Abstract

We report the design of an artificial flower-like structure that supports a magnetic plasma in the optical domain. The structure is composed of alternating “petals” of conventional dielectrics (ε>0) and plasmonic materials (Re(ε)<0). The induced effective magnetic current on such a structure possesses a phase lag with respect to the incident TE-mode magnetic field, similar to the phase lag between the induced electric current and the incident TM-mode electric field on a metal wire. An analogy is thus drawn with an artificial electric plasma composed of metal wires driven by a radio frequency excitation. The effective medium of an array of flowers has a negative permeability within a certain wavelength range, thus behaving as a magnetic plasma.

© 2009 Optical Society of America

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References

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  1. M. Lapine and S. Tretyakov, "Contemporary notes on metamaterials," IET Microwaves Antennas Propagat. 1(1), 3-11 (2007).
    [CrossRef]
  2. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
    [CrossRef] [PubMed]
  3. W. Rotman, "Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media," IRE Trans. Antennas Propagat. 10(1), 82-95 (1962).
  4. J. B. Pendry, A. J. Holden, D. J. Robbins, andW. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  5. A. Alu, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," Opt. Express 14, 1557-1567 (2006).
    [CrossRef] [PubMed]
  6. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
    [CrossRef] [PubMed]
  7. A. K. Sarychev, G. Shvets, and V. M. Shalaev, "Magnetic Plasmon Resonance," Phys. Rev. E 73, 036,609 (2006).
    [CrossRef]
  8. N. Engheta, A. Salandrino, and A. Al`u, "Circuit Elements at Optical Frequencies: Nanoinductors, Nanocapacitors, and Nanoresistors," Phys. Rev. Lett. 95, 095,504 (2005).
    [CrossRef]
  9. M. G. Silveirinha, A. Alu, J. Li, and N. Engheta, "Nanoinsulators and nanoconnectors for optical nanocircuits," J. Appl. Phys. 103, 064,305 (2008).
    [CrossRef]
  10. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, New York, NY, 1983).
  11. L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE Press, Piscataway, NJ, USA, 1994).
    [CrossRef]
  12. P. B. Johnson and R. W. Christy, "Optical Constants of the Nobel Metals," Phys. Rev. B 6(12), 4370-4379 (1972).
    [CrossRef]
  13. S. Tretyakov, Analytical Modeling in Applied Electromagnetics, (Artech House, INC, Norwood, MA, USA, 2003), pp. 164-175. In this reference the current coefficient αe of a wire of perfect electric conductor is used, written as a function of the radius of the wire. In our paper, no analytical formula for αm, thus the equation for μr is revised to have αm in it explicitly.

2008 (1)

M. G. Silveirinha, A. Alu, J. Li, and N. Engheta, "Nanoinsulators and nanoconnectors for optical nanocircuits," J. Appl. Phys. 103, 064,305 (2008).
[CrossRef]

2007 (1)

M. Lapine and S. Tretyakov, "Contemporary notes on metamaterials," IET Microwaves Antennas Propagat. 1(1), 3-11 (2007).
[CrossRef]

2006 (2)

2005 (1)

N. Engheta, A. Salandrino, and A. Al`u, "Circuit Elements at Optical Frequencies: Nanoinductors, Nanocapacitors, and Nanoresistors," Phys. Rev. Lett. 95, 095,504 (2005).
[CrossRef]

2004 (1)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, andW. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

1972 (1)

P. B. Johnson and R. W. Christy, "Optical Constants of the Nobel Metals," Phys. Rev. B 6(12), 4370-4379 (1972).
[CrossRef]

1962 (1)

W. Rotman, "Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media," IRE Trans. Antennas Propagat. 10(1), 82-95 (1962).

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Christy, R.W.

P. B. Johnson and R. W. Christy, "Optical Constants of the Nobel Metals," Phys. Rev. B 6(12), 4370-4379 (1972).
[CrossRef]

Engheta, N.

N. Engheta, A. Salandrino, and A. Al`u, "Circuit Elements at Optical Frequencies: Nanoinductors, Nanocapacitors, and Nanoresistors," Phys. Rev. Lett. 95, 095,504 (2005).
[CrossRef]

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, andW. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical Constants of the Nobel Metals," Phys. Rev. B 6(12), 4370-4379 (1972).
[CrossRef]

Lapine, M.

M. Lapine and S. Tretyakov, "Contemporary notes on metamaterials," IET Microwaves Antennas Propagat. 1(1), 3-11 (2007).
[CrossRef]

Padilla, W. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Pendry, J. B.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, andW. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, andW. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Rotman, W.

