Abstract

The concept of a layered metasurface constructed from loop nanoantennas for beam scanning in space is explored. Each layer of the metasurface can be envisioned as a shunt impedance sheet designable by modifying the loop configuration cell by cell. The single and concentric loop nanoantennas made of silver provide capacitive and inductive impedances, respectively, with negligible loss at 1.5 μm, managing full control of the beam phase and amplitude. A telecom metasurface for beam scanning in 3D space is presented. The complex structure is modeled with an in-house-developed finite-difference time-domain method considering interactions among elements, in contrast to many designs in which isolated elements are simulated by assuming local periodicity.

© 2014 Optical Society of America

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  1. M. Farmahini-Farahani, J. R. Cheng, and H. Mosallaei, J. Opt. Soc. Am. B 30, 2365 (2013).
    [CrossRef]
  2. N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
    [CrossRef]
  3. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 339, 1232009 (2013).
    [CrossRef]
  4. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
    [CrossRef]
  5. E. Carrasco and J. Perruisseau-Carrier, IEEE Antennas Wireless Propag. Lett. 12, 253 (2013).
    [CrossRef]
  6. P. Y. Chen and A. Alu, Phys. Rev. B 84, 205110 (2011).
    [CrossRef]
  7. Y. Nanfang, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J. P. Tetienne, Z. Gaburro, and F. Capasso, IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
    [CrossRef]
  8. B. Memarzadeh and H. Mosallaei, Opt. Lett. 36, 3623 (2011).
    [CrossRef]
  9. A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
    [CrossRef]
  10. J. A. Encinar and J. A. Zornoza, IEEE Trans. Antennas Propag. 51, 1662 (2003).
    [CrossRef]
  11. M. Pasian, S. Monni, A. Neto, M. Ettorre, and G. Gerini, IEEE Trans. Antennas Propag. 58, 43 (2010).
    [CrossRef]
  12. F. Monticone, N. M. Estakhri, and A. Alù, Phys. Rev. Lett. 110, 203903 (2013).
    [CrossRef]
  13. A. Alu and N. Engheta, IEEE Trans. Antennas Propag. 55, 3027 (2007).
    [CrossRef]
  14. B. Memarzadeh and H. Mosallaei, J. Opt. Soc. Am. B 30, 1827 (2013).
    [CrossRef]
  15. C. Pfeiffer and A. Grbic, Appl. Phys. Lett. 102, 231116 (2013).
    [CrossRef]
  16. A. E. H. Love, Phil. Trans. R. Soc. A 197, 1 (1901).
    [CrossRef]

2014

N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
[CrossRef]

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

2013

Y. Nanfang, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J. P. Tetienne, Z. Gaburro, and F. Capasso, IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[CrossRef]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 339, 1232009 (2013).
[CrossRef]

E. Carrasco and J. Perruisseau-Carrier, IEEE Antennas Wireless Propag. Lett. 12, 253 (2013).
[CrossRef]

F. Monticone, N. M. Estakhri, and A. Alù, Phys. Rev. Lett. 110, 203903 (2013).
[CrossRef]

C. Pfeiffer and A. Grbic, Appl. Phys. Lett. 102, 231116 (2013).
[CrossRef]

B. Memarzadeh and H. Mosallaei, J. Opt. Soc. Am. B 30, 1827 (2013).
[CrossRef]

M. Farmahini-Farahani, J. R. Cheng, and H. Mosallaei, J. Opt. Soc. Am. B 30, 2365 (2013).
[CrossRef]

2011

B. Memarzadeh and H. Mosallaei, Opt. Lett. 36, 3623 (2011).
[CrossRef]

P. Y. Chen and A. Alu, Phys. Rev. B 84, 205110 (2011).
[CrossRef]

2010

M. Pasian, S. Monni, A. Neto, M. Ettorre, and G. Gerini, IEEE Trans. Antennas Propag. 58, 43 (2010).
[CrossRef]

2007

A. Alu and N. Engheta, IEEE Trans. Antennas Propag. 55, 3027 (2007).
[CrossRef]

2003

J. A. Encinar and J. A. Zornoza, IEEE Trans. Antennas Propag. 51, 1662 (2003).
[CrossRef]

2000

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

1901

A. E. H. Love, Phil. Trans. R. Soc. A 197, 1 (1901).
[CrossRef]

Aieta, F.

