Optics Communications 277 (2007) 433–439
www.elsevier.com/locate/optcom
Influence of multiphoton events in measurement
of two-photon absorption cross-sections and optical
nonlinear parameters under femtosecond pumping
Rallabandi Sailaja a, Prem B. Bisht
b
a,*
, C.P. Singh b, K.S. Bindra b, S.M. Oak
b
a
Department of Physics, Indian Institute of Technology Madras, Chennai 600 036, India
Ultrafast Studies Section, A-Block, Raja Ramanna Center for Advanced Technology, Indore 452 013, India
Received 11 January 2007; received in revised form 29 March 2007; accepted 14 May 2007
Abstract
Absolute values of two-photon absorption cross-sections of some laser dyes in methanol solution have been measured by using the
transmission method. From the fluorescence yield measurements under multiphoton excitation, the number of involved photons in the
process has also been estimated. It is found that the presence of higher photon events may lead to erroneous values of measured twophoton absorption cross-sections. It is shown here that the Z-scan technique is capable of differentiating between the two- and three-photon absorption processes. Nonlinear optical parameters under femtosecond pumping by multiphoton resonant excitation at 800 nm are
also given here.
2007 Elsevier B.V. All rights reserved.
PACS: 42.65.k; 42.65.Re; 42.65.An
Keywords: Two-photon absorption cross-section; Femtosecond pumping; Open aperture Z-scan; Nonlinear optical parameters
1. Introduction
Multiphoton absorption processes offer technologically
relevant applications in medical science, three-dimensional
spatially-resolved optical data storage, optical switching
and micro fabrication [1–5]. These processes require high
peak powers which are available from ultrashort pulsed
lasers. Two-photon absorption (TPA) is a third order nonparametric process in which simultaneous absorption of
two photons takes place via virtual state in a medium.
The organic molecules have small values of TPA crosssections, typically of the order of 10 GM (1 GM = 1050
cm4 s). The selection rules for TPA process are different
from that of single-photon absorption [6]. Therefore, it
opens up the possibility of probing the transitions that
*
Corresponding author. Tel.: +91 2257 4866; fax: +91 2257 0545.
E-mail address: [email protected] (P.B. Bisht).
0030-4018/$ - see front matter 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.optcom.2007.05.033
are inaccessible under single-photon excitation [7–9]. Multiphoton processes also contribute to the white light continuum generation [10].
TPA cross-sections of the molecules can be determined
by measuring the transmittance of the sample by changing
the incident flux density [11,12]. Incident flux can be varied
either by using the neutral density filters, or by translating
the sample along the focal plane of a double convex lens.
The later is known as Z-scan technique that has been popularly used to determine the nonlinear optical parameters
of various media [13–17].
Several organic dyes have traditionally been used as
laser materials due to their high fluorescence yield and
large emission bandwidths. In recent years these dyes have
also found applications in biological and medical applications [18,19]. A large class of molecules absorbs in the
ultraviolet and visible regions and has a tendency to get
bleached under single-photon excitation. This problem
434
R. Sailaja et al. / Optics Communications 277 (2007) 433–439
can be overcome by using the near infrared wavelengths
(under multiphoton pumping) with no photodamage in
the areas that are out of focus. Multiphoton absorption
takes place at high concentrations and at large photon densities. However, in order to understand the photophysics of
suitable fluorescent dyes which can be used for various
applications, it is important to measure their TPA crosssections.
In the past, a few laser dyes have been used for standardization of measurement techniques [20,21]. There
are independent reports available on (i) measurement of
emission spectra under multiphoton excitation [18,22],
(ii) determination of number of photons involved in
absorption by measuring the fluorescence intensity vs.
the pump flux density [12], and (iii) measurement of
higher order absorption cross-sections [6]. In this paper,
we have deduced the TPA cross-sections by transmission
method for various selected dyes. However, the fluorescence intensity vs. the pump flux density plots have been
found to deviate from a pure two-photon absorption
event. In such cases, multiphoton Z-scan profiles reveal
the presence of three-photon (ThP) absorption. The nonlinear optical parameters have also been studied from the
Z-scan profiles obtained under multiphoton resonant case
at 800 nm as the optical absorption of these dyes lie below
this energy.
ture Z-scan (Fig. 1) was measured. A small portion of the
incident beam was used to monitor the input laser energy.
