Abstract

We investigated theoretically chiral negatively refractive fibers that guide transverse electromagnetic modes. In this Letter, novel properties of such fibers are presented, including arbitrariness of modal field and arbitrarily scalable core radius. Based on these novel properties, we conceptually propose a new type of space-division multiplexing that uses different spatial positions of the core of such fascinating fibers as different data paths.

© 2014 Optical Society of America

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References

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  1. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  2. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
    [CrossRef]
  3. J. B. Pendry, Science 306, 1353 (2004).
    [CrossRef]
  4. V. M. Shalaev, Nat. Photonics 1, 41 (2007).
    [CrossRef]
  5. I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
    [CrossRef]
  6. J. Schelleng, C. Monzon, P. F. Loschialpo, D. W. Forester, and L. N. Medgyesi-Mitschang, Phys. Rev. E 70, 066606 (2004).
    [CrossRef]
  7. A. Alu and N. Engheta, IEEE Trans. Microwave Theory Tech. 52, 199 (2004).
  8. G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. E 71, 046603 (2005).
    [CrossRef]
  9. A. V. Novitsky, J. Opt. A 8, 864 (2006).
    [CrossRef]
  10. S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, J. Opt. Soc. Am. B 30, 851 (2013).
    [CrossRef]
  11. N. Engheta and P. Pelet, Opt. Lett. 14, 593 (1989).
    [CrossRef]
  12. C. F. Bohren, Chem. Phys. Lett. 29, 458 (1974).
    [CrossRef]
  13. One might conclude that Eq. (3) is incorrect, as it seemingly implies the identity of two perpendicular vectors. But note that “perpendicular” should be applied only for real electromagnetic fields, never for complex-represented ones. Also necessarily distinguished are vectors in Euclidean space and the vector representation of complex numbers in a complex plane. Similarly, one cannot conclude that Eq. (4) means the parallelity of real electric and magnetic fields. Actually, the real electric and magnetic fields of TEM modes (obtained by taking either the real part or the Fourier transform of complex modal fields, depending on how we view the modal analysis, solving the eigenstates of time-harmonic fields or frequency-domain analysis) are perpendicular.
  14. Y. Cao, J. Li, and Q. Su, J. Opt. Soc. Am. B 28, 319 (2011).
    [CrossRef]
  15. T. G. Mackay and A. Lakhtakia, Phys. Rev. E 69, 026602 (2004).
    [CrossRef]
  16. C. Monzon and D. W. Forester, Phys. Rev. Lett. 95, 123904 (2005).
    [CrossRef]
  17. C.-W. Qiu, L.-W. Li, H.-Y. Yao, and S. Zouhdi, Phys. Rev. B 74, 115110 (2006).
    [CrossRef]
  18. C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 245214 (2007).
    [CrossRef]
  19. C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 155120 (2007).
    [CrossRef]
  20. C. Zhang and T. J. Cui, Appl. Phys. Lett. 91, 194101 (2007).
    [CrossRef]
  21. C.-W. Qiu, N. Burokur, S. Zouhdi, and L.-W. Li, J. Opt. Soc. Am. A 25, 55 (2008).
    [CrossRef]
  22. L. Jelinek, R. Marqués, F. Mesa, and J. D. Baena, Phys. Rev. B 77, 205110 (2008).
    [CrossRef]
  23. E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407 (2009).
    [CrossRef]
  24. C. Zhang and T. J. Cui, Opt. Commun. 280, 359 (2007).
    [CrossRef]
  25. J. Dong and J. Li Chin, Opt. Lett. 8, 1032 (2010).
  26. J. Dong, Opt. Commun. 283, 532 (2010).
    [CrossRef]
  27. D. R. Smith and N. Kroll, Phys. Rev. Lett. 85, 2933 (2000).
    [CrossRef]
  28. C. R. Brewitt-Taylor, P. G. Lederer, F. C. Smith, and S. Haq, IEEE Trans. Antennas Propag. 47, 692 (1999).
    [CrossRef]
  29. D. Richardson, J. Fini, and L. Nelson, Nat. Photonics 7, 354 (2013).
    [CrossRef]

2013 (2)

2011 (1)

2010 (2)

J. Dong and J. Li Chin, Opt. Lett. 8, 1032 (2010).

J. Dong, Opt. Commun. 283, 532 (2010).
[CrossRef]

2009 (1)

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407 (2009).
[CrossRef]

2008 (2)

L. Jelinek, R. Marqués, F. Mesa, and J. D. Baena, Phys. Rev. B 77, 205110 (2008).
[CrossRef]

C.-W. Qiu, N. Burokur, S. Zouhdi, and L.-W. Li, J. Opt. Soc. Am. A 25, 55 (2008).
[CrossRef]

2007 (5)

C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 155120 (2007).
[CrossRef]

