ARTICLE IN PRESS

Physica B 405 (2010) 2848–2851

Contents lists available at ScienceDirect

Physica B

0921-45

doi:10.1

n Corr

E-m

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

MATLAB-based experimental analysis of optical limiting properties of Cu/Agmixture nanoparticles

Y.H. Wang a, Y.M. Wang b,n, C.J. Han a, J.D. Lu a, L.L. Ji a, R.W. Wang a

a Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science & Technology, Wuhan 430081, Chinab Department of Nephrology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan 430022, China

a r t i c l e i n f o

Article history:

Received 22 February 2010

Received in revised form

6 April 2010

Accepted 7 April 2010

Keywords:

Ion implantation

Nanoparticles

Optical limiting

26/$ - see front matter & 2010 Elsevier B.V. A

016/j.physb.2010.04.010

esponding author. Tel.: +86 27 61094568.

ail address: wyh61@163.com (Y.M. Wang).

a b s t r a c t

The evolution of nanoclusters in sequentially ion-implanted Cu/Ag into silica glasses has been studied.

Third-order nonlinear optical properties of the nanoclusters were measured at 1064 nm excitations

using the Z-scan technique. Results of the investigation of nonlinear refraction by the off-axis Z-scan

configuration were presented and the mechanisms responsible for the nonlinear response were

discussed. The innovative point of this paper is that we carried out curve fitting analysis, which is based

on MATLAB features, for Cu/Ag optical limiting experiment. Our results showed that Cu/Ag mixture

nanoclusters have refractive optical limiting effect at 1064 nm.

& 2010 Elsevier B.V. All rights reserved.

1. Introduction

Potential applications of optical limiters in the protection ofsensors from intense laser pulses have motivated many efforts todesign new nonlinear optical systems [1]. Recently, increasingattention has been focued on the third-order nonlinear suscept-ibility and the photorefractive effect of noble–metal clustersembedded in dielectric matrices [2,3]. Third-order nonlinearitiesof metal/dielectric composite materials are influenced not only bythe type and size of the embedded metal nanoclusters but alsoby the dielectric constant, thermal conductivity and heat capacity ofthe dielectric matrices [2–6]. Amongst the nanoclusters studied inearlier papers, high nonlinear absorption and nonlinear refractioncoefficients are found in copper and copper containing nanoma-terials [7,8]. For silver, nonlinear refractive index n2 changes frompositive to negative upon the cluster’s growth [9].

Ion implantation has been utilized to produce high-densitymetal colloids in glasses. The high precipitate volume fraction andthe small size of nanoclusters in glasses lead to a greater third-order susceptibility than those of metal doped solid [10]. Thethird-order nonlinear optical responses of the metal nanocluster–glass composites can be understood from the framework ofdielectric and quantum confinement effects. Optical nonlinea-rities and optical limiting effects of the nanocomposites withmetal nanoparticles can be significantly enhanced by increasingthe number density and the size of metal particles [11].

ll rights reserved.

Application aspects of the material are closely related to thechange of optical properties versus the nanocluster structure.

Currently, optical limiting results obtained by the analysis ofexperimental practice including the completion of the researchtasks, engineers and technicians draw, are usually analyzed byauxiliary tools, such as Microcal Origin, Microsoft Excel, and so on.Although these analysis tools provide great help to variousexperimental results, all of these tools are direct applicationsoftware, which is not comprehensive enough to fitting curve, andsome limitations still remain on analysis of experimental data.

MATLAB incorporates engineering calculation, visual functionof figure into an organic whole, and offers Windows interfacedesign method of a figure. MATLAB has stronger operation ability,powerful and intelligent mapping, and higher programmingefficiency; in particular, it can be used for application develop-ment in this field. In this study, MNCGs were prepared bysequential implanted Cu/Ag ions into silica according to theexperimental protocol. We focused our interest on studying thenonlinear optical properties and optical limiting properties of thiskind of metal nanoclusters herein.

2. Experiments

Silica slides were implanted at room temperature sequentiallywith 5�1016 Cu+ ions/cm2 and 5�1016 Ag+ ions/cm2. Thecurrent density of ion implantation was lower than 1.5 mA/cm2 forCu and 2.5 mA/cm2 for Ag. According to the transport and range ofions in matter (TRIM) [12] calculation, the energies of implanta-tion (180 keV for Cu and 200 keV for Ag) are chosen to obtain

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2000.0

0.5

1.0

1.5

2.0

418 nm

570 nm

445 nm

1064 nm

Opt

ical

den

sity

(a.u

.)

