Abstract

It is established theoretically that racemic substances characterized by isomers with strong optical rotatory power are capable of producing negative refraction and focusing of arbitrarily polarized waves. A slab of such racemic material, while not chiral, acts just like Veselago’s hypothetical left-handed media slab, providing subwavelength resolution as Pendry’s ideal lens does and opening an avenue for optical and IR realizations. RF-microwave implementations in random and lattice fashion are also proposed.

© 2009 Optical Society of America

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  1. L. Pasteur, “Recherches sur les propriétes spécifiques de deux acides qui composent l'acide racémique,” Ann. Chim. Phys. 28, 56-117 (1850).
  2. K. F. Lindman, “Über eine durch ein isotropes System von spiralförmigen Resonatoren erzeugte Rotations-polarisation der elektromagnetischen Wellen,” Ann. Phys. 63, 621-644 (1920).
    [CrossRef]
  3. A. Sommerfeld, Optics (Academic, 1954).
  4. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ɛ and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  5. P. M. Valanju, R. M. Walser, and A.P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
    [CrossRef] [PubMed]
  6. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  7. J. B. Pendry and S. A. Ramakrishna, “Near field lenses in two dimensions,” J. Phys.: Condens. Matter 14, 8463-8479 (2002).
    [CrossRef]
  8. D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933-2936 (2000).
    [CrossRef] [PubMed]
  9. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  10. D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, “Direct calculation of permeability and permittivity for a left-handed metamaterial,” Appl. Phys. Lett. 77, 2246-2248 (2000).
    [CrossRef]
  11. R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a twodimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489-491 (2001).
    [CrossRef]
  12. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).
    [CrossRef] [PubMed]
  13. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and Enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  14. J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353-1355 (2004).
    [CrossRef] [PubMed]
  15. 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]
  16. M. G. Silveirinha, “Design of linear-to-circular polarization transformers made of long densely packed metallic helices,” IEEE Trans. Antennas Propag. 56, 390-401 (2008).
    [CrossRef]
  17. C. Monzon. Unpublished work, available from the author (Cesar.Monzon@verizon.net). Research carried out in 1999, while with the Raytheon's Antenna/Non-Metallics group, McKinney, Texas.
  18. B. D. H. Tellegen, “The Gyrator: A new electric network element,” Philips Res. Rep. 3, 81-101 (1948).
  19. C. Monzon, “Radiation and scattering in homogeneous general biisotropic regions,” IEEE Trans. Antennas Propag. AP-38, 227-235 (1990) .
    [CrossRef]
  20. C. Monzon, “New reciprocity theorems for chiral, nonactive and biisotropic media,” IEEE Trans. Microwave Theory Tech. 44, 2299-2301 (1996).
    [CrossRef]
  21. C. Monzon, “Scattering by a biisotropic body,” IEEE Trans. Antennas Propag. AP-43, 1288-1296(1995).
  22. C-W. Qiu, H-Y. Yao, L-W. Li, S. Zouhdi, and T-S. Yeo, “Routes to left-handed materials by magnetoelectric couplings,” Phys. Rev. B 75, 245214 (2007).
    [CrossRef]
  23. C-W. Qiu, H-Y. Yao, L-W. Li, S. Zouhdi, and T-S. Yeo, “Backward waves in magnetoelectrically chiral media: Propagation, impedance, and negative refraction,” Phys. Rev. B 75, 155120 (2007)
    [CrossRef]
  24. S. Zhang, Y-S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
    [CrossRef] [PubMed]
  25. S. Tretyakov, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695-706 (2003).
    [CrossRef]
  26. J. Psipopoulos, C. Meiners, and A. F. Jacob, “A scattering approach for the characterization of composite materials,” IEEE Trans. Antennas Propag. 53, 1507-1513 (2005).
    [CrossRef]
  27. G. Busse, J. Reinert, and A. F. Jacob, “Waveguide characterization of chiral material: experiments,” IEEE Trans. Microwave Theory Tech. MTT-47, 297-301 (1999).
    [CrossRef]
  28. Y. Tajitsu, R. Hosoya, T. Maruyama, M. Aoki, Y. Shikinami, M. Date, and E. Fukada, “Huge optical rotatory power of uniaxially oriented film of poly-L-lactic acid,” J. Mater. Sci. Lett. 18, 1785-1787 (1999).
    [CrossRef]

