nanomaterials

Article Selective Metasurfaces Based on Directional Conditions of Silicon Nanopillars

José Francisco Algorri 1,* , Braulio García-Cámara 1, Alexander Cuadrado 2, José Manuel Sánchez-Pena 1 and Ricardo Vergaz 1 1 GDAF-UC3M, Displays and Photonics Applications Group, Electronic Technology Department, Carlos III University of Madrid, Leganés, 28911 Madrid, Spain; [email protected] (B.G.-C.); [email protected] (J.M.S.-P.); [email protected] (R.V.) 2 Laser Processing Group, Instituto de Óptica, CSIC, C/Serrano 121, 28006 Madrid, Spain; [email protected] * Correspondence: [email protected]; Tel.: +34-916-245-964

Received: 12 May 2017; Accepted: 6 July 2017; Published: 7 July 2017

Abstract: Dielectric metasurfaces based on high materials have been proposed recently. This type of structure has several advantages over their metallic counterparts. In this work, we demonstrate that dielectric metasurfaces can be theoretically designed satisfying Kerker’s zero-forward condition. This is the first time that a dielectric metasurface based on this principle has been designed. A selective dielectric metasurface of silicon nanopillars is designed to work at 632.8 nm. This structure could work both as a dielectric and a reject band filter. Furthermore, by scaling up the structure, it could be possible to manufacture a terahertz (THz) dielectric mirror.

Keywords: nanophotonics; nanoparticles; ; silicon photonics

1. Introduction During the past years, metamaterials have gained increasing interest [1]. Metamaterials are artificial media composed of periodic structures smaller than the wavelength of the external stimuli. In classic materials, the electromagnetic field interacts with the atoms and molecules, and depending on their structural characteristics, the material shows specific electromagnetic properties. Metamaterials enable the design of surfaces or bulks with custom electromagnetic characteristics, even producing properties that cannot be found in nature (e.g., negative refractive index), by tailoring their basic constituents. Engineered wavelength resonance, bandwidth, or scattering phase and amplitude can also be obtained [2]. The design of metamaterials and their optical characteristics can be performed by using homogenization techniques [3], by averaging the electromagnetic fields over a subwavelength volume. Some research lines about these engineered media are in a mature stage, e.g., negative-index or chiral metamaterials, however, there are still some emerging directions of research, such as quantum [4], non-linear [5], sensor [6], or active [7] metamaterials, photonic hypercrystals [8] and metasurfaces [9]. In particular, metasurfaces are the two dimensional (2D) version of 3D metamaterials. These structures produce those effects observed in three dimensional (3D) metamaterials with the unique capability to tune the with planar components, thus obtaining a “planar photonics” device. These types of structures were studied in the past by the microwave community [10]. Recent improvements in nanofabrication processes allows transfering this knowledge to the visible spectrum. Several devices, such as super/hyper-lensing [11], cloaking [12], dielectric [13], etc., have been proposed. Specifically, the study of dielectric nanostructures has been a hot research topic in the past years [14,15]. The low absorption in the visible range and the compatibility with traditional CMOS (Complementary Metal Oxide Semiconductor) techniques of fabrication make them a suitable candidate to create flat

Nanomaterials 2017, 7, 177; doi:10.3390/nano7070177 www.mdpi.com/journal/nanomaterials Nanomaterials 2017, 7, 177 2 of 7 optical components. Flat optical components have the evident advantage of compactness, which is very important for new portable and wearable photonic devices. Apart from the CMOS compatibility, the use of silicon (Si) allows considerable reductions of thickness (<100 nm), and a high aspect ratio is possible [16]. Other examples of high efficiency achieved through high aspect ratio structure can be found in vortex beam generators [17]. In this work, a novel approach to the design of dielectric metasurfaces is proposed. Kerker’s conditions were theoretically proposed for spherical particles in 1983 [18]. Two possible conditions were predicted, the first condition (zero backscattering) and a second one (minimum forward scattering). The latter condition appears when a destructive interference in the forward direction produces a near-cancelation of light scattering in this direction. This is not a complete cancelation as stated by Kerker, due to the fulfilment of the Optical Theorem [19]. In order to design dielectric mirrors, this condition should be satisfied. Kerker’s theory was experimentally demonstrated in the microwave spectrum in 2012 [20] and in the visible spectrum in 2013 [21]. Shortly after, a deeper minimum forward scattering for disks [22] and spheroidal [23] (tuning the shape to overlap the spectral position of the electric and magnetic dipole resonances) was found. Additionally, a recent study on silicon nanopillars (Si NPs) demonstrates an optimized forward scattering condition for an optimum aspect ratio [24]. These results demonstrate even more intense light scattering for nanopillars than those produced by previous structures (spheroids and disks). Moreover, a study of the substrate effect revealed that the use of low refractive index substrates is required in order to exploit the minimum forward condition. It was also suggested that the arrangement in metasurfaces may overcome the overall substrate effect. In this work, this hypothesis is demonstrated by looking for the minimum forward condition of Si nanopillars and arranging them in an optimized metasurface configuration. By optimizing the size of the component particles (and their distance between each other), a dielectric metasurface with a selected reflection frequency (and a maximum reflection) can be designed. This structure could be used both as a dielectric mirror and a reject band filter.

