Abstract

There is an upper limit to the number of electromagnetic communication channels in two-dimensional linear passive components that depends only on the geometrical dimensions but is independent of the permittivity function, the actual external shape, or the internal design. The limit applies to both weakly and strongly scattering waves. When the permittivity contrast is low, a tighter limit exists that includes only multiple scattering waves. A detailed analysis helps compare these two limits and leads to insights that apply to devices, such as photonic crystals and microresonators, as well as lossless metamaterials, superlenses, and cloaking devices. As an example, we establish a rigorous scaling relation for the upper bound of the number of demultiplexing channels in superprisms.

© 2009 Optical Society of America

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2007 (1)

2006 (2)

2003 (2)

B. Momeni and A. Adibi, Appl. Phys. B 77, 555 (2003).
[CrossRef]

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 045115 (2003).
[CrossRef]

2000 (1)

1999 (3)

1998 (1)

1997 (1)

O. M. Bucci and T. Isernia, Radio Sci. 32, 2123 (1997).
[CrossRef]

1982 (1)

Adibi, A.

B. Momeni and A. Adibi, Appl. Phys. B 77, 555 (2003).
[CrossRef]

Brancaccio, A.

Bucci, O. M.

Chu, S. T.

S. T. Chu, B. E. Little, W. T. Pan, T. Kaneko, S. Sato, and Y. Kokubun, J. Endovasc. Ther. 11, 691 (1999).

Crocco, L.

Devaney, A. J.

Foster, M. A.

Gaeta, A. L.

Hanson, G. W.

G. W. Hanson and A. B. Yakovlev, Operator Theory for Electromagnetics (Springer, 2002).

Isernia, T.

Joannopoulos, J. D.

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Johnson, S. G.

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Kaneko, T.

S. T. Chu, B. E. Little, W. T. Pan, T. Kaneko, S. Sato, and Y. Kokubun, J. Endovasc. Ther. 11, 691 (1999).

Kawakami, S.

Kawashima, T.

Kokubun, Y.

S. T. Chu, B. E. Little, W. T. Pan, T. Kaneko, S. Sato, and Y. Kokubun, J. Endovasc. Ther. 11, 691 (1999).

Kosaka, H.

Leone, G.

Lipson, M.

Little, B. E.

S. T. Chu, B. E. Little, W. T. Pan, T. Kaneko, S. Sato, and Y. Kokubun, J. Endovasc. Ther. 11, 691 (1999).

Lohmann, A. W.

A. W. Lohmann, in Research Paper RJ-438 (IBM San Jose Research Lab, 1967), p. 1.

Luo, C. Y.

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Miller, D. A. B.

Momeni, B.

B. Momeni and A. Adibi, Appl. Phys. B 77, 555 (2003).
[CrossRef]

Notomi, M.

Okawachi, Y.

Pan, W. T.

S. T. Chu, B. E. Little, W. T. Pan, T. Kaneko, S. Sato, and Y. Kokubun, J. Endovasc. Ther. 11, 691 (1999).

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Pierri, R.

Piestun, R.

Porter, R. P.

Sato, S.

S. T. Chu, B. E. Little, W. T. Pan, T. Kaneko, S. Sato, and Y. Kokubun, J. Endovasc. Ther. 11, 691 (1999).

Sato, T.

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Sharping, J. E.

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Tamamura, T.

Tomita, A.

Xu, Q. F.

Yakovlev, A. B.

G. W. Hanson and A. B. Yakovlev, Operator Theory for Electromagnetics (Springer, 2002).

Appl. Phys. B (1)

B. Momeni and A. Adibi, Appl. Phys. B 77, 555 (2003).
[CrossRef]

J. Endovasc. Ther. (1)

S. T. Chu, B. E. Little, W. T. Pan, T. Kaneko, S. Sato, and Y. Kokubun, J. Endovasc. Ther. 11, 691 (1999).

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

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

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Phys. Rev. B (1)

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Radio Sci. (1)

O. M. Bucci and T. Isernia, Radio Sci. 32, 2123 (1997).
[CrossRef]

Science (1)

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Other (2)

G. W. Hanson and A. B. Yakovlev, Operator Theory for Electromagnetics (Springer, 2002).

A. W. Lohmann, in Research Paper RJ-438 (IBM San Jose Research Lab, 1967), p. 1.

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Figures (3)

Fig. 1
Fig. 1

Basic 2D configuration of an optical element bounded by a cylindrical domain.

Fig. 2
Fig. 2

(a) Transmitting singular functions Re { u n ( r , θ ) } for n = 0 , 3, 10, and 50 and a transmitting volume with R S = 10 λ . (b) Squares of the singular values for transmitting domain of different sizes showing their steplike behavior.

Fig. 3
Fig. 3

Upper bounds for a total number of communication channels ( N T ) and for multiple-scattering modes ( N MS ) . (a) Comparison for a specific transmitting volume versus the permittivity contrast χ max . (b) Comparison as a function of the transmitting volume for different values of the permittivity contrast χ max . In all cases Δ R = λ 4 .

Equations (7)

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E scat ( r , θ ) = j 4 β 2 0 2 π 0 R s H 0 ( 2 ) [ β r r ] χ ( r , θ ) E ( r , θ ) r d r d θ ,
u n ( r , θ ) = B n J n ( β r ) exp ( j n θ ) ,
v n ( r , θ ) = C n H n ( 2 ) ( β r ) exp ( j n θ ) ;
σ n 2 σ 0 2 = J n 2 ( β R S ) J n 1 ( β R S ) J n + 1 ( β R S ) J 0 2 ( β R S ) + J 1 2 ( β R S ) ,
σ 0 2 = π 4 β 3 R s 2 Δ R [ J 0 2 ( β R S ) + J 1 2 ( β R S ) ] 2 π 2 R S Δ R λ 2 ,
N T σ n 2 σ 0 2 = 1 J 0 2 ( β R S ) + J 1 2 ( β R S ) π 2 R S λ ,
N MS σ 0 N T χ max = π 2 R S λ 2 Δ R λ χ max ,

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