Abstract

We study the propagation of electromagnetic waves through a transition layer between positive-index and negative-index media theoretically. We consider three models where both the dielectric permittivity ε and the magnetic permeability µ change linearly from positive values to negative values. At the positions where ε or µ vanishes, the mode conversion of the incident electromagnetic waves into longitudinal plasma oscillations can occur. Using the invariant imbedding theory of mode conversion in inhomogeneous media, we calculate the mode conversion coefficient and the electromagnetic field profile in a numerically exact manner. We find that strong mode conversion can occur for both s- and p-polarized incident waves. The dependence of mode conversion on polarization is influenced very sensitively by the spatial profiles of ε and µ. We also discuss the interaction effects between mode conversion phenomena occurring at two resonance points located nearby.

© 2008 Optical Society of America

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    [CrossRef]
  5. D. E. Hinkel-Lipsker, B. D. Fried, and G. J. Morales, "Analytic expressions for mode conversion in a plasma with a linear density profile," Phys. Fluids B 4, 559-575 (1992).
    [CrossRef]
  6. K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. I. Exact calculation of the mode conversion coefficient in cold, unmagnetized plasmas," Phys. Plasmas 12, 062101 (2005).
    [CrossRef]
  7. S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
    [CrossRef] [PubMed]
  8. E. Mjølhus, "On linear mode conversion in a magnetized plasma," Radio Sci. 25, 1321-1339 (1990).
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    [CrossRef]
  10. E. H. Kim, I. H. Cairns, and P. A. Robinson, "Extraordinary-mode radiation produced by linear-mode conversion of Langmuir waves," Phys. Rev. Lett. 99, 015003 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. 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]
  13. F. Magnus, B. Wood, J. Moore, K. Morrison, G. Perkins, J. Fyson, M. C. K. Wiltshire, D. Caplin, L. F. Cohen, and J. B. Pendry, "A d.c. magnetic metamaterial," Nat. Mater. 7, 295-297 (2008).
    [CrossRef] [PubMed]
  14. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  15. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
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  16. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
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  19. V. I. Klyatskin, "The imbedding method in statistical boundary-value wave problems," Prog. Opt. 33, 1-127 (1994).
    [CrossRef]
  20. R. Rammal and B. Doucot, "Invariant-imbedding approach to localization. I. General framework and basic equations," J. Phys. (Paris) 48, 509-526 (1987).
    [CrossRef]
  21. K. Kim, D.-H. Lee, and H. Lim, "Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media," Europhys. Lett. 69, 207-213 (2005).
    [CrossRef]
  22. K. Kim, D. K. Phung, F. Rotermund, and H. Lim, "Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses," Opt. Express 16, 1150-1164 (2008).
    [CrossRef] [PubMed]
  23. K. Kim, F. Rotermund, and H. Lim, "Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: Exact calculation based on the invariant imbedding method," Phys. Rev. B 77, 024203 (2008).
    [CrossRef]
  24. A. K. Sarychev, D. J. Bergman, and Y. Yagil, "Theory of the optical and microwave properties of metal-dielectric films," Phys. Rev. B 51, 5366-5385 (1995).
    [CrossRef]
  25. L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and G. H. Derrick, "Periodic models for thin optimal absorbers of electromagnetic radiation," Phys. Rev. B 55, R16072-R16075 (1997).
    [CrossRef]

2008

F. Magnus, B. Wood, J. Moore, K. Morrison, G. Perkins, J. Fyson, M. C. K. Wiltshire, D. Caplin, L. F. Cohen, and J. B. Pendry, "A d.c. magnetic metamaterial," Nat. Mater. 7, 295-297 (2008).
[CrossRef] [PubMed]

K. Kim, D. K. Phung, F. Rotermund, and H. Lim, "Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses," Opt. Express 16, 1150-1164 (2008).
[CrossRef] [PubMed]

K. Kim, F. Rotermund, and H. Lim, "Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: Exact calculation based on the invariant imbedding method," Phys. Rev. B 77, 024203 (2008).
[CrossRef]

2007

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
[CrossRef]

E. H. Kim, I. H. Cairns, and P. A. Robinson, "Extraordinary-mode radiation produced by linear-mode conversion of Langmuir waves," Phys. Rev. Lett. 99, 015003 (2007).
[CrossRef] [PubMed]

A. M. D. McDougall and A. W. Hood, "A new look at mode conversion in a stratified isothermal atmosphere," Solar Phys. 246, 259-271 (2007).
[CrossRef]

