SURFACE PLASMON EXCITATIONAND MANIPULATION IN DISORDERED

TWO-DIMENSIONAL NANOPARTICLE ARRAYS

VICTOR COELLO* and RODOLFO CORTESCentro de Investigaci�on Cient�{¯ca y de EstudiosSuperiores de Ensenada BC, Unidad Monterrey

Km 9.5 Carretera Aeropuerto, Parque de Investigacion eInnovacion Tecnologica (PIIT) Apodaca

Nuevo Leon 66629, Mexico*vcoello@cicese.mx

CESAR E. GARCIA-ORTIZ and NORA ELIZONDOUniversidad Autonoma de Nuevo Leon, Doctorado en Ingenieria

Fisica Industrial-FCFM, Pedro de Alba S/NSan Nicolas de los Garza, Nuevo Leon 66451, Mexico

Received 15 November 2012Accepted 8 April 2013Published 14 May 2013

We present experimental and numerical results of simultaneous surface plasmon polariton (SPP)excitation and in-plane manipulation with random arrays of gold nanoparticles. The recordedimages were obtained by using leakage radiation microscopy (LRM) for the excitation wave-length of 633 nm and for di®erent densities of particles. The numerical model makes use of acomposed analytic Green dyadic which takes into account near- and far-¯eld regions, with thelatter being approximated by the part describing the scattering via excitation of SPP. The LRMoptical images obtained are related to the calculated SPP intensity distributions demonstratingthat the developed approach can be successfully used in studies of systems of closely spacedarrays.

Keywords: Surface plasmon polaritons, green dyadic, multiple scattering.

1. Introduction

Plasmonics is a very active research area dealing

with fundamental studies of surface plasmon

polaritons (SPPs),1 and opening promising techno-

logical perspectives within nano-optics, e.g., in

miniaturized photonic components.2 SPPs are elec-

tromagnetic excitations coupled to electron plasma

oscillations, which have the property of propagating

along a metal/dielectric interface as quasi two-dimensional (2D) interface waves. Even though thephenomenon of SPP has been known for a long time3

its local study is relatively recent and has beenstrongly motivated by the development of imagingtechniques such as the scanning near-¯eld opticalmicroscopy (SNOM),4,5 and the °uorescence micro-scopy.6 The two techniques each had their own dis-advantages. SNOM has a resolution which mostly

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NANO: Brief Reports and ReviewsVol. 8, No. 4 (2013) 1350044 (11 pages)© World Scienti¯c Publishing CompanyDOI: 10.1142/S1793292013500446

depends on tip quality, and an optical mapping thatis relatively slow whereas °uorescence microscopyexhibits molecular photobleaching and thereforedoes not allow quantitative analysis. An alternativedeveloped recently that overcome these limitations isthe so-called leakage radiation microscopy (LRM).7

The technique is simple in conception and provides arapid 2D SPP mapping, and the possibility of sim-ultaneous access to direct and reciprocal space. LRMhas stimulated plasmonics research in various direc-tions, one of them being SPP interaction and ma-nipulation with nanostructures. In this context, theinteraction of SPP waves with nanostructures hasbeen investigated ranging from individual nan-ometer-sized ¯lm structures,7 including quantumdots,8 to more complex plasmonic elements such asBragg mirrors,9 beam splitters,10 waveguides,11,12

refracting elements,13 etc. In general, the aforemen-tioned phenomena are related to the propagationof SPP waves through periodic or nanostructuredplasmonic elements. Considering the SPP interactionwith randomly 2D nanoparticles arrays, extensivetheoretical studies have been conducted.14�16 How-ever, experimental evidences of related phenomenasuch as localization17 and photon bandgap e®ect ofSPPs18 are still scarce. The experimental frameworkis not trivial since the unwanted process of SPPscattering into a free space is always present duringthe course of SPP propagation. Those radiative los-ses increase as the volume fraction of nanoparticlesbecomes larger, and as a consequence rather com-plicated and misleading ¯eld patterns may appear inthe surface plane. On the other hand, a relativelylarge density of nanoparticles is necessary in order toa®ect the transport of the light, and therefore, loca-lize electromagnetic modes in standing rather thantravelling waves.17 This suggests a trade-o® thatneeds to be explored further. In this context, using avectorial dipolar model for multiple SPP scatter-ing,19 we have numerically demonstrated the possi-bility of simultaneous SPP excitation and in-planemanipulation with square-lattice arrays of nano-particles.20 The main idea was in avoiding the usageof local SPP excitation elements as for example, in-coupling ridges,21 subwavelength hole arrays on athick metal ¯lm,22,23 or nanotubes.24 Therefore, itseems plausible that reducing the number of com-ponents could help not only in the miniaturization ofplasmonics circuits but also in minimizing unwantedSPP scattering and interference e®ects. Recently,we extended the aforementioned approach, by

