2_metamaterials

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Laser Phys. Lett. 7, No. 4, 259269 (2010) /DOI10.1002/lapl.200910140 259

Abstract: While three-dimensional photonic metamaterials are

difficult to fabricate, many new concepts and ideas in the meta-

material optics can be realized in two spatial dimensions using

planar optics of surface plasmon polaritons. In this paper we re-

view recent progress in this direction. Two-dimensional photonic

crystals, hyperbolic metamaterials, and plasmonic focusing de-

vices are demonstrated and used in novel microscopy and waveg-

uiding schemes.

1 m

Superposition of optical and AFM images of the flat hyperlens

c 2010 by Astro Ltd.

Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA

Two-dimensional metamaterial optics

I.I. Smolyaninov

Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA

Received: 9 November 2009, Revised: 12 November 2009, Accepted: 15 November 2009

Published online: 8 February 2010

Key words: metamaterial; surface plasmon; hyperlens

PACS: 42.70.-a, 78.67.-n

1. Introduction

Current metamaterial revolution in optics has been ignitedby introduction of such concepts as photonic crystals [1],negative refractive index metamaterials [2], etc., and re-alization that these novel materials with unusual opticalproperties may become very useful in signal processing,sensing, microscopy and lithography devices. For exam-ple, John Pendrys suggestion [3] that a negative refractiveindex metamaterial may be used in making a perfect lensinitiated an explosion of experimental activities directed atsuperlens and hyperlens realization. Relatively soonthese activities came to fruition [4]. However, fabricationof photonic crystals and negative refractive index meta-materials for the visible and near infrared remains a very

challenging technological task. Multiple alternating layers

of nanostructured materials with strongly different opticalproperties are required in most cases. Due to fabricationdifficulties, typical experiments with negative refractiveindex metamaterials reported so far deal with periodic lay-ered structures composed of only a few layers [5]. The sit-uation is almost the same in the field of three-dimensionalphotonic crystals (see for example [6] and the referencestherein). Thus, many important theoretical ideas in meta-material and transformation optics are waiting for experi-mental verification.

On the other hand, we may pursue a different strat-egy to fabricate and explore optical metamaterials. Two-dimensional optics of surface plasmon polaritons (SPP)may be used. Surface plasmons may be understood as a

two-dimensional (2D) light, which propagates along metal

Corresponding author: e-mail: [email protected]




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260 I.I. Smolyaninov : Two-dimensional metamaterial optics

Mutilayer 2D photonic crystal / metamaterial

Surface plasmon

Gold filmDielectric nanoparticle / nanohole

Figure 1 (online color at www.lphys.org) A multilayer two-

dimensional plasmonic metamaterial may be made using a

nanostructured layer of dielectric (or holes) on the surface of a

metal film. Such 2D metamaterials are much easier to fabricate

than their respective 3D analogues

surface. The basic properties of surface plasmons, such asdifferent means of plasmon excitation, coupling betweenSPP and ordinary light and plasmon field visualization aredescribed in detail in [7]. Over recent years various 2Doptical elements, such as mirrors, lenses, prisms, waveg-uides, etc., as well as more complicated compound de-vices such as plasmon microscopes and waveguide cou-plers has been demonstrated (see for example [710] andthe references therein). These simple and compound SPPdevices behave similar to their 3D optical counterparts. If

we wish to create a multilayer 2D plasmonic metamate-rial (Fig. 1), it would consist of only a single layer nanos-tructured metal film possibly covered with some dielectricpattern, which is much easier to fabricate. Let us demon-strate that such two-dimensional plasmonic metamaterialsoften behave in a manner, which is similar to the behaviorof their respective 3D counterparts.

Let us consider a SPP which propagates over a flatmetal-dielectric interface. If the metal film is thick, theSPP wave vector is defined by the expression

kp =

c

dmd+m

, (1)

wherem() and d() are the frequency-dependent di-electric constants of the metal and dielectric, respectively[7]. The spatial distribution of dielectric material on themetal surface may be set at will using various lithographytechniques. Let us introduce an effective 2D dielectric con-stant2D [8], which characterizes the way in which SPPsperceive the dielectric material deposited onto the metalsurface. Similar to the 3D case, we can introduce 2D sothatkp=

2D/c, and thus

2D = dmd+m

. (2)

This effective dielectric constant 2D parameter is usefulif we want to understand the behavior of SPPs which prop-

agate over an interface between the metal and the nanos-tructured dielectric film, such as the one shown in Fig. 1.

