Optics Communications 286 (2013) 347–352

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Optics Communications

0030-40

http://d

n Corr

E-m

journal homepage: www.elsevier.com/locate/optcom

Evaluation of the third-order optical nonlinearity of Au:SiO2 nanocompositesin the off-resonant spectral region

Hwang Woon Lee a, Kwangjin Lee a, Sunghun Cho a, John Kiran Anthony b, Soonil Lee a,Hanjo Lim c, Kihong Kim a, Valdas Pasiskevicius d, Fabian Rotermund a,n

a Department of Physics & Division of Energy Systems Research, Ajou University, Suwon 443-749, Republic of Koreab Department of Applied Physics and Chemistry, The University of Electro-Communications, Chofu, Tokyo 182 8585, Japanc Department of Electrical Engineering, Ajou University, Suwon 443-749, Republic of Koread Department of Applied Physics, Royal Institute of Technology (KTH), Stockholm 10691, Sweden

a r t i c l e i n f o

Article history:

Received 9 March 2012

Received in revised form

14 August 2012

Accepted 4 September 2012Available online 17 September 2012

Keywords:

Nanocomposite

Au:SiO2

Nonlinear refraction

Nonlinear absorption

Invariant imbedding method

18/$ - see front matter & 2012 Elsevier B.V. A

x.doi.org/10.1016/j.optcom.2012.09.009

esponding author. Tel.: þ82 31 219 2576; fax

ail address: rotermun@ajou.ac.kr (F. Rotermu

a b s t r a c t

The third-order nonlinear optical susceptibility (w(3)) of Au:SiO2 nanocomposite films with different

Au particle sizes was measured to be on the order of 10�10 esu to 10�9 esu in the off-resonant spectral

region, and the particle size-dependent behavior of w(3) was observed. The results were found to deviate

substantially from those of the conventional Maxwell-Garnet theory. By adapting the modified

invariant imbedding method, which takes into account the effect of interparticle interactions on the

nonlinear response, we successfully explain the enhanced third-order nonlinear susceptibility of

metal–dielectric nanocomposites at off-resonant wavelengths.

& 2012 Elsevier B.V. All rights reserved.

1. Introduction

Metal–dielectric nanocomposites have emerged as promisingefficient nonlinear optical (NLO) materials, with their intriguing largeand fast optical response stemming from the well-known surfaceplasmon resonance (SPR) phenomenon [1,2]. Various techniques suchas ion implantation [3], melting and heat treatment [4], photoreduc-tion [5], and sputtering [6] have been widely used to prepare high-quality nanocomposites, in which fine particles of metals such as Au,Ag, and Cu are embedded in transparent dielectric matrices. Thesenanocomposites are known to exhibit quite large third-order non-linearities (w(3)410�7 esu) near their SPR peaks. They are also knownto exhibit size-dependent optical properties, especially in theirquantum-size confinement regime. These size-tunable optical proper-ties of nanoparticles are of current interest because they can have asignificant impact on the development of nanophotonic devices. Formost practical fast photonic applications, however, NLO materialsneed to possess large w(3) values with as low absorption as possible atthe wavelengths of interest.

Over the past two decades, the nonlinear optical properties ofAu:SiO2 nanocomposite films, prepared with varying Au particle

ll rights reserved.

: þ82 31 219 1615.

nd).

sizes and volume fraction, have been intensively investigatedusing degenerate four wave mixing (DFWM) and z-scan techni-ques [3,7,8]. The enhancement of third-order nonlinearity atfrequencies close to SPR is mainly attributed to the local fieldenhancement, which could be predicted by the Maxwell-Garnett(MG) theory, and also to strong interparticle interactions [9]. Mostinvestigations reported up to now, however, have been primarilylimited to a spectral range around the SPR wavelength, wherethe absorption increases rapidly. However, by using single beamz-scan method, we showed that the particle size-dependentenhanced nonlinear optical response of the Au:SiO2 nanocompo-site films can also be observed in off-resonant spectral regionsnear 800 nm [10]. We found that the results deviated substan-tially from what was expected by the MG theory if we treated oursamples as MG media. In the present work, we utilize a relativelynew technique, called the invariant embedding method, byconsidering the samples as homogeneous effective media in orderto explain the third-order nonlinear optical response of theAu:SiO2 nanocomposite at 800 nm and 1250 nm. This numericalcalculation takes into account the local field factors inside themetal–dielectric nanocomposites that are analyzed through thedielectric constants, the linear transmittance, and the reflectance.The possible mechanisms for the sign reversal, the magnitude ofw(3), and the reason for the deviation of the results from the MGtheoretical analysis are discussed. Special attention is given to