introducing a composed analytic Green dyadic whichtakes into account near- and far-¯eld regions, andused to calculate simultaneous SPP excitation andin-plane propagation inside square-random arrays ofnanoparticles.25 The composed Green dyadic rep-resented an improvement of previous SPP simu-lations for random nanoparticles arrays since itpermitted SPP scattering simulations for more rea-listic systems with relatively large number of close, oreven in contact, nanoparticles. A system of closelyspaced arrays of nanoparticles is desirable in, forexample, plasmonic ¯eld enhancement for sensitivedetection of biological samples.26

Here, using a LRM, we experimentally investigatethe possibility of simultaneous SPP excitation andpropagation control in random 2D arrays of nano-particles illuminated by a normally incident Gaus-sian beam. We compare our optical images with thepreviously reported25 and the additionally obtainednumerical results. The paper is organized as follows.In Sec. 2, the main relationships used in our calcu-lations are given and explained. The experimentalsetup and the techniques for sample preparation, ingeneral terms, are presented in Sec. 3. Typical ex-perimental LRM images of the SPP excitation bynearly isolated particles are presented in Sec. 4. InSec. 5, numerical and experimental images of severalregimes of multiple scattering are presented forrandomly situated nanoparticles and the correlationbetween the regimes and their corresponding spatialFourier spectra are discussed. In Sec. 6, a simpleoptical refracting system composed of randomlysituated nanoparticles is considered. Finally, inSec. 7, we summarize the results obtained and o®erour conclusions.

2. The Model

The model is based on the assumptions that the in-plane SPP scattering is dominant with respect to theSPP scattering out of the plane, and that if the lightis incident on a metal/dielectric interface withscattering objects, the objects can be modeled aspoint-like dipoles.25 For out of plane scattering ofSPPs, we will consider propagating ¯eld componentsscattered away from the surface decreasing the totalenergy stored in SPPs. In-plane scattering of SPPsoccurs when SPPs are scattered by surface imper-fections along the surface plane, i.e., into other SPPspreserving the total SPP energy. These assumptionsled to the construction of an approximate Green's

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V. Coello et al.

tensor describing SPP-to-SPP scattering by a dipo-lar point-like nanoparticle located at a metal/dielectric interface. The validity of the model hasbeen established for relatively large inter-particledistances, whereas for smaller distances it is moreaccurate to use a composed analytic Green dyadicwhich takes into account near- and far-¯eld regions(SPP to SPP scattering) with the ¯rst being ap-proximated by the near-¯eld electrostatic approxi-mation of the total Green dyadic.25

The self-consistent polarization of each scattererestablished in the process of multiple scattering isobtained by solving the following equation:

Pi ¼ ®i �E0ðriÞ þk20

"0

Xn6¼i

®i �Gðri; rnÞ �Pn; ð1Þ

where Pi is the polarization of the particle i, �i isthe polarizability tensor for particle i with themultiple scattering between the particle and themetal surface taken into account (surface dressinge®ect), E0 is an incoming electric ¯eld, k0 is the freespace wave number, "0 is the vacuum permittivityand G(ri, rnÞ is the Green's tensor for the referencestructure (total ¯eld propagator). The Green'stensor G is the sum of a direct contribution Gd, inthis case the free space Green's tensor, and anindirect contribution GS that describes bothre°ection from the metal/dielectric interface andexcitation of SPPs. In order to take into accountspatial distribution of the incident ¯eld, whichinteracts with the particles, we assume that theincoming electric ¯eld is determined by thefollowing expression E0 ¼ e expð�½x2 þ y2�=W 2Þ,where e is the unit polarization vector and W is thewaist of the incident light beam. In a general form,E0 should be a ¯eld for the reference geometry,which would include the re°ection from the surfaceand a phase di®erence between the incident and there°ected ¯elds at a height z above the surface. Thiswill in practice only result in a scaling factor andtherefore one can use the above expression for E0 todescribe the illumination conditions with reasonablyaccurate results. For a spherical particle made of thesame metal as the substrate, the polarizability ten-sor is given by28�30:

