Abstract

The problem solved here consists of estimating the effective-medium properties of a chiral composite made of a dilute concentration of small noninteracting chiral spheres, randomly suspended in free space. Volume integral equations, to determine the scattering characteristics of an inhomogeneous chiral scatterer, are obtained. These equations are used to derive the general electromagnetic polarizability matrix of a small, homogeneous, chiral sphere embedded in free space. Finally, from the polarizability matrix, several conclusions regarding the effective properties of the chiral composite are obtained.

© 1990 Optical Society of America

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References

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  1. M. P. Silverman, R. B. Sohn, “Effects of Circular Birefringence on Light Propagation and Reflection,” Am. J. Phys. 54, 69–76 (1986).
    [Crossref]
  2. A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer-Verlag, Berlin, 1989).
  3. K. F. Lindman, “Über die durch ein aktives Raumgitter erzeugte Rotations polarisation der elektromagnetischen Wellen,” Ann. Phys. Leipzig 69, 270–284 (1922).
    [Crossref]
  4. I. Tinoco, M. P. Freeman, “The Optical Activity of Oriented Copper Helices. I. Experimental,” J. Phys. Chem. 61, 1196–1200 (1957).
    [Crossref]
  5. T. Guire, M. Umari, V. V. Varadan, V. K. Varadan, “Microwave Measurements on Chiral Composites,” in Abstracts USNC/URSI Radio Science Meeting, Syracuse, NY (6–10 June 1988).
  6. O. Vogl, G. D. Jaycox, F. Xi, K. Hatada, “Helical Polymers: Optical Activity Based on Rigid Macromolecular Conformation,” Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem. 30, 435–436 (1989).
  7. V. V. Varadan, Y. Ma, V. K. Varadan, “Effects of Chiral Microstructure on EM Wave Propagation in a Lossy Dielectric Composite Material,” Radio Sci. 24, 785–792 (1989).
    [Crossref]
  8. D. S. Jones, “Low Frequency Electromagnetic Radiation,” J. Inst. Math. Appl. 23, 421–447 (1979).
    [Crossref]
  9. C. T. Tai, “A Note on the Integral Equations for the Scattering of a Plane Wave by an Electromagnetically Permeable Body,” Electromagnetics 5, 79–88 (1985).
    [Crossref]
  10. R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).
  11. H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, New York, 1983).
  12. W. Weiglhofer, “Delta-Function Identities and Electromagnetic Field Singularities,” Am. J. Phys. 57, 455–456 (1989).
    [Crossref]
  13. K. M. Chen, “Interaction of Electromagnetic Fields with Biological Bodies,” in Research Topics in Electromagnetic Wave Theory, J. A. Kong, Ed. (Wiley, New York, 1980).
  14. D. S. Jones, Methods in Electromagnetic Wave Propagation (Oxford, U.P., London, 1979).
  15. C. F. Bohren, “Light Scattering by an Optically Active Sphere,” Chem. Phys. Lett. 29, 459–462 (1974).
    [Crossref]
  16. S. B. Singham, “Intrinsic Optical Activity in Light Scattering From an Arbitrary Particle,” Chem. Phys. Lett. 130, 139–144 (1986).
    [Crossref]
  17. A. H. Sihvola, I. V. Lindell, “Chiral Maxwell-Garnet Mixing Formula,” Electron. Lett. 26, 118–119 (1990).
    [Crossref]
  18. C. Kittel, Introduction to Solid State Physics (Wiley Eastern, New Delhi, 1974).
  19. J. Applequist, “Optical Activity: Biot’s Bequest,” Am. Sci. 75, 59–68 (1987).
  20. J. C. Monzon, “Radiation and Scattering in Homogeneous General Biisotropic Regions,” IEEE Trans. Antennas Propag AP-38, 227–235 (1990).
    [Crossref]
  21. A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Influence of Impedance Mismatch Between a Chiral Scatterer and the Surrounding Chiral Medium,” J. Mod. Opt. 36, 1385–1392 (1989).
    [Crossref]
  22. V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple Scattering Theory for Waves in Discrete Random Media and Comparison with Experiments,” Radio Sci. 18, 321–327 (1983).
    [Crossref]
  23. V. K. Varadan, V. V. Varadan, Y. Ma, W. F. Hall, “Design of Ferrite-Impregnated Plastics (PVC) as Microwave Absorbers,” IEEE Trans. Microwave Theory Tech. MTT-34, 251–258 (1986).
    [Crossref]
  24. Y. Ma, V. V. Varadan, V. K. Varadan, “Scattered Intensity of a Wave Propagating in a Discrete Random Medium,” Appl. Opt. 27, 2469–2477 (1988).
    [Crossref] [PubMed]
  25. E. U. Condon, “Theories of Optical Rotatory Power,” Rev. Mod. Phys. 9, 432–457 (1937).
    [Crossref]
  26. E. J. Post, Formal Structure of Electromagnetics (North-Holland, Amsterdam, 1962).
  27. Y. Ma, V. K. Varadan, V. V. Varadan, “Prediction of Electromagnetic Properties of Ferrite Composites,” in Progress in Electromagnetics Research, Vol. 3, A. Priou, Ed. (Elsevier, New York, 1990), in press.

