *> . T h e results o f the b l e a c h i n g
[3,9]. T h e a b s o r p t i o n cross section o f really inter-
L
E
0 3 0 1 - 0 1 0 4 / 8 4 / $ 0 3 . 0 0 © Elsevier Science Publishers B . V .
( N o r t h - H o l l a n d Physics P u b l i s h i n g D i v i s i o n )
e
0
(OL is the stimulated
E
w i t h o n l y one S Q - S J transition level per molecule.
T h i s m o d e l l e d t o e n o r m o u s l y large a b s o r p t i o n
cross sections o f o (p) = a ( * > ) A * ' / W A j '
A
A^
a n d Az>
h
inh
A
H
0
where
i n h
are the homogeneous a n d i n h o m o -
geneous l i n e w i d t h s , respectively.
T h e effective stimulated emission cross section
o (P)
depends o n the radiative lifetime r
E
the
spectral
shape
r a d
JE(P)
di> = l) of the fluorescence signal [1]:
<JE(v)
=
E(
and
E{v) ( q u a n t u m d i s t r i b u t i o n
*>)/8iT'npCJ>2T
(i)
I
rad >
where c is the v a c u u m light velocity, T J
the m e a n
f
refractive i n d e x o f the s o l u t i o n i n the fluorescence
CROSS
-
SECTIONS
0
region, v = v/c = 1 / X is the w a v e n u m b e r i n c m
o
F i g . 1. (a) Potential energy diagram, (b) Apparent S -S
T h e radiative l i f e t i m e r
ab-
l
together with real absorption cross-section spectrum of interacting molecules (dashed curve).
_
the dashed curve. F o r v > p
Am
o (v)~o ( )
A
A
s
i
n
c
e
a l l molecules (thermally excited a n d i n h o m o g e neously broadened) take part i n the a b s o r p t i o n
jE(i>)v-
8TTT) FC
"
V
* j o
fE(p)v- dp
v
4
A
where T J
dp
1
3
a
T r a d
p
.
A
W * -
l
d v
(2)
9
J
is the m e a n refractive index o f the solu-
a
t i o n i n the a b s o r p t i o n region, o r b y m e a s u r i n g the
fluorescing l i f e t i m e T
f
a n d the fluorescence q u a n -
t u m efficiency q ,
F
w i t h a p p r o x i m a t e l y equal strength. F o r v < p
Am
the apparent a b s o r p t i o n cross section d (v) re-
- 1
m a y be calculated b y use
of the S t r i c k l e r - B e r g f o r m u l a [2],
sorption and stimulated emission cross sections (solid curves)
a c t i n g molecules versus wavelength is i n d i c a t e d b y
r a d
T
r a d
=
T
(3)
F / 4 F -
A
duces because o n l y a tail o f t h e r m a l l y excited a n d
The
theory
o f n o n - l i n e a r light transmission
i n h o m o g e n e o u s l y b r o a d e n e d molecules overcomes
t h r o u g h dyes i n the long-wavelength a b s o r p t i o n
the energy separation to the lowest states i n the S i
region f o l l o w s exactly the theory o f ref. [3] where
b a n d a n d c a n take part i n the a b s o r p t i o n process.
the possible S -S transitions are c o m p r i s e d i n a
I n the case o f v < p
two-level system (levels 1 a n d 2 o f f i g . l a , f o r
Fm
t h e r m a l l y excited
the transitions f r o m the
a n d i n h o m o g e n e o u s l y shifted
0
1
details see ref. [3]). O (P )
A
is o b t a i n e d b y c o m p a r -
L
m o i e t y i n the S b a n d t o the S b a n d are i d e n t i c a l
i n g experimental energy-transmission data
to the fluorescence transitions f r o m the t h e r m a l l y
calculated
relaxed S b a n d t o the S b a n d . Therefore, the
Af ).
a b s o r p t i o n cross section o f the really i n t e r a c t i n g
molecules
molecules i n the long-wavelength tail
°A( L)
0
l
1
0
(v^v )
Fm
The initial
L
V
energy-transmission
E
i s N^O, r, t — — oo, z ) =
0L
ot (p )/
f
n
with
T (I ,
c o n d i t i o n f o r the interacting
~^ (To)/lo (p )
=
curves
A
L
which
A
L
involves the
becomes equal to the apparent stimulated e m i s s i o n
parameter O (P )
cross section d (p),
t r a n s m i s s i o n depends o n the pulse parameters I
E
i.e. o (p) = d (v).
