An optical reflectarray nanoantenna: The concept and design

An optical reflectarray nanoantenna: The concept and design

Akram Ahmadi*, Shabnam Ghadarghadr, and Hossein Mosallaei

Applied EM and Optics Laboratory, ECE Department, Northeastern University Boston, Massachusetts 02115, U.S.A.

*[email protected]

Abstract: This paper presents the concept and design of a reflectarray nanoantenna at optical frequencies whose elements are nano-sized concentric spherical particles with the core made of ordinary dielectrics and the shell made of a plasmonic material. Modeling approaches based on finite difference time domain (FDTD) numerical method and dipole-modes scattering theory are used to characterize and tune the reflectarray design. A

6 6× elements reflectarray nanoantenna operating at wavelength 357.1nm

with narrow beamwidth is presented, and its scanned radiation characteristics for 15° and 30° are demonstrated.

©2009 Optical Society of America

OCIS codes: (230.0230) Optical devices; (290.0290) Scattering.

References and links

1. J. A. Encinar, “Design of two-layer printed reflectarrays using patches of variable size,” IEEE Trans. Antenn. Propag. 49(10), 1403–1410 (2001).

2. P. W. Hannan, and M. A. Balfour, “Simulation of a phased-array antenna in waveguide,” IEEE Trans. Antenn. Propag. 13(3), 342–353 (1965).

3. N. Lenin, and P. H. Rao, “Evaluation of the reflected phase of a patch using waveguide simulator for reflectarray design,” Microw. Opt. Technol. Lett. 45(6), 528–531 (2005).

4. H. Rajagopalan, Y. Rahmat-Samii, and Y. A. Imbriale, “RF MEMS Actuated Reconfigurable Reflectarray Patch-Slot Element,” IEEE Trans. Antenn. Propag. 56(12), 3689–3699 (2008).

5. J. Li, and N. Engheta, “Core-shell nanowire optical antennas fed by slab waveguides,” IEEE Trans. Antenn. Propag. 55(11), 3018–3026 (2007).

6. N. Engheta, A. Alu, and A. Salandrino, “Nanocircuit elements, nano-transmission lines and nano-antennas using plasmonic materials in the optical domain,” in Proceedings of IEEE Conference on Antenna Technology: Small Antennas and Novel Metamaterials (2005), pp. 165–168.

7. J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76(24), 245403 (2007).

8. A. Alù, and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers,” J. Appl. Phys. 97(9), 094310 (2005).

9. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Leipzig Ann. Phys. 330(3), 377–445 (1908).

10. J. A. Stratton, Electromagnetic Theory (New York: McGraw-Hill, 1941). 11. U. Kreibig, and M. Vollmer, Optical Properties of Metal Clusters (Springer-Verlag Berlin Heidelberg, Germany,

1995). 12. Weng Cho Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, 1995). 13. S. Ghadarghadr, Z. Hao, and H. Mosallaei, “Plasmonic array nanoantennas on layered substrates: modeling and

radiation characteristics,” Opt. Express 17(21), 18556–18570 (2009). 14. L. Novotny, and B. Hecht, Principle of Nano-Optics (Cambridge University Press, United Kingdom, 2006). 15. H. Mosallaei, “FDTD-PLRC technique for modeling of anisotropic-dispersive media and metamaterial devices,”

IEEE Trans. Electromagn. Compat. 49(3), 649–660 (2007). 16. A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method,

3rd ed. (Artech House, Norwood, 2005). 17. C. A. Balanis, Antenna Theory, 3rd ed. (John Wiley and Sons, Inc., New Jersey, 2005).

