Abstract

We introduce the idea of discontinuous electric and magnetic fields at a boundary to design and shape wavefronts in an arbitrary manner. To create this discontinuity in the field we use orthogonal electric and magnetic currents which act like Huygens source to radiate the desired wavefront. These currents can be synthesized either by an array of electric and magnetic dipoles or by a combined impedance and admittance surface. A dipole array is an active implementation to impose discontinuous fields while the impedance/admittance surface acts as a passive one. We then expand on our previous work showing how electric and magnetic dipole arrays can be used to cloak an object demonstrating novel cloaking and anti-cloaking schemes. We also show how to arbitrarily refract a beam using a set of impedance and admittance surfaces. Refraction using the idea of discontinuous fields is shown to be a more general case of refraction than using simple phase discontinuities.

© 2013 OSA

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References

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  1. M. Selvanayagam and G. V. Eleftheriades, “An active electromagnetic cloak based on the equivalence principle,” IEEE Antennas and Wireless Propagation Letters11, 1226–1229 (2012).
    [CrossRef]
  2. C. G. M. Ryan, M. Chaharmir, J. Shaker, J. Bray, Y. M. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Transactions on Antennas and Propagation58, 1486–1493 (2010).
    [CrossRef]
  3. C. A. Balanis, Antenna Theory: Analysis and Design (Wiley-Interscience, 2005).
  4. B. Munk, Frequency Selective Surfaces: Theory and Design (Wiley-Interscience, 2000).
    [CrossRef]
  5. R. F. Harrington, Time-Harmonic Electromagnetic Fields (Wiley-Interscience, 2001).
    [CrossRef]
  6. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005), 3rd ed.
  7. J.-P. Berenger, “A Huygens subgridding for the FDTD method,” IEEE Trans. on Antennas and Propagation54, 3797–3804 (2006).
    [CrossRef]
  8. R. C. Hansen, Phased Array Antennas (Wiley-Interscience, 2009).
    [CrossRef]
  9. D.-H. Kwon and D. M. Pozar, “Optimal characteristics of an arbitrary receive antenna,” IEEE Transactions on Antennas and Propagation57, 3720–3727 (2009).
    [CrossRef]
  10. A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems (Prentice Hall, 1997).
  11. S. Tretyakov, Analytical Modeling in Applied Electromagnets (Artech House, 2003).
  12. A. Grbic and R. Merlin, “Near-field focusing plates and their design,” IEEE Transactions on Antennas and Propagation56, 3159–3165 (2008).
    [CrossRef]
  13. H. Chen, X. Luo, H. Ma, and C. Chan, “The anti-cloak,” Opt. Express16, 14603–14608 (2008).
    [CrossRef] [PubMed]
  14. I. Gallina, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “General class of metamaterial transformation slabs,” Phys. Rev. B81, 125124 (2010).
    [CrossRef]
  15. W. C. Gibson, The Method of Moments in Electromagnetics (Chapman and Hall/CRC, 2008).
  16. J. Du, S. Liu, and Z. Lin, “Broadband optical cloak and illusion created by the low order active sources,” Opt. Express20, 8608–8617 (2012).
    [CrossRef] [PubMed]
  17. D. A. Miller, “On perfect cloaking,” Opt. Express14, 12457–12466 (2006).
    [CrossRef] [PubMed]
  18. F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” Phys. Rev. Lett.103, 073901 (2009).
    [CrossRef] [PubMed]
  19. J. Lau and S. Hum, “Reconfigurable transmitarray design approaches for beamforming applications,” IEEE Transactions on Antennas and Propagation60, 5679–5689 (2012).
    [CrossRef]
  20. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science334, 333–337 (2011).
    [CrossRef] [PubMed]
  21. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science339(2013).
    [CrossRef] [PubMed]
  22. Y.-J. Tsai, S. Larouche, T. Tyler, G. Lipworth, N. M. Jokerst, and D. R. Smith, “Design and fabrication of a metamaterial gradient index diffraction grating at infrared wavelengths,” Opt. Express19, 24411–24423 (2011).
    [CrossRef] [PubMed]
  23. H. Steyskal, A. Hessel, and J. Shmoys, “On the gain-versus-scan trade-offs and the phase gradient synthesis for a cylindrical dome antenna,” IEEE Trans. on Antennas and PropagationAP-27, 825–831 (1979).
    [CrossRef]
  24. M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999), 7th ed.
  25. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14, 9794–9804 (2006).
    [CrossRef] [PubMed]
  26. A. Alú and N. Engheta, “Plasmonic and metamaterial cloaking: physical mechanisms and potentials,” Journal of Optics A: Pure and Applied Optics10, 093002 (2008).
    [CrossRef]
  27. D. Sievenpiper, L. Zhang, R. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Transactions on Microwave Theory and Techniques47, 2059–2074 (1999).
    [CrossRef]
  28. N. Engheta, “Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials,” Science317, 1698–1702 (2007).
    [CrossRef] [PubMed]
  29. L. Novotny and N. van Hulst, “Antennas for light,” Nature Photonics5, 83–90 (2011).
    [CrossRef]
  30. J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature493, 195–199 (2013).
    [CrossRef] [PubMed]
  31. C. Pfieffer and A. Grbic, “Metamaterial huygens’ surfaces: Tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett.110, 197401 (2013).
    [CrossRef]
  32. F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett.110, 203903 (2013).
    [CrossRef]