1990 (2)

A. H. Sihvola, I. V. Lindell, “Chiral Maxwell-Garnet Mixing Formula,” Electron. Lett. 26, 118–119 (1990).
[Crossref]

J. C. Monzon, “Radiation and Scattering in Homogeneous General Biisotropic Regions,” IEEE Trans. Antennas Propag AP-38, 227–235 (1990).
[Crossref]

1989 (4)

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Influence of Impedance Mismatch Between a Chiral Scatterer and the Surrounding Chiral Medium,” J. Mod. Opt. 36, 1385–1392 (1989).
[Crossref]

O. Vogl, G. D. Jaycox, F. Xi, K. Hatada, “Helical Polymers: Optical Activity Based on Rigid Macromolecular Conformation,” Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem. 30, 435–436 (1989).

V. V. Varadan, Y. Ma, V. K. Varadan, “Effects of Chiral Microstructure on EM Wave Propagation in a Lossy Dielectric Composite Material,” Radio Sci. 24, 785–792 (1989).
[Crossref]

W. Weiglhofer, “Delta-Function Identities and Electromagnetic Field Singularities,” Am. J. Phys. 57, 455–456 (1989).
[Crossref]

1988 (1)

1987 (1)

J. Applequist, “Optical Activity: Biot’s Bequest,” Am. Sci. 75, 59–68 (1987).

1986 (3)

S. B. Singham, “Intrinsic Optical Activity in Light Scattering From an Arbitrary Particle,” Chem. Phys. Lett. 130, 139–144 (1986).
[Crossref]

V. K. Varadan, V. V. Varadan, Y. Ma, W. F. Hall, “Design of Ferrite-Impregnated Plastics (PVC) as Microwave Absorbers,” IEEE Trans. Microwave Theory Tech. MTT-34, 251–258 (1986).
[Crossref]

M. P. Silverman, R. B. Sohn, “Effects of Circular Birefringence on Light Propagation and Reflection,” Am. J. Phys. 54, 69–76 (1986).
[Crossref]

1985 (1)

C. T. Tai, “A Note on the Integral Equations for the Scattering of a Plane Wave by an Electromagnetically Permeable Body,” Electromagnetics 5, 79–88 (1985).
[Crossref]

1983 (1)

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple Scattering Theory for Waves in Discrete Random Media and Comparison with Experiments,” Radio Sci. 18, 321–327 (1983).
[Crossref]

1979 (1)

D. S. Jones, “Low Frequency Electromagnetic Radiation,” J. Inst. Math. Appl. 23, 421–447 (1979).
[Crossref]

1974 (1)

C. F. Bohren, “Light Scattering by an Optically Active Sphere,” Chem. Phys. Lett. 29, 459–462 (1974).
[Crossref]

1957 (1)

I. Tinoco, M. P. Freeman, “The Optical Activity of Oriented Copper Helices. I. Experimental,” J. Phys. Chem. 61, 1196–1200 (1957).
[Crossref]

1937 (1)

E. U. Condon, “Theories of Optical Rotatory Power,” Rev. Mod. Phys. 9, 432–457 (1937).
[Crossref]

1922 (1)

K. F. Lindman, “Über die durch ein aktives Raumgitter erzeugte Rotations polarisation der elektromagnetischen Wellen,” Ann. Phys. Leipzig 69, 270–284 (1922).
[Crossref]

Applequist, J.