2006

K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity," Phys. Plasmas 13, 042103 (2006).
[CrossRef]

S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
[CrossRef] [PubMed]

2005

K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. I. Exact calculation of the mode conversion coefficient in cold, unmagnetized plasmas," Phys. Plasmas 12, 062101 (2005).
[CrossRef]

K. Kim, D.-H. Lee, and H. Lim, "Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media," Europhys. Lett. 69, 207-213 (2005).
[CrossRef]

2004

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

2000

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

1999

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]

1997

L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and G. H. Derrick, "Periodic models for thin optimal absorbers of electromagnetic radiation," Phys. Rev. B 55, R16072-R16075 (1997).
[CrossRef]

1995

A. K. Sarychev, D. J. Bergman, and Y. Yagil, "Theory of the optical and microwave properties of metal-dielectric films," Phys. Rev. B 51, 5366-5385 (1995).
[CrossRef]

1994

V. I. Klyatskin, "The imbedding method in statistical boundary-value wave problems," Prog. Opt. 33, 1-127 (1994).
[CrossRef]

1992

D. E. Hinkel-Lipsker, B. D. Fried, and G. J. Morales, "Analytic expressions for mode conversion in a plasma with a linear density profile," Phys. Fluids B 4, 559-575 (1992).
[CrossRef]

1990

E. Mjølhus, "On linear mode conversion in a magnetized plasma," Radio Sci. 25, 1321-1339 (1990).
[CrossRef]

1987

R. Rammal and B. Doucot, "Invariant-imbedding approach to localization. I. General framework and basic equations," J. Phys. (Paris) 48, 509-526 (1987).
[CrossRef]

1975

D. W. Forslund, J. M. Kindel, K. Lee, E. L. Lindman, and R. L. Morse, "Theory and simulation of resonant absorption in a hot plasma," Phys. Rev. A 11, 679-683 (1975).
[CrossRef]

1968

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Bergman, D. J.

A. K. Sarychev, D. J. Bergman, and Y. Yagil, "Theory of the optical and microwave properties of metal-dielectric films," Phys. Rev. B 51, 5366-5385 (1995).
[CrossRef]

Botten, L. C.

L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and G. H. Derrick, "Periodic models for thin optimal absorbers of electromagnetic radiation," Phys. Rev. B 55, R16072-R16075 (1997).
[CrossRef]

Cairns, I. H.

E. H. Kim, I. H. Cairns, and P. A. Robinson, "Extraordinary-mode radiation produced by linear-mode conversion of Langmuir waves," Phys. Rev. Lett. 99, 015003 (2007).
[CrossRef] [PubMed]

Caplin, D.

F. Magnus, B. Wood, J. Moore, K. Morrison, G. Perkins, J. Fyson, M. C. K. Wiltshire, D. Caplin, L. F. Cohen, and J. B. Pendry, "A d.c. magnetic metamaterial," Nat. Mater. 7, 295-297 (2008).
[CrossRef] [PubMed]

Cohen, L. F.

F. Magnus, B. Wood, J. Moore, K. Morrison, G. Perkins, J. Fyson, M. C. K. Wiltshire, D. Caplin, L. F. Cohen, and J. B. Pendry, "A d.c. magnetic metamaterial," Nat. Mater. 7, 295-297 (2008).
[CrossRef] [PubMed]

Derrick, G. H.

L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and G. H. Derrick, "Periodic models for thin optimal absorbers of electromagnetic radiation," Phys. Rev. B 55, R16072-R16075 (1997).
[CrossRef]

Doucot, B.

R. Rammal and B. Doucot, "Invariant-imbedding approach to localization. I. General framework and basic equations," J. Phys. (Paris) 48, 509-526 (1987).
[CrossRef]

Forslund, D. W.

D. W. Forslund, J. M. Kindel, K. Lee, E. L. Lindman, and R. L. Morse, "Theory and simulation of resonant absorption in a hot plasma," Phys. Rev. A 11, 679-683 (1975).
[CrossRef]

Fried, B. D.

D. E. Hinkel-Lipsker, B. D. Fried, and G. J. Morales, "Analytic expressions for mode conversion in a plasma with a linear density profile," Phys. Fluids B 4, 559-575 (1992).
[CrossRef]

Fyson, J.