2009

S. Zhang, Y-S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[CrossRef] [PubMed]

2008

M. G. Silveirinha, “Design of linear-to-circular polarization transformers made of long densely packed metallic helices,” IEEE Trans. Antennas Propag. 56, 390-401 (2008).
[CrossRef]

2007

C-W. Qiu, H-Y. Yao, L-W. Li, S. Zouhdi, and T-S. Yeo, “Routes to left-handed materials by magnetoelectric couplings,” Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C-W. Qiu, H-Y. Yao, L-W. Li, S. Zouhdi, and T-S. Yeo, “Backward waves in magnetoelectrically chiral media: Propagation, impedance, and negative refraction,” Phys. Rev. B 75, 155120 (2007)
[CrossRef]

2005

J. Psipopoulos, C. Meiners, and A. F. Jacob, “A scattering approach for the characterization of composite materials,” IEEE Trans. Antennas Propag. 53, 1507-1513 (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]

2004

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353-1355 (2004).
[CrossRef] [PubMed]

2003

S. Tretyakov, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695-706 (2003).
[CrossRef]

2002

P. M. Valanju, R. M. Walser, and A.P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef] [PubMed]

J. B. Pendry and S. A. Ramakrishna, “Near field lenses in two dimensions,” J. Phys.: Condens. Matter 14, 8463-8479 (2002).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a twodimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489-491 (2001).
[CrossRef]

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

2000

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, “Direct calculation of permeability and permittivity for a left-handed metamaterial,” Appl. Phys. Lett. 77, 2246-2248 (2000).
[CrossRef]

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

1999

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and Enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Y. Tajitsu, R. Hosoya, T. Maruyama, M. Aoki, Y. Shikinami, M. Date, and E. Fukada, “Huge optical rotatory power of uniaxially oriented film of poly-L-lactic acid,” J. Mater. Sci. Lett. 18, 1785-1787 (1999).
[CrossRef]

1996

C. Monzon, “New reciprocity theorems for chiral, nonactive and biisotropic media,” IEEE Trans. Microwave Theory Tech. 44, 2299-2301 (1996).
[CrossRef]

1990

C. Monzon, “Radiation and scattering in homogeneous general biisotropic regions,” IEEE Trans. Antennas Propag. AP-38, 227-235 (1990) .
[CrossRef]

1968

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

1948

B. D. H. Tellegen, “The Gyrator: A new electric network element,” Philips Res. Rep. 3, 81-101 (1948).

1920

K. F. Lindman, “Über eine durch ein isotropes System von spiralförmigen Resonatoren erzeugte Rotations-polarisation der elektromagnetischen Wellen,” Ann. Phys. 63, 621-644 (1920).
[CrossRef]

1850

L. Pasteur, “Recherches sur les propriétes spécifiques de deux acides qui composent l'acide racémique,” Ann. Chim. Phys. 28, 56-117 (1850).

Aoki, M.

Y. Tajitsu, R. Hosoya, T. Maruyama, M. Aoki, Y. Shikinami, M. Date, and E. Fukada, “Huge optical rotatory power of uniaxially oriented film of poly-L-lactic acid,” J. Mater. Sci. Lett. 18, 1785-1787 (1999).
[CrossRef]

Busse, G.

G. Busse, J. Reinert, and A. F. Jacob, “Waveguide characterization of chiral material: experiments,” IEEE Trans. Microwave Theory Tech. MTT-47, 297-301 (1999).
[CrossRef]

Date, M.

Y. Tajitsu, R. Hosoya, T. Maruyama, M. Aoki, Y. Shikinami, M. Date, and E. Fukada, “Huge optical rotatory power of uniaxially oriented film of poly-L-lactic acid,” J. Mater. Sci. Lett. 18, 1785-1787 (1999).
[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]

Fukada, E.

Y. Tajitsu, R. Hosoya, T. Maruyama, M. Aoki, Y. Shikinami, M. Date, and E. Fukada, “Huge optical rotatory power of uniaxially oriented film of poly-L-lactic acid,” J. Mater. Sci. Lett. 18, 1785-1787 (1999).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and Enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Hosoya, R.

Y. Tajitsu, R. Hosoya, T. Maruyama, M. Aoki, Y. Shikinami, M. Date, and E. Fukada, “Huge optical rotatory power of uniaxially oriented film of poly-L-lactic acid,” J. Mater. Sci. Lett. 18, 1785-1787 (1999).
[CrossRef]

Jacob, A. F.