J. Applequist, “Optical Activity: Biot’s Bequest,” Am. Sci. 75, 59–68 (1987).

Bohren, C. F.

C. F. Bohren, “Light Scattering by an Optically Active Sphere,” Chem. Phys. Lett. 29, 459–462 (1974).
[Crossref]

Bringi, V. N.

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple Scattering Theory for Waves in Discrete Random Media and Comparison with Experiments,” Radio Sci. 18, 321–327 (1983).
[Crossref]

Chen, H. C.

H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, New York, 1983).

Chen, K. M.

K. M. Chen, “Interaction of Electromagnetic Fields with Biological Bodies,” in Research Topics in Electromagnetic Wave Theory, J. A. Kong, Ed. (Wiley, New York, 1980).

Condon, E. U.

E. U. Condon, “Theories of Optical Rotatory Power,” Rev. Mod. Phys. 9, 432–457 (1937).
[Crossref]

Freeman, M. P.

I. Tinoco, M. P. Freeman, “The Optical Activity of Oriented Copper Helices. I. Experimental,” J. Phys. Chem. 61, 1196–1200 (1957).
[Crossref]

Guire, T.

T. Guire, M. Umari, V. V. Varadan, V. K. Varadan, “Microwave Measurements on Chiral Composites,” in Abstracts USNC/URSI Radio Science Meeting, Syracuse, NY (6–10 June 1988).

Hall, W. F.

V. K. Varadan, V. V. Varadan, Y. Ma, W. F. Hall, “Design of Ferrite-Impregnated Plastics (PVC) as Microwave Absorbers,” IEEE Trans. Microwave Theory Tech. MTT-34, 251–258 (1986).
[Crossref]

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

Hatada, K.

O. Vogl, G. D. Jaycox, F. Xi, K. Hatada, “Helical Polymers: Optical Activity Based on Rigid Macromolecular Conformation,” Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem. 30, 435–436 (1989).

Ishimaru, A.

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple Scattering Theory for Waves in Discrete Random Media and Comparison with Experiments,” Radio Sci. 18, 321–327 (1983).
[Crossref]

Jaycox, G. D.

O. Vogl, G. D. Jaycox, F. Xi, K. Hatada, “Helical Polymers: Optical Activity Based on Rigid Macromolecular Conformation,” Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem. 30, 435–436 (1989).

Jones, D. S.

D. S. Jones, “Low Frequency Electromagnetic Radiation,” J. Inst. Math. Appl. 23, 421–447 (1979).
[Crossref]

D. S. Jones, Methods in Electromagnetic Wave Propagation (Oxford, U.P., London, 1979).

Kittel, C.

C. Kittel, Introduction to Solid State Physics (Wiley Eastern, New Delhi, 1974).

Lakhtakia, A.

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Influence of Impedance Mismatch Between a Chiral Scatterer and the Surrounding Chiral Medium,” J. Mod. Opt. 36, 1385–1392 (1989).
[Crossref]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer-Verlag, Berlin, 1989).

Lindell, I. V.

A. H. Sihvola, I. V. Lindell, “Chiral Maxwell-Garnet Mixing Formula,” Electron. Lett. 26, 118–119 (1990).
[Crossref]

Lindman, K. F.

K. F. Lindman, “Über die durch ein aktives Raumgitter erzeugte Rotations polarisation der elektromagnetischen Wellen,” Ann. Phys. Leipzig 69, 270–284 (1922).
[Crossref]

Ma, Y.