W. Rotman, "Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media," IRE Trans. Antennas Propagat. 10(1), 82-95 (1962).

Salandrino, A.

N. Engheta, A. Salandrino, and A. Al`u, "Circuit Elements at Optical Frequencies: Nanoinductors, Nanocapacitors, and Nanoresistors," Phys. Rev. Lett. 95, 095,504 (2005).
[CrossRef]

Sarychev, A. K.

A. K. Sarychev, G. Shvets, and V. M. Shalaev, "Magnetic Plasmon Resonance," Phys. Rev. E 73, 036,609 (2006).
[CrossRef]

Shalaev, V. M.

A. K. Sarychev, G. Shvets, and V. M. Shalaev, "Magnetic Plasmon Resonance," Phys. Rev. E 73, 036,609 (2006).
[CrossRef]

Shvets, G.

A. K. Sarychev, G. Shvets, and V. M. Shalaev, "Magnetic Plasmon Resonance," Phys. Rev. E 73, 036,609 (2006).
[CrossRef]

Silveirinha, M. G.

M. G. Silveirinha, A. Alu, J. Li, and N. Engheta, "Nanoinsulators and nanoconnectors for optical nanocircuits," J. Appl. Phys. 103, 064,305 (2008).
[CrossRef]

Smith, D. R.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Tretyakov, S.

M. Lapine and S. Tretyakov, "Contemporary notes on metamaterials," IET Microwaves Antennas Propagat. 1(1), 3-11 (2007).
[CrossRef]

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Yen, T. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Zhang, X.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, andW. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

IET Microwaves Antennas Propagat. (1)

M. Lapine and S. Tretyakov, "Contemporary notes on metamaterials," IET Microwaves Antennas Propagat. 1(1), 3-11 (2007).
[CrossRef]

IRE Trans. Antennas Propagat. (1)

W. Rotman, "Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media," IRE Trans. Antennas Propagat. 10(1), 82-95 (1962).

J. Appl. Phys. (1)

M. G. Silveirinha, A. Alu, J. Li, and N. Engheta, "Nanoinsulators and nanoconnectors for optical nanocircuits," J. Appl. Phys. 103, 064,305 (2008).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, "Optical Constants of the Nobel Metals," Phys. Rev. B 6(12), 4370-4379 (1972).
[CrossRef]

Phys. Rev. E (1)

A. K. Sarychev, G. Shvets, and V. M. Shalaev, "Magnetic Plasmon Resonance," Phys. Rev. E 73, 036,609 (2006).
[CrossRef]

Phys. Rev. Lett. (2)

N. Engheta, A. Salandrino, and A. Al`u, "Circuit Elements at Optical Frequencies: Nanoinductors, Nanocapacitors, and Nanoresistors," Phys. Rev. Lett. 95, 095,504 (2005).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Science (1)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Other (3)

S. Tretyakov, Analytical Modeling in Applied Electromagnetics, (Artech House, INC, Norwood, MA, USA, 2003), pp. 164-175. In this reference the current coefficient αe of a wire of perfect electric conductor is used, written as a function of the radius of the wire. In our paper, no analytical formula for αm, thus the equation for μr is revised to have αm in it explicitly.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, New York, NY, 1983).

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE Press, Piscataway, NJ, USA, 1994).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

(a) An artificial medium composed of flower structures. (b)A single flower with TE0 incident radiation. (c) Left: the cross section of a flower. Dark: plasmonic petals; light: dielectric petals. Right: the equivalent RLC circuit for the structure. Each side represents one period in the structure. The capacitors (C) model the dielectric sectors, the inductors (L) together with the resistors (R) model the lossy plasmonic sectors, and the voltage sources (V) represents the incident electric field.

Fig. 2.
Fig. 2.

Magnitude (solid lines) and phase (red dashed lines) of γ 00, for the lossless (bold) and the lossy (thin) case.

Fig. 3.
Fig. 3.

(a)The distribution of the instantaneous scattered magnetic field (normalized to the the incident magnetic field at the origin) at resonance, for lossless plasmonic sectors. (b) γ 00 (thin solid) and γ 11 (thin dashed) of the cylindrical structure made of silver and SiO2; and Re(µr ) (bold solid), Im(µr ) (bold dashed) for the artificial material composed of an array of such cylindrical structures.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Hiz(r,ϕ)=𝓗0Σn=anJn(k0r)einϕ
Hsz(r,ϕ)=𝓗0Σn=(Σm=γmnam)Hn(1)(k0r)einϕ
μr=12πc2d2ω21A+M
A=2πωε0Im(αm1) + log ωd4πc + C + i (2πωε0Re(αm1)π2)

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