H.W. Lee et al. / Optics Communications 286 (2013) 347–352348

verify if the thermal accumulation could modify the opticalnonlinearities of Au:SiO2 samples, by using the thermally mana-ged z-scan method [11].

2. Experiment

2.1. Sample preparation

Au:SiO2 nanocomposite films with different Au particle sizeswere deposited on fused silica substrates by alternating sputter-ing of SiO2 and Au at room temperature, while the volumefraction of Au was kept constant at 2%. The nominal thicknessesof the Au layers in samples denoted as NC0.2, NC1.0, NC2.0, andNC2.5 were chosen to be 0.2 nm, 1.0 nm, 2.0 nm and 2.5 nm,respectively. To achieve an equal overall film thickness of 1.5 mmfor all the samples, different deposition rates were applied bycontrolling the thickness of the SiO2 layers. Details of the designparameters for each film and the estimated morphology after thefilm preparation are listed in Table 1.

Table 1Design parameters and estimated morphologies of the Au:SiO2 nanocomposites

(NCs).

Sample Nominal

thickness

(nm)

Mean diameter of

Au (nm)

Number

of layers

Volume

fraction

(%)

Film

thickness

(nm)

Au SiO2 Au SiO2 Au SiO2

NC0.2 0.2 19.54 1.08 75 76

NC1.0 1.0 92.81 2.00 15 16

NC2.0 2.0 165 3.03 8 9 2 98 1500

NC2.5 2.5 212.14 3.23 6 7

Fig. 1. Top-view TEM images of the SiO2/Au/SiO2 nanocomposite films with Au

The plan-view TEM images of four separate SiO2/Au/SiO2 films(see Fig. 1), which were grown on carbon-coated Cu grids, wererecorded for verifying the size of the embedded Au particle. Thedeposition procedure for similar Au:SiO2 nanocomposite films isdescribed in detail elsewhere [12,13]. The linear optical absorp-tion spectra and the refractive indices were estimated by employ-ing a spectrophotometer and a variable angle spectroscopicellipsometer (VASE, Woollam), respectively.

2.2. Conventional/thermally managed z-scan

The z-scan technique [14] was used to determine thenonlinear refractive indices (n2) and nonlinear absorptioncoefficients (b) of the Au:SiO2 nanocomposites. A Ti:sapphireoscillator and an optical parametric oscillator (OPO) were usedas the excitation sources. The Ti:Sa laser (Chameleon, CoherentInc.) operates at 80 MHz and delivers 150 fs pulses at 800 nm,and the synchronously-pumped OPO (Mira OPO, Coherent Inc.)delivers 200 fs pulses at 1250 nm with the same repetitionrate as that of the Ti:sapphire oscillator. The output pulses fromthe oscillator were focused on the sample by a lens with a focallength of 5 cm. The sample was translated around the focal pointand the transmission changes were recorded in both the closed-aperture (CA) and open-aperture (OA) z-scan geometries. Thebeam waist at the focal point was measured by the knife-edgemethod. To improve the signal-to-noise ratio, the pulses weremodulated by using a chopper, and the transmitted signalwas measured by a photodetector that was connected to a lock-in amplifier (SR850, SRS). Subsequently, the measured signalwas corrected by the reference signal from the same source,which was detected by a separate photodetector in front of thefocusing lens.

mean diameters of (a) 1.08 nm, (b) 2.00 nm, (c) 3.03 nm, and (d) 3.23 nm.