The dyes viz., Rubrene (RUB), Eosin, Pryridin1 (PY1),
Fluorescein 27 (F27), Rhodamine 6G (R6G) and Rhodamine B (RhB) used in this study were purchased from
Aldrich chemical co. and were used as received. All dyes
were dissolved in spectroscopic grade methanol except
RUB, which does not dissolve in methanol. We used spectroscopic grade benzene for RUB. A dilute concentration
of 105 M was used for taking the absorption and emission
spectra. The absorption spectra of the dyes were recorded
in a 5 mm thick quartz cell by using a spectrophotometer
(JASCO, V570). The fluorescence spectra were recorded
with a spectrofluorometer (JASCO, FP-6600) by exciting
at 400 nm. For the time-resolved measurements, a 40 ps
pulsed laser at 408 nm (Pilas, Advanced Photonics) was
used as an excitation source.
Multiphoton fluorescence measurements were also done
by exciting the samples with the fs pulses at 800 nm. The
laser beam was focused on to the sample and the fluorescence was collected by a fiber coupled spectrometer (Ocean
Optics, HR-4000). Incident laser energy was varied by
using neutral density filters to monitor fluorescence at various laser irradiances.
2. Experimental
3.1. Two-photon absorption (TPA) cross-section
The experiments were carried out at the pump wavelength of 800 nm with 100 fs duration pulses operating at
the repetition rate of 1 kHz. The laser pulses were generated by a Kerr-lens mode-locked Ti:sapphire laser (Spectra
Physics, Tsunami), which seeded a Ti:sapphire regenerative
amplifier (Quantronics, Titan). The energy of the fs pulse
was 83 nJ. The laser pulses were focused by a lens on
to the sample. The beam waist at the focal plane of the lens
(x0) was 47.5 ± 2.5 lm giving a Rayleigh range
(z0 ¼ px20 =k) of 9.8 mm. A 5 mm quartz cell containing
the sample was translated across the focal region for transmission measurements. For the closed-aperture Z-scans
(Fig. 1), the transmittance of the sample was detected
through an aperture placed at the far field. Simultaneously,
by using a beam splitter before the aperture, the open-aper-
To obtain the TPA cross-section (r2), the pump beam is
focused by a lens and the transmitted intensity of the pump
is measured as a function of the scanning distance (z) of the
sample. r2 depends on the number density of the molecules
(N), the pump wavelength (k), the pump pulsewidth (s) and
the inverse of the number of transmitted photons (NT)
from the sample. It can be related with these parameters
as follows [9],
1
0:66N r2
1
¼
ð1Þ
Z dep ðzÞ þ
NT
Ni
ðk=gÞs
F1
Ti:sapphire laser
(800 nm, ~ 100 fs
83 nJ, 1 kHz)
L1
3. Theory
where
1
Z dep ðzÞ ¼ tan
S
BS
ðz þ l=2Þk
1 ðz þ l=2 l=gÞk
tan
px20
px20
A
F2
D1
z
D2
L2
F3
Fig. 1. Experimental setup used for the measurement of nonlinear optical parameters. A = aperture, F1, F2 and F3 = neutral density filters, L1 and
L2 = double convex lenses, S = sample, BS = beam splitter, D1 and D2 = detectors.
R. Sailaja et al. / Optics Communications 277 (2007) 433–439
and Ni represents the number of incident photons. The value of the TPA cross-section can be obtained from the slope
of the plot of 1/NT versus the Zdep(z).
3.2. Calculation of optical nonlinear parameters
From the measured value of r2 we can calculate the nonlinear absorption coefficient (b) [12]
b¼
r2 kN
hc
ð2Þ
where h is the Planck’s constant and c is the velocity of
light. The imaginary part of the third order nonlinear susð3Þ
ceptibility (vIm ) in units of m2/V2 can be calculated by
cg2 k
b
108 109 p2
ð3Þ
0. 5
b
RUB in benzene
c
a
Optical density
1. 0
0. 4
0. 8
0. 3
0. 6
0. 4
0. 2
0. 2
0. 1
0. 0
400
500
600
700
Normalized fluo. int. (arb. units)
ð3Þ
vIm ¼
800
Wavelength / nm
Fig. 2. Absorption spectrum (curve a) of RUB in benzene. Fluorescence
spectrum obtained on pumping with kexc = 400 nm (curve b) and
kexc = 800 nm (curve c). The concentration for curves a and b is
0.01 mM. Higher concentration (10 mM) is needed for two-photon
induced fluorescence emission (curve c).
