Nonlinear absorption of light: Two-photon absorption and optical saturation in metalloporphyrin-doped boric acid glass

Article abstract of DOI:10.1016/S0301-0104(02)00958-8

The nonlinear absorption of five metal TMPPs (TMPP: tetrakis-(3,4,5-trimethoxyphenyl)porphyrin) doped in boric acid glass are measured with the linear polarized nanosecond laser pulses at different wavelengths by Z-scan; the two-photon absorption (TPA) is dominant in the near infrared, while the characteristic of saturation absorption (SA) is observed close to the Q(0,0) band of porphyrin. The symmetry allowed two-photon π* ← π transitions are suggested to be ¹B*_1g ← S₀ and ¹B*_2g ← S₀, with the cross-sections δ ranging from 25 x 10^-50 to 114 x 10^-50 cm⁴ s/photon. We analyze the property of SA with a four-level system, and find that the magnitudes of excited-state absorptivity and saturation intensity are not affected by changing the central metal ion in these experiments.

Full text of DOI:10.1016/S0301-0104(02)00958-8

Chemical Physics 286 (2003) 293–302
www.elsevier.com/locate/chemphys
Nonlinear absorption of light: two-photon absorption
and optical saturation in metalloporphyrin-doped
boric acid glass
T.C. Wen*, L.C. Hwang, W.Y. Lin, C.H. Chen, C.H. Wu
Department of Chemistry, Kaohsiung Medical University, P.O. Box 72-94, Kaohsiung, Taiwan, ROC
Received 4 June 2002
Abstract
The nonlinear absorption of five metal TMPPs (TMPP: tetrakis-(3,4,5-trimethoxyphenyl)porphyrin) doped in boric
acid glass are measured with the linear polarized nanosecond laser pulses at different wavelengths by Z-scan; the two-
photon absorption (TPA) is dominant in the near infrared, while the characteristic of saturation absorption (SA) is
observed close to the Q(0,0) band of porphyrin. The symmetry allowed two-photon pꢀ p transitions are suggested
ꢀ
ꢀ
1
1
to be B1g S0 and B2g S0, with the cross-sections d ranging from 25 Â 10À50 to 114 Â 10À50 cm4 s=photon. We
analyze the property of SA with a four-level system, and find that the magnitudes of excited-state absorptivity and
saturation intensity are not affected by changing the central metal ion in these experiments.
Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction
Meanwhile, the nonlinear transmission of metal
free porphyrin (H2TPP) derivatives are studied at
different wavelengths; for example, in a solid ma-
trix environment (doped in boric acid glass), they
display saturation absorption at the argon-ion la-
ser wavelengths of 458 and 476.5 nm [9], whereas
in toluene solutions, no transmittance variations
are observed using 784 nm (60 fs) pulses from a
self-mode-locked Ti:sapphire laser [10]. The pres-
ent paper is devoted to the investigation of non-
linear absorption of metal TMPP (TMPP:
For the porphyrin derivatives such as tetra-
benzoporphyrin (TBP) and tetraphenylporphyrin
(TPP), large third-order nonlinear susceptibility
vð3Þ and cross-sections of the excited-state ab-
sorption (RSA) have been recognized with both
nanosecond and picosecond laser pulses at 532 nm
[1–4]. More recently, the RSA in TPP complexes
including a variety of central metal ions (e.g.
Cd(II), Sn(II), Pb(II) and PðVÞCl2) are measured
with the Z-scan technique at 532 nm; enhancement
of RSA by the heavy-atom effect is revealed [5–8].
tetrakis-(3,4,5-trimethoxyphenyl)porphyrin)
in-
cluding chlorogallium(III), chloroindium(III),
chlorothallium(III), tin(II) and lead(III) as central
metal ions. These materials are doped in a solid
matrix (boric acid) and measured with nanosecond
laser pulses from 650 to 1350 nm (see Fig. 1).
* Corresponding author. Tel.: +886-7-312-1101; fax: +7-312-
5339.
E-mail address: tschwe@cc.kmu.edu.tw (T.C. Wen).
0301-0104/03/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved.
PII: S0301-0104(02)00958-8