H.W. Lee et al. / Optics Communications 286 (2013) 347–352 349

Because the operation of a laser at high pulse-repetition ratesmay give rise to cumulative thermal effects in the materials,which would result in modification of the optical nonlinearities,such thermal effects should be verified in advance. The thermallymanaged z-scan setup, suggested by Falconieri et al. [11], wasconstructed by altering the single beam z-scan scheme. Theexposure of the sample to the incident beam was controlled bya chopping wheel acting as an optical shutter (the wheel wasplaced at the focal point in order to minimize the beam waist ofthe incident beam on the wheel). The chopper wheel, whoseopening time was 25 ms, operated with a duty cycle of 20 Hz. Thetransient transmittance of the incident beam was detected bythe photodetector in both the OA and CA z-scan schemes. Thetime evolution of the pulse train envelope was processed by adigital storage oscilloscope (TDS 3000, Tektronix) at every posi-tion around the focal point.

Fig. 2. Linear absorption coefficients of the Au:SiO2 nanocomposite films.

2.3. Theoretical analysis

One of the limitations of the MG model as applied to the metal–dielectric composites is that it does not explicitly consider the effectof interparticle interaction on the local field enhancement, eventhough the model could correctly predict the location of the SPR andthe resulting local filed enhancement around the nanoparticles.Consequently, the model predicts that the enhancement of the localfield decreases significantly in the off-resonance region. Variousnumerical models have been suggested to explain the local fieldenhancement by considering the interparticle interaction of metalparticles [15,16]. In the present work, we have adopted the invariantimbedding method to extract the exact magnitude of the local fieldaround the interacting metal particles by using the linear dielectricpermittivity estimated through the linear transmittance and reflec-tance of the nanocomposites. The invariant imbedding method isapplied to cases in which the dielectric permittivity varies in onedirection in space in an arbitrary manner to derive a set of first-order ordinary differential equations called the invariant imbeddingequations. The exact reflection and transmission coefficients and thefield amplitudes can be obtained by solving the initial value problemof the invariant imbedding equations.

Consider a plane electromagnetic wave with a vacuum wavenumber of k0¼o/c (c is the speed of light in vacuum) thatpropagates with frequency o in a dielectric medium whosedielectric permittivity e is assumed to vary in space along thedirection of wave propagation. The medium is supposed to lie in0rzrL, where z and L represent the position and thickness ofthe medium, respectively, and the wave propagates in the x–z

plane. In this case, the complex amplitude of the electric field,E¼E(z), satisfies the wave equation

d2E

dz2þ k2

0eðzÞ�q2h i

E¼ 0 ð1Þ

Applying the invariant imbedding method, the exact differen-tial equations satisfied by the reflection coefficient r(l) for anormalized variable of medium size l can be derived as

drðlÞ

dl¼ 2ik0cos yrðlÞþ

ik0

2cos yeðlÞ�1� �

½1þrðlÞ�2, ð2Þ

where q is k0 siny and the initial condition for r(l) is given byr(0)¼0.

The amplitude of the electric field E(z) inside the medium iscalculated by the assumption of E as a function of both z and L, i.e.,E¼E(z, L).

Then,

dEðz,lÞ

dl¼ ik0 cosyEðz,lÞþ

ik0

2 cosyeðlÞ�1� �

1þrðlÞ� �

Eðz,lÞ: ð3Þ

For a given value of z, such that 0ozoL, the field amplitudeE(z, L) is obtained by integrating this equation from l¼z to l¼L

using the initial condition E(z, z)¼1þr(z).In this work, a Gaussian beam was used as the optical source,

rather than a monochromatic wave, which means we shouldcalculate the averaged electric field intensity for all the incidentangles and over the volume of the medium. An effective medium(layer) that is a mixture of the dielectric medium (SiO2) and thegold nanoparticles is considered, where the medium thicknessand the volume fraction are 1500 nm and 0.02, respectively. TheDrude model is used to obtain the dielectric constant of goldnanoparticles whose plasma frequency is 11�1015 Hz. By apply-ing the effective medium theory (Maxwell-Garnett theory), theeffective dielectric permittivity of the medium is obtained. Thenthe calculation of the intensity of the electric field at points allover the medium is carried out by using the invariant imbeddingtheory. The value of the electric field intensity averaged over thewhole medium size and incident angles can be calculated accord-ing to

/9E92S¼

R L0

R p=20 9Eðz,yÞ92

dzdyR L0

R p=20 dzdy

, ð4Þ

where the brackets denote averaging over the incident angle andthe medium size. Thus, the average local electric field intensitycould be calculated using Eqs. (2)–(4). These results are shown inFig. 7.