V. V. Varadan, Y. Ma, V. K. Varadan, “Effects of Chiral Microstructure on EM Wave Propagation in a Lossy Dielectric Composite Material,” Radio Sci. 24, 785–792 (1989).
[Crossref]

Y. Ma, V. V. Varadan, V. K. Varadan, “Scattered Intensity of a Wave Propagating in a Discrete Random Medium,” Appl. Opt. 27, 2469–2477 (1988).
[Crossref] [PubMed]

V. K. Varadan, V. V. Varadan, Y. Ma, W. F. Hall, “Design of Ferrite-Impregnated Plastics (PVC) as Microwave Absorbers,” IEEE Trans. Microwave Theory Tech. MTT-34, 251–258 (1986).
[Crossref]

Y. Ma, V. K. Varadan, V. V. Varadan, “Prediction of Electromagnetic Properties of Ferrite Composites,” in Progress in Electromagnetics Research, Vol. 3, A. Priou, Ed. (Elsevier, New York, 1990), in press.

Monzon, J. C.

J. C. Monzon, “Radiation and Scattering in Homogeneous General Biisotropic Regions,” IEEE Trans. Antennas Propag AP-38, 227–235 (1990).
[Crossref]

Post, E. J.

E. J. Post, Formal Structure of Electromagnetics (North-Holland, Amsterdam, 1962).

Sihvola, A. H.

A. H. Sihvola, I. V. Lindell, “Chiral Maxwell-Garnet Mixing Formula,” Electron. Lett. 26, 118–119 (1990).
[Crossref]

Silverman, M. P.

M. P. Silverman, R. B. Sohn, “Effects of Circular Birefringence on Light Propagation and Reflection,” Am. J. Phys. 54, 69–76 (1986).
[Crossref]

Singham, S. B.

S. B. Singham, “Intrinsic Optical Activity in Light Scattering From an Arbitrary Particle,” Chem. Phys. Lett. 130, 139–144 (1986).
[Crossref]

Sohn, R. B.

M. P. Silverman, R. B. Sohn, “Effects of Circular Birefringence on Light Propagation and Reflection,” Am. J. Phys. 54, 69–76 (1986).
[Crossref]

Tai, C. T.

C. T. Tai, “A Note on the Integral Equations for the Scattering of a Plane Wave by an Electromagnetically Permeable Body,” Electromagnetics 5, 79–88 (1985).
[Crossref]

Tinoco, I.

I. Tinoco, M. P. Freeman, “The Optical Activity of Oriented Copper Helices. I. Experimental,” J. Phys. Chem. 61, 1196–1200 (1957).
[Crossref]

Umari, M.

T. Guire, M. Umari, V. V. Varadan, V. K. Varadan, “Microwave Measurements on Chiral Composites,” in Abstracts USNC/URSI Radio Science Meeting, Syracuse, NY (6–10 June 1988).

Varadan, V. K.

V. V. Varadan, Y. Ma, V. K. Varadan, “Effects of Chiral Microstructure on EM Wave Propagation in a Lossy Dielectric Composite Material,” Radio Sci. 24, 785–792 (1989).
[Crossref]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Influence of Impedance Mismatch Between a Chiral Scatterer and the Surrounding Chiral Medium,” J. Mod. Opt. 36, 1385–1392 (1989).
[Crossref]

Y. Ma, V. V. Varadan, V. K. Varadan, “Scattered Intensity of a Wave Propagating in a Discrete Random Medium,” Appl. Opt. 27, 2469–2477 (1988).
[Crossref] [PubMed]

V. K. Varadan, V. V. Varadan, Y. Ma, W. F. Hall, “Design of Ferrite-Impregnated Plastics (PVC) as Microwave Absorbers,” IEEE Trans. Microwave Theory Tech. MTT-34, 251–258 (1986).
[Crossref]

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple Scattering Theory for Waves in Discrete Random Media and Comparison with Experiments,” Radio Sci. 18, 321–327 (1983).
[Crossref]

Y. Ma, V. K. Varadan, V. V. Varadan, “Prediction of Electromagnetic Properties of Ferrite Composites,” in Progress in Electromagnetics Research, Vol. 3, A. Priou, Ed. (Elsevier, New York, 1990), in press.