Wavelength (nm)400 600 800 1000 1200

C

B

A

ABC

AgCuCu/Ag

Fig. 1. Linear absorption spectra of the Ag, Cu and Cu/Ag mixture nanoparticles.

Y.H. Wang et al. / Physica B 405 (2010) 2848–2851 2849

similar ion distribution with consideration of surface sputteringeffect. Optical absorption spectra were recorded at room tem-perature using a UV–vis dual-beam spectrophotometer withwavelengths from 1200 to 200 nm. The measurements of third-order optical nonlinearities of these samples were carried outusing the standard Z-scan method. The excitation source is amode-locked Nd:YAG laser (PY61-10, Continnum), with a pulseduration of 38 ps and a repetition frequency of 10 Hz. 1064 nmwavelength is used for excitation in the experiment. The detectoris a dual-channel energy meter (EPM2000). With a converginglens of f¼260 mm, the radius of the Gaussian beam spot at focalwaist $0 is 44.7 mm. In the Z-scan test, the sample was movedstep by step along the propagation direction of the Gaussian beamunder the control of a computer. Meanwhile, a detectormonitored the transmitted laser power and the signals were sentback to the computer and recorded. Nonlinear refraction andnonlinear absorption were performed by both open- and closed-aperture Z-scans of a series of the samples at room temperature.Liquid CS2 in a fused-silica cell, 1 mm in thickness, was used as areference sample (gffi2�10�14 cm2/W in 1064 nm).

We carried out curve fitting analysis of Cu/Ag mixturenanoparticles optical limiting experimental results based onMATLAB features. According to the Cu/Ag mixture nanoparticlesexperimental data obtained, we applied the polynomial curvefitting method to get the fitting procedure and the fittingprocedure, which is as follows:

program Cu/Ag.mx10¼[0:0.4:3.2];x11¼[4.0:0.4:20.8];x12¼[22.4:0.4:35.2];x¼[x10,x11,x12]0;y¼[]; here [] is the output data of Z-scanp1¼polyfit(x,y,3);yy¼polyval(p1,x);plot(x,yy,x,y,‘+ ’),grid onFig.(2)X¼[ones(size(x)) exp(�x) x.nexp(�x)];a¼X\y;Y¼[ones(size(x)) exp(�x) x.nexp(�x)]na;plot(x,Y,‘� ’,x,y,‘.’),grid on

The valuable data of the experiments were shown in theprogram, while the non-value ones were removed. Furthermore,the distribution of valuable data points was analyzed by indexregression equation.

3. Results and discussion

Fig.1. shows the optical absorption spectra of Cu/Agsequentially implanted samples. For comparison, opticalabsorption spectra of 5�1016 Ag+ ions/cm2 and 5�1016 Cu+

ions/cm2 are also presented in Fig. 1. Surface plasmon resonance(SPR) peak positions are at 445 and 570 nm for the samples5�1016 Ag+ ions/cm2 (Ag sample) and 5�1016 Cu+ ions/cm2

(Cu sample). SPR peak at 445 nm with two shoulders around 400and 570 nm is observed in the Ag sample. However, the resonancepeak position (418 nm) is found in Cu/Ag sample. Compared toMie’s case (�400 nm), we think implanted Ag ions with firstimplanted Cu ions bring out collision and very little nanoparticleshave coalesced. Overall, collision produces a lot of scatteredsingle-phase particles, which lead to SPR peak being blueshifted.Our previous work [13] shows the cross-sectional TEM imageof Cu/Ag sample. There is no information of alloying betweenthe two implanted metal samples. Dual-layer distribution of

nanoparticles has been formed, where the shallower implantedlayer contains smaller spherical Ag nanoparticles with sizes lessthan 10 nm. The SPR peak in the present (Ag-445 nm) case is dueto larger Ag nanoparticles. The left shoulder band around 400 nmis the resonance absorption peak of the non-interacting smallnanoparticles.