2013 (4)

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science339(2013).
[CrossRef] [PubMed]

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature493, 195–199 (2013).
[CrossRef] [PubMed]

C. Pfieffer and A. Grbic, “Metamaterial huygens’ surfaces: Tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett.110, 197401 (2013).
[CrossRef]

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett.110, 203903 (2013).
[CrossRef]

2012 (3)

J. Lau and S. Hum, “Reconfigurable transmitarray design approaches for beamforming applications,” IEEE Transactions on Antennas and Propagation60, 5679–5689 (2012).
[CrossRef]

M. Selvanayagam and G. V. Eleftheriades, “An active electromagnetic cloak based on the equivalence principle,” IEEE Antennas and Wireless Propagation Letters11, 1226–1229 (2012).
[CrossRef]

J. Du, S. Liu, and Z. Lin, “Broadband optical cloak and illusion created by the low order active sources,” Opt. Express20, 8608–8617 (2012).
[CrossRef] [PubMed]

2011 (3)

Y.-J. Tsai, S. Larouche, T. Tyler, G. Lipworth, N. M. Jokerst, and D. R. Smith, “Design and fabrication of a metamaterial gradient index diffraction grating at infrared wavelengths,” Opt. Express19, 24411–24423 (2011).
[CrossRef] [PubMed]

L. Novotny and N. van Hulst, “Antennas for light,” Nature Photonics5, 83–90 (2011).
[CrossRef]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

2010 (2)

I. Gallina, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “General class of metamaterial transformation slabs,” Phys. Rev. B81, 125124 (2010).
[CrossRef]

C. G. M. Ryan, M. Chaharmir, J. Shaker, J. Bray, Y. M. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Transactions on Antennas and Propagation58, 1486–1493 (2010).
[CrossRef]

2009 (2)

D.-H. Kwon and D. M. Pozar, “Optimal characteristics of an arbitrary receive antenna,” IEEE Transactions on Antennas and Propagation57, 3720–3727 (2009).
[CrossRef]

F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” Phys. Rev. Lett.103, 073901 (2009).
[CrossRef] [PubMed]

2008 (3)

A. Alú and N. Engheta, “Plasmonic and metamaterial cloaking: physical mechanisms and potentials,” Journal of Optics A: Pure and Applied Optics10, 093002 (2008).
[CrossRef]

A. Grbic and R. Merlin, “Near-field focusing plates and their design,” IEEE Transactions on Antennas and Propagation56, 3159–3165 (2008).
[CrossRef]

H. Chen, X. Luo, H. Ma, and C. Chan, “The anti-cloak,” Opt. Express16, 14603–14608 (2008).
[CrossRef] [PubMed]

2007 (1)

N. Engheta, “Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials,” Science317, 1698–1702 (2007).
[CrossRef] [PubMed]

2006 (3)

1999 (1)

D. Sievenpiper, L. Zhang, R. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Transactions on Microwave Theory and Techniques47, 2059–2074 (1999).
[CrossRef]

1979 (1)

H. Steyskal, A. Hessel, and J. Shmoys, “On the gain-versus-scan trade-offs and the phase gradient synthesis for a cylindrical dome antenna,” IEEE Trans. on Antennas and PropagationAP-27, 825–831 (1979).
[CrossRef]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

Alexopolous, N.

