Antiresonant ring interferometry as a sensitive technique
for measuring nonlinear optical properties of thin films
Parinda Vasa a, B.P. Singh b, Praveen Taneja a, Pushan Ayyub
a
a,*
Department of Condensed Matter Physics and Material Science, Tata Institute of Fundamental Research, Homi Bhabha Road,
Mumbai 400005, India
b
Physics Department, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
Abstract
There is a critical need for a simple technique for the accurate measurement of weak optical nonlinearities such as the
nonlinear coefficients of thin films. We discuss the experimental set-up and provide a realistic analysis for a sensitive and
single beam technique based on an antiresonant ring interferometer for measuring nonlinear optical coefficients in thin
films. The technique was benchmarked using toluene and its superiority was demonstrated by measuring the effective
nonlinear absorption coefficient of a 1.3 lm thick CdS film, which could not be detected using standard techniques such
as z-scan. We show that this technique can, in principle, be used for films with thickness down to the nanometer
regime.
PACS: 42.65.An; 42.70.Nq; 78.66.Hf
1. Introduction
Considerable scientific research has been focussed on the development of novel materials for
nonlinear optical and optoelectronic device applications. These include band gap engineered
low-dimensional quantum confined semiconductors and polymers. It is particularly advantageous to grow these materials in the form of thin
films, a geometry that inherently favors the integration of devices in the system architecture.
Various techniques have been developed to study
the nonlinear optical response of materials.
Though z-scan is one of the simplest and most
popular single beam techniques [1], it does not
provide the sensitivity usually necessary for
studying thin films. In a 1 lm thick film, for
example, z-scan either fails to detect the nonlinearity or requires intensities high enough to
cause undesirable processes such as excited state
absorption, thermal effects [2] and optical damage [3]. Other methods such as degenerate four
wave mixing (DFWM) [2] or interferometric
298
measurements [4,5] are more sensitive but difficult to implement, requiring careful spatial and
temporal alignment of two or more beams. Lee
and Hughes (LH) [6] proposed a simple, sensitive, single beam technique based on an antiresonant ring (Sagnac) interferometer for
simultaneously measuring the real and imaginary
contributions to optical nonlinearity, and called
it Antiresonant Ring Nonlinear Spectroscopy
(ARINS). Used for measuring very small changes in a variety of physical properties, the antiresonant ring (ARR) is sensitive enough to
detect changes of less than 0.005% in the laser
amplitude. Due to its high sensitivity, ARR allows measurements to be performed at low intensities, eliminating unwanted processes that
may complicate measurements. It also offers selective probing of the nonlinear optical processes
by discriminating against their response time. As
both the beams in the ARR traverse the same
path, it is simpler to align than other interferometric techniques and is intrinsically immune to
thermal fluctuations and mechanical vibrations
[7]. Such a combination of properties makes
ARR an ideal technique for studying the nonlinear response in thin films.
This technique utilizes the dressing of two unequal-intensity counter-propagating beams with
differential nonlinear phase, which occurs upon
traversing the sample. This difference in phase
manifests itself in the intensity dependent transmission. Thus it is important to note that the
measurement of cubic nonlinearity requires the use
of pulsed laser beams only. Most nonlinear optical
measurements are performed using ultrashort laser
pulses with Gaussian temporal and spatial profile.
The transmission of the ARR resulting from the
interference of the two counter-propagating pulses
varies nonlinearly both in space and time in a
complex manner. Photodetection of the transmission of the ARR yields spatially and temporally
integrated response. Consequently, it is the pulse
energy and not the instantaneous power that is
detected.
The analysis of ARINS by LH [6] does not
cover these crucial aspects and treats the transmission of ARR for CW beams. As pointed out
above, it is not actually possible to make the
measurement with a CW beam or even with
pulsed beams having a long pulse duration. The
treatment of LH is thus applicable to the somewhat academic problem of square pulses with a
top hat spatial profile. Since LH had applied their
analysis to data obtained using Gaussian pulses
from an ultrafast Ti:sapphire laser, the results
obtained were probably not accurate. This aspect
presumably went unnoticed because LH had not
benchmarked the technique using a standard
nonlinear sample. We have, in fact, confirmed
that in the case of a common system such as
toluene, their analysis yields a value of the thirdorder nonlinearity that is lower than the literature
value by a factor of 25. It is, therefore, imperative
to modify the analysis to consider pulsed excitation with realistic shapes.