435
3.3. Estimation of number of photons from multiphoton
induced fluorescence yield
By measuring the fluorescence intensity at various flux
densities of the pump beam, the number of photons
involved at the pump wavelength can be estimated. The
fluorescence signal I ifl , from a molecule (in the absence of
stimulated emission at high incident laser excitation) can
be related to the experimental parameters as [6],
/
I ifl ¼ g fl Nlri qiexc
ð4Þ
i
where g is the refractive index of the solvent, /fl is the fluorescence yield of the molecule, N is the molecular number
density and l is the optical path length. qiexc is the flux density for i photon excitation, and ri is the corresponding
absorption cross-section.
3.4. Z-scan technique for measurement of optical
nonlinearity
As the sample is moved along the propagation direction
of a focused laser beam (Z-axis), the beam consequently
experiences a phase and intensity modulation, which can
be observed in its transmittance measured as a function
of the sample position (z). When a finite aperture is kept
before the detector it is referred to as a closed-aperture
(CA) Z-scan, whereas the geometry in which the aperture
is replaced by a double convex lens to focus all the transmitted light into the detector is known as an open-aperture
(OA) Z-scan.
CA Z-scan experiment is used to estimate the refractive
nonlinearity, while an OA Z-scan experiment is used to
estimate the presence of absorptive nonlinearities of the
sample [13]. Under thin-sample approximation, the phase
shift due to nonlinear refraction (DU) and nonlinear
absorption (DW), can be calculated respectively as
Table 1
Photophysical parameters of the laser dyes in methanol under single- and two-photon excitation
Dye
PY1
F27
Eosin
RUBk
R6G
RhB
a
b
c
d
e
f
g
h
k
kabsa (nm)
482
510
522
528
528
544
kexc = 400 nmb (±2 nm)
kemc
fwhmd
667
533
545
568
556
574
91
37
37
33
37
40
rabse (·1016 cm2)
0.77
1.21
1.47
1.63
2.36
2.29
remf (·1017 cm2)
5.6
2.0
2.9
4.4
2.8
4.5
kabs is the peak wavelength of the absorption maximum [23].
kexc is the pump wavelength.
kem is the peak wavelength of the fluorescence maximum.
fwhm is the full width at half maximum.
rabs is the absorption cross-section at the peak wavelength of the absorption.
rem is the emission cross-section at the peak wavelength of fluorescence.
/ is the fluorescence quantum yield (from Ref. [24]).
s is the fluorescence lifetime.
In benzene.
/g
0.50
0.91
0.67
0.98
0.93
0.89
sh (±0.1 ns)
2.0
4.3
2.9
16.4
3.5
2.8
kexc = 800 nmb (±2 nm)
kemc
fwhmd
677
547
574
591
587
615
93
41
43
58
42
45
R. Sailaja et al. / Optics Communications 277 (2007) 433–439
DU0 2ðx þ 3Þ
ðx2 þ 9Þðx2 þ 1Þ
DW0
ð6Þ
-1
4x
ðx2 þ 9Þðx2 þ 1Þ
where x = z/z0 and z0 is the Rayleigh range. Eq. (6) can be
used as a model to analyze the CA profiles for combined
contribution of refractive and absorptive nonlinearity in
which the absorptive nonlinearity is only due to either
TPA or SA. For these values of DU0 and DW0, one can calculate the values of n2 and b by using Eq. (5). The real part
ð3Þ
of the third order nonlinear susceptibility (vR ) in units of
2
2
m /V can be calculated as
ð3Þ
vR ¼
cg2
n2
270 108 p
4.68
4.64
4.60
4.56
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Zdep(z)
-13
11.7
ð7Þ
By knowing the three-photon absorption coefficient (c)
from the fit, the corresponding absorption cross-section
(r3) in units of cm6 s2 is calculated as [4,12],
r3 ¼ cðhcÞ2 =k2 N
4.72
ð8Þ
slope = (2.4 ± 0.1) x 10
11.6
-13
T ðzÞ ¼ 1 þ
2
-14
slope = (6.2 ± 0.5) x 10
-13
Here f(t) is the temporal profile of the incident pulse, Leff =
[1 exp(a0L)]/a0 is the effective length of the sample, I0 is
the irradiance of the pulse, n2 is the nonlinear refractive index, b is the nonlinear absorption coefficient, a0 is the linear
absorption coefficient, and k is the wave vector.