F. Magnus, B. Wood, J. Moore, K. Morrison, G. Perkins, J. Fyson, M. C. K. Wiltshire, D. Caplin, L. F. Cohen, and J. B. Pendry, "A d.c. magnetic metamaterial," Nat. Mater. 7, 295-297 (2008).
[CrossRef] [PubMed]

Hanada, K.

S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
[CrossRef] [PubMed]

Hasegawa, M.

S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
[CrossRef] [PubMed]

Hinkel-Lipsker, D. E.

D. E. Hinkel-Lipsker, B. D. Fried, and G. J. Morales, "Analytic expressions for mode conversion in a plasma with a linear density profile," Phys. Fluids B 4, 559-575 (1992).
[CrossRef]

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]

Hood, A. W.

A. M. D. McDougall and A. W. Hood, "A new look at mode conversion in a stratified isothermal atmosphere," Solar Phys. 246, 259-271 (2007).
[CrossRef]

Idei, H.

S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
[CrossRef] [PubMed]

Kasahara, H.

S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
[CrossRef] [PubMed]

Kim, E. H.

E. H. Kim, I. H. Cairns, and P. A. Robinson, "Extraordinary-mode radiation produced by linear-mode conversion of Langmuir waves," Phys. Rev. Lett. 99, 015003 (2007).
[CrossRef] [PubMed]

Kim, K.

K. Kim, D. K. Phung, F. Rotermund, and H. Lim, "Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses," Opt. Express 16, 1150-1164 (2008).
[CrossRef] [PubMed]

K. Kim, F. Rotermund, and H. Lim, "Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: Exact calculation based on the invariant imbedding method," Phys. Rev. B 77, 024203 (2008).
[CrossRef]

K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity," Phys. Plasmas 13, 042103 (2006).
[CrossRef]

K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. I. Exact calculation of the mode conversion coefficient in cold, unmagnetized plasmas," Phys. Plasmas 12, 062101 (2005).
[CrossRef]

K. Kim, D.-H. Lee, and H. Lim, "Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media," Europhys. Lett. 69, 207-213 (2005).
[CrossRef]

Kindel, J. M.

D. W. Forslund, J. M. Kindel, K. Lee, E. L. Lindman, and R. L. Morse, "Theory and simulation of resonant absorption in a hot plasma," Phys. Rev. A 11, 679-683 (1975).
[CrossRef]

Klyatskin, V. I.

V. I. Klyatskin, "The imbedding method in statistical boundary-value wave problems," Prog. Opt. 33, 1-127 (1994).
[CrossRef]

Lee, D.-H.

K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity," Phys. Plasmas 13, 042103 (2006).
[CrossRef]

K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. I. Exact calculation of the mode conversion coefficient in cold, unmagnetized plasmas," Phys. Plasmas 12, 062101 (2005).
[CrossRef]

K. Kim, D.-H. Lee, and H. Lim, "Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media," Europhys. Lett. 69, 207-213 (2005).
[CrossRef]

Lee, K.

D. W. Forslund, J. M. Kindel, K. Lee, E. L. Lindman, and R. L. Morse, "Theory and simulation of resonant absorption in a hot plasma," Phys. Rev. A 11, 679-683 (1975).
[CrossRef]

Lim, H.

K. Kim, F. Rotermund, and H. Lim, "Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: Exact calculation based on the invariant imbedding method," Phys. Rev. B 77, 024203 (2008).
[CrossRef]

K. Kim, D. K. Phung, F. Rotermund, and H. Lim, "Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses," Opt. Express 16, 1150-1164 (2008).
[CrossRef] [PubMed]

K. Kim, D.-H. Lee, and H. Lim, "Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media," Europhys. Lett. 69, 207-213 (2005).
[CrossRef]

Lindman, E. L.

D. W. Forslund, J. M. Kindel, K. Lee, E. L. Lindman, and R. L. Morse, "Theory and simulation of resonant absorption in a hot plasma," Phys. Rev. A 11, 679-683 (1975).
[CrossRef]

Magnus, F.

F. Magnus, B. Wood, J. Moore, K. Morrison, G. Perkins, J. Fyson, M. C. K. Wiltshire, D. Caplin, L. F. Cohen, and J. B. Pendry, "A d.c. magnetic metamaterial," Nat. Mater. 7, 295-297 (2008).
[CrossRef] [PubMed]

McDougall, A. M. D.

A. M. D. McDougall and A. W. Hood, "A new look at mode conversion in a stratified isothermal atmosphere," Solar Phys. 246, 259-271 (2007).
[CrossRef]

McPhedran, R. C.