1. Introduction

Reflectarray antennas are a class of antennas that combine the features of reflectors and phased arrays providing a directive beam in a desired scanned angle. The most important advantages of reflect arrays over phased arrays are the elimination of complexity and losses of

#118732 - $15.00 USD Received 20 Oct 2009; revised 9 Dec 2009; accepted 10 Dec 2009; published 22 Dec 2009

(C) 2010 OSA 4 January 2010 / Vol. 18, No. 1 / OPTICS EXPRESS 123

the feeding network and the higher efficiency [1]. Also they are easier for manufacturing in compared to reflector antennas. To design a reflectarray, the phase of the reflected wave should have a progressive variation over the whole surface such that the total phase delay from the feed to a fixed aperture plane is constant for all the elements. Then, a critical feature in the design of a reflectarray is the choice of elements for obtaining the required phase distribution.

In microwave, various potential reflectarray element designs are considered, which include variable size patches, patches with variable length slot, and patches with fixed slot fed by variable length stripline [1–4]. Introducing radiating elements that can work in optics is of great interest which will be explored in this paper for making a reflectarray nanoantenna. An optical reflectarray nanoantenna can enable successful wireless communication in optics.

Recently, Engheta et al suggested a method of realizing nanoantennas system at optical frequencies by using nanoparticles of concentric structures with cores made of ordinary dielectrics and shell of plasmonic materials [5]. In another study, subwavelength particles at plasmonic scattering resonance were suggested as antenna elements for Yagi-Uda antennas at optical frequencies [6,7]. The scattering resonance of these concentric structures can be tailored at different wavelength range by adjusting the core and shell radii or the material properties [5–8].

In this paper, we illustrate the concept of a reflectarray nanoantenna implemented in optics with the use of array of core-shell dielectric-plasmonic materials, each of them optimized properly to achieve the required phase shift. The concept and radiation performance are investigated. A 3-D finite difference time domain (FDTD) technique is applied to obtain the required reflection phase for a periodic array of a specific nanoparticle design. Then, the

obtained result is integrated into the making a 6 6× array of nanoparticles, see Fig. 1,

scanning successfully a narrow beam optical radiation. To remove the back radiation, the array is pinned on top of a dielectric-silver layer which removes wave penetration to the other side of the nanoantenna. The radiation pattern demonstrates a successfully designed optical reflectarray performance.

2. Array of core-shell nanoparticles

The general solution for the diffraction problem of a single sphere of arbitrary material with the frame of electrodynamics was first given by Mie in 1908 [9] and then refined by Stratton [10]. Mie applied Maxwell's equations with appropriate boundary conditions in spherical coordinates using multipole expansions of the incoming electric and magnetic fields. Clusters can be composed of more than one element forming core-shell particles [11].

εcore

εshell

a b

εcore

εshell

a b

(a) (b)

εs

z

dl θ0

x

εd

Fig. 1. Schematic of the system: (a) A concentric dielectric-plasmonic nanoparticle, and (b) Reflectarray nanoantenna structure.

Engheta et al demonstrated the scattering performance of a sphere particle made of plasma and dielectric materials with the goal of making a Yagi-Uda antenna [6,7]. Here, we integrate the obtained characteristic into the design of a reflectarray antenna for optical frequencies.



The scattering resonant frequency of the core-shell structure depends on material properties and radii of core and shell. Then, by adjusting these parameters one can control the resonant performance. A small particle can be modeled as an induced electric dipole with polarizability α that relates the induced dipole to the incident field as =p Eα . The scattered

field by this particle is equivalent to the radiated field from the induced dipole. The polarizability can be related to the scattering coefficient of the dipolar term given by Engheta et al in [7,8]:

0

13

0

6=

TMic

k

πεα − (1)

where 0

k is the wavenumber in the surrounding medium and 1

TMc is the scattering coefficient

of the TM mode of order 1 in the Mie scattering analysis. If one follows the closed form

equation which has been obtained for 1

TMc in [7,8], it will be obtained that by adjusting the

ratio b/a or the permittivities of core and shell, the scattering resonance can be tailored at different wavelength range. In this study, a Drude material is used to describe the frequency dependence of the permittivity of silver which is the shell material, i.e.