For propagation of a Gaussian beam profile in the low
irradiance limit (for small changes in phase), the normalized transmittance T(z) up to first order in irradiance is
given by [11,13]
of TPA cross-sections (from Eq. (1)) for various dyes are
given in Table 2.
From the measured TPA cross-sections, the nonlinear
absorption coefficient (b) and the imaginary part of the
ð3Þ
third order nonlinear susceptibility (vIm ) were also
(N T ) / 10
ð5aÞ
ð5bÞ
11.5
-1
DU ¼ kn2 I 0 Leff f ðtÞ ¼ DU0 f ðtÞ
and DW ¼ bI 0 Leff f ðtÞ=2 ¼ DW0 f ðtÞ
(N) / 10
436
11.4
4. Results and discussion
11.3
0.03
0.09
0.12
0.15
0.18
0.21
-13
7.4
slope = (3.1 ± 0.1) x 10
-13
7.2
-1
4.1. Measurement of TPA cross-sections
0.06
Zdep(z)
(NT ) / 10
Absorption spectra of the dyes were recorded at various
concentrations ranging from 105 to 102 M. The observed
absorption spectra match well with those reported in the
literature [23]. It was confirmed that these dyes do not have
any absorption at 800 nm. As for an example, the absorption spectrum of RUB in benzene is given in Fig. 2. The
fluorescence spectra were recorded by pumping at 400 nm
(under single-photon excitation) and at 800 nm (wavelength corresponding to multiphoton excitation). The fluorescence maxima, fwhm, absorption and emission crosssections, fluorescence quantum yield [24] and lifetimes of
various dyes are given in Table 1.
7.0
6.8
As shown in the experimental setup, the pump beam was
focused with a lens on the sample. Transmittance was measured by translating the sample on the focal plane of the
lens to vary the irradiance. Fig. 3 gives a typical transmission at the wavelength of 800 nm as a function of the distance (z) for a few dyes. For RhB according to Eq. (1), a
plot of inverse of number of transmitted photons with
the Zdep(z) gives a slope of 3 · 1013. The calculated values
6.6
0.00
0.05
0.10
0.15
0.20
0.25
Zdep(z)
Fig. 3. Plot of 1/NT () versus Zdep(z) for PY1 (a), RhB (b) and RUB (c).
The slopes are also given in the figures and indicate the strength of r2.
Straight line is the linear fit with Eq. (1).
R. Sailaja et al. / Optics Communications 277 (2007) 433–439
ð3Þ
Dye
ia
r2b (GM)
bc (·1014 m/W)
vIm d (·1023 m2/V2)
PY1
F27
Eosin
RUB
R6Gf
RhB
e
10 ± 1
4±1
11 ± 2
33 ± 3
26 ± 3
50 ± 4
2.4 ± 0.4
1.0 ± 0.3
2.7 ± 0.7
8±1
6±1
12 ± 1
1.0 ± 0.2
0.4 ± 0.1
1.0 ± 0.3
4.0 ± 0.5
2.5 ± 0.4
4.8 ± 0.4
a
b
c
d
e
f
2.6 ± 0.3
2.0 ± 0.2
2.5 ± 0.2
1.7 ± 0.1
1.7 ± 0.1
i is the number of photons involved in absorption at 800 nm excitation.
r2 is the two-photon absorption cross-section.
b is the nonlinear absorption coefficient.
ð3Þ
vIm is the imaginary part of third order nonlinear susceptibility.
Too weak to be observed.
r2 = 16 GM [9].
calculated by using Eqs. (2) and (3), respectively. It is
observed that RhB has the highest value of TPA cross-section, while F27 has the lowest at 800 nm.
absorbed by a molecule. Fig. 4 gives such a plot of fluorescence intensity versus the incident flux density for eosin and
RhB in methanol and for RUB in benzene. The obtained
values of the slopes are approximately 2.0 for eosin and
RhB, but slightly larger (2.5) for RUB.
a
1.02
RhB
1.00
0.98
Transmittance
Table 2
Experimentally obtained nonlinear optical parameters on pumping with
100 fs duration pulses at 800 nm
437
0.96
0.94
0.92
0.90
0.88
0.86
4.2. Fluorescence yield measurements at 800 nm
-4
-3
-2
-1
0
1
2
3
4
z/z 0
b
1.02
RUB
0.99
Transmittance
On excitation at 800 nm, dilute concentrations of dyes
do not show any fluorescence emission. However, when
the sample of a high concentration (102 M) is kept at
the focus of the incident laser beam, multiphoton induced
fluorescence is observed. A comparison of one- and twophoton fluorescence spectra of RUB in benzene is shown
in Fig. 2. The fluorescence peak is red shifted in the case
of two-photon pumping. Since there exists a reasonable
value of the ground state absorption cross-section near
the emission peak, self absorption effect (at higher concentrations) is responsible for this red shift.