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer-Verlag, Berlin, 1989).

T. Guire, M. Umari, V. V. Varadan, V. K. Varadan, “Microwave Measurements on Chiral Composites,” in Abstracts USNC/URSI Radio Science Meeting, Syracuse, NY (6–10 June 1988).

Varadan, V. V.

V. V. Varadan, Y. Ma, V. K. Varadan, “Effects of Chiral Microstructure on EM Wave Propagation in a Lossy Dielectric Composite Material,” Radio Sci. 24, 785–792 (1989).
[Crossref]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Influence of Impedance Mismatch Between a Chiral Scatterer and the Surrounding Chiral Medium,” J. Mod. Opt. 36, 1385–1392 (1989).
[Crossref]

Y. Ma, V. V. Varadan, V. K. Varadan, “Scattered Intensity of a Wave Propagating in a Discrete Random Medium,” Appl. Opt. 27, 2469–2477 (1988).
[Crossref] [PubMed]

V. K. Varadan, V. V. Varadan, Y. Ma, W. F. Hall, “Design of Ferrite-Impregnated Plastics (PVC) as Microwave Absorbers,” IEEE Trans. Microwave Theory Tech. MTT-34, 251–258 (1986).
[Crossref]

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple Scattering Theory for Waves in Discrete Random Media and Comparison with Experiments,” Radio Sci. 18, 321–327 (1983).
[Crossref]

Y. Ma, V. K. Varadan, V. V. Varadan, “Prediction of Electromagnetic Properties of Ferrite Composites,” in Progress in Electromagnetics Research, Vol. 3, A. Priou, Ed. (Elsevier, New York, 1990), in press.

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer-Verlag, Berlin, 1989).

T. Guire, M. Umari, V. V. Varadan, V. K. Varadan, “Microwave Measurements on Chiral Composites,” in Abstracts USNC/URSI Radio Science Meeting, Syracuse, NY (6–10 June 1988).

Vogl, O.

O. Vogl, G. D. Jaycox, F. Xi, K. Hatada, “Helical Polymers: Optical Activity Based on Rigid Macromolecular Conformation,” Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem. 30, 435–436 (1989).

Weiglhofer, W.

W. Weiglhofer, “Delta-Function Identities and Electromagnetic Field Singularities,” Am. J. Phys. 57, 455–456 (1989).
[Crossref]

Xi, F.

O. Vogl, G. D. Jaycox, F. Xi, K. Hatada, “Helical Polymers: Optical Activity Based on Rigid Macromolecular Conformation,” Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem. 30, 435–436 (1989).

Am. J. Phys. (2)

M. P. Silverman, R. B. Sohn, “Effects of Circular Birefringence on Light Propagation and Reflection,” Am. J. Phys. 54, 69–76 (1986).
[Crossref]

W. Weiglhofer, “Delta-Function Identities and Electromagnetic Field Singularities,” Am. J. Phys. 57, 455–456 (1989).
[Crossref]

Am. Sci. (1)

J. Applequist, “Optical Activity: Biot’s Bequest,” Am. Sci. 75, 59–68 (1987).

Ann. Phys. Leipzig (1)

K. F. Lindman, “Über die durch ein aktives Raumgitter erzeugte Rotations polarisation der elektromagnetischen Wellen,” Ann. Phys. Leipzig 69, 270–284 (1922).
[Crossref]

Appl. Opt. (1)

Chem. Phys. Lett. (2)

C. F. Bohren, “Light Scattering by an Optically Active Sphere,” Chem. Phys. Lett. 29, 459–462 (1974).
[Crossref]

S. B. Singham, “Intrinsic Optical Activity in Light Scattering From an Arbitrary Particle,” Chem. Phys. Lett. 130, 139–144 (1986).
[Crossref]

Electromagnetics (1)

C. T. Tai, “A Note on the Integral Equations for the Scattering of a Plane Wave by an Electromagnetically Permeable Body,” Electromagnetics 5, 79–88 (1985).
[Crossref]