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T.C. Wen et al. / Chemical Physics 286 (2003) 293–302
range ꢁ50–100 lm as measured with a microme-
ter, and the concentration of the porphyrin mole-
cules is ꢁ 10À2 M (i.e. ꢁ8:0 Â 1018 number of
molecules=cm3).
The UV-Vis absorption spectra are measured
with a Shimadsu UV-160A spectrophotometer,
while the oscillator strength f is evaluated from the
data by the formula f ¼ 4:33 Â 10À9eDt, where e is
the maximum molar extinction coefficient in
ðcm mol=LÞÀ1 and Dt is the band width at half-
maximum in cmÀ1
.
The nonlinear optical responses are performed
from 650 to 1350 nm. These laser pulses are
generated by an optical parametric oscillator
(OPO) (Continuum Surelite) pumped by the third
harmonic of a Nd:YAG laser. The beam from
the OPO laser (with 5 ns pulse width) is ex-
panded to 20 mm in diameter and subsequently
passed through a 3.0 mm-diam aperture, which
gives the beam a nearly flat top intensity profile
[15,16]. To turn the linear-polarized light from
OPO (which is horizontally polarized) into cir-
cularly polarized light, a k=4 zero-order wave-
plate (from CVI Laser Corporation) is inserted
between the source and the Glan-laser calcite
polarizer ranging from 1000 to 1550 (from New-
port) which is also horizontally polarized as the
input light. The waveplate is rotated around
the beam axis to find the orientation that retains
the extinction, then rotate this plate 45° from
this position to obtain half the input light pass-
ing through the Glan-laser polarizer. The quality
of the circularly polarized light is also adjusted
by tilting the waveplate about its fast (or slow)
axis.
For an open aperture Z-scan, a focal lens
(76 mm in diameter) is mounted 15 cm just behind
the focal point of the incident laser pulses
(x0 ꢂ 20 lm) which is focused with a lens of 10 cm
focal length. The incident and transmitted energies
are detected simultaneously by two energy probes
Rjp-735 (pyroelectric based) and Rjp-765 (silicon
based), then averaged with RJ-7620 (Laser Preci-
sion) energy meter individually. Each data point is
an average of over 50 shots with 0.5 Hz repetition
rate. The experimental errors are estimated to be
Æ15% from the variations of laser energies and
sample concentrations.
Fig. 1. Molecular structures of metal TMPPs.
2. Experimental
The free base H2TMPP is prepared from pyr-
role and 3,4,5-trimethoxybenzadehyde by the
method of Chan et al. [11] Chromatographic pu-
rification is repeated on silica gel columns and the
final products are identified by NMR and ele-
mental analysis. The metal TMPP is prepared by
refluxing H2TMPP and one of the metal halides
(e.g. GaCl3 and InCl3) or metal acetate (e.g.
ðCH3CO2Þ Pb Á 3H2O) in benzonitrile or dimeth-
2
ylformamide [12], and the crystallized products are
identified by NMR and UV-Vis spectroscopy. The
preparation of metal TMPP-doped boric acid glass
that we adopted is different from that used previ-
ously [13,14]. Appropriate quantities of porphyrin
and boric acid are measured and mixed thoroughly
and a suitable amount of this mixture is spread
uniformly over the microscopic glass slide. An-
other microscope slide is used to make a sandwich
of the sample. This sample is then heated in a high
temperature oven at 190 Æ 2 °C for an hour. After
that, the temperature is raised to 200 Æ 2 °C and
the sample is heated for one more hour. The
samples obtained are of good linear transmittance
(ꢁ70–90%), and most of the porphyrin molecules
are not decomposed according to their UV-Vis
absorption spectra. Sample thickness is in the