2

0( ) = 1

( )

p

pi

ωε ω ε

ω ω γ

− +

(2)

where p

ω is the bulk resonant frequency of the material, and damping factor p

γ represents

the losses present. (In this study, = 2 2000p

THzω π × and = 0.001p p

γ ω )

Figure 2 shows the magnitude and phase of the polarizability α of a concentric nanoshell

particle for different core materials and for different b/a ratios (see Fig. 1(a) for the geometry

of particle). Operating wavelength is 357.1 nm and 0

= ( 4.67 .01 )shell

iε ε− + . The outer radius

is a = 22.5 nm and in Fig. 2(a), b/a is assumed to be 0.533. Figure 2(b) shows the performance

versus b/a when 0

= 3coreε ε . As seen, due to the shift in resonant frequency, the phase

performance changes and these particles can be used for a reflectarray antenna. In this paper we use the same b/a for all the elements and change the core permittivity to control the phase (as this will be easier for our FDTD analysis).

(a) (b)

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

88

εεεεcore

| αα αα|

(10

-2εε εε 0

λλ λλ03)

0

0.2

0.4

0.6

0.8

11

Arg

(αα αα

) ( ππ ππ

)

Magnitude Phase

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

7

8

b/a

| αα αα|

(10

-2εε εε 0

λλ λλ03)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

Arg

( αα αα

) ( ππ ππ

)

PhaseMagnitude

Fig. 2. . Magnitude and phase of the polarizability α of a concentric nanoshell particle vs: (a)

the permittivity of core when b/a = 0.533 and, (b) the ratio of radii b/a when 0

= 3coreε ε .

Operating wavelength is 357.1 nm and the shell is made of silver [0

= ( 4.67 .01 )shell

iε ε− + ].

If a non-periodic array of plasmonic core-shells are placed over a layered material, with the presence of an incident field, each nano-particle can be viewed as an induced dipole



around the scattering resonance of that nano core-shell. The induced dipole on each nano core-shell is proportional to the total field upon that particle. In this scenario, the total field upon each nano core-shell can be expressed as the summation of three terms. The first part is

associated with the total incident field in the absence of the nano core-shells ( total

incE ), the

second part is the electric field due to the couplings between the nano core-shells in the

absence of the layered material ( ( , )l q

dipole l qG r r p ). Since this term represents the couplings

between the nano core-shells, for the thl nano core-shell we consider the fields of all other

nano core-shell except itself (excluding the field of the thl particle). The last term, is

associated with the reflected fields from the layered substrate ( ( , )l q

reflected l qG r r p ). Note that for

computing the last two terms we approximate each nano core-shell with an electric dipole. Hence for the second term we calculate the dipolar couplings and the Green's function analysis of dipoles over layered material is applied for evaluation of the final part [12,13]. Also, it is worth mentioning that the field associated with every nano core-shell (both couplings and reflected field) is directly proportional to the induced dipole moment, thus the induced dipole moment for each particle is derived by solving the following linear system of

equations. For , {1,2,..., }l q N∈ with N being the total number of particles, we obtain:

,

= ( ) ( , ) ( , ) ,l total l q l q

l inc l dipole l q reflected l q

q q l q

G Gα≠

+ +

∑ ∑p E r r r p r r p (3)

where total

incE denotes the sum of the incident field and its reflection from the layered material

in the absence of the nano-spheres. l

dipoleG is the dyadic Green's function of the thq nano core-

shell evaluated at the position of the thl particle. l

reflectedG is the reflected Green’s function of

the thq nano-sphere (from the layered material) computed at the location of the thl one, i.e.,

2 2 22

1 2

| |2 2 2 12

1 2

1

2 2 22

1 2

( )

( , ) = ( ) ,4 | |

( )

ikl q

l

dipole l q

l q

kx y x zx

eG k

x y y zy

kx z y z z

πε

−

∂ ∂ ∂+ ∂ ∂ ∂ ∂∂

∂ ∂ ∂+

∂ ∂ ∂ ∂ −∂ ∂ ∂ ∂ +

∂ ∂ ∂ ∂ ∂

r r

r rr r

(4a)

( ) ( ) ( )

( , ) = ( ) ( ) ( ) .