D. Sievenpiper, L. Zhang, R. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Transactions on Microwave Theory and Techniques47, 2059–2074 (1999).
[CrossRef]

Alú, A.

A. Alú and N. Engheta, “Plasmonic and metamaterial cloaking: physical mechanisms and potentials,” Journal of Optics A: Pure and Applied Optics10, 093002 (2008).
[CrossRef]

Alù, A.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett.110, 203903 (2013).
[CrossRef]

I. Gallina, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “General class of metamaterial transformation slabs,” Phys. Rev. B81, 125124 (2010).
[CrossRef]

Antar, Y. M. M.

C. G. M. Ryan, M. Chaharmir, J. Shaker, J. Bray, Y. M. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Transactions on Antennas and Propagation58, 1486–1493 (2010).
[CrossRef]

Balanis, C. A.

C. A. Balanis, Antenna Theory: Analysis and Design (Wiley-Interscience, 2005).

Berenger, J.-P.

J.-P. Berenger, “A Huygens subgridding for the FDTD method,” IEEE Trans. on Antennas and Propagation54, 3797–3804 (2006).
[CrossRef]

Boltasseva, A.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science339(2013).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999), 7th ed.

Bray, J.

C. G. M. Ryan, M. Chaharmir, J. Shaker, J. Bray, Y. M. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Transactions on Antennas and Propagation58, 1486–1493 (2010).
[CrossRef]

Broas, R.

D. Sievenpiper, L. Zhang, R. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Transactions on Microwave Theory and Techniques47, 2059–2074 (1999).
[CrossRef]

Capasso, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

Castaldi, G.

I. Gallina, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “General class of metamaterial transformation slabs,” Phys. Rev. B81, 125124 (2010).
[CrossRef]

Chaharmir, M.

C. G. M. Ryan, M. Chaharmir, J. Shaker, J. Bray, Y. M. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Transactions on Antennas and Propagation58, 1486–1493 (2010).
[CrossRef]

Chan, C.

Chen, H.

Du, J.

Eleftheriades, G. V.

M. Selvanayagam and G. V. Eleftheriades, “An active electromagnetic cloak based on the equivalence principle,” IEEE Antennas and Wireless Propagation Letters11, 1226–1229 (2012).
[CrossRef]

Engheta, N.

I. Gallina, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “General class of metamaterial transformation slabs,” Phys. Rev. B81, 125124 (2010).
[CrossRef]

A. Alú and N. Engheta, “Plasmonic and metamaterial cloaking: physical mechanisms and potentials,” Journal of Optics A: Pure and Applied Optics10, 093002 (2008).
[CrossRef]

N. Engheta, “Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials,” Science317, 1698–1702 (2007).
[CrossRef] [PubMed]

Estakhri, N. M.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett.110, 203903 (2013).
[CrossRef]

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

Galdi, V.

I. Gallina, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “General class of metamaterial transformation slabs,” Phys. Rev. B81, 125124 (2010).
[CrossRef]

Gallina, I.

I. Gallina, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “General class of metamaterial transformation slabs,” Phys. Rev. B81, 125124 (2010).
[CrossRef]

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

Gibson, W. C.

W. C. Gibson, The Method of Moments in Electromagnetics (Chapman and Hall/CRC, 2008).

Grbic, A.

C. Pfieffer and A. Grbic, “Metamaterial huygens’ surfaces: Tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett.110, 197401 (2013).
[CrossRef]

A. Grbic and R. Merlin, “Near-field focusing plates and their design,” IEEE Transactions on Antennas and Propagation56, 3159–3165 (2008).
[CrossRef]

Hagness, S. C.

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

Hansen, R. C.

R. C. Hansen, Phased Array Antennas (Wiley-Interscience, 2009).
[CrossRef]

Harrington, R. F.

R. F. Harrington, Time-Harmonic Electromagnetic Fields (Wiley-Interscience, 2001).
[CrossRef]

Hessel, A.