T.C. Wen et al. / Chemical Physics 286 (2003) 293–302
295
3. Results and discussion
order, Table 1. Similar results are observed for
metal TMPP-doped in boric acid except
TlClTMPP and PbTMPP: their Q(0,0) and Q(1,0)
bands (usually appear in liquid solution) are re-
placed with much broader bands peaked at 692 and
715 nm, respectively. This property could be in-
duced by the acidic environment of the boric acid
[18]. For example, protonation by trifluoroacetic
acid of a free-based TPP in CH2Cl2 gives rise to
new types of spectra: the spectrum of the centrally
protonated porphyrin shows a broad and flat ab-
sorption in the visible (with kmax ꢂ 654 nm) for its
Q-bands [19]. This behavior is interpreted as a
‘‘hyperporphyrin spectra’’ in terms of charge-
transfer excited states which involve charge move-
ment either into or out of the porphyrin ring [19].
The absorption spectra of all metal TMPPs
doped in boric acid are shown in Fig. 2(a), and the
absorption spectra of these compounds in CH2Cl2
solutions are also plotted in Fig. 2(b) for compar-
ison. Due to the interaction between the pp (or dp)
metal orbital and the ring a2u (or eg) orbital, the
intensity of the Q(0,0) absorption band is sensitive
to variations of the coordinated central metal ion
and ligand [17]. For the metal TMPP in solution,
its oscillator strength of Q(0,0) band is enhanced by
the metal ion following the order of GaClðIIIÞ <
InClðIIIÞ < TlClðIIIÞ; SnðIIÞ < PbðIIÞ, while the
kmax of Q(0,0) band shifts to the red with the same
3.1. The nonlinear absorptions dominated by the
TPA
(a)
The open aperture Z-scan traces of the sample
at four different wavelengths are recorded. The
excitation energy is approximately 10 lJ (ꢁ13:2 Â
107 W=cm2 at the focus). As displayed in Fig. 3, all
the transmission curves are symmetric with respect
to the focus (z ¼ 0), where they exhibit a nonlinear
absorption that we suggested to be caused by the
TPA.
The molecular orbital ordering and the one-
and two-photon properties of porphyrins have
been investigated theoretically [17,20–22]. A semi-
empirical SCF-MO calculation indicates that, for a
free base porphyrin dianion molecule belonging to
(b)
the D4h point group, its lowest-lꢀying two-photon
ꢀ
1
1
allowed states belong to the B1g and B2g irre-
ducible representations [20]. The calculated pꢀ p
transition energy, DE (eV), is 3.17 eV (1B1ꢀg S0)
and 3.52 eV (1B2ꢀg S0), which are lying in the
Soret (B-band) region. However, these states are
highlyꢀsensitive to environment; [20] for example,
1
the B1g state of a D2h free base porphyrin moves
from 3.134 to 2.53 eV as the external electric field
intensities increase from 1 Â 106 to 5 Â 107 V=cm.
As emphasized in [20], such field intensities are
experienced by porphyrins embedded in proteins,
as typical polar group-to-chromophore distances
Fig. 2. The ground state absorption bands B(0,0), Q(1,0) and
Q(0,0) of metal TMPP (a) doped in boric acid, and (b) in
CH2Cl2 solutions. kmax of Q(0,0) band is indicated in each of
them.
ꢀ
of <5 A can generate field intensities greater than
5 Â 107 V=cm. Besides, the focused laser radiation