J. Psipopoulos, C. Meiners, and A. F. Jacob, “A scattering approach for the characterization of composite materials,” IEEE Trans. Antennas Propag. 53, 1507-1513 (2005).
[CrossRef]

G. Busse, J. Reinert, and A. F. Jacob, “Waveguide characterization of chiral material: experiments,” IEEE Trans. Microwave Theory Tech. MTT-47, 297-301 (1999).
[CrossRef]

Kroll, N.

D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, “Direct calculation of permeability and permittivity for a left-handed metamaterial,” Appl. Phys. Lett. 77, 2246-2248 (2000).
[CrossRef]

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Li, J.

S. Zhang, Y-S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[CrossRef] [PubMed]

Li, L-W.

C-W. Qiu, H-Y. Yao, L-W. Li, S. Zouhdi, and T-S. Yeo, “Routes to left-handed materials by magnetoelectric couplings,” Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C-W. Qiu, H-Y. Yao, L-W. Li, S. Zouhdi, and T-S. Yeo, “Backward waves in magnetoelectrically chiral media: Propagation, impedance, and negative refraction,” Phys. Rev. B 75, 155120 (2007)
[CrossRef]

Lindman, K. F.

K. F. Lindman, “Über eine durch ein isotropes System von spiralförmigen Resonatoren erzeugte Rotations-polarisation der elektromagnetischen Wellen,” Ann. Phys. 63, 621-644 (1920).
[CrossRef]

Lu, X.

S. Zhang, Y-S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[CrossRef] [PubMed]

Maruyama, T.

Y. Tajitsu, R. Hosoya, T. Maruyama, M. Aoki, Y. Shikinami, M. Date, and E. Fukada, “Huge optical rotatory power of uniaxially oriented film of poly-L-lactic acid,” J. Mater. Sci. Lett. 18, 1785-1787 (1999).
[CrossRef]

Meiners, C.

J. Psipopoulos, C. Meiners, and A. F. Jacob, “A scattering approach for the characterization of composite materials,” IEEE Trans. Antennas Propag. 53, 1507-1513 (2005).
[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]

C. Monzon, “New reciprocity theorems for chiral, nonactive and biisotropic media,” IEEE Trans. Microwave Theory Tech. 44, 2299-2301 (1996).
[CrossRef]

C. Monzon, “Radiation and scattering in homogeneous general biisotropic regions,” IEEE Trans. Antennas Propag. AP-38, 227-235 (1990) .
[CrossRef]

C. Monzon, “Scattering by a biisotropic body,” IEEE Trans. Antennas Propag. AP-43, 1288-1296(1995).

C. Monzon. Unpublished work, available from the author (Cesar.Monzon@verizon.net). Research carried out in 1999, while with the Raytheon's Antenna/Non-Metallics group, McKinney, Texas.

Nemat-Nasser, S. C.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a twodimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489-491 (2001).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Park, Y-S.

S. Zhang, Y-S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[CrossRef] [PubMed]

Pasteur, L.

L. Pasteur, “Recherches sur les propriétes spécifiques de deux acides qui composent l'acide racémique,” Ann. Chim. Phys. 28, 56-117 (1850).

Pendry, J. B.

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353-1355 (2004).
[CrossRef] [PubMed]

J. B. Pendry and S. A. Ramakrishna, “Near field lenses in two dimensions,” J. Phys.: Condens. Matter 14, 8463-8479 (2002).
[CrossRef]

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

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and Enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Psipopoulos, J.

J. Psipopoulos, C. Meiners, and A. F. Jacob, “A scattering approach for the characterization of composite materials,” IEEE Trans. Antennas Propag. 53, 1507-1513 (2005).
[CrossRef]

Qiu, C-W.

C-W. Qiu, H-Y. Yao, L-W. Li, S. Zouhdi, and T-S. Yeo, “Routes to left-handed materials by magnetoelectric couplings,” Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C-W. Qiu, H-Y. Yao, L-W. Li, S. Zouhdi, and T-S. Yeo, “Backward waves in magnetoelectrically chiral media: Propagation, impedance, and negative refraction,” Phys. Rev. B 75, 155120 (2007)
[CrossRef]

Ramakrishna, S. A.