H. Steyskal, A. Hessel, and J. Shmoys, “On the gain-versus-scan trade-offs and the phase gradient synthesis for a cylindrical dome antenna,” IEEE Trans. on Antennas and PropagationAP-27, 825–831 (1979).
[CrossRef]

Hosseini, E. S.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature493, 195–199 (2013).
[CrossRef] [PubMed]

Hum, S.

J. Lau and S. Hum, “Reconfigurable transmitarray design approaches for beamforming applications,” IEEE Transactions on Antennas and Propagation60, 5679–5689 (2012).
[CrossRef]

Ittipiboon, A.

C. G. M. Ryan, M. Chaharmir, J. Shaker, J. Bray, Y. M. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Transactions on Antennas and Propagation58, 1486–1493 (2010).
[CrossRef]

Jokerst, N. M.

Kats, M. A.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

Kildishev, A. V.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science339(2013).
[CrossRef] [PubMed]

Kwon, D.-H.

D.-H. Kwon and D. M. Pozar, “Optimal characteristics of an arbitrary receive antenna,” IEEE Transactions on Antennas and Propagation57, 3720–3727 (2009).
[CrossRef]

Larouche, S.

Lau, J.

J. Lau and S. Hum, “Reconfigurable transmitarray design approaches for beamforming applications,” IEEE Transactions on Antennas and Propagation60, 5679–5689 (2012).
[CrossRef]

Lin, Z.

Lipworth, G.

Liu, S.

Luo, X.

Ma, H.

Merlin, R.

A. Grbic and R. Merlin, “Near-field focusing plates and their design,” IEEE Transactions on Antennas and Propagation56, 3159–3165 (2008).
[CrossRef]

Miller, D. A.

Milton, G. W.

F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” Phys. Rev. Lett.103, 073901 (2009).
[CrossRef] [PubMed]

Monticone, F.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett.110, 203903 (2013).
[CrossRef]

Munk, B.

B. Munk, Frequency Selective Surfaces: Theory and Design (Wiley-Interscience, 2000).
[CrossRef]

Nawab, S. H.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems (Prentice Hall, 1997).

Novotny, L.

L. Novotny and N. van Hulst, “Antennas for light,” Nature Photonics5, 83–90 (2011).
[CrossRef]

Onofrei, D.

F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” Phys. Rev. Lett.103, 073901 (2009).
[CrossRef] [PubMed]

Oppenheim, A. V.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems (Prentice Hall, 1997).

Pendry, J. B.

Pfieffer, C.

C. Pfieffer and A. Grbic, “Metamaterial huygens’ surfaces: Tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett.110, 197401 (2013).
[CrossRef]

Pozar, D. M.

D.-H. Kwon and D. M. Pozar, “Optimal characteristics of an arbitrary receive antenna,” IEEE Transactions on Antennas and Propagation57, 3720–3727 (2009).
[CrossRef]

Ryan, C. G. M.

C. G. M. Ryan, M. Chaharmir, J. Shaker, J. Bray, Y. M. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Transactions on Antennas and Propagation58, 1486–1493 (2010).
[CrossRef]

Schurig, D.

Selvanayagam, M.

M. Selvanayagam and G. V. Eleftheriades, “An active electromagnetic cloak based on the equivalence principle,” IEEE Antennas and Wireless Propagation Letters11, 1226–1229 (2012).
[CrossRef]

Shaker, J.

C. G. M. Ryan, M. Chaharmir, J. Shaker, J. Bray, Y. M. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Transactions on Antennas and Propagation58, 1486–1493 (2010).
[CrossRef]

Shalaev, V. M.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science339(2013).
[CrossRef] [PubMed]

Shmoys, J.

H. Steyskal, A. Hessel, and J. Shmoys, “On the gain-versus-scan trade-offs and the phase gradient synthesis for a cylindrical dome antenna,” IEEE Trans. on Antennas and PropagationAP-27, 825–831 (1979).
[CrossRef]

Sievenpiper, D.

D. Sievenpiper, L. Zhang, R. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Transactions on Microwave Theory and Techniques47, 2059–2074 (1999).
[CrossRef]

Smith, D. R.

Steyskal, H.