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T.C. Wen et al. / Chemical Physics 286 (2003) 293–302
used in two-photon studies will typically produce
transient electric fields in the range 104–105 V=cm
and field intensities from 106 to >107 V=cm are
possible [21]. On the other hand, the all valence
electron SCF-MO calculations indicate that,
among those porphyrins and metal porphyrins
that possess D4h, D2h or C4v symmetry point
groups, the energies of their highest filled a1uðpÞ
and a2uðpÞ states are almost the same [22].
The TPA in metal TMPPs, therefore, is sug-
1
gested tentatively to initiate from the S0 (i.e. A1g)
state, and attend one of the final states following
ꢀ
1
the processes of B1g S0 (for 840 and 900 nm
ꢀ
1
laser light) and B2g S0 (for 1200 and 1350 nm
light), as illustrated in Fig. 4(a).
During the TPA, the rate equation of light
propagation in the sample is
dI
dz
¼ Àða0 þ bIÞI;
ð1Þ
where a0 is the linear absorption coefficient
(a0 ¼ ðlnð1=TÞÞ=L), and b is the two-photon ab-
sorption coefficient. The values of a0 and b can be
assumed as constants at certain light intensities,
thus Eq. (1) is integrated to give
Z
Z
Iout
Iout
1
1
dI À
dI ¼ Àa0L;
ð2Þ
I
I þ ða=bÞ
Iin
Iin
where Iin and Iout are the input and output inten-
sities, respectively. The solution gives
Ioutðz; r; tÞ ¼ Iinðz; r; tÞeÀa L
0
ꢁꢀ
ꢂ
Iinðz; r; tÞbð1 À ea L
Þ
0
1 þ
:
ð3Þ
a0
The normalized transmittance for the open aper-
ture Z-scan is then obtained by integrating of Eq.
(3) over the spatial extent of the laser beam [23]
q0
pffiffiffi
T ðzÞ ¼ 1 À
for jq0j < 1;
ð4Þ
2 2
where
1
q0ðz; tÞ ¼ bI0Leff
;
ð5Þ
1 þ z2=z20
I0 is the on-axis instantaneous intensity at focus
(z ¼ 0) and Leff is the effective sample thickness
given by Leff ¼ ð1 À exp½Àa0LŠÞ=a0.

T.C. Wen et al. / Chemical Physics 286 (2003) 293–302
297
(a)
(b)
Fig. 3. Normalized transmittances from boric acid glasses doping with (a) InClTMPP and (b) PbTMPP. The curves are moved from
their original positions for the clear vision. The solid curves are the fit with Eq. (4).
sured d are ranging from 25 Â 10À50 to 54 Â 10À50
The TPA coefficient b (in units of cm/GW) is
ꢀ
1
cm4 s= photon (for the process of B1g S0), and
therefore deduced from the best fitting of our Z-
scan data with Eqs. (4) and (5), and the TPA cross-
section d (in units of cm4 s=photon) is evaluated by
using the following relationship:
from 31 Â 10À50 to 114 Â 10À50 cm4 s=photon (for
ꢀ
1
the process of B2g S0). As we mentioned be-
fore, the near infrared light from our OPO laser is
linear polarized with horizontal polarization (i.e.
the transmission axis is parallel to the surface of
our laser table). Under the same arrangements,
they predict that d in a free base porphyrin diaꢀnion
hvb
NAd0 Á 10À3
d ¼
;
ð6Þ
where hv is the energy of an incident photon, d0 is
the concentration of the dopant compound in
boric acid (in units of M/L), and finally NA the
Avogadro number. As listed in Table 2, the mea-
are around 20:8 Â 10À50 cm4 s=photon (for 1B1g
ꢀ
S0) and 1:7 Â 10À50 cm4 s=photon (for B2g S0)
1
[20].