� � I� "� 1

"þ 1

"� 1

"þ 2

1

8xx þ 1

8yy þ 1

4zz

� �� ��1

� �0;

ð2Þ

where I is the unit dyadic tensor, " is the metaldielectric constant, x; y; z are unit vectors in aCartesian coordinate system with z being perpen-dicular to the air�metal interface, and �0 ¼"0I4�a

3"�1"þ2 is the free space polarizability tensor in

the long-wave electrostatic approximation with abeing the sphere radius. The polarizations [seeEq. (1)] and the total ¯eld,

EðrÞ ¼ E0ðrÞ þ k20

"0

Xn

Gðr; rnÞ �Pn; ð3Þ

can be calculated using the appropriate Green'stensor for the reference structure Gðr; r 0Þ. Finally,based on the initial assumptions, we have used theanalytic representations of the Green dyadic in thenear- and far-¯eld (SPP to SPP propagator) regions.The complete analysis of the validity domain of suchan approximation as well as the suitable limit todistinguish between the uses of these expressionswere presented in detail elsewhere.25

3. Experimental Techniques

3.1. Sample preparation

In order to prepare the sample, a small drop con-taining a water solution of colloidal gold nano-particles (spheres) was then deposited on a goldthin ¯lm (50 nm), which was previously thermallyevaporated on a glass substrate. The drop evapor-ates after some minutes leaving a high-density cir-cular region with gold nanoparticles. When a dropof colloidal solution of nanoparticles dries on asurface it leaves behind a stain-like ring (\co®eestain") of material with clumps of particles in theinterior and a few number of them on the outside ofthe ring. Thus, the ¯nal sample structure consistedof both a high- and a low-density scattering regionscomposed of gold bumps randomly distributed overthe thin gold ¯lm [see Figs. 1(a)�1(c)]. The scat-tering regions densities were approximately of 10(low) and 50 (high) particles per 1�m2. The col-loidal gold nanoparticles were synthesized by usingthe green chemical method which is a simple, coste®ective and environmental friendly technique(more information about our procedure is found inRef. 27). The transmission electron and atomicforce microscopy studies revealed an average par-ticles size distribution ranging from 20 nm to100 nm [see Fig. 1(a)�1(c)].

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Surface Plasmon Excitation and Manipulation in Disordered 2D Nanoparticle Arrays

3.2. Leakage radiation microscopy

The experimental setup used for SPP imaging isshown in Fig. 2. SPPs are excited locally by focusingpolarized light from a He�Ne laser (633 nm)through a 20� (NA ¼ 0:4) microscope objective(O1) onto the surface of the arti¯cially nanos-tructured gold ¯lm (S). The image of leakage radi-ation is collected on a CCD camera after passingthrough a 63� (NA ¼ 1:25) oil-immersion objective(O2). The system allows one to study SPP propa-gation in both the direct and indirect space (Fourierspace, ’). Imaging Fourier space is possible byrecording the LRM ¯eld in the back focal plane ofthe oil immersion objective. A ¯lter (BB) in Fourierspace may be used to help that only the wavescorresponding to LRM are resolved, in order to

maximize the CCD image contrast and reduce noise.To facilitate observation of the surface structure, alamp illumination is conjugated with the 20�objective. A neutral density ¯lter (NDF) was usedto attenuate the probe laser intensity in order toavoid saturation in the CCD camera.