( ) ( ) ( )

lx lx lx

rx l q ry l q rz l q

l ly ly ly

reflected l q rx l q ry l q rz l q

lz lz lz

rx l q ry l q rz l q

Ge Ge Ge

G Ge Ge Ge

Ge Ge Ge

− − −

− − −

− − −

r r r r r r

r r r r r r r r

r r r r r r

(4b)

where for example, lz

rxGe is Green's function for the z-directed electric field associated with a

x-directed dipole [12,13]. By obtaining dipole polarizations from Eq. (3), one can comprehensively characterize the

radiation performance of the array of core-shell nanoparticles antenna deposited over a layered structure. This needs the sommerfeld integrals calculations for the array of dipoles (with arbitrary polarization) located on a layered substrate. This has carefully been addressed

in [13]. Hence, for each dipole ( , , )x y z

p p p located at 0 0 0

( , , )x y z above a substrate instance,



the upper half-space and lower half-space far-field radiation patterns can be represented as [14]:

2 12

3

( cos sin )cos sin= = .

( sin sin ) 4

ik rJ

x y J z JJ

x y JJ

E p p pk e

E p pr

θ

ϕ

ϕ ϕ θ θϕ ϕπε

+ Φ − Φ

− − ΦE (5)

where the index [1, ]J N∈ is to distinguish between the upper-half 1 1

( , )ε µ and lower-half

( , )N Nε µ . The potential parameters are defined in [13,14]. Notice that, each potential is

composed of two terms, whereas the first term can be interpreted as the far zone radiation pattern of a dipole, while the second term can be identified as the radiation from a dipole located at the image plane weighted by generalized reflection coefficients.

3. Optical reflectarray nanoantenna

To establish an optical reflectarray nanoantenna, one needs to design an array of nano-radiators where each of them is tailored properly to provide a desired reflection phase, where as a result the array can re-direct and scan the beam in a specific direction. Having an array of nanoradiators allows narrowing the radiation beam. Thus, the reflectarray nanoantenna can successfully scan a directive optical radiation beam. This will be of significant interest for optical far-field engineering.

Assuming the excitation is achieved by a feed located in the far-field of the array antenna,

the phase of the incident wave at each particle is proportional to the distance l

d from that

particle [see Fig. 1(b)]. Then, the required phase of the reflected field for this element to

achieve a reflected beam in a given direction 0 0

( , )θ φ is obtained by [1]

0 0 0 0

= [ sin ( cos sin )]l l l l

k d x yθ φ φΦ − + (6)

where ( , )l l

x y is the coordinate of the center of element l and 0 0 0

k ω µ ε= . The required

phase can successfully be achieved by optimizing core-shell dielectric-plasmonic nanoparticles. Basically, one can change the radii of the configuration or its materials parameters to achieve this importance. Here, for the sake of simplicity in FDTD analysis, the material core is considered as the variable for obtaining the required reflection phase.

3.1 Reflection-phase synthesis

In order to characterize the radiating element of an array, the effect of the surrounding elements needs to be taken into account. To achieve this, one can envision a nanoparticle inside the array as a periodic configuration and then apply a full wave numerical analysis to demonstrate the reflection phase from the array configuration [1–3]. A 3-D finite difference time domain (FDTD) [15,16] approach with periodic boundary condition (PBC) is applied to characterize the performance of periodic array of nanoparticles.

