Abstract

Since the discovery of backward-wave materials, people have tried to realize a strong chiral medium, which is traditionally thought impossible mainly for the reason of energy and spatial dispersion. We compare the two most popular descriptions of a chiral medium. After analyzing several possible reasons for the traditional restriction, we show that a strong chirality parameter leads to positive energy without any frequency-band limitation in the weak spatial dispersion. Moreover, strong chirality does not result in a strong spatial dispersion, which occurs only around the traditional limit point. For strong spatial dispersion where higher-order terms of spatial dispersion need to be considered, the energy conservation is also valid. Finally, we show that realization of strong chirality requires the conjugated type of spatial dispersion.

© 2007 Optical Society of America

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References

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  1. L. Pasteur, Researches on the molecular asymmetry of natural organic products, English translation of French original, (Alembic Club Reprints Vol. 14, pp. 1–461905), facsimile reproduction by SPIE in a 1990 book.
  2. A. J. Fresnel, in OEvres comple’tes dAugustin Fresnel, edited by H. d. Senarmont, E. Verdet, and L. Fresnel (Imprimerie imperiale, Paris, 1866), Vol. 1.
  3. W. A. Shurcliff and S. S. Ballard, Polarized light, (Van Nostrand Co., Princeton, 1964).
  4. Eugene Hecht, Optics, 3rd Ed. (Addison-Wesley, 1998).
  5. L. D. Landau and E. M. Lifshitz, Electromagnetics of continous media, vol. 8 of Course of Theoretical Physics, 2nd edition, English, (Pergamon Press, 1984).
    [PubMed]
  6. A. Sommerfeld, Lectures on Theoretical Physics: Optics (Academic, New York, 1952).
  7. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Boston, 1994).
  8. A. Serdukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science Publishers, Amsterdam, 2001).
  9. A. Lakhtakia, Beltrami Fields In Chiral media (World Scientific Publishing Co. Pte. Ltd., Singapore, 1994).
    [Crossref]
  10. A. Ishimaru, Electromagnetic Wave Propagation, Radiation and Scattering (Prentice Hall, Englewood Cliffs, NJ, 1991).
  11. J. A. Kong, Electromagnetic Wave Theory (Wiley, NY, 1986).
  12. S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, Waves and energy in chiral nihility, J. Electromagn. Waves Appl. 17, 695 (2003).
    [Crossref]
  13. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968).
    [Crossref]
  14. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).
    [Crossref] [PubMed]
  15. Y. Jin and S. He, “Focusing by a slab of chiral medium,” Opt. Express 13, 4974 (2005).
    [Crossref] [PubMed]
  16. T. G. Mackay and A. Lakhtakia, “Plane waves with negative phase velocity in Faraday chiral mediums,” Phys. Rev. E 69, 026602 (2004).
    [Crossref]
  17. S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
    [Crossref]
  18. C. Monzon and D. W. Forester, “Negative refraction and focusing of circularly polarized waves in optically active media,” Phys. Rev. Lett. 95, 123904 (2005).
    [Crossref] [PubMed]
  19. T. G. Mackay and A. Lakhtakia, “Negative phase velocity in a material with simultaneous mirror-conjugated and racemic chirality characteristics,” New J. Phys. 7, 165 (2005).
    [Crossref]
  20. Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B 73, 113104 (2006).
    [Crossref]
  21. Q. Cheng and T. J. Cui, “Negative refractions and backward waves in biaxially anisotropic chiral media,” Opt. Express 14, 6322 (2006).
    [Crossref] [PubMed]

2006 (2)

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B 73, 113104 (2006).
[Crossref]

Q. Cheng and T. J. Cui, “Negative refractions and backward waves in biaxially anisotropic chiral media,” Opt. Express 14, 6322 (2006).
[Crossref] [PubMed]

2005 (4)

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[Crossref]

C. Monzon and D. W. Forester, “Negative refraction and focusing of circularly polarized waves in optically active media,” Phys. Rev. Lett. 95, 123904 (2005).
[Crossref] [PubMed]

T. G. Mackay and A. Lakhtakia, “Negative phase velocity in a material with simultaneous mirror-conjugated and racemic chirality characteristics,” New J. Phys. 7, 165 (2005).
[Crossref]

Y. Jin and S. He, “Focusing by a slab of chiral medium,” Opt. Express 13, 4974 (2005).
[Crossref] [PubMed]

2004 (1)

T. G. Mackay and A. Lakhtakia, “Plane waves with negative phase velocity in Faraday chiral mediums,” Phys. Rev. E 69, 026602 (2004).
[Crossref]

2003 (1)

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, Waves and energy in chiral nihility, J. Electromagn. Waves Appl. 17, 695 (2003).
[Crossref]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).
[Crossref] [PubMed]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968).
[Crossref]

Ballard, S. S.