The third-order nonlinear absorption and refraction areinvestigated by Z-scan techniques [14]. This technique is simpleand sensitive for studying nonlinear optical properties anddetermining the sign of the nonlinear refractive and absorptionindices. The open- and closed- aperture Z-scan curves aretheoretically fitted by [14]:

TðzÞ ¼X1

m ¼ 0

½�q0ðzÞ�m

ð1þx2Þmðmþ1Þ3=2

ðmZ0Þ ð1Þ

TðzÞ ¼ 1þ4DF0 x

ðx2þ9Þðx2þ1Þð2Þ

where x¼z/z0, T is the normalized transmittance and z is thedistance along the lens axis in the far field. The nonlinearrefractive index is calculated by DF0¼(2p/l)gI0Leff, where 2p/lis the wave vector of the incident laser, I0 is the intensity of thelaser beam at the focus (z¼0), Leff is the effective thickness ofthe sample, which can be calculated from the real thickness L

and the linear absorption coefficient a0, in the form of Leff ¼

1�exp �a0Lð Þ½ �=a0.Third-order nonlinear optical property of the sample at

1064 nm is shown in Fig. 2; the open-aperture Z-scan shows nononlinear signal, which indicates that the sample has no nonlinearabsorption at 1064 nm. In Fig. 2, the peak–valley configurationindicates the negative sign of the nonlinear refractive index(n2o0). A self-defocusing refraction is verified from the peak–valley curve of closed-aperture data. It is considered this comesfrom the optical Kerr effect. The nonlinear property of the baresilica substrate is measured and there is no detectable change ofthe transmitted intensity under the same Z-scan conditions.

In our experiments, Leff (nm) for the sample is 64 nm. The peakintensity of 0.38 GW/cm2 is selected for the sample. Fitting theZ-scan data of the closed-aperture with Eq. (2), we get a value ofgE�1.6�10-10 cm2/W for 1064 nm. The absolute value of third-order nonlinear susceptibility w(3) for Cu/Ag mixture nanoparticlesimplanted sample is calculated using the following equations[14,15]:

DTp�v ¼ 0:406ð1�SÞ0:259Dj09 ð3Þ

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-300.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

a

Nor

mal

ized

Tra

nsm

ittan

ce

Z (mm)

Experiment Theoritical fit

-20 -10 0 10 20 30

Fig. 2. Z-scan experiment results for 1064 nm normalized close-aperture. Solid

line: theoretical curve.

0 0.5 1 1.5 2 2.5 3 3.5 4x 10-5

-0.5

0

0.5

1

1.5

2

2.5 x 10-5

Out

put (

kJ/c

m2 )

Input (kJ/cm2)

Fig. 3. Cu/Ag mixture nanoparticles’s three times polynomial fitting curve.

0 0.5 1 1.5 2 2.5 3 3.5 4x 10-5

-0.5

0

0.5

1

1.5

2

2.5x 10-5

Input (kJ/cm2)

Out

put (

kJ/c

m2 )

Fig. 4. Cu/Ag mixture nanoparticles exponential regression analysis curve.

Y.H. Wang et al. / Physica B 405 (2010) 2848–28512850

Re w 3ð Þ ¼ 2n20e0cg ð4Þ

Thus, we obtain the absolute value of w(3) as 1.1�10�7 esu for1064 nm.

We carried out optical limiting measurement for the samplehaving no nonlinear absorption at 1064 nm. The results ofrunning the MATLAB program Cu/Ag.m obtained fitting curveare shown in Figs. 3 and 4.

As shown in Fig. 3, we found that the fitting sample imageoutput values increases along with the increase of x. However,when the increasing rate of the output value gradually reduce tozero, there is a drop in the curve tail section. Nevertheless, thefitting curve is still a very good line to reflect the optical limitingcharacteristics of the curve, indicating the Cu/Ag mixturenanoparticles with the optical limiting effect. Moreover, the indexof regression analysis, which is shown in Fig. 4, is a typicaloptical limiting characteristic curve. It appeared in a certainturning point only in the initial segment because of theexperimental error.

From the figures above, it is clear that Cu/Ag mixturenanoparticles exhibited a certain degree of optical limitingproperties. MATLAB, as a fitting tool, has successfullyaccomplished the completion of fit tasks and is a good helper tostudy the materials optical limiting.

4. Conclusion

In this paper, metal nanoparticles in silica have beensynthesized by sequential implantation of silver and copper ions.We report the experimental observations of the nonlinear opticalresponses of Cu/Ag mixture nanoparticles using pecosecond laserpulses. During the 1064 nm excitation, the sample had nononlinear absorption and w(3) is �1.1�10�7 esu, which comefrom nonlinear refraction contribution. Moreover, the opticallimiting effect in the 1064 nm was also observed in this study. Weapplied the polynomial curve fitting method and made indexregression analysis by using MATLAB software. Basically, thecurve fitting reflects that the sample has optical limiting propertyat near-infrared field. MATLAB, in the study materials aboutoptical limiting performance, is effective. Further studies aboutCu/Ag mixture nanoparticles are in progress.

Acknowledgment

This work was supported by the National Natural ScienceFoundation of China (No. 10805035).

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