Electron. Lett. (1)

A. H. Sihvola, I. V. Lindell, “Chiral Maxwell-Garnet Mixing Formula,” Electron. Lett. 26, 118–119 (1990).
[Crossref]

IEEE Trans. Antennas Propag (1)

J. C. Monzon, “Radiation and Scattering in Homogeneous General Biisotropic Regions,” IEEE Trans. Antennas Propag AP-38, 227–235 (1990).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

V. K. Varadan, V. V. Varadan, Y. Ma, W. F. Hall, “Design of Ferrite-Impregnated Plastics (PVC) as Microwave Absorbers,” IEEE Trans. Microwave Theory Tech. MTT-34, 251–258 (1986).
[Crossref]

J. Inst. Math. Appl. (1)

D. S. Jones, “Low Frequency Electromagnetic Radiation,” J. Inst. Math. Appl. 23, 421–447 (1979).
[Crossref]

J. Mod. Opt. (1)

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Influence of Impedance Mismatch Between a Chiral Scatterer and the Surrounding Chiral Medium,” J. Mod. Opt. 36, 1385–1392 (1989).
[Crossref]

J. Phys. Chem. (1)

I. Tinoco, M. P. Freeman, “The Optical Activity of Oriented Copper Helices. I. Experimental,” J. Phys. Chem. 61, 1196–1200 (1957).
[Crossref]

Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem. (1)

O. Vogl, G. D. Jaycox, F. Xi, K. Hatada, “Helical Polymers: Optical Activity Based on Rigid Macromolecular Conformation,” Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem. 30, 435–436 (1989).

Radio Sci. (2)

V. V. Varadan, Y. Ma, V. K. Varadan, “Effects of Chiral Microstructure on EM Wave Propagation in a Lossy Dielectric Composite Material,” Radio Sci. 24, 785–792 (1989).
[Crossref]

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple Scattering Theory for Waves in Discrete Random Media and Comparison with Experiments,” Radio Sci. 18, 321–327 (1983).
[Crossref]

Rev. Mod. Phys. (1)

E. U. Condon, “Theories of Optical Rotatory Power,” Rev. Mod. Phys. 9, 432–457 (1937).
[Crossref]

Other (9)

E. J. Post, Formal Structure of Electromagnetics (North-Holland, Amsterdam, 1962).

Y. Ma, V. K. Varadan, V. V. Varadan, “Prediction of Electromagnetic Properties of Ferrite Composites,” in Progress in Electromagnetics Research, Vol. 3, A. Priou, Ed. (Elsevier, New York, 1990), in press.

K. M. Chen, “Interaction of Electromagnetic Fields with Biological Bodies,” in Research Topics in Electromagnetic Wave Theory, J. A. Kong, Ed. (Wiley, New York, 1980).

D. S. Jones, Methods in Electromagnetic Wave Propagation (Oxford, U.P., London, 1979).

C. Kittel, Introduction to Solid State Physics (Wiley Eastern, New Delhi, 1974).

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, New York, 1983).

T. Guire, M. Umari, V. V. Varadan, V. K. Varadan, “Microwave Measurements on Chiral Composites,” in Abstracts USNC/URSI Radio Science Meeting, Syracuse, NY (6–10 June 1988).

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer-Verlag, Berlin, 1989).

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Figures (1)

Fig. 1
Fig. 1

Schematic of the scattering problem for which the coupled volume integral equations are developed in Sec. II.

Equations (56)