W. A. Shurcliff and S. S. Ballard, Polarized light, (Van Nostrand Co., Princeton, 1964).

Cheng, Q.

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B 73, 113104 (2006).
[Crossref]

Q. Cheng and T. J. Cui, “Negative refractions and backward waves in biaxially anisotropic chiral media,” Opt. Express 14, 6322 (2006).
[Crossref] [PubMed]

Cui, T. J.

Q. Cheng and T. J. Cui, “Negative refractions and backward waves in biaxially anisotropic chiral media,” Opt. Express 14, 6322 (2006).
[Crossref] [PubMed]

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B 73, 113104 (2006).
[Crossref]

Forester, D. W.

C. Monzon and D. W. Forester, “Negative refraction and focusing of circularly polarized waves in optically active media,” Phys. Rev. Lett. 95, 123904 (2005).
[Crossref] [PubMed]

Fresnel, A. J.

A. J. Fresnel, in OEvres comple’tes dAugustin Fresnel, edited by H. d. Senarmont, E. Verdet, and L. Fresnel (Imprimerie imperiale, Paris, 1866), Vol. 1.

He, S.

Hecht, Eugene

Eugene Hecht, Optics, 3rd Ed. (Addison-Wesley, 1998).

Ishimaru, A.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation and Scattering (Prentice Hall, Englewood Cliffs, NJ, 1991).

Jin, Y.

Jylha, L.

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[Crossref]

Kong, J. A.

J. A. Kong, Electromagnetic Wave Theory (Wiley, NY, 1986).

Lakhtakia, A.

T. G. Mackay and A. Lakhtakia, “Negative phase velocity in a material with simultaneous mirror-conjugated and racemic chirality characteristics,” New J. Phys. 7, 165 (2005).
[Crossref]

T. G. Mackay and A. Lakhtakia, “Plane waves with negative phase velocity in Faraday chiral mediums,” Phys. Rev. E 69, 026602 (2004).
[Crossref]

A. Lakhtakia, Beltrami Fields In Chiral media (World Scientific Publishing Co. Pte. Ltd., Singapore, 1994).
[Crossref]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Electromagnetics of continous media, vol. 8 of Course of Theoretical Physics, 2nd edition, English, (Pergamon Press, 1984).
[PubMed]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Electromagnetics of continous media, vol. 8 of Course of Theoretical Physics, 2nd edition, English, (Pergamon Press, 1984).
[PubMed]

Lindell, I. V.

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Boston, 1994).

Mackay, T. G.

T. G. Mackay and A. Lakhtakia, “Negative phase velocity in a material with simultaneous mirror-conjugated and racemic chirality characteristics,” New J. Phys. 7, 165 (2005).
[Crossref]

T. G. Mackay and A. Lakhtakia, “Plane waves with negative phase velocity in Faraday chiral mediums,” Phys. Rev. E 69, 026602 (2004).
[Crossref]

Maslovski, S.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, Waves and energy in chiral nihility, J. Electromagn. Waves Appl. 17, 695 (2003).
[Crossref]

Monzon, C.

C. Monzon and D. W. Forester, “Negative refraction and focusing of circularly polarized waves in optically active media,” Phys. Rev. Lett. 95, 123904 (2005).
[Crossref] [PubMed]

Nefedov, I.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, Waves and energy in chiral nihility, J. Electromagn. Waves Appl. 17, 695 (2003).
[Crossref]

Pasteur, L.

L. Pasteur, Researches on the molecular asymmetry of natural organic products, English translation of French original, (Alembic Club Reprints Vol. 14, pp. 1–461905), facsimile reproduction by SPIE in a 1990 book.

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).
[Crossref] [PubMed]

Semchenko, I.

A. Serdukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science Publishers, Amsterdam, 2001).

Serdukov, A.

A. Serdukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science Publishers, Amsterdam, 2001).

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).
[Crossref] [PubMed]

Shurcliff, W. A.

W. A. Shurcliff and S. S. Ballard, Polarized light, (Van Nostrand Co., Princeton, 1964).

Sihvola, A.

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[Crossref]

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, Waves and energy in chiral nihility, J. Electromagn. Waves Appl. 17, 695 (2003).
[Crossref]

A. Serdukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science Publishers, Amsterdam, 2001).

Sihvola, A. H.

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Boston, 1994).

Simovski, C.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, Waves and energy in chiral nihility, J. Electromagn. Waves Appl. 17, 695 (2003).
[Crossref]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).
[Crossref] [PubMed]

Sommerfeld, A.