3. Results and discussion

The linear optical properties of the Au:SiO2 nanocompositeswere evaluated by measuring the linear transmission and reflec-tion by taking into account the Fresnel reflection losses at thesurface (Fig. 2). The absorption peak due to SPR continuouslyshifted toward longer wavelengths with increasing Au particlesize, with the peak becoming more enhanced and sharper, asreported in the previous work [17]. The refractive indices of theAu:SiO2 nanocomposite films measured through variable-angleellipsometry are shown in Fig. 3. The overall film thickness, theaverage particle diameter and the volume fraction of Au wereused as the fitting parameters for determining the optical con-stants such as the linear refractive index n and the extinctioncoefficient k.

The z-scan measurements were performed with a peak pulseintensity as high as �1 GW/cm2 at the focal point. This value wasapproximately a factor of 10 less than the damage threshold of the

Fig. 3. Refractive indices of the Au:SiO2 nanocomposite films.

0.96

1.00

1.04

0.96

1.00

1.04

0.96

1.00

1.04

-10 -5 0 5 10

0.96

1.00

1.04

-10 -5 0 5 10

AOAC NC0.2

NC1.0

NC2.0

NC2.5

NC1.0

NC2.0

Nor

mal

ized

tra

nsm

itta

nce

[a.u

.]

NC2.5

Z [mm]

NC0.2

NC1.0

NC2.0

NC2.5

Fig. 4. Normalized z-scan traces of the Au:SiO2 nanocomposite films with closed

(left column) and open (right column) apertures and measured at 1250 nm. The

solid lines correspond to the theoretical fits.

H.W. Lee et al. / Optics Communications 286 (2013) 347–352350

sample. Fig. 4 shows the OA (with S¼1) and CA (with S¼0.4)z-scan traces, measured for four Au:SiO2 nanocomposite films at1250 nm. In the case of NC2.5, the incident power was reduced to50% as compared with the other cases to avoid the signal satura-tion problem. The peak-valley CA z-scan traces indicate the self-defocusing and, hence, the negative nonlinear refraction. TheOA z-scan traces indicate the saturable absorption and, hence,a negative nonlinear absorption. By fitting the experimental

data with the z-scan theory [14], nonlinear refractive indices(n2) of �2.85�10�11 cm2/W, �3.82�10�11 cm2/W, �7.52�10�11 cm2/W and �8.56�10�11 cm2/W were obtained for theNC0.2, NC1.0, NC2.0, and NC2.5 samples at 800 nm, respectively.Measurements at 1250 nm delivered n2 values ranging from�0.94�10�11 cm2/W to �5.22�10�11 cm2/W, and these valuesare listed in Table 2. The absolute n2 values of the samples werefound to increase with increasing Au particle size. The OA z-scantransmission curves in the right column of Fig. 4 were also theore-tically fitted. The magnitude of the nonlinear absorption was found toincrease with increasing Au particle size, from �0.22�10�6 cm/Wto �4.08�10�6 cm/W at 800 nm and from �0.59�10�7 cm/W to�2.63�10�7 cm/W at 1250 nm (Table 2). The source of saturableabsorption shown in Fig. 4 is expected because the collective electronresonance absorption tail extends into the infrared region [18]. Forgold and silver, the SPR has a peak in the visible light region, and thetail of this absorption band extends well into the infrared region,which is the low-energy end of the visible light region (Fig. 2). The tailon this low-energy side is observed as a very broad backgroundabsorption in the infrared region. Consequently we observed satur-able absorption at both 800 nm and 1250 nm.

As an important step, we analyzed the possible contribution ofthermal effects to the observed nonlinear response of the sampleby using the thermally managed z-scan technique. The timeevolution of the transient transmission of the z-scan traces forevery position around the focal point during the opening time isshown in Fig. 5. The time evolution of the normalized transmis-sion at the peak and valley of the z-scan were extracted asdescribed in Ref. [16]and we found no significant modificationsto the magnitudes of n2 and b. This result enabled us to rule outany dominating contribution from the thermal effects to thenonlinear response of samples.

