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.

© 2010 Optical Society of America

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References

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  1. J. A. Encinar, "Design of two-layer printed reflectarrays using patches of variable size," IEEE Trans. Antenn. Propag. 49(10), 1403-1410 (2001).
    [CrossRef]
  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).
    [CrossRef]
  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).
    [CrossRef]
  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).
    [CrossRef]
  5. J. Li, and N. Engheta, "Core-shell nanowire optical antennas fed by slab waveguides," IEEE Trans. Antenn. Propag. 55(11), 3018-3026 (2007).
    [CrossRef]
  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).
    [CrossRef]
  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).
    [CrossRef]
  9. Q1. G. Mie, "Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen," Leipzig Ann. Phys. 330(3), 377-445 (1908).
    [CrossRef]
  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).
    [CrossRef]
  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).
    [CrossRef]
  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).

2009 (1)

2008 (1)

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).
[CrossRef]

2007 (3)

J. Li, and N. Engheta, "Core-shell nanowire optical antennas fed by slab waveguides," IEEE Trans. Antenn. Propag. 55(11), 3018-3026 (2007).
[CrossRef]

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).
[CrossRef]

H. Mosallaei, "FDTD-PLRC technique for modeling of anisotropic-dispersive media and metamaterial devices," IEEE Trans. Electromagn. Compat. 49(3), 649-660 (2007).
[CrossRef]

2005 (2)

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).
[CrossRef]

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).
[CrossRef]

2001 (1)

J. A. Encinar, "Design of two-layer printed reflectarrays using patches of variable size," IEEE Trans. Antenn. Propag. 49(10), 1403-1410 (2001).
[CrossRef]

1965 (1)

P. W. Hannan, and M. A. Balfour, "Simulation of a phased-array antenna in waveguide," IEEE Trans. Antenn. Propag. 13(3), 342-353 (1965).
[CrossRef]

1908 (1)

Q1. G. Mie, "Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen," Leipzig Ann. Phys. 330(3), 377-445 (1908).
[CrossRef]

Alù, A.

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).
[CrossRef]

Balfour, M. A.

P. W. Hannan, and M. A. Balfour, "Simulation of a phased-array antenna in waveguide," IEEE Trans. Antenn. Propag. 13(3), 342-353 (1965).
[CrossRef]

Encinar, J. A.

J. A. Encinar, "Design of two-layer printed reflectarrays using patches of variable size," IEEE Trans. Antenn. Propag. 49(10), 1403-1410 (2001).
[CrossRef]

Engheta, N.

J. Li, and N. Engheta, "Core-shell nanowire optical antennas fed by slab waveguides," IEEE Trans. Antenn. Propag. 55(11), 3018-3026 (2007).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

Ghadarghadr, S.

Hannan, P. W.

P. W. Hannan, and M. A. Balfour, "Simulation of a phased-array antenna in waveguide," IEEE Trans. Antenn. Propag. 13(3), 342-353 (1965).
[CrossRef]

Hao, Z.

Imbriale, Y. A.

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).
[CrossRef]

Lenin, N.

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).
[CrossRef]

Li, J.

J. Li, and N. Engheta, "Core-shell nanowire optical antennas fed by slab waveguides," IEEE Trans. Antenn. Propag. 55(11), 3018-3026 (2007).
[CrossRef]

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).
[CrossRef]

Mie, G.

Q1. G. Mie, "Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen," Leipzig Ann. Phys. 330(3), 377-445 (1908).
[CrossRef]

Mosallaei, H.

S. Ghadarghadr, Z. Hao, and H. Mosallaei, "Plasmonic array nanoantennas on layered substrates: modeling and radiation characteristics," Opt. Express 17(21), 18556-18570 (2009).
[CrossRef]

H. Mosallaei, "FDTD-PLRC technique for modeling of anisotropic-dispersive media and metamaterial devices," IEEE Trans. Electromagn. Compat. 49(3), 649-660 (2007).
[CrossRef]

Rahmat-Samii, Y.

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).
[CrossRef]

Rajagopalan, H.

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).
[CrossRef]

Rao, P. H.

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).
[CrossRef]

Salandrino, A.