A. Sommerfeld, Lectures on Theoretical Physics: Optics (Academic, New York, 1952).

Tretyakov, S.

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[Crossref]

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, Waves and energy in chiral nihility, J. Electromagn. Waves Appl. 17, 695 (2003).
[Crossref]

A. Serdukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science Publishers, Amsterdam, 2001).

Tretyakov, S. A.

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Boston, 1994).

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968).
[Crossref]

Viitanen, A. J.

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Boston, 1994).

J. Electromagn. Waves Appl. (1)

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, Waves and energy in chiral nihility, J. Electromagn. Waves Appl. 17, 695 (2003).
[Crossref]

New J. Phys. (1)

T. G. Mackay and A. Lakhtakia, “Negative phase velocity in a material with simultaneous mirror-conjugated and racemic chirality characteristics,” New J. Phys. 7, 165 (2005).
[Crossref]

Opt. Express (2)

Photonics Nanostruct. Fundam. Appl. (1)

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[Crossref]

Phys. Rev. B (1)

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B 73, 113104 (2006).
[Crossref]

Phys. Rev. E (1)

T. G. Mackay and A. Lakhtakia, “Plane waves with negative phase velocity in Faraday chiral mediums,” Phys. Rev. E 69, 026602 (2004).
[Crossref]

Phys. Rev. Lett. (1)

C. Monzon and D. W. Forester, “Negative refraction and focusing of circularly polarized waves in optically active media,” Phys. Rev. Lett. 95, 123904 (2005).
[Crossref] [PubMed]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).
[Crossref] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968).
[Crossref]

Other (11)

L. Pasteur, Researches on the molecular asymmetry of natural organic products, English translation of French original, (Alembic Club Reprints Vol. 14, pp. 1–461905), facsimile reproduction by SPIE in a 1990 book.

A. J. Fresnel, in OEvres comple’tes dAugustin Fresnel, edited by H. d. Senarmont, E. Verdet, and L. Fresnel (Imprimerie imperiale, Paris, 1866), Vol. 1.

W. A. Shurcliff and S. S. Ballard, Polarized light, (Van Nostrand Co., Princeton, 1964).

Eugene Hecht, Optics, 3rd Ed. (Addison-Wesley, 1998).

L. D. Landau and E. M. Lifshitz, Electromagnetics of continous media, vol. 8 of Course of Theoretical Physics, 2nd edition, English, (Pergamon Press, 1984).
[PubMed]

A. Sommerfeld, Lectures on Theoretical Physics: Optics (Academic, New York, 1952).

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Boston, 1994).

A. Serdukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science Publishers, Amsterdam, 2001).

A. Lakhtakia, Beltrami Fields In Chiral media (World Scientific Publishing Co. Pte. Ltd., Singapore, 1994).
[Crossref]

A. Ishimaru, Electromagnetic Wave Propagation, Radiation and Scattering (Prentice Hall, Englewood Cliffs, NJ, 1991).

J. A. Kong, Electromagnetic Wave Theory (Wiley, NY, 1986).

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Figures (2)

Fig. 1.
Fig. 1.

The strength relationship of chirality and spatial dispersion. The point of κ μ ε = 1 is singularity, corresponding infinite spatial dispersion coefficient β. When κ μ ε > 1 , β becomes negative for keeping the positive rotation term coefficients with negative εDBF and μDBF .

Fig. 2.
Fig. 2.

With chirality strength increases, εDBF and μDBF reduces quickly from ε and μ to -∞

Equations (16)

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

D ¯ = ε DBF E ¯ + ε DBF β × E ¯ ,
B ¯ = μ DBF H ¯ + μ DBF β × H ¯ .
D ¯ = ε E ¯ + ( χ + i κ ) H ¯ ,
B ¯ = μ H ¯ + ( χ i κ ) E ¯ ,
D ¯ = ε E ¯ + i κ H ¯ ,
B ¯ = μ H ¯ i κ E ¯ .
ε DBF = ε ( 1 κ 2 μ ε ) ,
μ DBF = μ ( 1 κ 2 μ ε ) ,
β = κ ω ( μ ε κ 2 ) .
[ ε i κ i κ μ ] .
w = w e + w m
= D ¯ E ¯ 2 + B ¯ H ¯ 2
= ε E ¯ 2 2 + i κ H ¯ E ¯ + μ H ¯ 2 2 i κ E ¯ H ¯
= ε E ¯ 2 2 + μ H ¯ 2 2 .
D ¯ = ε DBF ( E ¯ + β 1 × E ¯ + β 2 × × E ¯ + ) ,
B ¯ = μ DBF ( H ¯ + β 1 × H ¯ + β 2 × × H ¯ + ) ,

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