Here we present a generalized analysis of ARINS valid for the measurement of real and imaginary components of nonlinear susceptibility and
discuss the interpretation of our results. We incorporate linear as well as nonlinear absorption
(two-photon absorption or saturation of absorption). We have also taken account of the actual
reflectivities of the two mirrors (viz., 80% and 4%)
used in the ARR, while LH had assumed both
mirrors to have 100% reflectivity, a situation under
which ARINS cannot function. To test the efficacy
of our formulation and benchmark the technique,
we have measured the nonlinear susceptibility of
toluene. Our results are in excellent agreement
with earlier values of the electronic nonlinearity.
We also report the measurement of the effective
nonlinear absorption coefficient (bÞ of a 1.3 lm
thick CdS film, which demonstrates the superior
sensitivity of ARINS compared to z-scan.
Even though the ARINS technique was proposed more than a decade ago and has found
applications in mode locking [8] and fiber optics
[9–11], it has subsequently never been applied to
the measurement of nonlinearity in spite of its
simplicity, elegance, versatility and extremely high
sensitivity. We believe that the physically realistic
formulation proposed here will allow this powerful
technique to be used widely for the determination
of small nonlinear optical responses (such as in
thin films) and help to elucidate their corresponding mechanisms.
299
2. Experimental setup and formulation
The ARR can be setup in different configurations based on the Sagnac interferometer [12].
Fig. 1 shows the ARINS setup used in our experiments. A 50–50 beam splitter divides the input
pulse into two counter-propagating pulses having
p phase difference. Reflections from a high reflectivity mirror and an uncoated flat with 6° wedged
rear surface close the ring and the two pulses again
recombine at the beam splitter to yield ARR
2
2
transmission, jEout j / jEcw þ Eccw j . Here Ecw and
Eccw are the optical fields traveling in clockwise
and counterclockwise directions respectively. Inside the ring there is a unit magnification telescope
comprised of a pair of identical lenses in 2f configuration. One of the lenses focuses the pulses into
the sample placed at its focus while the other one
re-collimates them. Two counter propagating
fields traversing the ring acquire linear as well as
intensity dependent nonlinear phase shifts. Since
both the fields traverse the same optical path
through the ring and encounter the same interactions with the optical elements, linear interactions
would affect their amplitude and phase in identical
manner. For an exactly 50% beam splitter, in the
absence of any nonlinear interactions, the two returning fields with the same amplitude and phase
difference will interfere destructively at the beam
splitter to yield zero transmission. In this ÔbalancedÕ condition all the input power is reflected
back to the incident direction. Measurement
Fig. 1. Schematic diagram of the experimental set-up for antiresonant ring nonlinear spectroscopy (ARINS).
against this dark background provides the basis
for the improved sensitivity essential for measuring
relatively weak signals. Any small deviation from
the ideal splitting ratio (d) results in a leakage from
the ARR and is responsible for the background
that limits the sensitivity of the measurement.
In the case of nonlinear interaction, the two unequal intensity counter propagating pulses in the
sample will undergo different phase changes. Their
superposition on the beam splitter will result in the
intensity dependent transmission of the ARR,
which is related to the nonlinear response of the
sample. The difference of nonlinear phases picked
up by two counter propagating pulses and hence the
transmission of ARR will be maximum when only
one of these is intense enough to cause an appreciable nonlinear polarization in the medium. This
can be achieved if one of the pulses emerging from
the 50–50 beam splitter is sufficiently attenuated by
a neutral density filter before passing through the
sample. In our setup this is implemented for the
clockwise beam using an uncoated flat as a 4% reflector. We point out that the differential dressing of
counter propagating pulses with nonlinear phases is
possible only when the two do not interact simultaneously in the sample. Else, the same nonlinear
phase will be impressed on both by the cross action
phenomenon. The temporal overlap of the two
pulses in the sample can be prevented by spatially
offsetting the sample with respect to the center of the
ARR. The time difference between the arrivals of
the two pulses (Dsarr ) determines the nature of the
nonlinear optical process that can be studied depending on its response time. Nonlinear processes
with decay time longer than Dsarr do not contribute
to the intensity dependent transmission of the ARR
as both the pulses are affected identically. The delay
window thus acts as an ultrafast gate. This gives
ARR the unique ability to filter the nonresonant
electronic contributions from integrating (or slow,
e.g. thermal) nonlinearities or those arising from
long lived (resonant) states and makes it ideal for
time resolved studies and ultrafast gating. If the
arrival times of the two pulses in the sample are reversed, one would measure the unfiltered response.