Let us first highlight the scattering performance of a core-shell nanosphere. Figure 3

illustrates the FDTD simulation of the particle having a = 22.5nm , b/a = 0.533 , silver as the

shell material and 0

= 3coreε ε . In the FDTD model, the computational domain is configured

with cubical Yee cells with 0.75nm∆ = and the core-shell structure is illuminated by a plane

wave having x-polarized electric field and traveling in the –z direction. The sphere is placed

at the center of computational domain (0,0,0) and the scattered field is stored at (0,0,100 )∆

in front of the concentric sphere. The scattered field is plotted in Fig. 3. The polarizability α

of the same particle based on Mie theory is also shown in Fig. 3. These two graphs can be compared in regard of the position of resonances. A good comparison between the full wave

numerical analysis and theoretical model is established. At resonance point (0

357.1nmλ = )

the error is less than 4% which can be smaller by choosing a smaller Yee cell.



250 300 350 400 450 500 550 600 650 700 7500

1

2

3

4

5

6

7

8

Wavelength (nm)| αα αα

| (1

0-2εε εε 0

λλ λλ03)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

|Scatt

ere

d F

ield

|

Mie Theory FDTD

Fig. 3. Resonance performance of a concentric nanoshell particle, 0

b/a = 0.533, = 3coreε ε .

Close comparison between Mie-theory and FDTD is illustrated.

The array of nanoparticles is investigated next. The objective is to successfully tailor the reflection phase from a nanoparticle located inside the array to the value of interest. To accomplish this, the FDTD is applied to characterize one unit-cell of the periodic structure (array of particles in free-space) and determine the phase of the reflected field. The unit-cell

size is considered to be 150 150nm nm× (in x and y directions) and the same Yee cell is used.

The required phase is manipulated by changing the core material of the nanoparticle. Figure 4 shows the reflection amplitude and phase for different core materials (b/a is fixed at 0.533). As observed, the resonance performance depends on the material properties. Careful selection of the operating wavelength gives a better control over the reflected phase swing. If we

choose operating wavelength0

357.1nmλ = (f = 840 THz) as the design wavelength, we can

realize a relatively large phase swing of about 115°. Figure 5 illustrates the reflection phase variation in terms of change in the material parameter of core. This is a very useful curve that will be used in next section to realize a reflectarray of interest.

300 325 350 375 400 425 450 475 5005000

0.1

0.2

0.3

0.4

0.5

Wavelength (nm)

Re

fle

cti

on

Co

eff

icie

nt

εεεεcore

= 1εεεε0

εεεεcore

= 2εεεε0

εεεεcore

= 3εεεε0

300 325 350 375 400 425 450 475 500500-200

-150

-100

-50

0

50

100

150

200

Wavelength (nm)

Re

fle

cti

on

Ph

as

e (

de

g)

εεεεcore

= 1εεεε0

εεεεcore

= 2εεεε0

εεεεcore

= 3εεεε0

Phase swing

(a) (b)

Fig. 4. FDTD simulated results for different core materials and construction of phase design curve: (a) Reflection amplitude and, (b) Reflection phase.



1 1.5 2 2.5 3 3.5 4 4.5-120

-100

-80

-60

-40

-20

0

20

εεεεcore

Refl

ecti

on

Ph

ase (

deg

)

Fig. 5. Phase of reflection coefficient vs the core permittivity at 0

357.1nmλ = .

3.2 Scanned-beam characteristics

In this paper, two reflectarray designs (including 6 6× elements) for beam scanning at 15° and

30° are considered. The geometry of reflectarray is depicted in Fig. 1(b). The center of array

is placed at (0,0,0) . For the first design the feed is located at

( , , ) = ( 400 ,0,2250 )f f f

x y z nm nm− , and for the second design it is at

( , , ) = ( 400 ,0,4500 )f f f

x y z nm nm− . The feed excitation is modeled with an infinitesimal

electric dipole which is polarized along the x-direction and operates at 0

357.1nmλ = .

In order to ensure field radiation only in one side of the antenna, the array antenna is deposited on a silver layer coated by a dielectric material. The silver layer has a thickness of

035.71 0.1nm λ= and the same material as the shell ( = 4.67 .01

rsiε − + ). The dielectric

material is made of a thin 2

SiO film with = 2.2rdε and thickness of 3.571nm. Considering

the thin thicknesses of the substrate layers, they do not have much effects on the reflection phase, and they will only help to suppress the back radiation. Hence, one can still use the reflection phase curve demonstrated in Fig. 5 for an array of core-shell nanoparticles located in free-space. This will be validated later by both our theoretical and full-wave numerical models.

