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. 1-46 1905), facsimile reproduction by SPIE in a 1990 book.
  2. A. J. Fresnel, in OEvres comple‘tes dAugustin Fresnel, H. d. Senarmont, E. Verdet, and L. Fresnel, eds., (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, 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

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

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

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

2003

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

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

1968

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

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]

He, S.

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]

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]

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]

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]

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]

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]

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]

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]

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]

J. Electromagn. Waves Appl.

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.

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

Photonics Nanostruct. Fundam. Appl.

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

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

Phys. Rev. E

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.

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

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.

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

Other

L. Pasteur, Researches on the molecular asymmetry of natural organic products, English translation of French original, (Alembic Club Reprints Vol. 14, pp. 1-46 1905), facsimile reproduction by SPIE in a 1990 book.

A. J. Fresnel, in OEvres comple‘tes dAugustin Fresnel, H. d. Senarmont, E. Verdet, and L. Fresnel, eds., (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, 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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