We also point out that the weak nonlinear lens
induced by the tightly focused Gaussian beam
does not significantly affect the beam parameters
300
upon propagation, when the sample is situated at
the beam waist (f the Rayleigh range) [13]. This
is amply illustrated by the fact that no variation in
transmittance occurs in closed aperture z-scan
when the sample is at the focus [1]. Thus the spot
sizes at the beam splitter can be taken to be the
same as in the linear interaction case. It then
transpires that for the evaluation of the transmitted pulse energy one only needs to consider the
nonlinear phase change due to the sample. Any
linear phase effects due to propagation inside the
ring can be completely omitted or at best an arbitrary phase function can be plugged into the field
expression for the sake of completeness.
To calculate Iout we consider a collimated, spatially and temporally Gaussian pulse with electric
field amplitude E0 , incident on the beam splitter,
where it is split into two counter-propagating
beams with electric fields Ecw and Eccw . The general
form for the electric field of a Gaussian beam is:
w0
r2
Eðz; r; tÞ ¼ E0
exp
exp ½i/ðzÞF ðtÞ;
wðzÞ
w2 ðzÞ
ð1Þ
where z is the distance of propagation, r is the
transverse coordinate, w0 is the beam waist (z ¼ 0),
/ðzÞ ¼exp½iðkz tan1 ðz=z0 ÞÞ is the phase of the
Gaussian beam (with pulse duration sp and wave
vector k and the function F ðtÞ ¼ exp½ð2 ln 2Þt2 =s2p gives the temporal variation. The spot size at a distance z is w2 ðzÞ ¼ w20 ½1 þ ðz2 =z20 Þ, where z0 is the
Rayleigh range. For simplicity, we assume that the
Rayleigh range is larger than the sample thickness
(thin sample approximation). We ignore the slight
difference in the spot sizes for the CW and CCW
beams at the lenses (which arises because the sample
is offset from the center of the ARR). If the intensity
splitting ratio in CW and CCW directions are
(1=2 d) and (1=2 þ d) respectively and the spot
size at the focal point is w0 , then the electric field at
the incident face for the two counter propagating
beams can be expressed as:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pffiffiffi
Ecw ¼ 1=2 dE0 expðr2 =w20 ÞF ðtÞ R and
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Eccw ¼ 1=2 þ dE0 expðr2 =w20 ÞF ðtÞ;
ð2Þ
where R is the reflectivity of the uncoated flat. The
field propagation through the sample is governed
by dI=dz ¼ aðIÞI and d/=dz ¼ knðIÞ. For the
weaker CW beam, aðIÞ ¼ a, the coefficient of linear absorption and nðIÞ ¼ n0 , the linear refractive
index. For the CCW beam aðIÞ ¼ a þ bI, and
nðIÞ ¼ n0 þ n2 I, where b is the effective nonlinear
absorption coefficient and n2 is the nonlinear index
of refraction. The electric field of a pulsed
Gaussian beam at the exit face of the sample
(thickness ¼ L) with a nonlinear absorption and
nonlinear refractive index is
E0 ðr; tÞ
Eexit ðr; tÞ ¼ pffiffiffiffiffiffiffiffiffiffiffi expðaL=2Þ expðikn0 LÞ
1þq
expðikn2 lnð1 þ qÞ=bÞ;
ð3Þ
where E0 ðr; tÞ is the incident electric field,
q ¼ bIin Leff , Leff ¼ ½1 expðaLÞ=a is the effective
length of the sample and Iin ¼ ð1=2 þ dÞKI0 is the
intensity incident on the sample, I0 is the intensity
incident on the beam splitter and K is a constant
(<1) accounting for the reflection losses at the
sample and lens surfaces. In our experimental
setup Iin 0:4I0 and jdj 0:02. Using Eqs. (2) and
(3), the electric field of the two counter propagating beams at the corresponding exit faces of the
sample can be expressed as
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
exit
Ecw
¼ ð1=2 dÞE0
2
r
exp
expðaL=2Þ
w20
pffiffiffi
ð4Þ
expðikn0 LÞF ðtÞ R;
2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E0
r
exit
Eccw
¼ ð1=2 þ dÞ pffiffiffiffiffiffiffiffiffiffi exp
expðaL=2Þ
w20
1þq
expðikn0 LÞ expðikn2 Iin Leff ÞF ðtÞ;
ð5Þ
where q 1 and lnð1 þ qÞ q. When the two
beams arrive again at the beam splitter after one
trip round the ring, the electric fields in the
transmission branch are given by multiplying Eqs.