Depending on the frequency, SPPs perceive the dielectricmaterial bounding the metal surface in drastically differentways. At low frequencies 2D

d. Both plasmons and

photons perceive the dielectric material similarly. On theother hand, if the imaginary part ofmis neglected, underthe resonant condition

m() = d() (3)the effective2D of the dielectric layer diverges. This fre-quency corresponds to the frequency of the surface plas-mon resonance for the metal-dielectric interface. Abovethis frequency 2D changes sign and becomes negative.This means that plasmons propagating over metal-vacuuminterface perceive small dielectric particles as if they aremetallic. Thus, by choosing the SPP frequency, and thecomposition and geometry of the nanostructured dielectric

film on top of the metal surface we may span a very widerange of the effective dielectric constants2D, which maybe necessary to make a particular composite optical meta-material. As a result, two-dimensional photonic crystals,strongly anisotropic hyperbolic metamaterials with differ-ent symmetries [11], etc. become very easy to fabricate.Below we will discuss experimental realizations of someof these 2D metamaterials in more detail.

2. 2D photonic crystals

Early examples of experimental work devoted to the study

of 2D plasmonic Bloch waves, forbidden zones, plasmoniccrystal gap waveguides, etc. may be found in [12,13]. Anexample of the plasmonic crystal gap waveguides is shownin Fig. 2, which is reproduced from [14]. In this paper ex-perimental observation of a very strong polarization su-perprism effect in a surface polaritonic crystal has beenreported. Directional demultiplexing of the SPP waveguid-ing modes on a periodic surface structure with orthogonalline defects has been observed, which occurs at very smallchanges of polarization state of the external illuminatinglight. This effect is somewhat similar to the superprismeffect in 3D photonic crystals in the wavelength domain,but in this realization it occurs because of a very strongpolarization dependence of the SPP dispersion in a peri-odic structure. Fig. 2 demonstrates that light directly illu-minating a SPP band gap structure can be efficiently cou-pled into SPP waveguiding modes of line defects in thestructure. By controlling polarization of the incident lightwithin only a few degrees range, the SPP coupling intoone or another mutually perpendicular waveguides can beachieved providing a possibility of polarization switchingbetween the waveguides [14].

The plasmonic crystal behavior of such nanostructuredmetallic films can be used to enhance molecular fluores-cence. In the plasmonic crystal geometry the fluorescenceenhancement is achieved through enhancement of pump-ing light at the substrate because of surface plasmon ex-

citation facilitated by the surface gratings. This configu-ration may be potentially useful in sensing applications.


Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA www.lphys.org


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decomposed intoxandycomponents ask0sin sinandk0sin cos, respectively. The grating k-vector 2n/acan provide momentum matching along the x directionas shown in Eq. (4), while the y component remains un-changed as shown in Eq. (5). If a surface plasmon is ex-cited, the k-vector of the incoming photons mediated bythe grating periodicity should match the k-vector of sur-face plasmons as shown in Eq. (6):

kx = k0sin sin+2n

a =ksp, (4)

ky =k0sin cos= ksp (5)

k2

= (6)

=k0sin cos

2+

k0sin sin+2n

a

2=ksp

2 ,

wheren is an integer, and k is the SPP Bloch wave vec-tor in the x y plane. The observed fluorescence max-ima in Fig. 4 correspond to small integer values of n.Thus, the fluorescence enhancement mechanism is consis-tent with excitation of the SPP Bloch waves on the surfaceof 2D photonic crystal. The observed phenomenon may bepromising in sensing applications. More recent examplesof photonic crystal effects in 2D plasmonic crystals can befound in [16].