4. Random Particles Arrays:

Low-Density Area

First we imaged the LRM ¯eld created by an inci-dent (linear polarized) Gaussian beam, x-pol,� ¼ 633 nm, FWHM ¼ 2�m, and impinging on asmall area of the low-density region of nano-particles. Hereafter all the images are presented inlinear grayscale. Two extended lobes similar tothose related to dipole-like damped radiation fromsingle nanoparticles are clearly seen in the directspace image [see Fig. 3(a)]. This is achieved byfocusing the illumination beam to a cluster of a fewparticles since our imaging system cannot provideenough information of spatial resolution about theposition of a single nanoparticle [see Fig. 3(b)]. SuchSPP beam scattering was numerically simulated [seeFig. 3(c)] using the total Green's tensor formalismdescribed in Sec. 2. Hereafter, the entire systems aresimulated on a gold surface with dielectric constant" ¼ �11þ 1:4i and the illumination conditions arekept the same for all the calculations. The calcu-lated images show grayscale representations of thedistributions of the intensity jEj2 for the illumina-tion wavelength (633 nm). The total intensity ¯eldwas calculated 80 nm above the air�gold interface,and the incident beam has been removed; i.e., onlyscattered SPP appear in the pictures. The con-¯guration and the illumination conditions can beconsidered as fairly similar to the experimental ones,for example we have used a cluster system of 10particles. The radius of the particles (30 nm) is a¯tting parameter which is chosen to match the ex-perimental images. This is because the size of theparticles used in simulations is only relevant within

(a) (b)

(c)

Fig. 1. (a) TEM image of gold nanoparticles synthesized bythe green synthesis method. AFM images (65� 65�m2Þ of thegold sample surface showing (b) a high- and a low-densityscattering regions composed of gold bumps randomly dis-tributed and (c) zoom (10� 10�m2Þ on the low-density areashowing individual particles.

Fig. 2. Experimental setup for LRM.

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V. Coello et al.

the model and in°uences the polarizability of theparticles,19,25 but does not bear a direct relation tothe size of the scatterers in the experiment. Theleakage radiation recorded in the Fourier plane ofthe microscope [see Fig. 3(d)] exhibits two crescentsthat are characteristic of the Au/Air SPP mode,and which also indicate the polarization direction.31

In the calculated Fourier spectrum of Fig. 3(e), onecan see a very good agreement with the main fea-tures of Fig. 3(d). In order to get a more realisticnumerical calculation, the numerical aperture ofthe collection objective was taken into account, i.e.,in our calculations, the Fourier image is limited

toffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffik2x þ k2

y

q=k0 � N:A. The ¯eld distribution dis-

played in Fig. 3(a) mainly shows the ¯eld com-ponent parallel to the polarization of the incident¯eld. However, the horizontal orthogonal com-ponent though being weaker is di®erent from zero.In order to map such component and therefore tostudy, in more detail, the near- and far-¯eld scat-tering contributions, we have performed LRMmeasurements in cross polarized detection. For this

reason, a linear polarizer was placed in front of theCCD camera of our experimental setup. Theintensity distributions of the horizontal componentbeing dictated by nondiagonal elements of the ¯eldpropagators may produce complicated patterns. Inaccordance with this, now we observed a four-lobepattern in both the recorded [see Fig. 4(a)] andcalculated images [see Fig. 4(b)]. Based on the pro-posed model, one should expect to distinguish atransition zone in the obtained pattern since we usea near-¯eld dyadic for distances shorter and a SPPdyadic for distances longer than a speci¯ed fractionof the illumination light wavelength.25 The centralpart of the calculated image clearly exhibited thatthe extended lobes are formed only after an initialtransition region [see Fig. 3(d)]. A similar transitionbetween bright spots and elongated lobes is evidentin the experimental obtained image [see Fig. 3(c)].The ¯eld distribution displayed in Fig. 3(a) mainlyshows the ¯eld component parallel to the polariz-ation of the incident ¯eld. However, the horizontalorthogonal component though being weaker isdi®erent from zero. In order to map such component

(a) (b) (c)

(d) (e)

Fig. 3. (a) LRM of a dipole-like damped radiation. (b) Topographic image of a small nanoparticle cluster. (c) Dipole-like dampedradiation calculated image. Fourier space (d) LRM and (e) calculated images of (a) and (c), respectively. The arrow indicates theincident light polarization in (a) and (c).