A
E
A l l ther-
A
L
t o be determined. T h e energy
0L
m a l l y relaxed molecules i n the S state have a p -
(peak intensity), s(r\ t') (temporal a n d spatial
p r o x i m a t e l y the same stimulated emission cross
pulse shape, gaussian shape used i n calculations),
1
section f o r v < p , i.e. o (v) = d (v). I n the case
A/
of v > p
°A( L)>
Fm
Fm
E
E
o n l y a high-frequency tail o f excited
molecules i n the S state c a n emit a n d the h i g h l
frequency tail o f a (v) results [d (p) < o (v)].
E
E
E
I n early studies [10] the SQ-S-^ a b s o r p t i o n b a n d
was considered t o consist o f a n inhomogeneous
distribution
o f homogeneously b r o a d e n e d
lines
L
V
(pulse d u r a t i o n ) a n d o n the dye parameters
T
F (fluorescence
cross-relaxation time), a
cross section), T
c x
e x
lifetime),
T
3
(spectral
(excited-state a b s o r p t i o n
(relaxation time o f levels p o p u -
lated b y excited-state absorption) a n d r
or
(reorien-
t a t i o n time o f t r a n s i t i o n d i p o l e moments).
T h e pulse parameters are measured i n the ex-
periments. T h e dye parameters o (v ) a n d o (v )
are determined f r o m the energy-transmission measurements. a ( ^ ) is obtained b y fitting the c a l c u lated energy-transmission curves at high i n p u t i n tensities to the energy-transmission data. It is given
by
A
ex
° A L)
C
ex
L
L
Kln[r (/ -»
= -
V
L
E
0 L
oo)]a (*> )/a (*> ),
A
L
A
L
w i t h K close to o n e [3], It s h o u l d be s m a l l c o m p a r e d to a A 0 L ). F o r o (v ) comparable to o (v )
the described p i c o s e c o n d bleaching technique c a n not be used. T h e Sj-state lifetime r has to be
measured separately, for example b y streak camera
measurements of the fluorescence decay after p i c o second pulse excitation o r b y absorption-recovery
analysis w i t h picosecond p u m p a n d probe techniques (methods reviewed i n refs. [9,11,12]). T h e
spectral cross-relaxation time T describes r e f i l l i n g
of depopulated levels i n the S b a n d b y thermalisat i o n a n d r e d i s t r i b u t i o n w i t h i n the inhomogeneous
p r o f i l e [3]. F o r T ^> A / n o r e f i l l i n g o f states i n
the interaction region o f the S b a n d occurs. C o m plete bleaching is observed w h e n half o f the i n i tially present molecules is transferred to the
state. T h e level p o p u l a t i o n s at complete b l e a c h i n g
are N = N = \N (t' = - oo). I n the case o f T < § c
A / the i n v o l v e d states i n the S - b a n d are refilled
f r o m the S reservoir a n d complete b l e a c h i n g is
observed for the level p o p u l a t i o n s
= N « N^/'
= — oo). A pulse energy o f a factor o f two higher
is necessary f o r I < A / c o m p a r e d to T » A /
i n order t o achieve the same b l e a c h i n g effect. I n
our calculations w e assumed 7 < A / . T h e rep o r t e d a values w o u l d be a factor o f two smaller
for T » A r . T h e S„ state p o p u l a t e d b y excitedstate a b s o r p t i o n is assumed to relax to the S state
w i t h a decay time T w h i c h is generally i n the
subpicosecond region [13-15]. r = 1 0 ~ s is used
i n the calculations. I n some dye molecules S -state
lifetimes i n the picosecond [16-22] a n d s u b nanosecond-to-nanosecond region [23,24] have
been f o u n d . T h e slight influence o f T o n o
d e t e r m i n a t i o n is discussed below.
ex
L
A
L
F
3
been measured. F o r the fluorescence technique
[eqs. ( l ) - ( 3 ) ] the S Q - S , a b s o r p t i o n spectra were
measured w i t h a c o n v e n t i o n a l spectrophotometer
[a (P)] a n d the fluorescence spectral shapes E(v)
were o b t a i n e d b y H e - N e - l a s e r excitation a n d f l u o rescence detection at right angles to the excitation
b e a m w i t h a spectrometer a n d a n o p t i c a l m u l t i c h a n n e l analyser.