Let us first consider the 15° scan angle case (0

15 , 0θ φ= =� � ). From Eq. (6), one can first

determine the required reflection phases for the array elements. Then, from Fig. 5 the required material parameters for the nanoparticles cores are evaluated, as given in Table 1(a). The

cores materials range from 1.2rε = to 3.9

rε = . The Mie theory formulations discussed in

section 2 is used to determine the equivalent dipole modes for each of the nanoshells as

illustrated in Table 2(a). Since the values of y

p s are much smaller than those of x

p and z

p

dipoles, they are not shown in this table. The values are normalized to maximum of |p|. The radiation pattern for the array of dipoles elements located above the layered substrate is obtained in Fig. 6(a). This validates a successful 15° beam scanning for the reflected field (25° difference compared to the beam illumination). The half-power beamwidth is 22° which is an improvement of about 4 times compared to dipole excitation itself (which has a 90° beamwidth). Note that, the obtained beamwidth for reflectarray is in good comparison with

the performance of a uniform array offering 19° beamwidth [17]. Thus, the 6 6× reflectarray

nanoparticles antenna successfully scans a narrow beam optical emission. One can reduce the beamwidth even much more by simply increasing the number of array elements [17].The

magnitude (dB) and phase of the x-directed electric field in an x-y plane located at 0

= 0.5z λ

above the plane of nano core-shells are also depicted in Figs. 7.



Table 1. Core relative permittivity of nanoantenna array elements: (a) 0

= 15θ �

, (b) 0

= 30θ �

.

(a) θ = 15° (b) θ = 30°

m = 1 m = 2 m = 3 m = 4 m = 5 m = 6 m = 1 m = 2 m = 3 m = 4 m = 5 m = 6

n = 1 1.2 2.25 2.7 2.8 2.84 2.8 1.2 2.1 2.7 2.88 3.47 3.91

n = 2 1.8 2.67 2.87 3.11 3.3 3.04 1.6 2.53 2.77 3.04 3.76 4.62

n = 3 2.09 2.76 3.0 2.59 3.69 3.51 1.7 2.59 2.81 2.27 3.92 4.77

n = 4 2.09 2.76 3.0 2.59 3.69 3.51 1.7 2.59 2.81 2.27 3.92 4.77

n = 5 1.8 2.67 2.87 3.11 3.3 3.04 1.6 2.53 2.77 3.04 3.76 4.62

n = 6 1.2 2.25 2.7 2.8 2.84 2.8 1.2 2.1 2.7 2.88 3.47 3.91

The similar procedure can be followed to design a 6 6× array for 30° scan angle.

Table 1(b) illustrates the required core material parameters where they range from 1.2rε = to

4.8rε = . Induced dipole modes for the nanoparticles are summarized in Table 2(b).

Figure 6(b) illustrates the radiation characteristic. The radiation pattern shows that the main

beam is directed along 0

= 30θ � whose half-power beamwidth is about 30°. Figures 8 show

the distribution of the x

E in an x y− plane, 0

0.5λ above the nano particles' plane.

Table 2. Induced dipoles, x

p s and z

p s: (a) 0

= 15θ �

, (b) 0

= 30θ �

.