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Surface Plasmon Excitation and Manipulation in Disordered 2D Nanoparticle Arrays

and therefore to study, in more detail, the near- andfar-¯eld scattering contributions, we have performedLRMmeasurements in cross polarized detection. Forthis reason, a linear polarizer was placed in front ofthe CCD camera of our experimental setup. Theintensity distributions of the horizontal componentbeing dictated by nondiagonal elements of the ¯eldpropagators may produce complicated patterns. Inaccordance with this, now we observed a four-lobepattern in both the recorded [see Fig. 4(a)] andcalculated images [see Fig. 4(b)]. Based on the pro-posed model, one should expect to distinguish atransition zone in the obtained pattern since we usea near-¯eld dyadic for distances shorter and a SPPdyadic for distances longer than a speci¯ed fractionof the illumination light wavelength.25 The centralpart of the calculated image clearly exhibited thatthe extended lobes are formed only after an initialtransition region [see Fig. 4(d)]. A similar transitionbetween bright spots and elongated lobes is evidentin the experimentally obtained image [see Fig. 4(c)].

A point dipole emitter not only excites a SPP,but also has its own dipolar emission and its dif-fraction pattern (similar to the one generated by acircular aperture) that overlay coherently on theleakage radiation image of the SPP.7 The inter-ference of these contributions, as well as the ¯nitenumerical aperture of the collection objective, leadto strong circular fringes at the image center ofFig. 4(c). Regarding the theoretical calculation, asit was mentioned in the total ¯eld calculationsthe incident beam has been removed; i.e., only scat-tered SPP appear in the pictures and therefore theexperimentally observed interference pattern is notpresent. Insets (a) and (b) of Fig. 5 show a directSPP excitation taking place at the center of a line-like surface structure with a certain inclinationangle with respect to axis light polarization. Wethink that such line is formed, in the low densityarea, by a short linear chain of the Au nanoparticles[see Fig. 5(a)]. The light-SPP coupling of Fig. 5(b)strongly resembles the classical coupling through aridge structure21 where the process results in aslightly diverging SPP beams propagating awayfrom the ridge. Figure 5(c) shows the result of thecorresponding modeling. There, as an incidentwave, we used a Gaussian beam having the waistsituated at the center of a 150-nm-period line ofnanoparticles (length ¼ 2:5�m). In a previouswork,20 we demonstrated that a similar array workse±ciently with a period of 150 nm. However, oneshould establish that as long as the array period issu±ciently smaller than the incident SPP wave-length, we consider this calculation method as a onegiving the correct result, provided that the size ofthe particles is adjusted appropriately. The line-likestructure has an angle orientation similar to thatobserved in the experimental image. The SPP ex-citation is evidenced by the SPP beam coming outof the line-like structure [see Figs. 5(b) and 5(c)],and by the corresponding Fourier transform [seeFigs. 5(d) and 5(e)]. Here, it is important to notethat not all the synthesized nanoparticles wereperfectly spherical. Bearing this fact in mind, in thecorresponding experimental real space image, oneshould expect that the SPP propagation leads to aslightly asymmetric double lobe structure [seeFig. 5(b)]. The same characteristics of plasmon ex-citation are seen in the corresponding Fourier spaceimage [see Fig. 5(d)]. In the ideal numerical case,the point-like particles are assumed perfect sym-metric [see Fig. 5(c)] and therefore one can observe

(a) (b)

(c) (d)

Fig. 4. Cross polarized (a) LRM and (b) calculated images ofa dipole-like radiation. (c) and (d) Zoom of the central part in(a) and (b), respectively. Incident light polarization is the sameas in Fig. 3.

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point-symmetric k-pace images [see Fig. 5(e)]. Thus,we showed that the developed numerical approachgives consistent results and can be used to modelSPP scattering on more complicated systems suchas high-density random arrays of nanoparticles.

4.1. Random particles arrays:High-density area

In general, the phenomena related to the regime ofSPP multiple scattering are rather complicated andtheir interpretation is far from being trivial. This isdue, at least partially, that the randomness of theinteractions yields a large number of scatteringevents. We studied SPP multiple scattering on asmall area (Area1) of the high-density region ofnanoparticles or clusters. Figure 6(a) shows intensitydistributions where the multiple interference e®ectsare already pronounced. For example, at the centerof the image in Fig. 6(a), i.e., within the area of thescatterers, one can appreciate bright and darkregions which are a collection of small and roundbright spots similar to those reported as evidence oflocalized SPPs.17 The corresponding Fourier spec-trum [see Fig. 6(b)] showed a ¯ngerprint of theexcited SPPs (which propagates almost in all poss-ible directions of Area1) and the interference

between such excited modes and SPP scattered in allpossible directions. In other words, the Fourierspectrum contains a nearly ¯lled circle that corre-sponds to the well-developed multiple scattering.17