J. B. Pendry and S. A. Ramakrishna, “Near field lenses in two dimensions,” J. Phys.: Condens. Matter 14, 8463-8479 (2002).
[CrossRef]

Reinert, J.

G. Busse, J. Reinert, and A. F. Jacob, “Waveguide characterization of chiral material: experiments,” IEEE Trans. Microwave Theory Tech. MTT-47, 297-301 (1999).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and Enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[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]

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a twodimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489-491 (2001).
[CrossRef]

D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, “Direct calculation of permeability and permittivity for a left-handed metamaterial,” Appl. Phys. Lett. 77, 2246-2248 (2000).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a twodimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489-491 (2001).
[CrossRef]

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

Shikinami, Y.

Y. Tajitsu, R. Hosoya, T. Maruyama, M. Aoki, Y. Shikinami, M. Date, and E. Fukada, “Huge optical rotatory power of uniaxially oriented film of poly-L-lactic acid,” J. Mater. Sci. Lett. 18, 1785-1787 (1999).
[CrossRef]

Silveirinha, M. G.

M. G. Silveirinha, “Design of linear-to-circular polarization transformers made of long densely packed metallic helices,” IEEE Trans. Antennas Propag. 56, 390-401 (2008).
[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]

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a twodimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489-491 (2001).
[CrossRef]

D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, “Direct calculation of permeability and permittivity for a left-handed metamaterial,” Appl. Phys. Lett. 77, 2246-2248 (2000).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Sommerfeld, A.

A. Sommerfeld, Optics (Academic, 1954).

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and Enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Tajitsu, Y.

Y. Tajitsu, R. Hosoya, T. Maruyama, M. Aoki, Y. Shikinami, M. Date, and E. Fukada, “Huge optical rotatory power of uniaxially oriented film of poly-L-lactic acid,” J. Mater. Sci. Lett. 18, 1785-1787 (1999).
[CrossRef]

Tellegen, B. D. H.

B. D. H. Tellegen, “The Gyrator: A new electric network element,” Philips Res. Rep. 3, 81-101 (1948).

Tretyakov, S.

S. Tretyakov, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695-706 (2003).
[CrossRef]

Valanju, A.P.

P. M. Valanju, R. M. Walser, and A.P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef] [PubMed]

Valanju, P. M.

P. M. Valanju, R. M. Walser, and A.P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef] [PubMed]

Veselago, V. G.

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

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, “Direct calculation of permeability and permittivity for a left-handed metamaterial,” Appl. Phys. Lett. 77, 2246-2248 (2000).
[CrossRef]

Walser, R. M.

P. M. Valanju, R. M. Walser, and A.P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef] [PubMed]

Yao, H-Y.

C-W. Qiu, H-Y. Yao, L-W. Li, S. Zouhdi, and T-S. Yeo, “Routes to left-handed materials by magnetoelectric couplings,” Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C-W. Qiu, H-Y. Yao, L-W. Li, S. Zouhdi, and T-S. Yeo, “Backward waves in magnetoelectrically chiral media: Propagation, impedance, and negative refraction,” Phys. Rev. B 75, 155120 (2007)
[CrossRef]

Yeo, T-S.

C-W. Qiu, H-Y. Yao, L-W. Li, S. Zouhdi, and T-S. Yeo, “Backward waves in magnetoelectrically chiral media: Propagation, impedance, and negative refraction,” Phys. Rev. B 75, 155120 (2007)
[CrossRef]

C-W. Qiu, H-Y. Yao, L-W. Li, S. Zouhdi, and T-S. Yeo, “Routes to left-handed materials by magnetoelectric couplings,” Phys. Rev. B 75, 245214 (2007).
[CrossRef]

Zhang, S.

S. Zhang, Y-S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[CrossRef] [PubMed]

Zhang, W.

S. Zhang, Y-S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[CrossRef] [PubMed]

Zhang, X.

S. Zhang, Y-S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[CrossRef] [PubMed]

Zouhdi, S.

C-W. Qiu, H-Y. Yao, L-W. Li, S. Zouhdi, and T-S. Yeo, “Backward waves in magnetoelectrically chiral media: Propagation, impedance, and negative refraction,” Phys. Rev. B 75, 155120 (2007)
[CrossRef]

C-W. Qiu, H-Y. Yao, L-W. Li, S. Zouhdi, and T-S. Yeo, “Routes to left-handed materials by magnetoelectric couplings,” Phys. Rev. B 75, 245214 (2007).
[CrossRef]

Ann. Chim. Phys.