Y. Nanfang, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J. P. Tetienne, Z. Gaburro, and F. Capasso, IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[CrossRef]

Alu, A.

P. Y. Chen and A. Alu, Phys. Rev. B 84, 205110 (2011).
[CrossRef]

A. Alu and N. Engheta, IEEE Trans. Antennas Propag. 55, 3027 (2007).
[CrossRef]

Alù, A.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

F. Monticone, N. M. Estakhri, and A. Alù, Phys. Rev. Lett. 110, 203903 (2013).
[CrossRef]

Aoust, G.

Y. Nanfang, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J. P. Tetienne, Z. Gaburro, and F. Capasso, IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[CrossRef]

Blanchard, R.

Y. Nanfang, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J. P. Tetienne, Z. Gaburro, and F. Capasso, IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[CrossRef]

Boltasseva, A.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 339, 1232009 (2013).
[CrossRef]

Capasso, F.

N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
[CrossRef]

Y. Nanfang, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J. P. Tetienne, Z. Gaburro, and F. Capasso, IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[CrossRef]

Carrasco, E.

E. Carrasco and J. Perruisseau-Carrier, IEEE Antennas Wireless Propag. Lett. 12, 253 (2013).
[CrossRef]

Castaldi, G.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

Chen, P. Y.

P. Y. Chen and A. Alu, Phys. Rev. B 84, 205110 (2011).
[CrossRef]

Cheng, J. R.

Encinar, J. A.

J. A. Encinar and J. A. Zornoza, IEEE Trans. Antennas Propag. 51, 1662 (2003).
[CrossRef]

Engheta, N.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

A. Alu and N. Engheta, IEEE Trans. Antennas Propag. 55, 3027 (2007).
[CrossRef]

Estakhri, N. M.

F. Monticone, N. M. Estakhri, and A. Alù, Phys. Rev. Lett. 110, 203903 (2013).
[CrossRef]

Ettorre, M.

M. Pasian, S. Monni, A. Neto, M. Ettorre, and G. Gerini, IEEE Trans. Antennas Propag. 58, 43 (2010).
[CrossRef]

Farmahini-Farahani, M.

Gaburro, Z.

Y. Nanfang, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J. P. Tetienne, Z. Gaburro, and F. Capasso, IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[CrossRef]

Galdi, V.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

Genevet, P.

Y. Nanfang, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J. P. Tetienne, Z. Gaburro, and F. Capasso, IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[CrossRef]

Gerini, G.

M. Pasian, S. Monni, A. Neto, M. Ettorre, and G. Gerini, IEEE Trans. Antennas Propag. 58, 43 (2010).
[CrossRef]

Grbic, A.

C. Pfeiffer and A. Grbic, Appl. Phys. Lett. 102, 231116 (2013).
[CrossRef]

Kats, M. A.

Y. Nanfang, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J. P. Tetienne, Z. Gaburro, and F. Capasso, IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[CrossRef]

Kildishev, A. V.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 339, 1232009 (2013).
[CrossRef]

Love, A. E. H.

A. E. H. Love, Phil. Trans. R. Soc. A 197, 1 (1901).
[CrossRef]

Memarzadeh, B.

Monni, S.

M. Pasian, S. Monni, A. Neto, M. Ettorre, and G. Gerini, IEEE Trans. Antennas Propag. 58, 43 (2010).
[CrossRef]

Monticone, F.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

F. Monticone, N. M. Estakhri, and A. Alù, Phys. Rev. Lett. 110, 203903 (2013).
[CrossRef]

Mosallaei, H.

Nanfang, Y.

Y. Nanfang, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J. P. Tetienne, Z. Gaburro, and F. Capasso, IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Neto, A.

M. Pasian, S. Monni, A. Neto, M. Ettorre, and G. Gerini, IEEE Trans. Antennas Propag. 58, 43 (2010).
[CrossRef]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Pasian, M.

M. Pasian, S. Monni, A. Neto, M. Ettorre, and G. Gerini, IEEE Trans. Antennas Propag. 58, 43 (2010).
[CrossRef]

Perruisseau-Carrier, J.

E. Carrasco and J. Perruisseau-Carrier, IEEE Antennas Wireless Propag. Lett. 12, 253 (2013).
[CrossRef]

Pfeiffer, C.