The MG theory is widely applied to predict the third-ordernonlinear response of nanocomposite materials with low metalvolume fractions. This theory utilizes the mean field approximation,in which the local field in a single isolated particle is assumed to bequasi-static. Subsequently, the third-order susceptibility is expressedby [19,20],

wð3Þ ¼ pwð3Þm 9f 92ðf Þ2 ð5Þ

where p is the metal volume fraction (p{1) and wð3Þm is the third-order nonlinear susceptibility of the bulk metal. Using the MG theory,the local field factor f is defined as the ratio between the electric fieldin the metal particle and the applied field, and it is given byf ðoÞ ¼ 3ed=emþ2ed, where ed and em denote the frequency-dependent dielectric functions of the host material and the bulkmetal, respectively. In the case of nanoparticle embedded composites,the complex dielectric constant can be expressed as

em ¼ e0m�ie00m ð6Þ

where

e0m � e0m-bulk, e00m ¼

o2p

o3t¼ e00bulkþ

3o2pnF

4o3r: ð7Þ

The real part of the dielectric constant of a metal nanoparticlecan be the same as that of the bulk metal, and o, op, nF, and r

represent the frequency of light, the plasma frequency, the Fermivelocity, and the radius of the metal particle, respectively. Wefirst calculated the w(3) values at various wavelengths using theMG theory (depicted in Fig. 6), and these values are comparedwith the experimentally obtained w(3) values at 800 nm and1250 nm (Tables 2 and 3). A clear discrepancy is noticed betweenthe magnitudes of the experimental and theoretical (MG) w(3)

values. The experimental values of 9w(3)9 are approximately threeorders of magnitude higher for all the nanocomposite films. Onereason for these results is that the MG theory does not consider

Table 2Estimated third-order nonlinear optical properties of the Au:SiO2 nanocomposite films.

Sample 800 nm 1250 nm

n2 (cm2/W) b (cm/W) FOM (esu cm) n2 (cm2/W) b (cm/W) FOM (esu cm)

NC0.2 �2.85�10�11�0.22�10�6 5.20�10�13

�0.94�10�11�0.59�10�7 3.13�10�13

NC1.0 �3.82�10�11�0.42�10�6 2.96�10�13

�2.26�10�11�1.55�10�7 7.58�10�13

NC2.0 �7.52�10�11�1.07�10�6 3.37�10�13

�2.56�10�11�2.29�10�7 9.59�10�13

NC2.5 �8.56�10�11�4.08�10�6 4.21�10�13

�5.22�10�11�2.63�10�7 15.2�10�13

Fig. 5. Time evolution of the nonlinear transmission for analyzing thermal

accumulation using thermally managed z-scan for Au:SiO2 nanocomposites.

Fig. 6. The calculated effective 9w(3)9 values of the Au:SiO2 nanocomposites with

different particle sizes using the Maxwell-Garnett model.

H.W. Lee et al. / Optics Communications 286 (2013) 347–352 351

the effect of interparticle interactions on the nonlinear responseof the nanocomposite. For a detailed explanation of our experi-mental results, therefore, a better theoretical analysis is required.Such a discrepancy between the experimental and theoreticalw(3) values can be understood if we consider the mutual interac-tions between the Au nanoparticles, which can greatly influencethe third-order nonlinear response through the local field enhance-ment. There have been several reports on the numerical evaluationof the contribution of interparticle interactions to the nonlinearresponse of particles [15,16]. In these reports, the redshift of the

plasmon resonance and the enhancement of the local field factor ofthe metal–dielectric structure were calculated by considering thecontribution of the interparticle interactions.