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).
[CrossRef]

IEEE Trans. Antenn. Propag. (4)

J. A. Encinar, "Design of two-layer printed reflectarrays using patches of variable size," IEEE Trans. Antenn. Propag. 49(10), 1403-1410 (2001).
[CrossRef]

P. W. Hannan, and M. A. Balfour, "Simulation of a phased-array antenna in waveguide," IEEE Trans. Antenn. Propag. 13(3), 342-353 (1965).
[CrossRef]

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).
[CrossRef]

J. Li, and N. Engheta, "Core-shell nanowire optical antennas fed by slab waveguides," IEEE Trans. Antenn. Propag. 55(11), 3018-3026 (2007).
[CrossRef]

IEEE Trans. Electromagn. Compat. (1)

H. Mosallaei, "FDTD-PLRC technique for modeling of anisotropic-dispersive media and metamaterial devices," IEEE Trans. Electromagn. Compat. 49(3), 649-660 (2007).
[CrossRef]

J. Appl. Phys. (1)

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).
[CrossRef]

Leipzig Ann. Phys. (1)

Q1. G. Mie, "Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen," Leipzig Ann. Phys. 330(3), 377-445 (1908).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

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).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

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).
[CrossRef]

Other (7)

A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, Norwood, 2005).

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

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.

J. A. Stratton, Electromagnetic Theory (New York: McGraw-Hill, 1941).

U. Kreibig, and M. Vollmer, Optical Properties of Metal Clusters (Springer-Verlag Berlin Heidelberg, Germany, 1995).

Weng Cho Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, 1995).

L. Novotny, and B. Hecht, Principle of Nano-Optics (Cambridge University Press, United Kingdom, 2006).

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Figures (10)

Fig. 1.
Fig. 1.

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

Fig. 2.
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 εcore = 3ε 0. Operating wavelength is 357.1 nm and the shell is made of silver [εshell = (-4.67 + .01i)ε 0].

Fig. 3.
Fig. 3.

Resonance performance of a concentric nanoshell particle, b/a = 0.533, εcore = 3ε 0. Close comparison between Mie-theory and FDTD is illustrated.

Fig. 4.
Fig. 4.

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

Fig. 5.
Fig. 5.

Phase of reflection coefficient vs the core permittivity at λ 0 = 357. 1nm.

Fig. 6.
Fig. 6.

Radiation pattern in the x-z plane at λ 0 = 357.1nm : (a) θ 0 = 15°, (b) θ 0 = 30°.

Fig. 7.
Fig. 7.

Near-field ( Ex ) of the reflectarray for 15° beam scanning [Fig. 6(a)] in a plane located at 0.5λ 0 above the nanoantenna: (a) Magnitude (dB), (b) Phase.

Fig. 8.
Fig. 8.

Near-field ( Ex ) of the reflectarray for 30° beam scanning [Fig. 6(b)] in a plane located at 0.5λ 0 above the nanoantenna: (a) Magnitude (dB), (b) Phase.

Fig. 9.
Fig. 9.

FDTD radiation pattern in the x-z plane at λ = 357.1nm : (a) θ 0 = 15°, (b) θ 0 = 30°. Good comparisons compared to dipole-modes theoretical results (Fig. 6) are observed.

Fig. 10.
Fig. 10.

Radiation patterns in the x-z plane at different frequencies for 30° beam scanning: (a) f = 0.9 f 0 , (b) f = 0.95 f 0 : (c) f = 1.05 f 0, and (d) f = 1.1 f 0, (f 0 = 840THz is the design frequency).

Tables (2)

Tables Icon

Table 1. Core relative permittivity of nanoantenna array elements: (a) θ 0 = 15°, (b) θ 0 = 30°.

Tables Icon

Table 2. Induced dipoles, px s and pz s: (a) θ 0 = 15°, (b) θ 0 = 30°.

Equations (7)

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α = 6 π ε 0 k 0 3 i c 1 TM
ε ( ω ) = ε 0 ( 1 ω p 2 ω ( ω + i γ p ) )
p l = α l ( E inc total ( r l ) + q , q l G ̿ dipole l r l r q p q + q G ̿ reflected l r l r q p q ) ,
G ̿ dipole l r 1 r q = [ ( k 1 2 + 2 2 x ) 2 x y 2 x z 2 x y ( k 1 2 + 2 2 y ) 2 y z 2 x z 2 y z ( k 1 2 + 2 2 z ) ] e i k 1 r l r q 4 π ε 1 r l r q ,
G ̿ reflected l r 1 r q = [ G e rx lx ( r l r q ) G e ry lx ( r 1 r q ) G e rz lx ( r l r q ) G e rx ly ( r l r q ) G e ry ly ( r l r q ) G e rz ly ( r l r q ) G e rx lz ( r l r q ) G e ry lz ( r l r q ) G e rz lz ( r l r q ) ] .
E = E θ E φ = k J 2 4 π ε J e i k J r r ( p x cos φ + p y sin φ ) cos θ Φ J 2 p z sin θ Φ J 1 ( p x sin φ p y sin φ ) Φ J 3 .
Φ l = k 0 [ d l sin θ 0 ( x l cos ϕ 0 + y l sin ϕ 0 ) ]

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