L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and G. H. Derrick, "Periodic models for thin optimal absorbers of electromagnetic radiation," Phys. Rev. B 55, R16072-R16075 (1997).
[CrossRef]

Mitarai, O.

S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
[CrossRef] [PubMed]

Mjølhus, E.

E. Mjølhus, "On linear mode conversion in a magnetized plasma," Radio Sci. 25, 1321-1339 (1990).
[CrossRef]

Moore, J.

F. Magnus, B. Wood, J. Moore, K. Morrison, G. Perkins, J. Fyson, M. C. K. Wiltshire, D. Caplin, L. F. Cohen, and J. B. Pendry, "A d.c. magnetic metamaterial," Nat. Mater. 7, 295-297 (2008).
[CrossRef] [PubMed]

Morales, G. J.

D. E. Hinkel-Lipsker, B. D. Fried, and G. J. Morales, "Analytic expressions for mode conversion in a plasma with a linear density profile," Phys. Fluids B 4, 559-575 (1992).
[CrossRef]

Morrison, K.

F. Magnus, B. Wood, J. Moore, K. Morrison, G. Perkins, J. Fyson, M. C. K. Wiltshire, D. Caplin, L. F. Cohen, and J. B. Pendry, "A d.c. magnetic metamaterial," Nat. Mater. 7, 295-297 (2008).
[CrossRef] [PubMed]

Morse, R. L.

D. W. Forslund, J. M. Kindel, K. Lee, E. L. Lindman, and R. L. Morse, "Theory and simulation of resonant absorption in a hot plasma," Phys. Rev. A 11, 679-683 (1975).
[CrossRef]

Nakamura, K.

S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
[CrossRef] [PubMed]

Nicorovici, N. A.

L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and G. H. Derrick, "Periodic models for thin optimal absorbers of electromagnetic radiation," Phys. Rev. B 55, R16072-R16075 (1997).
[CrossRef]

Nishino, N.

S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
[CrossRef] [PubMed]

Nozato, H.

S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
[CrossRef] [PubMed]

Pendry, J. B.

F. Magnus, B. Wood, J. Moore, K. Morrison, G. Perkins, J. Fyson, M. C. K. Wiltshire, D. Caplin, L. F. Cohen, and J. B. Pendry, "A d.c. magnetic metamaterial," Nat. Mater. 7, 295-297 (2008).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

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

Perkins, G.

F. Magnus, B. Wood, J. Moore, K. Morrison, G. Perkins, J. Fyson, M. C. K. Wiltshire, D. Caplin, L. F. Cohen, and J. B. Pendry, "A d.c. magnetic metamaterial," Nat. Mater. 7, 295-297 (2008).
[CrossRef] [PubMed]

Phung, D. K.

Rammal, R.

R. Rammal and B. Doucot, "Invariant-imbedding approach to localization. I. General framework and basic equations," J. Phys. (Paris) 48, 509-526 (1987).
[CrossRef]

Robbins, D. J.

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S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
[CrossRef] [PubMed]

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S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
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V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
[CrossRef]

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[CrossRef] [PubMed]

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D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
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S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
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V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

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F. Magnus, B. Wood, J. Moore, K. Morrison, G. Perkins, J. Fyson, M. C. K. Wiltshire, D. Caplin, L. F. Cohen, and J. B. Pendry, "A d.c. magnetic metamaterial," Nat. Mater. 7, 295-297 (2008).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

Wood, B.

F. Magnus, B. Wood, J. Moore, K. Morrison, G. Perkins, J. Fyson, M. C. K. Wiltshire, D. Caplin, L. F. Cohen, and J. B. Pendry, "A d.c. magnetic metamaterial," Nat. Mater. 7, 295-297 (2008).
[CrossRef] [PubMed]

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A. K. Sarychev, D. J. Bergman, and Y. Yagil, "Theory of the optical and microwave properties of metal-dielectric films," Phys. Rev. B 51, 5366-5385 (1995).
[CrossRef]

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S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
[CrossRef] [PubMed]

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S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
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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).
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[CrossRef] [PubMed]

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V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
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K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity," Phys. Plasmas 13, 042103 (2006).
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[CrossRef]

A. K. Sarychev, D. J. Bergman, and Y. Yagil, "Theory of the optical and microwave properties of metal-dielectric films," Phys. Rev. B 51, 5366-5385 (1995).
[CrossRef]