H. Steyskal, A. Hessel, and J. Shmoys, “On the gain-versus-scan trade-offs and the phase gradient synthesis for a cylindrical dome antenna,” IEEE Trans. on Antennas and PropagationAP-27, 825–831 (1979).
[CrossRef]

Sun, J.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature493, 195–199 (2013).
[CrossRef] [PubMed]

Taflove, A.

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

Tetienne, J.-P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

Timurdogan, E.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature493, 195–199 (2013).
[CrossRef] [PubMed]

Tretyakov, S.

S. Tretyakov, Analytical Modeling in Applied Electromagnets (Artech House, 2003).

Tsai, Y.-J.

Tyler, T.

van Hulst, N.

L. Novotny and N. van Hulst, “Antennas for light,” Nature Photonics5, 83–90 (2011).
[CrossRef]

Vasquez, F. G.

F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” Phys. Rev. Lett.103, 073901 (2009).
[CrossRef] [PubMed]

Watts, M. R.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature493, 195–199 (2013).
[CrossRef] [PubMed]

Willsky, A. S.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems (Prentice Hall, 1997).

Wolf, E.

M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999), 7th ed.

Yaacobi, A.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature493, 195–199 (2013).
[CrossRef] [PubMed]

Yablonovitch, E.

D. Sievenpiper, L. Zhang, R. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Transactions on Microwave Theory and Techniques47, 2059–2074 (1999).
[CrossRef]

Yu, N.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

Zhang, L.

D. Sievenpiper, L. Zhang, R. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Transactions on Microwave Theory and Techniques47, 2059–2074 (1999).
[CrossRef]

IEEE Antennas and Wireless Propagation Letters (1)

M. Selvanayagam and G. V. Eleftheriades, “An active electromagnetic cloak based on the equivalence principle,” IEEE Antennas and Wireless Propagation Letters11, 1226–1229 (2012).
[CrossRef]

IEEE Trans. on Antennas and Propagation (2)

J.-P. Berenger, “A Huygens subgridding for the FDTD method,” IEEE Trans. on Antennas and Propagation54, 3797–3804 (2006).
[CrossRef]

H. Steyskal, A. Hessel, and J. Shmoys, “On the gain-versus-scan trade-offs and the phase gradient synthesis for a cylindrical dome antenna,” IEEE Trans. on Antennas and PropagationAP-27, 825–831 (1979).
[CrossRef]

IEEE Transactions on Antennas and Propagation (4)

A. Grbic and R. Merlin, “Near-field focusing plates and their design,” IEEE Transactions on Antennas and Propagation56, 3159–3165 (2008).
[CrossRef]

J. Lau and S. Hum, “Reconfigurable transmitarray design approaches for beamforming applications,” IEEE Transactions on Antennas and Propagation60, 5679–5689 (2012).
[CrossRef]

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IEEE Transactions on Microwave Theory and Techniques (1)

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Journal of Optics A: Pure and Applied Optics (1)

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Nature (1)

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature493, 195–199 (2013).
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Phys. Rev. B (1)

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C. Pfieffer and A. Grbic, “Metamaterial huygens’ surfaces: Tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett.110, 197401 (2013).
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Figures (13)

Fig. 1
Fig. 1

An arbitrary boundary in free space upon which a discontinuity exists between the electric and magnetic fields on either side of the boundary. Electric and magnetic currents are imposed on the boundary to support the discontinuity. This is the motivating idea behind altering the fields using electric and magnetic currents.

Fig. 2
Fig. 2

How currents on a surface impose a discontinuity. Radiating electric currents create a magnetic field which curls around the current thus imposing a discontinuity in the magnetic field on either side of the boundary. Likewise, magnetic currents create an electric field which curls around the current imposing a discontinuity in the magnetic field

Fig. 3
Fig. 3

A schematic of the active cloak which is constructed by enforcing electric and magnetic dipoles on the boundary of the dielectric cylinder. In this section two cloaking schemes are demonstrated by altering the weights of the electric and magnetic dipoles on the boundary. In the first example the fields are canceled outside of the scatterer without disturbing the interior fields {Eint, Hint}. In the second example the electric and magnetic dipoles create a scattered field exterior to the cloak that looks like a metallic cylinder.