3. 2D hyperbolic metamaterials

A proposal to implement hyperbolic metamaterials in or-der to overcome the diffraction limit of resolution invarious microscopy and lithography techniques has beenput forward relatively recently by at least three differ-ent groups [11]. This proposal requires fabrication ofstrongly anisotropic 3D metal-dielectric optical metama-terials, which is quite challenging to achieve. Experimen-tal realization of this proposal came from two differ-ent approaches. In the 3D realization a multilayer metal-dielectric cylindrical structure was fabricated [17], whilesimultaneously published 2D plasmonic realization [18]required much simpler pattern of PMMA rings on a goldfilm substrate. It should be noted that the reported resolu-tion of the 2D hyperlens appeared to be better by a factorof two. Discussion of Eq. (1) and Eq. (2) in the Introduc-tion makes it clear that a 3D multilayer metal-dielectricnanostructure can indeed be emulated in 2D using a peri-odic dielectric pattern on a metal substrate. Fabrication ofsuch anisotropic metamaterials in two dimensions requiresonly very simple and common lithographic techniques. Inthe proper frequency range the right combination of metal-vacuum and metal-dielectric interfaces on a metal surfacewhich supports surface plasmon polaritons would emulatethe strongly anisotropic metal-dielectric metamaterial with

cylindrical symmetry, which is described in [11]. This ap-proach finds rigorous theoretical justification in [19].

(a) (b)

(d) (e)

400

700 500

6001000 800

600 900

700

(c)

Figure 4 (online color at www.lphys.org) The intensity com-

parison of R6G/PMMA gratings on (a) ITO/glass substrate and

(b) Au/glass substrate when observed in the fluorescence micro-

scope. When the grating periodicity is varied as shown in (c) flu-

orescence intensity exhibits pronounced dependence on the grat-

ing period, polarization of excitation light, and sample rotation.

Image (d) was taken under the polarized Hg lamp. E field is par-

allel to the grating trenches. Image (e) was taken after the sample

was rotated 90 degrees clockwise. E field is perpendicular to the

grating trenches in this case

Let us recall the basic properties of hyperbolic meta-materials. Let us start with a non-dispersive non-magnetic(= 1) uniaxial anisotropic material with dielectric permit-tivitiesx= y= 1andz= 2. The wave equation in sucha material can be written (see for example [20]) as

2E

c2t2 =

1E , (7)

where

is the inverse dielectric permittivity tensor. Anyelectromagnetic field propagating in this uniaxial materialcan be expressed as a sum of the ordinary and extraor-dinary contributions, each of these being a sum of an ar-

bitrary number of plane waves polarized in the ordinary(E perpendicular to the optical axis) and extraordinary




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Laser Phys. Lett. 7, No. 4 (2010) 265

Z,a.u.

-0.0

15

0.1

66

X, a.u.

0 0.045

(a)

(b)

1 m

Figure 9 (online color at www.lphys.org) (a) composite im-

age of the AFM image from Fig. 8a superimposed onto the cor-

responding optical image obtained using a conventional optical

microscope illustrating the imaging mechanism of the magnify-

ing hyperlens. Near the edge of the hyperlens the separation of

three rays (marked by arrows) is large enough to be resolved us-

ing a conventional optical microscope. (b) the cross section of

the optical image along the line shown in (a) indicates the three

rays

ventional optical microscope. The cross section analysisof this image across the plasmon rays (Fig. 3f) indicatesresolution of at least 70 nm or/7. The lateral separationbetween these rays increased by a factor of ten as the raysreached the outer rim of the hyperlens. This increase al-

lowed visualization of the triplet using a conventional mi-croscope. In a similar fashion, two rows of PMMA dots

No sampleNo image

Control #1

Control #2

Imageformed

Reverseorientation:no phasematching toplasmonsno images

(a)

(b)

1 m

Figure 10 (online color at www.lphys.org) (a) This image ob-

tained using a conventional optical microscope presents results

of two imaging experiments (top portion of the image) performed

simultaneously with four control experiments seen at the bottom

of the same image. The rows of PMMA dots shown in the inset

and in the AFM image (b) were fabricated near the two top and

two bottom hyperlenses. No such pattern was made near the two

hyperlenses visible in the center of the image. Upon illuminationwith an external laser, the two rows of PMMA dots separated by

130 nm gap gave rise to two divergent plasmon rays shown by

arrows, which are clearly visible in the top portion of the image.

The four control hyperlenses visible at the bottom do not produce

such rays because there is no sample to image for the two hyper-

lenses in the center, and the two bottom hyperlenses are inverted

shown in Fig. 8c gave rise to two plasmon rays, which arevisualized in Fig. 8e.

The composite image in Fig. 9 has been obtained as

a result of superposition of the AFM image from Fig. 8aand the corresponding optical image obtained using a con-

www.lphys.orgc 2010 by Astro Ltd.