(4) and (5) by the respective splitting ratios
t
Ecw
¼ ð1=2 dÞE0
w20
r2
exp
w2 ðzÞ
w2 ðzÞ
pffiffiffi
expðaL=2Þexpðikn0 LÞexpði/ðzÞÞF ðtÞ R;
ð6Þ
301
"
2 E0
w0
t
Eccw
¼ ð1=2 þ dÞ pffiffiffiffiffiffiffiffiffiffiffi
1 þ q w2 ðzÞ
r2
exp
expðaL=2Þ
w2 ðzÞ
expðikn0 LÞ expði/ðzÞÞ
pffiffiffi
expðikn2 Iin Leff ÞF ðtÞ R;
bLdIin
pffiffiffi
2 2
" 2 # 2 2 #
2
b
kn2
L Iin
pffiffiffi :
þ
þ
4
2
3 3
Iout ¼ ðexpðaLÞRIÞ 4d2 þ
ð7Þ
where wðzÞ is the spot size at the beam splitter after
one round trip. Both wðzÞ and w0 can be determined
experimentally. As mentioned earlier, the ARR
2
2
t
t
leakage is jEout ðr; tÞj ¼ jEcw
ðr; tÞ þ Eccw
ðr; tÞj . Sub2
stituting Eqs. (6) and (7), jEout j can be expressed as
2
w0
2r2
2
2
jEout j ¼
expð aLÞ exp
F ðtÞ
w2 ðzÞ
w2 ðzÞ
"
2
#
2
1
ð1=2 þ dÞ
1
2
þ 2d d þ
2
2
ð1 þ qÞ
2
jE0 j R cosðkn2 Iin Leff Þ
ð8Þ
for q 1, Eq. (8) becomes
2
w0
2r2
2
2
jEout j ¼
expð
aLÞ
exp
ðtÞ
F
w2 ðzÞ
w2 ðzÞ
"
"
2
bIin
4d2 þ bIin Ld þ
4
2 # #
kn2 Iin
2
þ
ð9Þ
L2 jE0 j R:
2
As has been stated earlier, the relevant measured quantity in this experiment is the transmitted
pulse energy:
Z 1Z 1
2
W ¼
Eout
2pr dr dt:
ð11Þ
For low intensity levels (q 1), the ARR
transmission Iout as a function of Iin is a cubic
polynomial. The coefficients are directly related to
the coefficient of nonlinear absorption (two-photon or saturation or excited state absorption) and
to n2 . As mentioned earlier, d is related to the
linear leakage and limits the sensitivity. For d ¼ 0,
Iout / Iin3 , in which case the simultaneous evaluation of b (or Is ) and n2 becomes difficult. However,
a small nonzero d makes the analysis much simpler
as each term of the polynomial can be evaluated
directly. In our geometry, Eccw Ecw , and if the
sample exhibits nonlinear absorption (not saturation), Eccw will be attenuated more than the Ecw .
For d > 0 and Eccw Ecw , all the coefficients of
the polynomial will be positive and Iout will be a
continuously increasing function of Iin . If the
sample exhibits saturation of absorption then Eccw
will be attenuated less than Ecw and the sign of d
opposes the increase in nonlinear leakage. The
quadratic term in the polynomial becomes negative, and Iout shows saturation at a relatively low
intensity, where the effect of d is cancelled by the
saturable absorption. At higher intensities Iout increases continuously. For d < 0, the curvature of
ARR leakage as a function of Iin is reversed for the
two processes. Thus, by carefully choosing d, both
the origin of nonlinearity and the values of nonlinear coefficients can be conveniently obtained.