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

× E - i ω μ 0 H = 0 ,             × H + i ω 0 E = 0.
D = [ E + β × E ] ,             B = μ [ H + β × H ] ,
× E = γ 2 β E + i ω μ ( γ / k ) 2 H ,             × H = γ 2 β H - i ω ( γ / k ) 2 E ,
× E - i ω μ 0 H = - K ,             × H + i ω 0 E = J ,
K = - γ 2 β E - i ω [ μ ( γ / k ) 2 - μ 0 ] H ,
J = γ 2 β H - i ω [ ( γ / k ) 2 - 0 ] E
B 0 ( r , r ) = ( J + / k 0 2 ) g 0 ( r , r ) ,
g 0 ( r , r ) = exp ( i k 0 r - r ) / 4 π r - r
E ( r ) - E inc ( r ) = - i ω μ 0 V d v B 0 ( r , r ) · J ( r ) - × V d v B 0 ( r , r ) · K ( r ) ,
H ( r ) - H inc ( r ) = i ω 0 V d v B 0 ( r , r ) · K ( r ) + × V d v B 0 ( r , r ) · J ( r ) .
g 0 ( r , r ) ~ exp ( - i k 0 u r · r ) exp ( i k 0 r ) / 4 π r ,
E ( r ) - E inc ( r ) ~ { i ω μ 0 ( J - u r u r ) · V d v exp ( - i k 0 u r · r ) J ( r ) - i k 0 u r × V d v exp ( - i k 0 u r · r ) K ( r ) } exp ( i k 0 r ) / 4 π r ,
H ( r ) - H inc ( r ) ~ { i ω 0 ( J - u r u r ) · V d v exp ( - i k 0 u r · r ) K ( r ) - i k 0 u r × V d v exp ( - i k 0 u r · r ) J ( r ) } exp ( i k 0 r ) / 4 π r .
E ( r ) = E inc ( r ) + J ( r ) / ( 3 i ω 0 ) + PV { i ω μ 0 V d v J ( r ) · B 0 ( r , r ) - J ( r ) / ( 3 i ω 0 ) - V d v K ( r ) · [ × B 0 ( r , r ) ] } ; r V ,
H ( r ) = H inc ( r ) + K ( r ) / ( 3 i ω μ 0 ) + PV { i ω 0 V d v K ( r ) · B 0 ( r , r ) - K ( r ) / ( 3 i ω μ 0 ) + V d v J ( r ) · [ × B 0 ( r , r ) ] } ; r V ,
- i ω p ( u r ) = V d v exp ( - i k 0 u r · r ) J ( r ) ,
- i ω m ( u r ) = V d v exp ( - i k 0 u r · r ) K ( r ) .
E sc ( r ) ~ [ ω 2 μ 0 ( J - u r u r ) · p ( u r ) - ω k 0 u r × m ( u r ) ] exp ( i k 0 r ) / 4 π r ,
H sc ( r ) ~ [ ω 2 0 ( J - u r u r ) · m ( u r ) + ω k 0 u r × p ( u r ) ] exp ( i k 0 r ) / 4 π r .
p 0 = ( i / ω ) V d v J ( r ) ,
m 0 = ( i / ω ) V d v K ( r ) .
p 0 = V d v ( γ 2 / k 2 - 0 ) E ( r ) + V d v ( i ω μ β γ 2 / k 2 ) H ( r ) ,
m 0 = V d v ( μ γ 2 / k 2 - μ 0 ) H ( r ) + V d v ( i ω μ β γ 2 / k 2 ) E ( r ) .
E ( 0 ) = E inc ( 0 ) + J ( 0 ) / ( 3 i ω 0 ) ,
H ( 0 ) = H inc ( 0 ) + K ( 0 ) / ( 3 i ω μ 0 ) .
E ( 0 ) = [ 3 ( μ r γ 2 / k 2 + 2 ) E inc ( 0 ) + 3 ( γ 2 β / i ω 0 ) H inc ( 0 ) ] / Δ ,
H ( 0 ) = [ 3 ( r γ 2 / k 2 + 2 ) H inc ( 0 ) - 3 ( γ 2 β / i ω μ 0 ) E inc ( 0 ) ] / Δ ,