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2.7 m

(a)

Z,a.u.

-0.2

39

0.7

30

X, a.u.

0 0.849

(b)

Figure 13 (online color at www.lphys.org) (a) optical micro-

scope image of the 44 array of the 2D focusing elements based

on the concentric ring structure illuminated with 532 nm laser

light. The inset shows the AFM image of an individual focus-

ing structure. (b) analysis of the image cross section along the

dashed line shown in (a) indicates considerable enhancement of

the field intensity in the focal spot, which is estimated to be ofthe order of 20

4. Conventional plasmon focusing devices

It is interesting to note that outside the hyperbolic fre-quency range plasmonic metamaterial devices describedabove may be used as efficient focusing elements for SPPs[23]. Fig. 13 demonstrates 2D focusing properties of theconcentric ring structure illuminated by 532 nm externallaser light. A 44 array of the focusing devices is shown.Analysis of the image cross section along the dashed line

shown in Fig. 13a indicates considerable enhancement ofthe field intensity in the focal spot, which is measured to be

(a)

(b)

(c)

Figure 14 (online color at www.lphys.org) (a) geometry of the

plasmonic focusing devices based on parabolic gratings. (b) and

(c) demonstrate the possibility to scan the focal spot as a function

of illumination angle

of the order of 20. The radius of the circular focusing areais limited by the propagation length of SPP in a given fre-quency range. Near 500 nm wavelengths, the Re(k)/Im(k)ratio for the gold-vacuum interface is of the order of 30[22], which means that plasmon energy may be collectedover a 30/2 2.5 m radius. Ideal focusing of thisenergy into the diffraction-limited/2n2effspot would pro-duce the field intensity enhancement of the order of 100.

However, surface plasmons are strongly scattered into 3Dphotons by surface defects. In reality, the reported field




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Figure 15 (online color at www.lphys.org) SEM image of an

array of double holes through a 500 nm thick gold membrane.

The holes have been milled from the backside using a 50 keV

focused ion beam. The size of gaps in between the hole pairs is

about 20 nm. Such gaps are supposed to support localized surface

plasmon modes

enhancement factors reach the 20 50 range [24]. Thisdesign of the SPP 2D focusing device is very well suitedfor sensing applications using fluorescence or SERS. Fluo-rescence enhancement by surface gratings due to couplingto SPPs is described above. Fluorescence and SERS detec-tion schemes benefit from exponential enhancement of theSPP field near the metal surface. Additional enhancementdue to SPP focusing is highly desirable in these applica-tions. We anticipate that the SPP focusing devices may becombined with metal nanostructures, which support local-ized surface plasmon modes. This will lead to further en-hancement of SERS signals. Other efficient geometries for

SPP focusing include parabolic gratings shown in Fig. 14.The latter geometry permits scanning of the focal spot asa function of the illumination angle, which would be use-ful if the position of the focal spot needs to be matchedwith the location of the nanofocusing plasmonic struc-ture, such as the one shown in Fig. 15 reproduced from[25].

5. Conclusion

We have reviewed various examples of two-dimensionalplasmonic metamaterials, which are reasonably easyto fabricate and study. While fabrication of three-

dimensional photonic metamaterials faces numerous tech-nological challenges, many new concepts and ideas in the

optics of metamaterials may be tested much easier in twospatial dimensions using planar optics of surface plas-mon polaritons. Based on this approach, we have demon-

strated two-dimensional plasmonic crystals which showgreat promise in sensing applications, hyperbolic meta-materials which improve optical resolution far beyond thediffraction limit, and many other interesting plasmonicnanodevices, such as 2D plasmonic cloaks [26]. Novelplasmonic metamaterials may be used in improved mi-croscopy, lithography and waveguiding schemes, whichare projected to exhibit spatial resolution down to /20level. They may also supplement regular 3D photonicmetamaterials [27] in such nonlinear optical applicationsas second harmonic generation [28], fluorescence en-hancement [15], and surface enhanced Raman scattering.

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Dr. Smolyaninov is Fellow of the Optical Society ofAmerica. He has published more than 100 refereed jour-nal articles in such areas as metamaterial optics, plasmon-ics, optical wireless communications, and low temperaturephysics.



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