Actually, in such SPP scattering regime, two imageswith a slightly di®erent number of particles anddistributions may exhibit distinct total intensity¯elds. Indeed, a small variation of the particles dis-tributions and/or parameters of the incident lightmay change signi¯cantly the total intensity ¯elddistribution. LRM images taken at a di®erent andsomewhat rougher surface area (Area2) of the gold¯lm showed a very complicated interference pattern[see Fig. 6(c)]. In fact, it is possible that only a fewbright spots should be directly related to the excitedand scattered SPPs. For example, if the nano-particles are very close to each other, the nanoarrayis almost symmetric over the extent of the incidentbeam and therefore cannot scatter e±ciently in theaxial direction since the incoming propagating vec-tor and the propagating SPP vector are hardlymatched. The above mentioned is also exhibited inthe Fourier spectrum where a clear SPP ¯ngerprintof the interference between the excited and thescattered SPP's is almost not present [see Fig. 6(d)].In this context, the corresponding numerical simu-lations where made for a total area of 27� 27�m2 in

(a) (b) (c)

(d) (e)

Fig. 5. (a) Topographic image of a line-like surface defect. (b) LRM image of the direct SPP excitation taking place at the center of theline-like defect, and (c) corresponding calculated image. (d) Fourier space LRM and (e) calculated images. The dotted circle and arrowin (a) indicate the incident Gaussian beam and its polarization, respectively. The solid line in (c) represents the line surface defect.

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Surface Plasmon Excitation and Manipulation in Disordered 2D Nanoparticle Arrays

which 100 (representing Area1) and 150 (repre-senting Area2) scatterers were randomly distributedin a central area of 10� 10�m2 [see Figs. 6(e) and6(g)]. Since we assume that the (point-like) particlesare perfectly symmetric and homogeneously dis-tributed in a square area, the calculated k-space

images present a point-symmetric behavior. It isclearly not the case in the experiments. However, ingeneral, the simulations showed a good agreementwith the corresponding above-mentioned exper-imental case [see Figs. 6(e)�6(h)]. Similar investi-gations were carried out in another region of the

Fig. 6. LRM and calculated images of Area1 (a, e) and Area2 (c, g) sections of nanoparticles illuminated with a free-spaceexcitation wavelength of 633 nm and (b, d, f, h) Fourier space images of (a, c, e, g), respectively. Incident light polarization is thesame as in Fig. 3.

(a) (b)

(c) (d)

Fig. 7. (a) LRM and (c) (15� 5�m2Þ calculated images of high density of nanoparticles illuminated with a free-space excitationwavelength of 633 nm. (b) LRM and (d) (8� 5�m2Þ calculated images of a SPP plane wave elastically scattered. The solid circle in(a) and (c) indicates the incident Gaussian beam. The white arrow in (b) and (d) indicates the SPP incident direction. Incident lightpolarization is the same as in Fig. 3.

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V. Coello et al.

random nanoarray that contains the high density ofparticles. LRM and calculated images have shownconsiderably less pronounced e®ects of multiple SPPscattering outside the random structures [seeFig. 7(a) and 7(c)]. Outside the nanoparticle cluster,where only a few scatterers are present, a nearlyplane SPP wave is propagating in the speculardirection with respect to an imaginary boundary ofthe region of nanoparticles [see Figs. 7(a) and 7(c)].Such SPP wave was achieved by using the cluster ofnanoparticles randomly distributed over the thin gold¯lm as a mechanism of simultaneous SPP excitationand propagation. Then, far from its excitation origin(�10�m), the SPP behave as a nearly plane SPPwave. A SPP plane wave impinging on a nanoparticleindeed shows a parabolic interference pattern in theresulting total intensity distribution (as long as theelastic scattering is preserved). Figures 7(b) and 7(d)show an LRM and calculated images that correspondto the interference between a SPP mode with a planephase front (originated outside the scatterer area)and a scattered SPP, due to a nearly isolated nano-particle, with a cylindrical phase front. The existenceof suchwell-pronounced parabolic interference fringesare the basis of the dipole multiple scattering vec-torial model.19