1 0
Using Eq. (9) it can be shown easily that
pffiffiffi 2
p pw ðzÞRsIðexpðaLÞÞ
pffiffiffiffiffiffiffi
W¼
2 ln 2
"
" 2 # 2 2 #
2
bLdIin
b
kn2
L Iin
2
pffiffiffi :
4d þ pffiffiffi þ
þ
4
2
3 3
2 2
ð10Þ
1=2
Defining Iout ¼ 2ðln 2Þ W =p3=2 sw2 ðzÞ which
has the dimensions of intensity, Eq. (10) can be
expressed as
3. Results and discussion
To verify our formulation and demonstrate the
application of ARINS, we measured the real and
imaginary contribution to the third order nonlinearity of toluene at 774 nm. A tunable, femtosecond Ti:Sapphire laser was used to generate a 100
MHz pulse train with a pulse duration of 68 fs. A
Pockels cell reduced the repetition rate to 3 Hz. A
lower repetition rate prevents the contribution of
thermal effects to the nonlinearity. The sample cell
302
2
ARR Output Intensity (KW/cm )
600
500
400
Transmision (Normalized)
was a 1 mm path length quartz cuvette. Fig. 2
shows the ARINS leakage as a function of incident
intensity, Iin , which was varied by a variable attenuator. Table 1 gives the nonlinear coefficients (b
and vð3Þ ) of toluene measured by us, and the values
calculated using our data but the old ARINS
formulation. For comparison, we also provide the
corresponding values reported earlier by Meredith
ð3Þ
et al. [14], who measured vxxxx
ð3x; x; x; xÞ by
using third harmonic generation of 1.91 lm fundamental wavelength, a technique that would
measure purely the electronic part of the nonlinearity. As all the interacting wavelengths are far
away from the resonance in toluene (nonresonant
ð3Þ
condition), vð3Þ
xxxx ð3x; x; x; xÞ ffi vxxxx ðx; x; x;
1.08
1.04
1.00
0.96
Closed aperture
Open aperture
0.92
-100
-50
0
50
100
Z (Arb. Units)
300
200
Quadratic fit
Linear transmission ( β = 0)
Experimental
100
0
0.0
0.5
1.0
1.5
2.0
2 .5
2
Incident Intensity (GW/cm )
Fig. 2. Antiresonant ring leakage signal for toluene. Inset
shows the closed and open aperture z-scan data (Imax ¼ 3 GW/
cm2 ) for the same sample.
xÞ. The fact that this indeed is the case is established by the excellent agreement of their
ð3Þ
value detervð3Þ
xxxx ð3x; x; x; xÞ value with the v
mined by Saikan and Marowky [15] using the
FWM (CARS Maker fringe) technique. Clearly,
the value of vð3Þ for toluene calculated using our
formulation is in very good agreement with these
reported values. However, the value calculated
from our experimental data but using the treatment of LH [6] is lower by a factor of 25 and is
obviously incorrect.
We point out that in our experiment, the maximum intensity at the sample (Iin ) was only 0.8
GW/cm2 , whereas a z-scan measurement with 3 Hz
repetition rate pulses fails to detect the nonlinear
refractive index and two-photon absorption in
toluene even at the much higher intensity of 3 GW/
cm2 (Fig. 2, inset). The scatter in the z-scan data is
about 4%, which obviously limits the sensitivity
of the technique. Note that the ARR leakage exhibits a point of inflexion, which – as explained
earlier – is due to the value of d being negative.
The values obtained in our experiments are estimated to have an error of about 7%. Various
external sources not related to ARINS, such as
variation in the sample thickness and reflectivity
also contribute to the error, often in ways difficult
to quantify.
On the other hand, z-scan experiments performed with 100 MHz pulse train yield
vð3Þ 2 1012 esu. This would imply that the
measured nonlinearity in this experiment is thermal in nature as a 100 MHz pulse train can cause
significant sample heating. However, the ARINS
experiment with 100 MHz pulse train still yields
the same vð3Þ value as obtained with 3 Hz pulses.
Table 1
Comparison of the values of the nonlinear coefficients for toluene and CdS from our present data (column 3) and literature (column 5)
Sample
Parameter
ARINS
(our analysis)
ARINS
(analysis of LH [6])
Values reported
earlier
Toluene
viiii (x; x, x; xÞ esu 1014
b cm/GW
ð3Þ
10.1
0.378
0.046
0.001
9.81 [12], 9.4 [13]
–
CdS thin film
viiii (x; x, x; xÞ
esu 1014
b cm/GW
ð3Þ
–
–
62
0.2
95 ([2], single
crystal)
6.4 ([2], single
crystal)
Values obtained from our data using the older analysis of Lee and Hughes (LH) [6] are given in column 4.