Fig. 4
Fig. 4

An active cloak which cancels the scattered field without disturbing the fields inside the dielectric. On the left is a plot of the total out-of-plane electric field, Ez for the bare dielectric cylinder without a cloak. The inset shows the fields inside the cylinder. The dielectric boundary is marked with a black circle. The right plot shows the cylinder with a cloak made up of electric and magnetic dipoles. We can see that the field pattern now resembles the incident plane-wave only. Note also that the fields in the dielectric are relatively undisturbed as shown in the inset. Finally the 2D radar cross section (RCS) is shown in the bottom plot indicating a decrease in the scattering off of the cylinder.

Fig. 5
Fig. 5

An active cloak which cancels the scattered field of the dielectric cylinder while making the dielectric cylinder look like a metallic cylinder. On the left is a plot of the total out-of-plane electric field, Ez for a bare metallic cylinder. The boundary is marked with a black circle and is the same size as our dielectric cylinder. The right plot shows the dielectric cylinder with a cloak made up of electric and magnetic dipoles. We can see that the field pattern now resembles the total field of our metallic cylinder, which disguises the dielectric cylinder. Note also that the fields in the dielectric are undisturbed as well. Finally the 2D radar cross section is shown on the bottom plot demonstrating quantitatively how the dielectric cylinder resembles a metallic cylinder when cloaked with the active dipole array.

Fig. 6
Fig. 6

Refraction and reflection at an interface. If the incident plane-wave is refracted or reflected at the boundary in free-space, a discontinuity exists at the interface which requires an electric and magnetic current at the interface. We can impose those currents using a discrete active electric and magnetic dipole array or we can use a passive impedance and admittance surface, provided we constrain the amplitudes of the fields.

Fig. 7
Fig. 7

An array of electric and magnetic dipoles at a surface which interfere to generate a negatively refracted plane-wave. The total electric field along the vertical axis is plotted. The incident field is along the θi = 20° direction and the refracted wave along the θt = 20°.

Fig. 8
Fig. 8

A plane-wave incident on an impedance surface. Shown are the incident and the scattered fields. On side 2 of the boundary the total fields are the scattered fields summed with the incident plane wave (not-shown).

Fig. 9
Fig. 9

A plane-wave incident on an admittance surface. Shown are the incident and the scattered fields. On side 2 of the boundary the total fields are the scattered fields summed with the incident plane wave (not-shown). To create a surface which primarily reflects the incident plane-wave as opposed to refracting it, the sign of Etm should be flipped.

Fig. 10
Fig. 10

A plane-wave incident on a combined impedance and admittance surface. Shown are the incident and the total fields on either side of the boundary. Because the impedance and admittance surface create induced electric and magnetic currents we can successfully refract the incident plane-wave without any other fields on side two of the boundary. Also note that the majority of the power is scattered into Et as the amplitude of Eis is much smaller as shown in Fig. 11

Fig. 11
Fig. 11

Design curves summarizing refraction through an impedance and admittance surface for an incident plane wave of amplitude Ei = 1. All plots are drawn with incident angle, θi, on the horizontal axis and the refracted angle, θt, on the vertical axis. The top-left plot gives us the amplitude of the refracted beam, Et while the top-right plot gives us the amplitude of the reflected beam Eis. The bottom two curves are contour plots of the impedance and admittance of the screen at a given point, (y = λ) for different incident and reflected angles.

Fig. 12
Fig. 12

Method of moments verification of an impedance and admittance surface to refract an incident plane-wave. Solid, coloured curves are calculated method of moments results. Dashed black curves are theoretical results from the previous section. The top-left and top-right figures are the calculated reactance and susceptance of the two surfaces. We can see good agreement with the theoretical results as well as their non-linear dependence on the spatial coordinate of the surface. The bottom-left and bottom-right plots show the calculated and theoretical electric field on side-two and side-one of the surface respectively (real and imaginary parts in red and blue respectively). Note the much larger amplitude of the the refracted beam compared to the reflected beam.