298
T.C. Wen et al. / Chemical Physics 286 (2003) 293–302
Fig. 4. Schematic representation of (a) the theoretical calculated two-photon states of a D4h free base porphyrin dianion [20].
Transitions proceeded by the laser beams of k1(1350 nm), k2(1200 nm), k3(900 nm) and k4(840 nm) are also illustrated. In (b), the
observed B(0,0)- and Q(0,0)-band energies of porphyrin derivatives are plotted according to 1. GaClTMPP, 2. InClTMPP, 3.
SnTMPP, 4. TlClTMPP and 5. PbTMPP.
firm these two-photon excited states, we are ar-
ranged to determine this polarization ratio at some
specific wavelengths (e.g. 840 and 1200 nm) in the
near future.
The behavior of TPA in the near infrared (1350
nm) is also observed from the incident intensity-
dependent experiments (see Fig. 6); we measure the
transmitted intensity I passing through a sample
by various input intensities I0, and fit the data with
a formula
In addition, the characteristics of two-photon
excited states can be verified from the polariza-
tion ratio X ¼ hdcirci=hdlini, where hdcirci and hdlini
are the two photon absorptivities under circular
ꢀ
1
and linear polarization, respectively. For B1g
ꢀ
1
and B2g (D4h) states, in the absence of vibronic
coupling
3ðSabSaꢀb þ SabSbꢀaÞ
3
X ¼
¼
;
ð7Þ
2ðSabSaꢀb þ SabSbꢀaÞ
2
where (SabSaꢀb) is a product of two second-rank
tensors which are functions of the internal molec-
ular Cartesian coordinates a and b and the photon
and state energies [20]. Using the Z-scan method,
we measure the absorptivities of InClTMPP and
GaClTMPP (doped in boric acid) with both cir-
cular and linear polarized light at 1320 nm. The
I0
I ¼
;
ð8Þ
ð1 þ I0bLÞ
where L is the thickness of the sample. Eq. (8) is
derived from the rate equation of light propaga-
tion (that is Eq. (1)) with the assumptions that
a0 ꢂ 0 (transparent sample) and the beam has a
nearly uniform transverse intensity distribution
within the sample [24]. As listed in Table 2, b ob-
tained here is in good agreement with its Z-scan
result.
results give X ¼ 1:40 ðX ¼ dcirc=dlin ¼ bcirc= blin
¼
ð0:21 cm=GWÞ=ð0:15 cm=GWÞÞ for InClTMPP
(see Fig. 5) and X ¼ 1:43 ðX ¼ ð0:20 cm=
GWÞ=ð0:14 cm=GWÞÞ for GaClTMPP. To con-

T.C. Wen et al. / Chemical Physics 286 (2003) 293–302
299
Table 2
Two-photon absorption coefficient b and cross-section d in metal TMPP doped in boric acid glass
Compound
Excitation wavelength TPA coefficient b
TPA cross-section
d ðÂ10À50 ðcm4 s=photonÞÞ
31
Imaginary part of third-order
vð3ÞImvð3Þ ðÂ10À12 esuÞ
0.67
0.85
2.37
1.39
(nm)
(cm/GW)
GaClTMPP
840
900
0.11
0.13
36
54
1200
1350
0.27
0.14 (0.12)
25 (22)
InClTMPP
TlClTMPP
SnTMPP
840
900
0.38
0.22
114
65
2.38
1.45
1.92
1.91
1200
1350
0.22
0.19 (0.22)
47
36 (39)
840
900
0.19
0.21
52
57
1.17
1.42
1.15
1.81
1200
1350
0.13
0.18 (0.21)
26
32 (36)
840
900
0.22
0.11
64
31
1.35
0.63
3.43
1.80
1200
1350
0.38
0.18 (0.22)
77
32 (39)
PbTMPP
840
900
0.19
0.16
56
43
1.19
1.12
2.98
1.70
1200
1350
0.34
0.18 (0.21)
67
32 (36)
Data in parenthesis are determined by the intensity-dependent transmittance method. All the excitation pulses are linear polarized
with horizontal polarization.
n20ꢀ0kC
2p
In cgs units, the imaginary part of the third-
order nonlinear susceptibility vð3Þ is related to the
TPA coefficient b through
Imvð3Þ
¼
b;
ð9Þ
where n0 is the linear index of refraction (n0 ¼ 1:37
for boric acid glass), ꢀ0 is the permittivity of
Fig. 5. Normalized transmittances from InClTMPP doped in
boric acid (ꢁ0.01 M). The input intensity is around 6 lJ at 1320
nm. Curve (1) is irradiated with circularly polarized pulses and
curve (2) is irradiated with linear polarized pulses, while curve
(2) is moved downward from original position for the clear
vision. Both solid curves are the fit with Eq. (4).
Fig. 6. Measured transmitted intensity as a function of the in-
cident intensity (at 1350 nm) for InClTMPP (open cycle) and
PbTMPP (open diamond). The solid curves are fitted with Eq. (7).