30
20
Transmission (Normalized)
2
This establishes that ARINS can discriminate
against slow nonlinear processes and can yield
purely the electronic nonlinearity.
Having benchmarked the ARINS technique as
well as our modified analysis procedure, we now
demonstrate the usefulness of ARINS for measuring the relatively weak nonlinear response in
thin films. We selected an optically flat, 1.3 lm
thick polycrystalline CdS film, rf-sputtered on a 1
mm thick quartz substrate [16]. The CdS film
showed a bandgap of 2.5 eV, which is close to its
bulk bandgap. The measurement was made at 774
nm using a pulse duration of 80 fs, and a low pulse
repetition rate of 3 Hz. The quartz substrate and
the sample cell did not show any nonlinearity at
the intensity levels used in our experiment. Fig. 3
shows the ARR leakage for the CdS film. The
monotonically increasing ARR output is related to
the positive d in this case. In the CdS thin film we
could not detect any intensity dependent refractive
index. In our experiment Dsarr was 2.5 ns, which
indicates that the relaxation time in CdS is longer.
The response in toluene could be detected since it
is purely nonresonant electronic nonlinearity.
Fig. 3 (inset) shows that closed and open aperture
z-scans – performed at an intensity of 3 GW/cm2 –
cannot detect the nonlinearity in CdS. This indicates the superiority of ARINS over z-scan for thin
films. Table 1 shows the values of the nonlinear
absorption cross-section for CdS measured by us,
as well as those reported earlier [2].
Values obtained using LH formulation are much
lower than the literature values because of problems in their formulation and because the technique
was not benchmarked using a standard material.
The value of the effective b obtained by us for the
nanocrystalline CdS film (average grain size ¼ 5
nm) is much larger than that reported for the
nonlinear absorption coefficient in single crystal
CdS. Further experiments (infrared photoconductivity, excited state absorption and dispersion of bÞ
aimed to understand the origin of the large observed nonlinear coefficients in CdS thin films suggest the existence of mechanisms different from that
in bulk CdS [17]. The enhancement can be ascribed
to the presence of mid-band gap defect states in the
sputter deposited nanocrystalline films [18]. Such
defect states can act as intermediate states for 774
ARR Output Intensity (KW/cm )
303
1.10
1.05
1.00
0.95
0.90
-60 -40 -20
Open aperture
Closed aperture
0
20
40
60
z (Arb. Units)
10
Quadratic fit
Linear transmission ( β = 0)
Experime ntal
0
0.0
0.5
1.0
1.5
2.0
2
Incident Intensity (GW/cm )
Fig. 3. Antiresonant ring leakage signal for CdS thin film. Inset
shows the closed and open aperture z-scan data (Imax ¼ 3 GW/
cm2 ) for the same sample.
nm incident photon energy and can increase the
two-photon absorption cross-section significantly.
Excited state absorption due to the defect states in
semiconductors also contributes to the nonlinear
coefficient. The presence of such states was confirmed by a measurement of the single-photon
photocurrent at IR wavelengths. In fact, nanocrystalline CdS thin films also show a stable photocurrent response at visible wavelengths [16].
Though we have discussed the use of ARINS for
ð3Þ
measuring the contribution to vjklm ðx; x; x; xÞ,
the method can be suitably modified to incorporate
different wavelengths and/or polarizations to meað3Þ
sure contributions to vjklm ðx4 ; x1 ; x2 ; x3 Þ. The
lowest value of b that could be successfully measured is 0.38 cm/GW for a 1 mm sample length of
toluene. For a polycrystalline CdS thin film, we
obtained b of 62 cm/GW. This implies that the
ARINS techniques can be used to measure the value of b in CdS film with a thickness as low as 60
nm. This is therefore an extremely powerful technique for measuring nonlinearity in films having
thickness in the nanometer range. Another technique that can measure such low nonlinearities is
DFWM, but the difficulty with this is that it in-
304
volves critical alignment of more than one beam. It
also does not give both real and imaginary parts of
the nonlinearity, which can be obtained simultaneously using ARINS.
In summary, we have provided a general formalism for using a simple, single beam interferometric technique to measure very weak nonlinear
signals. The ARINS technique is highly sensitive,
stable against thermal and mechanical perturbations, and can simultaneously measure real and
imaginary susceptibilities. We have also experimentally demonstrated the superiority of the
ARINS technique over the conventional z-scan
technique in detecting nonlinear optical coefficients in thin films.
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