Fig. 13
Fig. 13

Simulation results from HFSS for a physically realized impedance and admittance screen. On the left a schematic of the surface. The impedance screen is made of reactively loaded dipoles with the reactive loading shown in red. The admittance screen is made of reactively loaded loops with the loading shown in blue. In the middle is a plot of the total vertical electric field for a simulation of the impedance screen for an incident Gaussian beam. The plot on the right is a far-field plot of the scattered electric field.

Equations (34)

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n ^ × [ E 2 E 1 ] = M s ,
n ^ × [ H 2 H 1 ] = J s .
J s , d = n = p e ( n d u ) δ ( u n d u ) ,
M s , d = n = p m ( n d u ) δ ( u n d u ) .
n ^ × [ E 2 E 1 ] = 0 ,
n ^ × [ H 2 H 1 ] = J s ,
n ^ × E 1 = Z s J s
n ^ × [ E 2 E 1 ] = M s ,
n ^ × [ H 2 H 1 ] = 0 ,
n ^ × H 1 = Y s M s ,
M s = n × ( E s ) = k 2 n = n = A s n H n ( 2 ) ( k ρ ) e j n ( ϕ + π 2 ) ϕ ^ ,
J s = n × ( H s ) = j ω ε k n = n = A s n H n ( 2 ) ( k ρ ) e j n ( ϕ + π 2 ) z ^ ,
M s = n × ( E s + E sm ) = [ k 2 n = n = A s n H n ( 2 ) ( k ρ ) e j n ( ϕ + π 2 ) + k 2 n = n = A s m n H n ( 2 ) ( k ρ ) e j n ( ϕ + π 2 ) ] ϕ ^ ,
J s = n × ( H s + H sm ) = j ω ε k [ n = n = A s n H n ( 2 ) ( k ρ ) e j n ( ϕ + π 2 ) n = n = A s m n H n ( 2 ) ( k ρ ) e j n ( ϕ + π 2 ) ] z ^ ,
M s = y ^ [ E t e j k y cos θ t E i e j k y cos θ i ] ,
J s = z ^ [ 1 η cos θ t E t e j k y cos θ t 1 η cos θ i E i e j k y cos θ i ] ,
sin θ t sin θ i = 1 k o d Φ d y ,
E i e j k y sin θ i E i s e e j k y sin θ i + E t e e j k y sin θ t = Z s [ 1 η cos θ i E i e j k y sin θ i + 1 η cos θ i E i s e e j k y sin θ i 1 η cos θ t E t e e j k y sin θ t + 1 η cos θ i E i e j k y sin θ i + 1 η cos θ i E i s e e j k y sin θ i 1 η cos θ t E t e e j k y sin θ t ] ,
E i s e = E i cos θ t cos θ i + cos θ t
E t e = E i cos θ i cos θ i + cos θ t
X s = η ( cos θ t + cos θ i ) 4 cos θ t cos θ i cot ( Φ / 2 ) ,
E i s m = E t m = E i cos θ i cos θ i + cos θ t ,
B s = cos θ t 2 η cot ( Φ / 2 )
E t = E t e + E t m = 2 E i cos θ i cos θ i + cos θ t .
E i s = E i s m E i s e = E i ( cos θ i cos θ t ) cos θ i + cos θ t .
P = 1 2 S [ E × H * ] n ^ d S .
P = A 2 η ( | E i | 2 cos θ i E t 2 cos θ t E i s 2 cos θ i ) = 0
E tot | x = 0 = E i | x = 0 + E s | x = 0 .
E tot | x = 0 = E i e j k y sin θ i z ^ ω μ 4 L / 2 L / 2 J s ( y ) H o 2 ( k | y y | ) d y ,
n ^ × H tot | x = 0 = n ^ × H i | x = 0 + n ^ × H s | x = 0 .
n ^ × H tot | x = 0 = E i η cos θ i e j k y sin θ i x ^ 1 4 ω μ ( k 2 + 2 y 2 ) L / 2 L / 2 M s ( y ) H o 2 ( k | y y | ) d y ,
E s , elec = ω μ 4 L / 2 L / 2 J s ( y ) H o 2 ( k | ( y y ) 2 + z 2 | ) d y ,
E s , mag = j 4 L / 2 L / 2 × [ M s ( y ) H o 2 ( k | ( y y ) 2 + z 2 | ) ] d y ,
E s = E s , elec + E s , mag

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