A
T h e b l e a c h i n g technique was p e r f o r m e d w i t h
single picosecond pulses f r o m a m o d e - l o c k e d r u b y
laser. T h e energy transmission through the dyes
was measured w i t h photodetectors. T h e i n p u t - p u l s e
peak intensity w a s determined b y t w o - p h o t o n
transmission measurements through a C d S crystal
[25] (the error i n the single-shot peak-intensity
detection is « + 10%). T h e ruby-laser pulse d u r a t i o n was determined b y t w o - p h o t o n fluorescence
detection [26].
0
3
L
4. Results
0
x
2
A
3
L
0
0
2
3
L
3
3
T h e S Q - S J a b s o r p t i o n spectra o (v) a n d the
fluorescence spectra o (v) o f solutions o f d i c y a n i n e i n m e t h a n o l a n d oxazine 1 i n ethanol are
s h o w n i n figs. 2 a n d 3, respectively. T h e absorpt i o n cross sections at the ruby-laser frequency are
O (P ) = O (P ) = (3.1 ± 0 . 3 ) X 1 0 ~
c m for dic y a n i n e a n d (2.5 ± 0.3) X 1 0 ~
c m f o r oxazine 1.
T h e energy-transmission d a t a are depicted i n
A
E
A
L
E
1 6
l
1 6
L
L
L
3
2
2
WAVELENGTH
800
L
1
I
1
700
1
1
1
I
'
X
[nm ]
600
'
—
' "—I
1
500
'
'
1
T~
l
c x
ex
1 3
2
c x
A
3. Experiments
FREQUENCY
T h e a b s o r p t i o n cross sections of the dyes d i c y a n i n e i n m e t h a n o l a n d oxazine 1 i n ethanol have
v
[cm1]
F i g . 2. Absorption and fluorescence spectrum of dicyanine
( D O ' ) in methanol.
WAVELENGTH
X
(nml
values to the experimental points, a (dicyanine) =
(3 ± 0 . 4 ) X 1 0 "
c m a n d a ( o x a z i n e 1) = ( 2 . 2 ±
0.4)X10~
c m , are i n c l u d e d i n table 1. E a c h
d a t a p o i n t represents a n average over about ten
shots. T h e error bars indicate the standard deviat i o n . T h e influence of the S^-S, decay time T o n
the measurement of the long-wavelength absorpt i o n cross section was analysed for the dyes studied.
T h e influence is f o u n d to be s m a l l . F o r example, if
r = 10 ps is assumed instead of T = 0.1 ps the
best-fitting a a n d a values change b y less than
10% to a ( d i c y a n i n e ) = 3.0 X 1 0 "
cm , a (dicyanine) = 9.1 X 1 0 ~
c m , a ( o x a z i n e 1) = 2.4 X
10"
c m a n d a ( o x a z i n e 1) = 2 . 2 X 1 0 ~
cm .
T h e o (v ) data determined b y fluorescence techniques [a (j> )] a n d b y the b l e a c h i n g technique
agree quite well.
A
1 6
1 6
2
A
2
c x
ex
CX
A
ex
1 6
A
I
12000
tU
1
i
i
16000
14000
i
i
18000
FREQUENCY
F i g . 3. Absorption and
i
v
i
20000
1 7
.
22000
1 6
I cm"']
fluorescence
spectrum of oxazine 1
perchlorate in ethanol.
A
ex
i i i 1111
1—i
A
i
1—i
i i 111|
i
i i
111
2
ex
A
1 7
ex
2
L
E
figs. 4a a n d 4b. T h e curves are calculated w i t h the
dye a n d pulse parameters listed i n table 1. a a n d
a are v a r i e d for the different curves. T h e best-fit
0.81
2
2
L
I n the case of d i c y a n i n e r
A / a n d the energy transmission is strongly intensity dependent
[9,27]. F o r oxazine 1 we have T » A / so that the
energy transmission is determined b y the pulse
energy [9,28]. I n b o t h cases the measurement of
r E (/ 0 L , A / ) allows the d e t e r m i n a t i o n of the
long-wavelength a b s o r p t i o n cross section a .
F
L
f
L
L
A
Table 1
Parameters used and results
Parameter
Dicyanine
Oxazine 1
9.5
1
0.1
140
4600
1020
1
0.1
200
5200
time constants (ps)
a)
c)
T
T'ex
C)
e)
d )
or
T
cross sections
(cm )
2
1.4X10"
PEAK
INTENSITY
I
2
F i g . 4. Energy transmission of mode-locked ruby-laser pulses
versus input peak intensity, (a) Oxazine 1 in ethanol. Curves
are calculated for a
= 2 X10"
1 6
= 0.106
ex
cm ; 3 : a
2
5: CT = 8 X 1 0
a
- 1 6
A
a .