300
T.C. Wen et al. / Chemical Physics 286 (2003) 293–302
vacuum (ꢀ0 ¼ ð1=4pÞ esu2=erg=cm), k is the wave-
length of incident light and C is the speed of light
in vacuum. Thus Imvð3Þ / 0:63 Â 10À12–3:43 Â
10À12 esu from the calculations.
absorption. The change in intensity of the light as
it passing through this model is therefore governed
by dI=dz ¼ ÀaðIÞI, where aðIÞ ¼ a0 þ b0; a0 is the
linear and b0 is the nonlinear absorption coeffi-
cients arising from the transitions of 1 ! 3 and
2 ! 4, respectively. Furthermore, the value of b0 is
proportional to the number of molecules, NðtÞ, in
T1 state: b0 ¼ r24NðtÞ. Thus the equations gov-
erning the absorption can be expressed as:
3.2. The nonlinear absorptions dominated by the SA
When an organic dye (e.g. fluorescein-doped
boric acid glass) is irradiated by a strong laser
pulse, the large S0 ! S1 absorptivity (ꢂ10À16 cm2)
always leads to a substantial transient population
in the S1 state; meanwhile, the population builds
up in the lowest excited triplet state (T1) via in-
tersystem crossing. In addition, because many of
the quenching mechanisms that are present in li-
quid do not exist in a solid matrix, the lifetime of
T1 state is very long in a solid environment; for
examples, in fluorescein-doped boric acid glass, the
decay of its triplet state population is P100 ms,
[13] while the measured triplet lifetimes in por-
phyrin-doped boric acid glass is about 200 ls [9].
Thus, a four-level system (in Fig. 7) seems ade-
quate to describe the saturation absorption in solid
porphyrin samples [13,25]. For the sake of sim-
plicity, we assume that (1) the 3 ! 2 and 4 ! 2
transitions are fast (compared with the excitation
pulse duration), and (2) all of the initially excited
molecules (1 ! 3) are trapped in level 2 (T1),
which is the only state leading to excited-state
dI
dz
¼ Àða0 þ r24NðtÞÞI;
ð10Þ
dNðtÞ a0I
¼
;
ð11Þ
dt
ꢁhx
where ꢁhx is the energy of the laser pulse. Eqs. (8)
and (9) can be combined to yield
Z
t
dI
dz
r24a0I
ꢁhx
¼ Àa0I À
Iðt0Þdt0:
ð12Þ
À1
This equation is solved for the fluence and inte-
grated over the spatial extent of the laser beam to
yield the normalized transmission T, given by [2]
ꢃ
ꢄꢁ
q0
1 þ x2
q0
1 þ x2
r24a0F0Leff
2ꢁhx
T ¼ ln 1 þ
;
q0 ¼
;
ð13Þ
where x ¼ z=z0, z is the position of the sample and
z0 is the Rayleigh range of the lens and F0 is the
fluence (J=cm2) of the laser at focus (z ¼ 0).
Thus the behavior of saturation absorption can
be simulated with Eq. (13): let r13 ¼ 2Â 10À18 cm2,
F0 ¼ 1:733 J=cm2 (corresponding to E ¼ 17 lJ)
and ꢁhx ¼ 3:06 Â 10À19 J (at 650 nm) in this
equation. With the cross-section r24 decreases
from 3 Â 10À19 to 1 Â 10À19 cm2, we obtain a
normalized transmittance that increases from
ꢁ1.15 to ꢁ1.50 as a result. On the other hand,
when the size of r24 is larger than that of the
ground state r13, the characteristic of reverse sat-
urable absorption (RSA) is presented as plotted in
Fig. 7.
The normalized transmittances from metal
TMPPs at 650 nm are shown in Fig. 8, where each
of them has a maximum transmittance at the focal
point. The solid curves through the experimental
data represent the theoretical fits with Eq. (13); we
obtain r24 ranging from 3.36 to 3.91Â10À19 cm2.
Fig. 7. A four-level system (inset picture) together with the
change of transmitted light vs. different excited-state absorption
cross-sections as described in Section 3.2.