C. Zhang and T. J. Cui, Appl. Phys. Lett. 91, 194101 (2007).
[CrossRef]

C. Zhang and T. J. Cui, Opt. Commun. 280, 359 (2007).
[CrossRef]

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

2006 (2)

A. V. Novitsky, J. Opt. A 8, 864 (2006).
[CrossRef]

C.-W. Qiu, L.-W. Li, H.-Y. Yao, and S. Zouhdi, Phys. Rev. B 74, 115110 (2006).
[CrossRef]

2005 (2)

C. Monzon and D. W. Forester, Phys. Rev. Lett. 95, 123904 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. E 71, 046603 (2005).
[CrossRef]

2004 (4)

J. B. Pendry, Science 306, 1353 (2004).
[CrossRef]

J. Schelleng, C. Monzon, P. F. Loschialpo, D. W. Forester, and L. N. Medgyesi-Mitschang, Phys. Rev. E 70, 066606 (2004).
[CrossRef]

A. Alu and N. Engheta, IEEE Trans. Microwave Theory Tech. 52, 199 (2004).

T. G. Mackay and A. Lakhtakia, Phys. Rev. E 69, 026602 (2004).
[CrossRef]

2003 (1)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

2000 (2)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

D. R. Smith and N. Kroll, Phys. Rev. Lett. 85, 2933 (2000).
[CrossRef]

1999 (1)

C. R. Brewitt-Taylor, P. G. Lederer, F. C. Smith, and S. Haq, IEEE Trans. Antennas Propag. 47, 692 (1999).
[CrossRef]

1989 (1)

1974 (1)

C. F. Bohren, Chem. Phys. Lett. 29, 458 (1974).
[CrossRef]

1968 (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Alu, A.

A. Alu and N. Engheta, IEEE Trans. Microwave Theory Tech. 52, 199 (2004).

Argyros, A.

Atakaramians, S.

Baena, J. D.

L. Jelinek, R. Marqués, F. Mesa, and J. D. Baena, Phys. Rev. B 77, 205110 (2008).
[CrossRef]

Bloemer, M. J.

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. E 71, 046603 (2005).
[CrossRef]

Bohren, C. F.

C. F. Bohren, Chem. Phys. Lett. 29, 458 (1974).
[CrossRef]

Brewitt-Taylor, C. R.

C. R. Brewitt-Taylor, P. G. Lederer, F. C. Smith, and S. Haq, IEEE Trans. Antennas Propag. 47, 692 (1999).
[CrossRef]

Burokur, N.

Cao, Y.

Cui, T. J.

C. Zhang and T. J. Cui, Appl. Phys. Lett. 91, 194101 (2007).
[CrossRef]

C. Zhang and T. J. Cui, Opt. Commun. 280, 359 (2007).
[CrossRef]

D’Aguanno, G.

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. E 71, 046603 (2005).
[CrossRef]

Dong, J.

J. Dong and J. Li Chin, Opt. Lett. 8, 1032 (2010).

J. Dong, Opt. Commun. 283, 532 (2010).
[CrossRef]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407 (2009).
[CrossRef]

Engheta, N.

A. Alu and N. Engheta, IEEE Trans. Microwave Theory Tech. 52, 199 (2004).

N. Engheta and P. Pelet, Opt. Lett. 14, 593 (1989).
[CrossRef]

Fedotov, V. A.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407 (2009).
[CrossRef]

Fini, J.

D. Richardson, J. Fini, and L. Nelson, Nat. Photonics 7, 354 (2013).
[CrossRef]

Fleming, S. C.

Forester, D. W.

C. Monzon and D. W. Forester, Phys. Rev. Lett. 95, 123904 (2005).
[CrossRef]

J. Schelleng, C. Monzon, P. F. Loschialpo, D. W. Forester, and L. N. Medgyesi-Mitschang, Phys. Rev. E 70, 066606 (2004).
[CrossRef]

Haq, S.

C. R. Brewitt-Taylor, P. G. Lederer, F. C. Smith, and S. Haq, IEEE Trans. Antennas Propag. 47, 692 (1999).
[CrossRef]

Jelinek, L.

L. Jelinek, R. Marqués, F. Mesa, and J. D. Baena, Phys. Rev. B 77, 205110 (2008).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Koschny, T.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407 (2009).
[CrossRef]

Kroll, N.

D. R. Smith and N. Kroll, Phys. Rev. Lett. 85, 2933 (2000).
[CrossRef]

Kuhlmey, B. T.

Lakhtakia, A.

T. G. Mackay and A. Lakhtakia, Phys. Rev. E 69, 026602 (2004).
[CrossRef]

Lederer, P. G.

C. R. Brewitt-Taylor, P. G. Lederer, F. C. Smith, and S. Haq, IEEE Trans. Antennas Propag. 47, 692 (1999).
[CrossRef]

Li, J.