L. Pasteur, “Recherches sur les propriétes spécifiques de deux acides qui composent l'acide racémique,” Ann. Chim. Phys. 28, 56-117 (1850).

Ann. Phys.

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Other

C. Monzon. Unpublished work, available from the author (Cesar.Monzon@verizon.net). Research carried out in 1999, while with the Raytheon's Antenna/Non-Metallics group, McKinney, Texas.

A. Sommerfeld, Optics (Academic, 1954).

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Figures (4)

Fig. 1
Fig. 1

Proposed random racemic structures. (a) A racemic spherical unit cell, (b) a racemic structure of chiral unit cells. All helices are metallic and of identical size; the foam is shown transparent.

Fig. 2
Fig. 2

Example of Maxwell–Garnett estimate for densely packed composite spheres (each being a racemic random helix bundle in low density foam). (a) Dispersion relation, (b) constitutive parameters.

Fig. 3
Fig. 3

Proposed racemic cubical lattice structure. (a) Unit cell where antipodal springs have opposite helicity, (b) proposed structure (4 × 3 × 3 cells are shown).

Fig. 4
Fig. 4

Comparison of normalized wavenumber estimates using Maxwell–Garnett for a racemic random helix composite in low-density foam. Here ν ( f ) refers to the combination wherein the “cell” spheres are racemic, ν 1 ( f ) refers to the racemic combination wherein the cell spheres contain single helices, and ν + ( f ) is the purely chiral (L) scenario. In all cases the cell packing fraction and the number of helices per unit volume is the same.

Equations (14)

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D ¯ = ε E ¯ i χ H ¯ , B ¯ = μ H ¯ + i χ E ¯ ,
Re { ν + } < 0 ,
α E E = C h 2 1 ( f f 0 ) 2 i f f Q , α H H = C ( 2 π f μ S ) 2 1 ( f f 0 ) 2 i f f Q ,
α E H = i h C 2 π f μ S 1 ( f f 0 ) 2 i f f Q , α H E = α E H ,
ε ( f ) = 1 + N α E E ( f ) 3 ε 0 Δ ( f ) , μ ( f ) = 1 + N α H H ( f ) 3 μ 0 Δ ( f ) ,
Δ ( f ) = 1 N α E E ( f ) 9 ε 0 N α H H ( f ) 9 μ 0 .
E ¯ = e ¯ e i ν ¯ x ¯ , H ¯ = h ¯ e i ν ¯ x ¯ ,
ν ± = ω μ ε χ , η ± = μ ε = η e .
e ¯ ± = ± i η ± h ¯ ± , h ¯ ± = 1 2 ( s ̂ ± i u ̂ ) ,
[ P ¯ M ¯ ] = [ α E E α E H α H E α H H ] [ E ¯ H ¯ ] ,
ε ( f ) = 1 + N α E E ( f ) 3 ε 0 Δ ( f ) , μ ( f ) = 1 + N α H H ( f ) 3 μ 0 Δ ( f ) ,
χ ( f ) = i N α E H ( f ) 3 ε 0 μ 0 Δ ( f ) , Δ ( f ) = 1 N α E E ( f ) 9 ε 0 N α H H ( f ) 9 μ 0 .
ε eff ( f ) = 1 + 3 φ ( ε ( f ) 1 ) [ μ ( f ) + 2 φ ( μ ( f ) 1 ) ] [ χ ( f ) ] 2 ( 1 φ ) [ ε ( f ) + 2 φ ( ε ( f ) 1 ) ] [ μ ( f ) + 2 φ ( μ ( f ) 1 ) ] [ ( 1 φ ) χ ( f ) ] 2 ,
μ eff ( f ) = 1 + 3 φ ( μ ( f ) 1 ) [ ε ( f ) + 2 φ ( ε ( f ) 1 ) ] [ χ ( f ) ] 2 ( 1 φ ) [ ε ( f ) + 2 φ ( ε ( f ) 1 ) ] [ μ ( f ) + 2 φ ( μ ( f ) 1 ) ] [ ( 1 φ ) χ ( f ) ] 2 ,

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