In order to evaluate the local field enhancement in the off-resonant spectral regions, we used the invariant imbeddingmethod [21]. This method is used to obtain the local fieldamplitude inside the nanocomposite medium by solving theinitial value problem using the dielectric permittivity. The effec-tive w(3) values which were obtained from the calculation of thelocal field intensity for different Au:SiO2 nanocomposites areshown in Fig. 7. A summary of the comparison of the experi-mental results with these theoretical results is given in Table 3.The good match between the results within one order of magni-tude indicates that the interparticle interaction of the metalparticles could be one of the main contributions to the enhance-ment of the third-order nonlinear susceptibility in the off-resonant region. In addition to the large magnitude of w(3), weobserved its dependence on the size of the nanoparticles at both800 nm and 1250 nm. The theoretical calculation with Eq. (5) onthe basis of the invariant imbedding method could also describethe size dependent behavior of w(3) (Table 3). The redshift in theeffective w(3) resonance peak in Fig. 7 originates from the resonantfrequency shift of surface plasmon excitations. Thus, the invariantimbedding method can successfully evaluate the nonlinearresponse of metal–dielectric nanocomposites and can be a power-ful technique for estimating the enhancement of the opticalnonlinearity. We, however, remark that more work is necessaryto improvise the present invariant embedding method to includeinterparticle distance effects on the optical properties of thecomposite.

One can note from recent reports [22,23] that the intrinsicnonlinear susceptibility of the nanoparticle is especially influ-enced by the intraband transition of electrons, the interbandtransition, and the hot electron contribution, with the intrabandtransition being primarily responsible for the size-dependentbehavior of w(3) [19]. This intraband contribution has beenproposed for metal particles with diameters in the range of about1–10 nm, where the quantum size effects arise, and the changesin the electron mean-free path, which determine the thermal andelectrical conductivity, as well as the optical properties, will takeplace. Because the imaginary part of the dielectric constant of themetal nanoparticle can be expressed by Eq. (7), the third-orderoptical nonlinearity of the metal nanocomposite can be influ-enced by the size of the metal particles [4].

We calculated the figure of merit (FOM), which is a usefulparameter when assessing the suitability of a material forpractical applications, for all the composites (Table 2). The FOMcan be expressed as

wð3Þeff

a ¼p9f 92

f 2wð3Þm

p9f 92e00m

" #¼

f 2

e00mwð3Þm , ð8Þ

where a, p, f, and e00m represent the linear absorption coefficient,volume fraction of inclusion material, local field factor, and imaginarypart of the dielectric constant for the metal nanoparticle, respectively.

Table 3Estimated third-order nonlinear susceptibility of the Au:SiO2 nanocomposite films by the MG theory (MG), invariant imbedding method (IBD), and

experiment (EXP).

Sample 800 nm 1250 nm

9w(3)9 MG (esu) 9w(3)9IBD (esu) 9w(3)9EXP (esu) 9w(3)9MG (esu) 9w(3)9IBD (esu) 9w(3)9EXP (esu)

NC0.2 1.42�10�12 0.80�10�9 2.29�10�9 1.17�10�14 4.31�10�10 0.75�10�9

NC1.0 2.46�10�12 0.83�10�9 3.11�10�9 2.17�10�14 4.45�10�10 1.82�10�9

NC2.0 2.90�10�12 1.05�10�9 6.30�10�9 2.73�10�14 4.48�10�10 2.11�10�9

NC2.5 2.98�10�12 1.08�10�9 7.71�10�9 2.85�10�14 4.58�10�10 2.18�10�9

Fig. 7. The calculated effective 9w(3)9 values of the Au:SiO2 nanocomposites with

different particle sizes using the invariant imbedding method.

H.W. Lee et al. / Optics Communications 286 (2013) 347–352352

It can be noticed that the FOM is better at 1250 nm, which is due tothe lower linear absorption of particles at 1250 nm.

4. Conclusion

z-Scan measurements on Au:SiO2 nanocomposites were per-formed at off-resonant wavelengths of 800 nm and 1250 nm.The negative signs of Im[w(3)] and Re[w(3)] are observed forAu particles with mean diameters of r10 nm. The discrepancynoted between the w(3) values obtained from the experiment andthe conventional Maxwell-Garnett theory has been explained byusing the invariant imbedding method. The invariant imbeddingmethod enables us to precisely predict the value of 9w(3)9 in thenear infrared (NIR) and infrared (IR) wavelengths far from the SPRabsorption band. The theoretically estimated values from theinvariant imbedding method show good agreement with theexperimental results. The size-dependent variation of the third-order nonlinearity could be qualitatively confirmed at 800 nmand 1250 nm.

Acknowledgments

This work was supported by the National Research Foundation(NRF) funded by the Korean Government (MEST) (grant nos.2011-0017494, 2012-0000608, 2010-0018855, and 2010-220-C00013).

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