T.C. Wen et al. / Chemical Physics 286 (2003) 293–302
301
sample concentration. The results are listed in
Table 3.
For the porphyrin derivatives dissolved in
solution or doped in a solid matrix, the saturable
absorption has been determined at wavelengths
close to the kmax of B(0,0) band, and character-
ized by the smaller excited-state absorption
cross-section than that of the ground state [5,9].
Here we observe saturation absorption at 650
nm, which is close to the kmax of the Q(0,0)
bands (see Fig. 4(b)). The result also displays
that the ratio of r24=r13 is less than one; this
ratio is about 0.18 in average of five compounds
in Table 3.
The saturation intensity can be estimated from
Is ¼ ðhtÞ=ðs21r24Þ: for PbTMPP, we find Is ¼
3:92 Â 103 W=cm2 with s21 ꢂ 200 ls obtained
from the flash photolysis experiment [9]. Due to its
extremely long lifetime of the lowest triplet state
(P100 ms), the saturation intensity for a fluores-
cein-doped boric acid glass is only 1:5 Â
10À2 W=cm2 [13]. Data in Table 3 exhibit that
changing of the central metal ion has little or no
effect on those parameters such as the excited-
state absorption cross-section and saturation in-
tensity.
4. Conclusions
Fig. 8. The saturation absorption at 650 nm of five metal TMPP
samples. The solid curves are the fittings of data to Eq. (13).
In this study, the nonlinear response of five
metal porphyrins doped in boric acid glass are
measured with nanosecond laser pulses with linear
polarization. The results show two-photon ab-
sorption (TPA) at near infrared, and saturation
absorption (SA) at 650 nm. The values of TPA
The ground-state absorption cross-section r13 is
evaluated by r13 ¼ a0=N, where a0 is determined
from the absorption spectrum in boric acid at 650
nm, and N (in units of no. of molecules/cm3) is the
Table 3
Saturation absorption parameters of metal TMPP doped in boric acid glass at 650 nm
Compounds
Ground state absorption
cross-section
r13 ðÂ10À18 cm2Þ
Linear absorption
coefficient a0 ðcmÀ1
Excited-state absorption
cross-section
r24 ðÂ10À19 cm2Þ
Saturation intensity
Is ðÂ103 W=cm2Þ
Þ
GaClTMPP
InClTMPP
TlClTMPP
SnTMPP
2.05
2.12
1.93
1.99
2.00
119.1
119.1
113.9
116.5
120.4
3.74
3.83
3.63
3.36
3.91
4.10
4.02
4.21
4.55
3.92
PbTMPP
The excitation pulse is linear polarized with horizontal polarization.

302
T.C. Wen et al. / Chemical Physics 286 (2003) 293–302
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B.G. Maiya, R. Philip, G.R. Kumar, Opt. Commun. 182
(2000) 255.
cross-sections d are determined in this work, and
we also propose tentatively the two-photon al-
lowed transition states to be B1g and B2g. Using
both the circular and linear polarized light at 1320
ꢀ
ꢀ
1
1
[7] N. Ono, S. Ito, C.H. Wu, C.H. Chen, T.C. Wen, Chem.
Phys. 262 (2000) 467.
nm, we obtain the polarization ratio X ðX ¼ dcirc
=
[8] P.P. Kiran, N.K.M.N. Srinivas, D.R. Reddy, B.G. Maiya,
A. Dharmadhikari, A.S. Sandhu, G.R. Kumar, D.N. Rao,
Opt. Commun 202 (2002) 347.
dlinÞ equals 1.40 (from InClTMPP) and 1.43 (from
GaClTMPP). We are arranged to determine this
ratio from some specific wavelengths (e.g. 840 and
1200 nm) to confirm these excited states. The
characteristic of SA is demonstrated by the smaller
excited-state absorption cross-sections than that of
the ground state, and there are no significant
change of the excited-state absorptivity and the
saturation intensity Is by changing of the central
metal ion in this experiments.
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Acknowledgements
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(1993) 438.
We gratefully acknowledge the financial support
from the National Science Council of ROC, Tai-
wan (NSC 89-2113-M-037-008). We also appreci-
ate our refereeÕs valuable comments to this work.
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