Li, L.-W.

C.-W. Qiu, N. Burokur, S. Zouhdi, and L.-W. Li, J. Opt. Soc. Am. A 25, 55 (2008).
[CrossRef]

C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 155120 (2007).
[CrossRef]

C.-W. Qiu, L.-W. Li, H.-Y. Yao, and S. Zouhdi, Phys. Rev. B 74, 115110 (2006).
[CrossRef]

Li Chin, J.

J. Dong and J. Li Chin, Opt. Lett. 8, 1032 (2010).

Loschialpo, P. F.

J. Schelleng, C. Monzon, P. F. Loschialpo, D. W. Forester, and L. N. Medgyesi-Mitschang, Phys. Rev. E 70, 066606 (2004).
[CrossRef]

Mackay, T. G.

T. G. Mackay and A. Lakhtakia, Phys. Rev. E 69, 026602 (2004).
[CrossRef]

Marqués, R.

L. Jelinek, R. Marqués, F. Mesa, and J. D. Baena, Phys. Rev. B 77, 205110 (2008).
[CrossRef]

Mattiucci, N.

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. E 71, 046603 (2005).
[CrossRef]

Medgyesi-Mitschang, L. N.

J. Schelleng, C. Monzon, P. F. Loschialpo, D. W. Forester, and L. N. Medgyesi-Mitschang, Phys. Rev. E 70, 066606 (2004).
[CrossRef]

Mesa, F.

L. Jelinek, R. Marqués, F. Mesa, and J. D. Baena, Phys. Rev. B 77, 205110 (2008).
[CrossRef]

Monzon, C.

C. Monzon and D. W. Forester, Phys. Rev. Lett. 95, 123904 (2005).
[CrossRef]

J. Schelleng, C. Monzon, P. F. Loschialpo, D. W. Forester, and L. N. Medgyesi-Mitschang, Phys. Rev. E 70, 066606 (2004).
[CrossRef]

Nelson, L.

D. Richardson, J. Fini, and L. Nelson, Nat. Photonics 7, 354 (2013).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Novitsky, A. V.

A. V. Novitsky, J. Opt. A 8, 864 (2006).
[CrossRef]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Pelet, P.

Pendry, J. B.

J. B. Pendry, Science 306, 1353 (2004).
[CrossRef]

Plum, E.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407 (2009).
[CrossRef]

Qiu, C.-W.

C.-W. Qiu, N. Burokur, S. Zouhdi, and L.-W. Li, J. Opt. Soc. Am. A 25, 55 (2008).
[CrossRef]

C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 155120 (2007).
[CrossRef]

C.-W. Qiu, L.-W. Li, H.-Y. Yao, and S. Zouhdi, Phys. Rev. B 74, 115110 (2006).
[CrossRef]

Richardson, D.

D. Richardson, J. Fini, and L. Nelson, Nat. Photonics 7, 354 (2013).
[CrossRef]

Scalora, M.

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. E 71, 046603 (2005).
[CrossRef]

Schelleng, J.

J. Schelleng, C. Monzon, P. F. Loschialpo, D. W. Forester, and L. N. Medgyesi-Mitschang, Phys. Rev. E 70, 066606 (2004).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Shalaev, V. M.

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

D. R. Smith and N. Kroll, Phys. Rev. Lett. 85, 2933 (2000).
[CrossRef]

Smith, F. C.

C. R. Brewitt-Taylor, P. G. Lederer, F. C. Smith, and S. Haq, IEEE Trans. Antennas Propag. 47, 692 (1999).
[CrossRef]

Soukoulis, C. M.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407 (2009).
[CrossRef]

Su, Q.

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Yao, H.-Y.

C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 155120 (2007).
[CrossRef]

C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C.-W. Qiu, L.-W. Li, H.-Y. Yao, and S. Zouhdi, Phys. Rev. B 74, 115110 (2006).
[CrossRef]

Yeo, T.-S.

C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 155120 (2007).
[CrossRef]

Zhang, C.

C. Zhang and T. J. Cui, Appl. Phys. Lett. 91, 194101 (2007).
[CrossRef]

C. Zhang and T. J. Cui, Opt. Commun. 280, 359 (2007).
[CrossRef]

Zheludev, N. I.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407 (2009).
[CrossRef]

Zhou, J.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407 (2009).
[CrossRef]

Zouhdi, S.