According to Eq. (4), the slope of the log–log plot of the
fluorescence signal from the sample versus the incident
photon flux density gives the number of photons that are
0.96
0.93
0.90
0.87
0.84
-4
-3
-2
-1
0
1
2
3
4
1
2
3
4
z/z 0
c
RhB in methanol
RUB in benzene
PTP
1.00
0.98
Transmittance
Fluo. Int. (arb. units)
eosin in methanol
1
0.96
0.94
0.92
0.90
0.1
-4
-2
-1
Flux density (cm s )
1
Fig. 4. The log–log plot of fluorescence intensity versus the incident flux
density for RhB (s) in methanol, RUB in benzene (D), and eosin in
methanol (d) on pumping at 800 nm. The straight line is the linear fit to
the data points. The slopes are 1.7 ± 0.1 for RhB, 2.5 ± 0.2 for RUB, and
2.0 ± 0.2 for eosin.
-3
-2
-1
0
z/z0
Fig. 5. OA Z-scans obtained by pumping at 800 nm for RhB in methanol
(Panel A), RUB in benzene (Panel B) and PTP in cyclohexane (Panel C).
Open circles denote the data points. The fittings for two-photon
absorption by using Eq. (6) (—), and for three-photon absorption (- - -)
[4] are also shown here.
438
R. Sailaja et al. / Optics Communications 277 (2007) 433–439
4.3. Determination of nonlinear optical parameters at
800 nm by Z-scan technique
To compare the nonlinear optical parameters obtained
from the transmission technique, we also performed the
OA Z-scan experiments at 800 nm for these dyes. It is
observed that the OA Z-scan profile is sharper in the case
of RUB as compared to that of RhB (Fig. 5). Panel A of
Fig. 5 gives the fitting of the OA Z-scan profile obtained
in RhB with Eq. (6). Since the OA Z-scan profile contains
the phase shift only due to NLA, while fitting it by Eq. (6)
the value of DU has been taken to be zero. With the measured value of DW we can obtain the value of the nonlinear
absorption coefficient (b) by using Eq. (5b). From these
values of b, the imaginary part of third order nonlinear susð3Þ
ceptibility (vIm ) was obtained by using Eq. (3). Table 3
ð3Þ
gives the obtained values of vIm and r2. It can be seen that
r2 values are reasonably close to those obtained by the
transmission technique except for RUB in benzene.
As mentioned above, the slope of log–log plot for the
fluorescence intensity versus the pump flux density is not
equal to 2 or 3 in a few samples (Table 2). It is well known
that both the dyes R6G and RhB show two-photon
absorption upon excitation at 800 nm. Fluorescence yield
measurements show a slope of 1.7 contrary to the expected
value of 2.0. The normalized transmittance obtained from
an OA Z-scan reaches to 0.9 at focus indicative of
Table 3
Nonlinear optical parameters obtained from OA Z-scan at 800 nm
ð3Þ
Dye
b(·1014 m/W)
vIm (·1023 m2/V2)
r2 (GM)
PY1
F27
Eosin
RUBa
R6G
RhB
2.2 ± 0.1
1.7 ± 0.1
3.2 ± 0.2
13.6 ± 0.6
5.4 ± 0.3
12.0 ± 0.6
0.9 ± 0.1
0.7 ± 0.1
1.3 ± 0.1
7.0 ± 0.4
2.2 ± 0.1
4.8 ± 0.2
9±1
7±1
13 ± 2
56 ± 6
22 ± 2
50 ± 5
a
In benzene.
a
10% absorption of the excitation beam itself. The maximum value of the irradiance used in the fluorescence
measurements was two times higher than that used in the
Z-scan experiments. This results in a higher absorption of
the excitation beam due to the nonlinear absorption in
the medium itself; resulting in the lowering of the slope.