(a) θ = 15°

m = 1 m = 2 m = 3 m = 4 m = 5 m = 6

n = 1 0.57e-i0.99π 0.30e-i0.3π

0.84e-i0.67π 0.25ei0.06π

0.63e-i0.41π 0.27ei0.45π

0.68e-i0.31π 0.20ei0.8π

0.67e-i0.01π 0.20e-i0.88π

0.56ei0.18π 0.07e-i0.65π

n = 2 0.79e-i0.97π 0.39e-i0.19π

0.66e-i0.74π 0.40ei0.14π

0.55e-i0.57π 0.39ei0.45π

0.56e-i0.48π 0.30ei0.87π

0.5e-i0.07π 0.27e-i0.87π

0.5ei0.07π 0.08e-i0.59π

n = 3 0.76e-i0.95π 0.26e-i0.04π

0.61e-i0.78π 0.39ei0.29π

0.56e-i0.63π 0.32ei0.5π

0.94e-i0.61π 0.33ei0.97π

0.33ei0.01π 0.18e-i0.92π

0.28ei0.15π 0.03ei0.16π

n = 4 0.76e-i0.95π 0.26e-i0.04π

0.61e-i0.78π 0.39ei0.29π

0.56e-i0.63π 0.32ei0.5π

0.94e-i0.61π 0.33ei0.97π

0.33ei0.01π 0.18e-i0.92π

0.28ei0.15π 0.03ei0.16π

n = 5 0.79e-i0.97π 0.39e-i0.19π

0.66e-i0.74π 0.40ei0.14π

0.55e-i0.57π 0.39ei0.45π

0.56e-i0.48π 0.30ei0.87π

0.5e-i0.07π 0.27e-i0.87π

0.5ei0.07π 0.08e-i0.59π

n = 6 0.57e-i0.99π 0.30e-i0.3π

0.84e-i0.67π 0.25ei0.06π

0.63e-i0.41π 0.27ei0.45π

0.68e-i0.31π 0.20ei0.8π

0.67e-i0.01π 0.20e-i0.88π

0.56ei0.18π 0.07e-i0.65π

(b) θ = 30°

m = 1 m = 2 m = 3 m = 4 m = 5 m = 6

n = 1 0.74ei0.86π 0.58e-i0.4π

0.82e-i0.61π 0.39e-i0.05π

0.74e-i0.16π 0.33ei0.62π

0.41ei0.17π 0.25e-i0.89π

0.55ei0.55π 0.12e-i0.38π

0.24e-i0.93π 0.04ei0.46π

n = 2 0.77ei0.9π 0.88e-i0.34π

0.37e-i0.55π 0.57e-i0.02π

0.68e-i0.24π 0.41ei0.57π

0.30e-i0.01π 0.33e-i0.94π

0.48ei0.55π 0.14e-i0.42π

0.12e-i0.95π 0.02ei0.46π

n = 3 0.78ei0.9π 0.71e-i0.34π

0.51e-i0.5π 0.58ei0.02π

0.54e-i0.26π 0.42ei0.54π

0.31e-i0.04π 0.26e-i0.8π

0.53ei0.55π 0.12e-i0.19π

0.10e-i0.85π 0.07ei0.84π

n = 4 0.78ei0.9π 0.71e-i0.34π

0.51e-i0.5π 0.58ei0.02π

0.54e-i0.26π 0.42ei0.54π

0.31e-i0.04π 0.26e-i0.8π

0.53ei0.55π 0.12e-i0.19π

0.10e-i0.85π 0.07ei0.84π

n = 5 0.77ei0.9π 0.88ei0.34π

0.37e-i0.55π 0.57e-i0.02π

0.68e-i0.24π 0.41ei0.57π

0.30e-i0.01π 0.33e-i0.94π

0.48ei0.55π 0.14e-i0.42π

0.12e-i0.95π 0.02ei0.46π

n = 6 0.74ei0.86π 0.58e-i0.4π

0.82e-i0.61π 0.39e-i0.05π

0.74e-i0.16π 0.33ei0.62π

0.41ei0.17π 0.25e-i0.89π

0.55ei0.55π 0.12e-i0.38π

0.24e-i0.93π 0.04ei0.46π



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-9

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0

60

120

30

150

0

180

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90 90

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-9

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0

60

120

30

150

0

180

30

150

60

120

90 90

(a) (b)

Fig. 6. Radiation pattern in the x-z plane at 0

= 357.1nmλ : (a) 0

= 15θ�

, (b) 0

= 30θ�

.