C.-W. Qiu, N. Burokur, S. Zouhdi, and L.-W. Li, J. Opt. Soc. Am. A 25, 55 (2008).
[CrossRef]

C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 155120 (2007).
[CrossRef]

C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C.-W. Qiu, L.-W. Li, H.-Y. Yao, and S. Zouhdi, Phys. Rev. B 74, 115110 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

C. Zhang and T. J. Cui, Appl. Phys. Lett. 91, 194101 (2007).
[CrossRef]

Chem. Phys. Lett. (1)

C. F. Bohren, Chem. Phys. Lett. 29, 458 (1974).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

C. R. Brewitt-Taylor, P. G. Lederer, F. C. Smith, and S. Haq, IEEE Trans. Antennas Propag. 47, 692 (1999).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

A. Alu and N. Engheta, IEEE Trans. Microwave Theory Tech. 52, 199 (2004).

J. Opt. A (1)

A. V. Novitsky, J. Opt. A 8, 864 (2006).
[CrossRef]

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

J. Opt. Soc. Am. B (2)

Nat. Photonics (2)

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

D. Richardson, J. Fini, and L. Nelson, Nat. Photonics 7, 354 (2013).
[CrossRef]

Opt. Commun. (2)

C. Zhang and T. J. Cui, Opt. Commun. 280, 359 (2007).
[CrossRef]

J. Dong, Opt. Commun. 283, 532 (2010).
[CrossRef]

Opt. Lett. (2)

J. Dong and J. Li Chin, Opt. Lett. 8, 1032 (2010).

N. Engheta and P. Pelet, Opt. Lett. 14, 593 (1989).
[CrossRef]

Phys. Rev. B (5)

C.-W. Qiu, L.-W. Li, H.-Y. Yao, and S. Zouhdi, Phys. Rev. B 74, 115110 (2006).
[CrossRef]

C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S. Yeo, Phys. Rev. B 75, 155120 (2007).
[CrossRef]

L. Jelinek, R. Marqués, F. Mesa, and J. D. Baena, Phys. Rev. B 77, 205110 (2008).
[CrossRef]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407 (2009).
[CrossRef]

Phys. Rev. E (4)

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. E 71, 046603 (2005).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

J. Schelleng, C. Monzon, P. F. Loschialpo, D. W. Forester, and L. N. Medgyesi-Mitschang, Phys. Rev. E 70, 066606 (2004).
[CrossRef]

T. G. Mackay and A. Lakhtakia, Phys. Rev. E 69, 026602 (2004).
[CrossRef]

Phys. Rev. Lett. (3)

C. Monzon and D. W. Forester, Phys. Rev. Lett. 95, 123904 (2005).
[CrossRef]

D. R. Smith and N. Kroll, Phys. Rev. Lett. 85, 2933 (2000).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Science (1)

J. B. Pendry, Science 306, 1353 (2004).
[CrossRef]

Sov. Phys. Usp. (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other (1)

One might conclude that Eq. (3) is incorrect, as it seemingly implies the identity of two perpendicular vectors. But note that “perpendicular” should be applied only for real electromagnetic fields, never for complex-represented ones. Also necessarily distinguished are vectors in Euclidean space and the vector representation of complex numbers in a complex plane. Similarly, one cannot conclude that Eq. (4) means the parallelity of real electric and magnetic fields. Actually, the real electric and magnetic fields of TEM modes (obtained by taking either the real part or the Fourier transform of complex modal fields, depending on how we view the modal analysis, solving the eigenstates of time-harmonic fields or frequency-domain analysis) are perpendicular.

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Figures (2)

Fig. 1.
Fig. 1.

TEM guiding fiber supporting N data paths.

Fig. 2.
Fig. 2.

(a) Schematic of a TEM-guiding fiber with five data paths located at (2a/3,π/2), (2a/3,0), (2a/3,π/2), (2a/3,π), and (0,0). Data encoding and corresponding modal pattern: (b) g(q)=0, (c) g(q)=1, (d) g(q)=q, and (e) g(q)=q(q2/3). The dashed circle indicates the interface.

Equations (13)

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

×F±=±k±F±,
E=(F++F)/2,H=(F+F)/(2iη).
iβz^×F±,t=±k±F±,t.
E=±iηH=F±/2.
F±1,2=(iβ±±k±1,2r^+θ^)f±(ra)nβ±±k±1,21einθ,
S1,2(r,θ,z,t)=R(1η1,2)β±k±1,2[f±2(ra)nβ±±k±1,21]2z^.
P=002πS·z^rdθdr=0
F+1=(ir^+θ^)f+e+iθqn1,F+2=(+ir^+θ^)f+eiθpn+1,
F+1=(ir^+θ^)e+iθg(q)F+2=(+ir^+θ^)eiθj=0[g(j)(0)/j!]pj+2
F+1,θ=eiθg(eiθ)=eiθj=0[g(j)(0)/j!](eiθ)j,F+2,θ=eiθj=0[g(j)(0)/j!](e+iθ)j+2=F+1,θ.
R(F+,x)/x=R(F+,y)/y,R(F+,y)/x=R(F+,x)/y,
F+1=(ix^+y^)g(q),F+2=(+ix^+y^)j=0[g(j)(0)/j!]pj+2.
g(q)=j=1M(qqj),

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