2. Structure and Operation Principle The control of light reflection and transmission is one of the most relevant features in the design of novel metasurfaces. We already showed that an optimum aspect ratio of a silicon nanopillar can be obtained to accomplish the minimum forward scattering condition. Figure1 reminds some of our previous results in [24] in order to clarify the optical response of the individual components of the proposed metasurface. In particular, Figure1 plots the aspect ratios of silicon nanoparticles, either pillars or disks, where their electric and magnetic dipolar contributions satisfy the minimum forward scattering condition (red lines). The plot considers both a normal incidence on its flat surface and a certain incident wavelength (632.8 nm corresponding with commercial He-Ne lasers). A shadowed region highlights the optimum geometries producing the most directional scattering with a strongly-attenuated scattering in the forward direction. The differences of the scattered field in the far-field region between the optimum and non-optimum aspect-ratio particles can be seen in the insets. A minimum forward scattering can be observed for h = 160 nm and r = 74 nm into the optimum region (lower inset). Values out of this region, e.g., h = 280 nm and r = 60 nm (upper inset) do not present a relevant directional scattering although the minimum forward condition is still satisfied. Figure2 shows the scattering of one of the previous nanopillars accomplishing the minimum- forward scattering condition. While Figure2a considers a low refractive index substrate (aerogel, n = 1.03), Figure2b is calculated over a substrate ( n = 1.5). As can be seen, the reduction of the refractive index contrast between the nanoparticle and the surrounding medium blurs the shape of the electric and magnetic Mie resonances excited in the particle, leading to a worse observation of the directional scattering. In order to overcome this limitation, in this work we design an ordered array (Figure3a) of these previous particles with an optimum aspect ratio as a metasurface with reflection and transmission control of a normal incident light. The excitation of Mie resonances in individual particles are also presented in the frequency Nanomaterials 2017, 7, 177 3 of 7

Nanomaterials 2017, 7, 177 3 of 7 response of the whole structure. However, the intensity of the peak, particularly in the analysis of the transmissiontransmissionNanomaterials and and2017 reflection, 7, reflection177 coefficients, coefficients, strongly stro dependsngly depends on the interparticle on the interparticle distance. Consequently, distance.3 of 7 theConsequently, design parameters the design of our parameters device are: of our the device radius are: (r), the the radius height (r), (h the), and height the ( distanceh), and the (d distance) between NPs(d) (Figurebetweentransmission3b). NPs (Figureand reflection 3b). coefficients, strongly depends on the interparticle distance. Consequently, the design parameters of our device are: the radius (r), the height (h), and the distance

(d) Nanomaterialsbetween NPs 2017, (Figure7, 177 3b). 3 of 7

transmission and reflection coefficients, strongly depends on the interparticle distance. Consequently, the design parameters of our device are: the radius (r), the height (h), and the distance (d) between NPs (Figure 3b).

FigureFigure 1. 1.Aspect Aspect ratio ratio (height (height vs.vs. radius)radius) of cylindrical cylindrical silicon silicon particles particles producing producing a aminimum minimum forward forward scatteringscatteringFigure at at 1. 632.8 632.8 Aspect nm ratio in in vacuum.(height vacuum. vs. The radius The optimum) optimum of cylindrical observation observation silicon region particles region is producingdeli ismited delimited aand minimum shadowed. and forward shadowed. Two Twospatial spatialscattering distributions distributions at 632.8 of nm the ofin scattered vacuum. the scattered Theelectric optimum electric field inob field servationthe infar-field the region far-field region is deli regionare mited included areand includedshadowed. as insets, as Twobeing insets, spatial distributions of the scattered electric field in the far-field region are included as insets, being beingas highest asFigure highest the 1. intensity Aspect the intensity ratio as (heightreddish as vs. reddish the radius color) of the incylindrical a color rainbowin silicon a scale. rainbow particles Labels producing scale. NP and Labels a minimumND NPrefer andforward to nanopillars ND refer to as highest the intensity as reddish the color in a rainbow scale. Labels NP and ND refer to nanopillars nanopillarsand nanodisks,scattering and nanodisks, respectivelyat 632.8 nm in respectively vacuum.and ℜ = The h/2 androptimum is the< =aspect obh/2servationr ratio.is the region aspect is deli ratio.mited and shadowed. Two andspatial nanodisks, distributions respectively of the scattered and ℜ = electrich/2r is fieldthe aspect in the far-fieldratio. region are included as insets, being as highest the intensity as reddish the color in a rainbow scale. Labels NP and ND refer to nanopillars and nanodisks, respectively and ℜ = h/2r is the aspect ratio.