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[CrossRef] [PubMed]

S. Shiraiwa, K. Hanada, M. Hasegawa, H. Idei, H. Kasahara, O. Mitarai, K. Nakamura, N. Nishino, H. Nozato, M. Sakamoto, K. Sasaki, K. Sato, Y. Takase, T. Yamada, H. Zushi, and TST-2@K Group, "Heating by an electron Bernstein wave in a spherical tokamak plasma via mode conversion," Phys. Rev. Lett. 96, 185003 (2006).
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[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Profiles of the dielectric permittivity and the magnetic permeability inside metamaterial media in (a) model A, (b) model B, and (c) model C. The squares designate the positions where both ε and µ vanish. At the position marked by a filled (empty) circle, only ε (µ) vanishes. The vertical dashed lines indicate the region where 0≤zL. The wave is assumed to be incident from the right side where z>L and transmitted to the left side where z<0.

Fig. 2.
Fig. 2.

Universal curve for the mode conversion coefficient A for model A plotted versus Q=ζsin2θ. The points B and C marked by square dots correspond to Q=0.44 and π respectively. Inset: Mode conversion coefficient versus incident angle for ζ=10π, 25π and 50π and for η=10-8.

Fig. 3.
Fig. 3.

Electric field intensity for model A plotted versus ζ1/2(z-z R )/h, when (a) Q=0.44 and (b) Q=π. An s wave is assumed to be incident from the right side and η=10-5.

Fig. 4.
Fig. 4.

Mode conversion coefficient for model B (solid line) versus incident angle, when ζ=25π and η=10-8 and when an s wave is incident. A is almost zero for all θ when a p wave is incident. The result for model A (dashed line), when ζ=25π and η=10-8, is shown for comparison.

Fig. 5.
Fig. 5.

(a) Reflectance and (b) mode conversion coefficient for model C (solid lines) versus incident angle, when ζ=10π and η=10-8. The points P and Q correspond to θ=6.53° and 10.53° respectively. The results for model A (dashed lines), when ζ=10π and η=10-8, are shown for comparison.

Fig. 6.
Fig. 6.

Spatial distributions of the electric field intensity for model C, when (a) θ=6.53° and (b) θ=10.53°. An s wave is assumed to be incident from the right side and η=10-5.

Equations (13)

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d 2 E d z 2 1 μ ( z ) d μ d z d E d z + [ k 0 2 ε ( z ) μ ( z ) q 2 ] E = 0 .
H x ( z ) = i k 0 μ ( z ) d E d z , H z ( z ) = q k 0 E ( z ) μ ( z ) .
ε ˜ ( z ) = μ ˜ ( z ) = { 1 if 0 z < L 2 ( z z R ) h + i η if L 2 z L ,
ε ˜ ( z ) = { 0 . 5 if 0 z < L 2 0 . 75 ( z z R 1 ) h + i η if L 2 z L ,
μ ˜ ( z ) = { 2 if 0 z < L 2 1 . 5 ( z z R 2 ) h + i η if L 2 z L ,
ε ˜ ( z ) = μ ˜ ( z ) = { ( z z r 1 ) h + i η if 0 z L 3 1 if L 3 < z < 2 L 3 ( z z r 2 ) h + i η if 2 L 3 z L ,
E ˜ ( x , z ) = { [ e i p ( L z ) + r ( L ) e i p ( z L ) ] e i q x , z > L t ( L ) e i p z + i q x , z < 0 .
1 i p d r ( l ) d l = 2 μ ˜ ( l ) r ( l ) + a ( l ) 2 [ 1 + r ( l ) ] 2 ,
1 i p d t ( l ) d l = μ ˜ ( l ) t ( l ) + a ( l ) 2 [ 1 + r ( l ) ] t ( l ) ,
a ( l ) = ε ˜ ( l ) μ ˜ ( l ) + [ ε ˜ ( l ) 1 μ ˜ ( l ) ] tan 2 θ .
1 i p = E ( z , l ) l = μ ˜ ( l ) E ( z , l ) + a ( l ) 2 [ 1 + r ( l ) ] E ( z , l ) ,
d 2 E d z ̂ 2 1 z ̂ + i η ̂ d E d z ̂ + [ ( z ̂ + i η ̂ ) 2 Q ] E = 0 .
E x ( z ) = i k 0 ε ( z ) d H d z , E z ( z ) = q k 0 H ( z ) ε ( z )

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