Similarly in the case of RUB, Z-scan OA data show
15% absorption of the excitation beam. In the fluorescence measurements, use of higher irradiance may also
have resulted in the reduced value of the slope from 3.0
to 2.5. Similarly, for eosin and F27, the observed slopes
of 2.0 and 2.6, indicate two- and three- photon absorptions, respectively.
The CA Z-scan profiles were also recorded for the dyes
at the pump wavelength of 800 nm and were fitted with Eq.
(6). This was done after the setup was standardized by performing the CA Z-scan of CS2. The nonlinear refractive
index for CS2 (2.2 · 1019 m2/W) was found to be in agreement with the reported value [17]. The nonlinear refractive
indices for the pure solvents (methanol and benzene) were
obtained as 0.3 · 1019 m2/W and 0.8 · 1019 m2/W,
respectively. The nonlinear refractive part for the dye solutions was obtained by dividing the CA Z-scan profile with
the OA Z-scan. Fig. 6 gives the CA Z-scan profiles for F27
in methanol (Panel A) and the solvent alone (methanol,
Panel B). It is seen that the values of the nonlinear refractive index for the dye solutions are close to those obtained
for the solvents at 800 nm. The values of the nonlinear
absorption coefficient (b) and the imaginary part of v(3)
obtained from two-photon absorption experiments are
found to be two orders less than those obtained under single-photon pumping at 532 nm [16].
4.4. Influence of higher photon absorption
In case of RUB (Panel B, Fig. 5), the OA Z-scan data do
not fit with Eq. (6) indicating the deviation from the twophoton induced optical nonlinearity. Instead, the data fit
b
1.3
Transmittance
Transmittance
1.2
1.1
1.0
0.9
1.2
1.1
1.0
0.9
0.8
0.7
0.8
-4
-3
-2
-1
0
z/z 0
1
2
3
4
-4
-3
-2
-1
0
1
2
3
4
z/z0
Fig. 6. CA Z-scan profile for (a) F27 in methanol of 10 mM concentration and (b) methanol at 800 nm excitation. Open circles represent the data points
and the solid line shows the fit with Eq. (6).
R. Sailaja et al. / Optics Communications 277 (2007) 433–439
well with the three-photon absorption indicating the presence of higher photon events at 800 nm. This is consistent
with the obtained value of number of photons as 2.5 from
the analysis of multiphoton induced fluorescence yield
(Table 2). Similar scans were obtained for the dyes PPO,
and POPOP in methanol and PTP in cyclohexane (Fig. 5,
Panel C). PTP has been reported to have three-photon
absorption at the pump wavelength of 800 nm [6]. The
measured OA Z-scan profile of PTP also fits with the
three-photon induced optical nonlinearity. By using Eq.
(8) the three-photon absorption cross-section for RUB
and PTP obtained by fitting the Z-scan profiles are
4.7 · 1078 cm6 s2 and 2.9 · 1078 cm6 s2, respectively.
These observations indicate the requirement of two-photon
excitation at 800 nm for eosin, but coexistence of threephoton processes in the case of RUB, PPO, POPOP and
PTP. This also justifies the assumption of simultaneous
absorption of two photons in r2 calculations for the case
of, for example, eosin by using Eq. (1). In contrast, for
the case of RUB in benzene, even though the plot of 1/
NT versus Zdep fits to a straight line, Eq. (1) is not suitable
for accurate determination of r2 from the transmission
technique under such circumstances. A glance at Table 2
indicates that the varying values of involved photons must
be taken into account before using Eq. (1) for r2 calculations from the measurement. The values of i greater than
2 indicate the presence of three- and more photon induced
emissions.
5. Conclusions
The TPA cross-sections of various dyes have been measured by using the transmission technique. The irradiance
dependence of the fluorescence intensity reveals that two
or more photons may be simultaneously absorbed by dyes
at 800 nm. At present, this poses the limitation on the exact
determination of TPA cross-section from the transmission
technique. Therefore a correction to this should be taken
into account. The nonlinear optical parameters were also
measured by the Z-scan technique at 800 nm for the multiphoton resonance case. We found that these parameters
439
obtained from the transmission technique match well with
those obtained from the OA Z-scan technique for the cases
of TPA free of other higher photon events.
Acknowledgements
RS and PBB thank DRDO, New Delhi for financial
assistance.
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