(a)( a) ((bb)) (a) (b) Figure 2. Far-field scattering (being as highest the intensity as reddish the color in a rainbow scale) of FigureFigure 2. 2.Far-field Far-fieldscattering scattering (being as as highest highest the the intensity intensity as asreddish reddish the the color color in a inrainbow a rainbow scale) scale) of Figure 2. Far-field scattering (being as highest the intensity as reddish the color in a rainbow scale) of an individualan individual nanoparticle nanoparticle (h =(h 160 = 160 nm, nm, r =r 72= 72 nm) nm) satisfying satisfying the the minimumminimum forwardforward condition condition at at λ λ= = of an individualan individual nanoparticle nanoparticle ( h(h == 160 nm, nm, r =r 72= nm) 72 nm) satisfying satisfying the minimum the minimum forward condition forward at conditionλ = at 632.8632.8 nm, nm,deposited deposited over over (a) (aa )low a low refractive refractive index index substrate substrate (aerogel) (aerogel) oror (b) glassglass substrate.substrate. λ = 632.8632.8 nm, nm, deposited deposited over over ((a) a a low low refractive refractive index index substrate substrate (aerogel) (aerogel) or (b) glass or substrate. (b) glass substrate.

(a) (b) (a) (b) Figure 3. (a) Schematic of the silicon (Si) nanopillars metasurface, which consist of subwavelength Si Figure 3. (a) Schematic of the silicon(a) (Si) nanopillars metasurface,(b which) consist of subwavelength Figurenanopillars 3. (a) Schematic on a glass ofsubstrate; the silicon and (Si) (b) nanopillarsthe geometry metasurface, for the incident which light consist vector of and subwavelength structural Si SiFigure nanopillarsnanopillars parameters3. (a) Schematic on on aof glass athe glass metasurface. of substrate; thesubstrate; silicon and and(Si) ( bnanopillars(b)) thethe geometrygeometry metasurface, for for the the incident incidentwhich consistlight light vector of vector subwavelength and and structural structural Si parametersnanopillars parameters of on the aof metasurface. glassthe metasurface. substrate; and (b) the geometry for the incident light vector and structural parameters of the metasurface.

Nanomaterials 2017, 7, 177 4 of 7

Our framework is a set of numerical simulations based on Maxwell equations solved by finite element method (COMSOL®) (Version 5.1, COMSOL Inc., Burlington, MA, USA). The refractive indices of the Si and glass are extracted from references [25,26], respectively. A plane TE-polarized electromagnetic wave is normally incident on a silicon nanopillar array placed over a glass substrate. The symmetry of the structure at the normal incidence produces the same response for both polarizations. Estimations of the reflection coefficient and transmission coefficient are based on S-parameters (scattering parameter). The scattered-field formulation applies the weak formulation (variational calculation). COMSOL® performs an eigenmode analysis on ports 1 and 2 (input and output of the light) estimating the respective electric field patterns E1, E2 of the fundamental modes on these ports. The computed electric field (Ec) of the input port is the sum of the excitation and the reflected field. The reflected and transmitted powers (Equations (1) and (3), R and T, respectively) are defined through S-parameters given by Equations (2) and (4) [27]:

2 R = |S11| (1)

where R ∗ ((Ec − E1) · E1 )dA1 port 1 S11 = R ∗ (2) (E1 · E1 )dA1 port 1

2 T = |S21| (3) where R ∗ (Ec · E2 )dA2 port 2 S21 = R ∗ (4) (E2 · E2 )dA2 port 2 where A is the area of each port.

3. Results As was mentioned, in order to observe clearly directional effects, and in particular the desired minimum forward scattering, low refractive index substrates under the nanoparticle are required [24] (see Figure2a). This is a consequence of the excitation of the electric and magnetic Mie resonances in the particles which requires a high refractive index contrast between the particles and the surrounding medium. Nevertheless, the growing or deposition of such nanoparticles over such substrates is not an easy experimental task. Commonly, silicon or glass substrates are used in the design and fabrication of such devices, appreciably reducing the observance of resonant and directional effects. In this work a glass substrate is used because although this could dispel the minimum forward scattering condition found (Figure2b), it will ease future fabrication. The main result of this work is the following: when nanoparticles are arranged in an array configuration forming a metasurface, the negative effect of increasing the index of the substrate may be overcome, as it will be demonstrated. This effect can be used in order to ease the creation of structures with a selected frequency of reflection. Once the structural dimensions of each individual nanoparticle is established by using the results of Figure1 to obtain the best directional scattering of each component, the optimum distance d between them in the metasurface must be determined. For this study, a numerical process determines the maximum power reflectance for a specific distance d. In Figure4, it is shown how this distance affects both power reflectance and transmittance coefficients of the structure, as expected. The power coefficients (reflectance: red solid line; transmittance: blue solid line) of a metasurface composed of silicon nanopillars with an optimum aspect ratio, a height of 160 nm and a radius of 74 nm, is plotted as a function of the array constant (d). Regarding the optimization of minimum-forward scattering of the metasurface, a minimum transmittance is expected. A maximum reflectance, and minimum transmittance, is found for an inter-particle distance of d = 100 nm. The longer the distance, Nanomaterials 2017, 7, 177 5 of 7 nm, is plotted as a function of the array constant (d). Regarding the optimization of minimum- forwardNanomaterials scattering2017, 7, 177 of the metasurface, a minimum transmittance is expected. A maximum5 of 7 reflectance, and minimum transmittance, is found for an inter-particle distance of d = 100 nm. The longerthe lower the thedistance, reflection; the thislower is mainlythe reflection; due to thethis direct is mainly transmission due to the of thedirect incoming transmission light through of the incomingthe nanoparticle light through gap. In the contrast, nanoparticle if the minimumgap. In contrast, forward if the condition minimum is notforward in the condition optimum is regionnot in the(Figure optimum4, dashed region line, (Figure nanoparticles 4, dashed of hline,= 280 nanoparticles nm), the power of h reflectance = 280 nm), coefficient the power is appreciablyreflectance coefficientlower. Once is theappreciably distance lower.d that produces nce the distance a maximum d that reflectance produces isa maximum selected, the reflectance three parameters is selected, of thethe three configurable parameters metasurface of the configurable (r, h, d) are established.metasurface (r, h, d) are established.

Figure 4. 4. ReflectedReflected (red) (red) and and transmitted transmitted power power (blue) (blue) for for a metasurface a metasurface of Si of nanoparticles Si nanoparticles with with h = 160h = 160nm, nmr = ,74r =nm 74 (solid nm (solid line) and line) h and= 280h nm,= 280 r = nm, 60 nmr = (dashed 60 nm (dashed line), as line),a function as a functionof distance of between distance nanoparticlesbetween nanoparticles (NPs). nly (NPs). transmission Only transmission with h = 160 with nmh =is160 shown. nmis shown.

Despite the complexity of the structure and the hi highgh number of different effects that govern the optical responseresponse ofof such such a a metasurface, metasurface, we we have have spectrally spectrally characterized characterized the selectedthe selected metasurface metasurface with withd = 100 d = nm. 100This nm. isThis computed is computed using Equationsusing Equations (1)–(4) (1)–(4) and the and method the method described described in Section in 2Section, and the 2, andresults the are results shown are in shown Figure 5in. TheFigure power 5. The reflectance power coefficientreflectance hascoefficient a maximum has a at maximum a wavelength at a wavelengthλ = 632.8 nm λ, as= 632.8 it was nm, designed as it was from designed Figure1 fromfor one Figure nanoparticle, 1 for one so nanoparticle, that the spectral so that performance the spectral of performancethe whole surface of the maintains whole thesurface spectral maintains signature the of spectral each one signature of its individual of each components, one of its asindividual expected. components,This result demonstrates as expected. how This the resonanceresult demonstrat reflectiones band how of the the resonance metasurface re canflection be engineered band of andthe metasurfacespectrally tuned can be just engineered by designing and their spectrally individual tuned components just by designing so that their they satisfyindividual the secondcomponents order soKerker’s that they condition satisfy the (minimum second order forward Kerker’s scattering). condition On (minimum the other hand, forward the sc highattering). value of n the the power other hand,reflectance the high coefficient value of obtained the power at the reflectance optimized coefficient wavelength obtained for which at the the optimized metasurface wavelength was designed for whichdemonstrates the metasurface the power ofwas the designed optimization demonstrates parameter dthe, regarding power of the the interparticle optimization distance, parameter to obtain d, regardingan optimized the flatinterparticle metasurface distance, in terms to ofobtain reflection an optimized properties. flat metasurface in terms of reflection properties.Finally, a remarkable result is concluded: the use of a glass substrate has not been a drawback in theFinally, reflection a remarkable properties result of the is metasurface, concluded: the as bothuse of the a wavelengthglass substrate at whichhas not the been maximum a drawback was indesigned the reflection to occur properties and the value of the of metasurface, the power reflectance as both the coefficient wavelength peak at has which been the maintained maximum in was the designedstep from to nanoparticle occur and the to value metasurface. of the power Several reflec anglestance have coefficient been studied peak has (from been 0 maintained◦ to 85◦), and in the stepresult from is that nanoparticle the wavelength to metasurface. at the maximum Several reflection angles have for which been thestudied metasurface (from 0° was to 85°), optimized and the is resultmaintained is that in the the wavelength whole angular at the range, maximum although reflection the value for ofwhich the power the metasurface could slightly was decrease.optimized is maintained in the whole angular range, although the value of the power could slightly decrease.

