Abstract

Applying the analytical closed-form solutions of the “quasi-static” potential distribution around two conjoined resonant half-cylinders with different permittivities, reported in the first part of this manuscript, here we interpret these results in terms of our nanocircuit paradigm applicable to nanoparticles at infrared and optical frequencies [Phys. Rev. Lett. 95, 095504 (2005) ]. We investigate the possibility of connecting in series and parallel configurations plasmonic and/or dielectric nanoparticles acting as nanocircuit elements, with a goal for the design of a more-complex nanocircuit system with the desired response. The present analysis fully validates the heuristic predictions regarding the parallel and series combination of a pair of nanocircuit elements depending on their relative orientation with respect to the field polarization. Moreover, the geometries under analysis present interesting peculiar features in their wave interaction, such as an “intermediate” stage between the parallel and series configurations, which may be of interest for certain applications. In particular, the resonant nanocircuit configuration analyzed here may dramatically change, in a continuous way, its effective total impedance by simply rotating its orientation with respect to the polarization of the impressed optical electric field, providing a novel optical nanodevice that may alter its function by rotation with respect to the impressed optical local field.

© 2007 Optical Society of America

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References

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2007 (2)

A. Alù and N. Engheta, "Three-dimensional nanotransmission lines at optical frequencies: a recipe for broadband negative-refraction optical metamaterials," Phys. Rev. B 75, 024304 (2007).
[CrossRef]

A. Salandrino, A. Alù, and N. Engheta, "Parallel, series, and intermediate interconnections of optical nanocircuit elements. 1. Analytical solution," J. Opt. Soc. Am. B 24, 3007-3013 (2007).
[CrossRef]

2006 (6)

2005 (4)

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature (London) 438, 335-338 (2005).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alù, "Circuit elements at optical frequencies: nano-inductors, nano-capacitors and nano-resistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

J. Gómez Rivas, C. Janke, P. Bolivar, and H. Kurz, "Transmission of THz radiation through InSb gratings of subwavelength apertures," Opt. Express 13, 847-859 (2005).
[CrossRef] [PubMed]

2000 (2)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B 62, 016356 (2000).
[CrossRef]

1998 (1)

1991 (1)

Appl. Opt. (1)

J. Opt. Soc. Am. B (3)

Nature (London) (1)

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature (London) 438, 335-338 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. B (3)

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B 62, 016356 (2000).
[CrossRef]

A. Alù and N. Engheta, "Theory of linear chains of metamaterial/plasmonic particles as sub-diffraction optical nanotransmission lines," Phys. Rev. B 74, 205436 (2006).
[CrossRef]

A. Alù and N. Engheta, "Three-dimensional nanotransmission lines at optical frequencies: a recipe for broadband negative-refraction optical metamaterials," Phys. Rev. B 75, 024304 (2007).
[CrossRef]

Phys. Rev. Lett. (2)

N. Engheta, A. Salandrino, and A. Alù, "Circuit elements at optical frequencies: nano-inductors, nano-capacitors and nano-resistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Science (1)

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Other (5)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

M. Silveirinha, A. Alù, J. Li, and N. Engheta, "Nanoinsulators and nanoconnectors at optical frequencies," http://www.arxiv.org/ftp/cond-mat/papers/0703/0703600.pdf.

This is why in Fig. we did not sketch any circuit model in the inset; in this more general configuration there is no standard equivalent circuit connection modeling the current flow and voltage drop across the nanocircuit elements.

A. Alu and N. Engheta, "Plasmonic resonant optical nanoswitch," http://arxiv.org/abs/0710.4895.

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Figures (7)

Fig. 1
Fig. 1

A basic optical nanocircuit as an isolated nanoparticle illuminated by the uniform electric field E 0 , as envisioned in [14]. Left, a nonplasmonic sphere with Re [ ϵ ] > 0 , which provides a nanocapacitor and a nanoresistor; right, a plasmonic sphere with Re [ ϵ ] < 0 , which gives a nanoinductor and a nanoresistor. The thinner field lines together with the arrows represent the fringe dipolar electric field from the nanosphere, which corresponds to the fringe capacitor in the circuit equivalence on the bottom of each case.

Fig. 2
Fig. 2

Heuristic sketch of a nanocircuit (a) series and (b) parallel configurations of nanoparticles and their circuit equivalence.

Fig. 3
Fig. 3

Two conjoined 2D half-cylinders with different permittivities, illuminated by a uniform electric field. Series (left) and parallel (right) configurations.

Fig. 4
Fig. 4

Exact “quasi-static” potential distribution for the 2D conjoined half-cylinders of Fig. 3 in the (a) series and (b) parallel resonant configurations. In both figures the uniform-impressed electric field is vertical pointing to the top and for the series configuration ϵ 1 = ϵ 2 = 2 ϵ 0 (for the parallel configuration the potential distribution is independent of the value of permittivities, as long as ϵ 1 = ϵ 2 ). Darker regions correspond to a lower potential.

Fig. 5
Fig. 5

Exact “quasi-static” potential distribution for a 2D half-cylinder with ϵ = ϵ 0 , consistent with the results of Fig. 4. In this case, the series or parallel combination is interestingly still present, even though the other nanocircuit element that supports the resonance is represented by the free-space half-cylinder “connected” to it.

Fig. 6
Fig. 6

“Half-series-half-parallel” intermediate interconnection obtained from the structure of Fig. 6 when γ = π 4 (the uniform-impressed electric field is vertical pointing to the top).

Fig. 7
Fig. 7

“Quasi-static” potential distribution for two 2D conjoined half-cylinders with ϵ 1 = 2 ϵ 0 , ϵ 2 = 3 ϵ 0 in their (a) series and (b) parallel interconnection. The small numerical noise along the horizontal axis in (b) is due to the small truncation errors.

Equations (4)

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ρ 2 2 Φ ( ρ , φ ) ρ 2 + ρ Φ ( ρ , φ ) ρ + 2 Φ ( ρ , φ ) φ 2 = 0 .
Φ i ( ρ , φ ) = Φ i parallel ( ρ , φ ) sin ( γ ) + Φ i series ( ρ , φ ) cos ( γ ) ,
{ Φ i parallel ( ρ , φ ) = E 0 ρ 2 + R 2 ρ sin φ Φ i series ( ρ , φ ) = E 0 ϵ 0 ϵ i ρ 2 R 2 ρ cos φ } ,
E φ E ρ ρ = R = Φ i parallel ( ρ , φ ) φ Φ i series ( ρ , φ ) ρ ρ = R = tan γ ,

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