A
= 3 X10"
1: a
1 6
A
(8.6±1)X10
°cx("L)°
[W/cm l
X
= 1 X10"
c m ; 4: a
2
A
1 6
c m ; 2:
2
= 4X10"
1 6
a
A
cm ;
2
c m , (b) Dicyanine in methanol. Curves for
2
- 1 6
(3.0 + 0.4) X 1 0 "
°A("L)°
3.8X10
(2.5±0.3)X10
(2.2 + 0.4) X 10~
-18
1 7
(3.1±0.3)X10
INPUT
b )
1 6
- 1 6
(2.3 ± 0.4) X 1 0 "
- 1 7
16
1 7
laser data
* (cm
L
_ 1
)
L
Ref. [6].
14403
gaussian
30
d/ (ps)
a )
14403
gaussian
b )
Ref. [8].
25
c )
Assumed.
d )
Ref.
[29].
a = 0.288 a . l : o = l x K T
cm ; 2:a = 2 x l O "
cm ;
3: a = 3 x l O ~ c m ; 4: a = 4x 10~
c m ; 5: o = 8 x K T
e) Estimated from the D e b y e - S t o k e s - E i n s t e i n hydrodynamic
cm .
0
ex
A
A
2
1 6
A
1 6
2
A
2
16
1 6
A
2
A
2
1 6
model
[30].
This work.
5. Conclusions
[8] G . S . Beddard, T . Doust and G . Porter, C h e m . Phys. 61
A picosecond pulse bleaching technique has
been described f o r the measurement o f the absorpt i o n cross section o f molecules absorbing at the
long-wavelength side o f the S -S^ absorption b a n d .
T h e technique is applicable i f the excited-state
a b s o r p t i o n a is smaller than the a b s o r p t i o n cross
section a a n d the S -state lifetime is k n o w n f r o m
other measurements. T h e excited-state a b s o r p t i o n
cross section a n d the ground-state a b s o r p t i o n cross
section are determined. T h e m e t h o d is applicable
independent of the d u r a t i o n o f the S s t a t e lifetime
c o m p a r e d to the p i c o s e c o n d p u m p pulse d u r a t i o n .
[9] A . Penzkofer and W . Blau, O p t . Quantum Electron. 15
(1981) 17.
0
e x
A
1
r
(1983) 325.
[10] M . Hercher, A p p l . Opt. 6 (1967) 947.
[11] S . L . Shapiro, ed., i n : Topics of applied physics, V o l . 18.
Ultrashort light pulses (Springer, Berlin, 1977).
[12] A . G . Doukas, J. Buchert and R . R . A l f a n o , i n : Biological
events probed b y ultrafast laser spectroscopy, ed. R . R .
A l f a n o (Academic Press, N e w Y o r k , 1982) p . 387.
[13] W . Falkenstein, A . Penzkofer and W . Kaiser, O p t . C o m mun. 27 (1978) 151.
[14] C . V . Shank, E . P . Ippen and O . Teschke, C h e m . Phys.
Letters 45 (1977) 291.
[15] M . Kasha, Discussions Faraday Soc. 9 (1950) 14.
[16] H . Tashiro and T . Yajima, C h e m . Phys. Letters 42 (1976)
553.
[17] H . Schuller and H . Puell, O p t . C o m m u n . 3 (1971) 352.
[18] C . L i n and A . Dienes, Opt. C o m m u n . 9 (1973) 21.
Acknowledgement
[19] J . R . H u b e r and M . Mahaney, C h e m . Phys. Letters 30
(1975) 410.
T h e authors thank D r . W . B l a u a n d M r . W .
D a n k e s r e i t e r f o r p r e l i m i n a r i l y measurements a n d
the R e c h e n z e n t r u m o f the U n i v e r s i t y for disposal
o f c o m p u t e r time. T h e y acknowledge f i n a n c i a l
support b y the D e u t s c h e Forschungsgemeinschaft.
[20] R . W . Anderson, R . M . Hochstrasser and H . J . Pownall,
C h e m . Phys. Letters 43 (1976) 224.
[21] T . Kobayashi a n d S. Nagakura, C h e m . Phys. 23 (1977)
153.
[22] K . Kasatani, M . Kawasaki and H . Sato, C h e m . Phys. 83
(1984) 461.
[23] M . Maciejewski a n d P.P. Steer, C h e m . Phys. Letters 100
(1983) 540.
[24] M . Beer and H . C . Longuet-Higgins, J. C h e m . Phys. 32
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