r = / 0 ,             μ r = μ / μ 0 ,             Δ = ( γ 2 / k 2 ) [ ( r + 2 ) ( μ r + 2 ) - 4 k 2 β 2 ] .
( p 0 m 0 ) = ( α ee i α em - i α em α mm ) ( E inc H inc ) = α · ( E inc H inc )
α ee = ( 4 π 0 a 3 ) [ ( r - 1 ) ( μ r + 2 ) + 2 k 2 β 2 ] / [ ( r + 2 ) ( μ r + 2 ) - 4 k 2 β 2 ] ,
α mm = ( 4 π μ 0 a 3 ) [ ( r + 2 ) ( μ r - 1 ) + 2 k 2 β 2 ] / [ ( r + 2 ) ( μ r + 2 ) - 4 k 2 β 2 ] ,
α em = ( 12 π 0 μ 0 a 3 ) [ ω r μ r β ] / [ ( r + 2 ) ( μ r + 2 ) - 4 k 2 β 2 ]
α ( - β ) = transpose { α ( β ) } .
P = N p 0 ,             M = N m 0 .
D = ( 0 + N α ee ) E + i N α em H ,
B = ( μ 0 + N α mm ) H - i N α em E ,
D = ( T ) E + ζ ( T ) H ,             B = μ ( T ) H - ζ ( T ) E
( T ) = 0 + N α ee ,             μ ( T ) = μ 0 + N α mm ,             ζ ( T ) = i N α em ,
D = ( DBF ) [ E + β ( DBF ) × E ] ,             B = μ ( DBF ) [ H + β ( DBF ) × H ] ,
( DBF ) = ( 0 + N α ee ) - ( N α em ) 2 / ( μ 0 + N α mm ) ,
μ ( DBF ) = ( μ 0 + N α mm ) - ( N α em ) 2 / ( 0 + N α ee ) ,
β ( DBF ) = ( N α em / ω ) / [ ( 0 + N α ee ) ( μ 0 + N α mm ) - ( N α em ) 2 ]
( DBF ) = ( T ) = 0 [ 1 + 4 π N a 3 ( r - 1 ) / ( r + 2 ) ] ,
μ ( DBF ) = μ ( T ) = μ 0 [ 1 + 4 π N a 3 ( μ r - 1 ) / ( μ r + 2 ) ] ,
D = ( C ) E + i ω χ ( C ) H ,             B = μ ( C ) H - i ω χ ( C ) E ;
( C ) = 0 + N a ee , μ ( C ) = μ 0 + N α mm , χ ( C ) = N α em / ω .
D = ( P ) E + i ξ ( P ) B ,             H = ( 1 / μ ( P ) ) B + i ξ ( P ) E ;
( P ) = ( 0 + N α ee ) - ( N α em ) 2 / ( μ 0 + N α mm ) ,
μ ( P ) = μ 0 + N α mm ,
ξ ( P ) = ( N α em ) / ( μ 0 + N α mm ) .
α ee = ( DBF ) - 0 ( 1 - ω 2 ( DBF ) μ ( DBF ) β ( DBF ) 2 ) N ( 1 - ω 2 ( DBF ) μ ( DBF ) β ( DBF ) 2 ) ,
α mm = μ ( DBF ) - μ 0 ( 1 - ω 2 ( DBF ) μ ( DBF ) β ( DBF ) 2 ) N ( 1 - ω 2 ( DBF ) μ ( DBF ) β ( DBF ) 2 ) ,
α em = ω ( DBF ) μ ( DBF ) β ( DBF ) N ( 1 - ω 2 ( DBF ) μ ( DBF ) β ( DBF ) 2 ) .
/ o = 8 π 2 a 6 μ 0 0 + 4 π a 3 ( α ee μ 0 + α mm 0 ) + 2 ( α ee α mm - α em 2 ) 8 π 2 a 6 μ 0 0 + 2 π a 3 ( 2 α mm 0 - α ee μ 0 ) - ( α ee α mm - α em 2 ) ,
μ / μ o = 8 π 2 a 6 μ 0 0 + 4 π a 3 ( a ee μ 0 + α mm 0 ) + 2 ( α ee α mm - α em 2 ) 8 π 2 a 6 μ 0 0 + 2 π a 3 ( 2 α ee μ 0 - α mm 0 ) - ( α ee α mm - α em 2 ) ,
β = 3 π a 3 α em / ω 4 π 2 a 6 μ 0 0 + 2 π a 3 ( α mm 0 + α ee μ 0 ) + ( α ee α mm - α em 2 ) ,

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