Nanomaterials 2017, 7, 177 6 of 7 Nanomaterials 2017, 7, 177 6 of 7

FigureFigure 5. 5.Power Power absorption, absorption, reflectance reflectance andand transmittancetransmittance coefficients coefficients for for a ametasurface metasurface made made of ofSi Si nanopillarsnanopillars with withh =h = 160 160 nm, nm,r r= = 7474 nmnm andand distance between between them them of of d d= =100 100 nm. nm.

4. Conclusions4. Conclusions InIn this this work, work, a a novel novel approachapproach toto thethe designdesign of dielectric metasurfaces metasurfaces is isproposed proposed and and theoreticallytheoretically demonstrated. demonstrated. When When optimized optimized Si nanoparticles Si nanoparticles producing produc a minimuming a minimum forward forward condition condition are arranged in an array configuration, the optical response of the overall structure is are arranged in an array configuration, the optical response of the overall structure is spectrally similar spectrally similar to that of each individual particle. to that of each individual particle. The use of non-low but easy-to-obtain refractive index substrates has been shown to degrade the The use of non-low but easy-to-obtain refractive index substrates has been shown to degrade the directional scattering for individual particles. However, in this work we have demonstrated that an directional scattering for individual particles. However, in this work we have demonstrated that an array configuration with an optimum design overcomes this limitation, producing an enhanced arrayreflection. configuration The power with reflectance an optimum coefficient design magnitud overcomese is related this limitation, to the inter-particle producing distance, an enhanced and reflection.neither the The peak power nor the reflectance intensity coefficient have been magnitudedegraded by is the related use toof thea simple inter-particle glass substrate. distance, andConsequently, neither the peakthe distance nor the intensityparameter have between been degradednanoparticles by thecan usebe ofoptimized a simple to glass provoke substrate. a Consequently,maximum power the distance reflectance parameter coefficient between at the nanoparticlesdesigned wavelength can be optimizedfor one individual to provoke nanoparticle. a maximum power reflectanceThe experimental coefficient community at the designed should wavelengthconsider that for this one result individual could nanoparticle.be scaled up to other frequencyThe experimental ranges, e.g., community THz, in order should to create consider extrem thately this flat result band could pass be filter scaleds or upselective to other dielectric frequency ranges,mirrors e.g., that THz, could in be order easy to to create build. extremely flat band pass filters or selective dielectric mirrors that could be easy to build. Acknowledgments: This work has been supported by Ministerio de Economía y Competitividad of Spain Acknowledgments:(grants no. TEC2013-47342-C2-2-RThis work has beenand supportedno. TEC2013- by50138-EXP) Ministerio and de Economthe R andía yD Competitividad Program SINF of T Spain N (grantsS2013/MIT-2790 no. TEC2013-47342-C2-2-R of the Comunidad de and Madrid) no. and TEC2013-50138-EXP) the funding from Agencia and the Estatal R and de Investigación D Program SINFOTON(AEI) and S2013/MIT-2790Fondo Europeo of de the Desarrollo Comunidad Regional de Madrid) (FEDER) and for the the funding Project TEC2016-77242-C3-1-R from Agencia Estatalde AEI/FEDER, Investigaci UE.ón (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) for the Project TEC2016-77242-C3-1-R AEI/FEDER, UE. Author Contributions: All authors contributed to scientific discussion and critical revision of the article. Author Contributions: All authors contributed to scientific discussion and critical revision of the article. 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