C. Pfeiffer and A. Grbic, Appl. Phys. Lett. 102, 231116 (2013).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Shalaev, V. M.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 339, 1232009 (2013).
[CrossRef]

Silva, A.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Tetienne, J. P.

Y. Nanfang, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J. P. Tetienne, Z. Gaburro, and F. Capasso, IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Yu, N.

N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
[CrossRef]

Zornoza, J. A.

J. A. Encinar and J. A. Zornoza, IEEE Trans. Antennas Propag. 51, 1662 (2003).
[CrossRef]

Appl. Phys. Lett.

C. Pfeiffer and A. Grbic, Appl. Phys. Lett. 102, 231116 (2013).
[CrossRef]

IEEE Antennas Wireless Propag. Lett.

E. Carrasco and J. Perruisseau-Carrier, IEEE Antennas Wireless Propag. Lett. 12, 253 (2013).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

Y. Nanfang, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J. P. Tetienne, Z. Gaburro, and F. Capasso, IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[CrossRef]

IEEE Trans. Antennas Propag.

J. A. Encinar and J. A. Zornoza, IEEE Trans. Antennas Propag. 51, 1662 (2003).
[CrossRef]

M. Pasian, S. Monni, A. Neto, M. Ettorre, and G. Gerini, IEEE Trans. Antennas Propag. 58, 43 (2010).
[CrossRef]

A. Alu and N. Engheta, IEEE Trans. Antennas Propag. 55, 3027 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Mater.

N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
[CrossRef]

Opt. Lett.

Phil. Trans. R. Soc. A

A. E. H. Love, Phil. Trans. R. Soc. A 197, 1 (1901).
[CrossRef]

Phys. Rev. B

P. Y. Chen and A. Alu, Phys. Rev. B 84, 205110 (2011).
[CrossRef]

Phys. Rev. Lett.

F. Monticone, N. M. Estakhri, and A. Alù, Phys. Rev. Lett. 110, 203903 (2013).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Science

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 339, 1232009 (2013).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic configuration of the three-layer cascaded metasurface with outer layer characterized by the susceptance B1 and inner layer B2. The distance in between is d=λ/4. The whole structure is immersed in the dielectric medium with εd=2.25. (b) The equivalent circuit model, from which the reflection and transmission coefficients are obtained. (c) Reflection amplitude and (d) phase as a function of B1 and B2. (e) Transmission amplitude and (f) phase as a function of B1 and B2. The white lines in (c)–(f) are the equal-amplitude contours where the phase is changing. The black lines are the equal-phase contours where the amplitude is changing.

Fig. 2.
Fig. 2.

Configurations of (a) the single loop antennas and (c) the concentric loop antennas. (b) Frequency response of the susceptance for the single loop element when D2=220nm, D1=40nm. (d) Frequency response of the susceptance for the concentric loop element when D4=350nm, D3=240nm, D2=100nm, D1=20nm. The period P and the thickness h are fixed as 400 and 20 nm for all the designs. The insets in (b) and (d) show the equivalent circuits at the corresponding frequencies.

Fig. 3.
Fig. 3.

(a) Normalized capacitive susceptance of the single loop element at 200 THz as a function of D1 and D2. (b) Normalized inductive susceptance of the concentric loop at 200 THz by tuning D3 and D1, where D4 and D2 are fixed as 350 and 100 nm, respectively.

Fig. 4.
Fig. 4.

(a) Definition of the focal point F using (f0, θ, φ). J is the projection of F onto the metasurface plane. Geometry of (b) the outer layer and (c) the inner layer composed of graded loop inclusions for beam focusing at f0=2.56λ, θ=13°, φ=225°.

Fig. 5.
Fig. 5.

(a) Designed phase shift profile for the three-layer metasurface to focus beam into the focal point f0=2.56λ, θ=13°, φ=225°. (b) Real phase shift profile after the three-layer finite metasurface obtained from one full-wave FDTD simulation. (c) Field distribution (amplitude) in the xy plane at the focal point. One can see beam scanning and concentration at the designed location.

Equations (1)

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Φ(x,y)=2πλ[(f0cosθ)2+(xf0sinθcosφ)2+(yf0sinθsinφ)2f0cosθ].

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