Fig. 7. Near-field (x

E ) of the reflectarray for 15° beam scanning [Fig. 6(a)] in a plane located

at 0

0.5λ above the nanoantenna: (a) Magnitude (dB), (b) Phase.

Fig. 8. Near-field (x

E ) of the reflectarray for 30° beam scanning [Fig. 6(b)] in a plane located

at 0

0.5λ above the nanoantenna: (a) Magnitude (dB), (b) Phase.

A full-wave FDTD numerical analysis is also applied to validate our dipole-modes modeling results, and further explore the effects of finite-size substrate on the radiation characteristics. To accurately model thin silver shells in FDTD, we need to use very small-

size Yee cells, hence characterizing the whole 6 6× array would be very huge and time-

consuming. Instead, we model the core-shell structures with their equivalent induced dipoles (using Mie analytical model), and then we integrate them with FDTD numerical technique.



This is called hybrid FDTD-dipolar mode technique. In the FDTD simulation, each

nanoparticle is modeled by its induced dipoles given in Table 2. There will be 6 6× sets of

dipoles on top of the finite-size layered substrate. Since the y

p is about ten times smaller than

xp and

zp , in our simulation we ignored the

yp s. At operating wavelength,

0357.1nmλ = ,

the slab size in transverse plane is 0 0

3 3λ λ× . The hybrid FDTD-dipolar modes is applied and

the radiation patterns are demonstrated in Fig. 9. Very good comparisons in compared to the full theoretical model are presented. The side lobes are slightly increased due to the wave diffractions from the substrate edges. The FDTD results validate successfully the concept and radiation performance of the optical reflectarray nanoantennas investigated in this paper.

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30

150

0

180

30

150

60

120

90 90

(a) (b)

Fig. 9. FDTD radiation pattern in the x-z plane at 0

= 357.1nmλ : (a) 0

= 15θ�

, (b) 0

= 30θ�

. Good

comparisons compared to dipole-modes theoretical results (Fig. 6) are observed.

Frequency sensitivity of the reflectarray design is also explored in this paper. The

radiation patterns for scanning 30° at different frequencies 0 0 0 0

= 0.9 ,0.95 ,1.05 ,1.1f f f f f are

plotted in Fig. 10. By changing the frequency, both the size and material (for the silver coatings) parameters of the nanoparticles will be changed affecting the radiation pattern and degrading the performance.

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0

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120

30

150

0

180

30

150

60

120

90 90

(c)

(a) (b)

(d)

Fig. 10. Radiation patterns in the x-z plane at different frequencies for 30° beam scanning: (a)

0= 0.9f f , (b)

0= 0.95f f : (c)

0= 1.05f f , and (d)

0= 1.1f f , (

0= 840f THz is the design

frequency).



4. Conclusions

This paper presents the concept of reflectarray nanoantenna implementation in optics for the first time, with the use of array of core-shell nanoparticles. Optimized geometry-material plasmonic nanoparticles determine successfully the required reflection phases for desired far-field manipulation. Efficient dipole-modes theoretical model and FDTD full-wave numerical method are applied to demonstrate the physics of array of nanoantennas and fully characterize the radiation characteristics. Successful narrow-beamwidth directive emission is demonstrated. The radiation pattern results illustrate that the reflectarray nanoantenna is able to very effectively shape the beam and scan desired directions. Increasing the number of array elements and optimizing the particles configurations will lead to an entirely new paradigm for efficient wireless communication in optics.

Acknowledgments

This work was supported in part by the U.S. Air Force Office of Scientific Research (AFOSR) and National Science Foundation (NSF). We would like to thank Prof. Nader Engheta at University of Pennsylvania for his great discussions and suggestions during this work.



An optical reflectarray nanoantenna: The concept and design

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Transcript of An optical reflectarray nanoantenna: The concept and design