5. SPPs Scattering by VariousNanoparticles

In the low nanoparticle density region, we oftenobserved regions of nearly isolated nanoparticleslying on the surface and relatively close to eachother. We took advantage of those random distri-butions in order to study near-¯eld interactionsbetween closely spaced particles, particularly e®ectsof SPP refraction.13 As mentioned previously, byfocusing the illumination beam to a nearly isolatednanoparticle, dipole-like damped radiation can beachieved. On the other hand, a line of nanoparticlescan act as a beam splitter10 or as a mirror9 mostlydepending on the inter-particle distance. We gen-erated a dipole-like SPP source which pointedtoward a line-like nanostructure [see Figs. 8(a) and8(b)]. Collective SPP refraction e®ects were clearlyexhibited during the course of SPP propagation. Forexample, the interaction between the dipole sourceand the line nanostructure showed a beam splittinge®ect. Far from its origin (�10�m), the transmittedbeam strikes a small cluster of nanoparticlesand parabolic interference fringes can be clearly

observed in the total intensity distribution. Com-parison between numerical and experimentalresults showed a good correlation [see Figs. 8(b)and 8(c)].

6. Conclusions

Summarizing, simultaneous SPP excitation andpropagation control in random 2D arrays of nano-particles have been investigated with the help ofLRM imaging. Numerical simulations based on theGreen's tensor formalism show a goodmatchwith theexperimental results. The numerical calculationswere carried out by using a relatively simple vectorialdipolar model for multiple SPP scattering25 thatallows one to explicitly formulate the set of linearequations for the self-consistent ¯eld, facilitating

(a) (b)

(c)

Fig. 8. SPP refractive e®ects. (a) Topography, (b) LRM and(c) (10� 15�m2Þ calculated images. The dotted circle in (a)indicates the incident Gaussian beam. The arrows in (a) help toguide the eye from the SPP excitation (solid) to the severalrefraction e®ects (dotted). The lines in (b) and (c) represent thesurface features of (a). Incident light polarization is the same asin Figs. 3(a) and 3(b).

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Surface Plasmon Excitation and Manipulation in Disordered 2D Nanoparticle Arrays

greatly computer aided design considerations. Ex-perimental results obtained for dipole-like radiationhave been presented. The corresponding cross polar-ized detection has exhibited four extended lobes thatare formed only after an initial transition region.Using a line-like surface defect, the experimentalfeasibility of simultaneous excitation, and propa-gation of SPP ¯elds was corroborated. For randomly(high-density) situated nanoparticles, the exper-imental and numerical results of simulations of dif-ferent scattering regimens and related phenomenahave been presented illustrating the interplay be-tween di®erent orders of scattering and SPPphenomena. We demonstrated the possibility toperform interactive refractive e®ects on a system ofparticles that are relatively near to each other. Eventhough the similar properties had already beenobserved on nanoshaped arrays, we believe that, ifproperly designed, the above-mentioned nanoparticlesystems o®er more capabilities for nanophotonicssystems integration. In general, theoretical modelingof multiple SPP scattering regimes is quite a chal-lenge in itself, because one has to deal with a largenumber of scattering events, however, the obtainedresults reproduced good all the qualitative ten-dencies found in the experimental study. A detailedcomparison between data from experimental mea-surements and numerical simulations is very di±cultto assess quantitatively. For example, in our con-¯guration, the direct evaluation of the optimumSPP coupling e±ciency using the vectorial dipolarmodel is cumbersome and typically omitted,32 sinceit should involve, among other things, a carefulanalysis of strong particle�surface interactionswhose accurate description might require goingbeyond the framework of dipole scattering approach.We would like to emphasize that the main idea of theproposed experimental approach was in avoiding theusage of additional interfacing elements such as, forexample, in-coupling ridges and focusing elements.However, we are clear that even though a certainunderstanding about multiple SPP scatteringphenomena was gained, the outcome of these in-vestigations clearly made calls for more systematicanalyses. A statistical study seems to be a di®erentand powerful approach in order to elucidate furtherin this ¯eld.33 Based on the results obtained here,we also conclude that a search of new experimentaland numerical approaches for plasmonic modes inrandom mediums remains to be an open problem.

Acknowledgments

The authors acknowledge ¯nancial support fromCONACyT project 127589 and scholarship 228959.

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