Abstract

Several aspects of electromagnetic wave propagation and scattering in isotropic chiral media (D = E + β∊▽ × E, B = μH + βμ▽× H) are explored here. All four field vectors, E, H, D, and B, satisfy the same governing differential equation, which reduces to the vector Helmholtz equation when β = 0. Vector and scalar potentials have been postulated. Conservation of energy and momentum are examined. Some properties, consequences, and computationally attractive forms of the applicable infinite-medium Green’s function have been explored. Finally, the mathematical expression of Huygens’s principle, as applicable to chiral media, has also been derived and employed to set up a scattering formalism and to establish the forward plane-wave-scattering amplitude theorems. Several of the results given that pertain to the field equations and Green’s dyadic are available for constitutive equations other than those mentioned above; these results, along with some others, have been given now for the above-mentioned constitutive equations. The derivations of Huygens’s principle and other developments described here have not been given earlier, to our knowledge, for any pertinent set of constitutive equations. With advances in polymer science, the formalisms developed here may be useful in the utilization of artificial chiral dielectrics at suboptical and microwave frequencies; application to vision research is also anticipated.

© 1988 Optical Society of America

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  1. E. J. Post, Formal Structure of Electromagnetics (North-Holland, Amsterdam, 1962), Chap. 8.
  2. A. Lakhtakia, V. V. Varadan, V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral-chiral interface,” IEEE Trans. Electromag. Compat. EC-28, 90–95 (1986).
    [CrossRef]
  3. M. P. Silverman, R. B. Sohn, “Effects of circular birefringence on light propagation and reflection,” Am. J. Phys. 54, 69–76 (1986).
    [CrossRef]
  4. E. Charney, The Molecular Basis of Optical Activity (Krieger, Tampa, Fla., 1979).
  5. L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, Cambridge, 1982).
  6. M. Born, Optik (Springer-Verlag, Heidelberg, 1972), p. 412.
  7. C. F. Bohren, “Light scattering by optically active particles,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1975).
  8. R. A. Satten, “Time-reversal symmetry and electromagnetic polarization fields,” J. Chem. Phys. 28, 742–743 (1958).
    [CrossRef]
  9. M. P. Silverman, “Reflection and refraction at the surface of a chiral medium: comparison of gyrotropic constitutive relations invariant or noninvariant under a duality transformation,” J. Opt. Soc. Am. A 3, 830–837 (1986).
    [CrossRef]
  10. M. P. Silverman, “Specular light scattering from a chiral medium: unambiguous test of gyrotropic constitutive equations,” Lett. Nuovo Cimento 43, 378–382 (1985).
    [CrossRef]
  11. C. F. Bohren, “Angular dependence of the scattering contribution to circular dichroism,” Chem. Phys. Lett. 40, 391–396 (1976).
    [CrossRef]
  12. F. I. Fedorov, “On the theory of optical activity in crystals. I. The law of conservation of energy and the optical activity tensors,” Opt. Spectrosc. (USSR) 6, 49–53 (1959).
  13. F. I. Fedorov, “On the theory of optical activity in crystals. II. Crystals of cubic symmetry and plane classes of central symmetry,” Opt. Spectrosc. (USSR) 6, 237–240 (1959).
  14. B. V. Bokut’, F. I. Fedorov, “On the theory of optical activity in crystals. III. General equations of normals,” Opt. Spectrosc. (USSR) 6, 342–344 (1959).
  15. C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
    [CrossRef]
  16. C. F. Bohren, “Scattering of electromagnetic waves by an optically active spherical shell,” J. Chem. Phys. 62, 1566–1571 (1975).
    [CrossRef]
  17. C. F. Bohren, “Scattering of electromagnetic waves by an optically active cylinder,” J. Colloid Interface Sci. 66, 105–109 (1978).
    [CrossRef]
  18. A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Scattering and absorption characteristics of lossy dielectric, chiral, non-spherical objects,” Appl. Opt. 24, 4146–4154 (1985).
    [CrossRef] [PubMed]
  19. E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
    [CrossRef]
  20. B. D. H. Tellegen, “The gyrator: a new electric network element,” Phillips Res. Rep. 3, 81–101 (1948).
  21. C. M. Krowne, “Electromagnetic theorems for complex anisotropic medium,” IEEE Trans. Antennas Propag. AP-32, 1224–1230 (1984).
    [CrossRef]
  22. LI. G. Chambers, “Propagation in a gyrational medium,” Q. J. Mech. Appl. Math. 9, 360–370 (1956).This paper contains several errors, chiefly as follows: Eqs. (4.6) are not a necessary consequence of Eqs. (4.5), and Sec. 8 appears to imply a Green’s function of the kind Fexp(ikr)/R, which is incorrect.
    [CrossRef]
  23. H. Unz, “Electromagnetic radiation in drifting Tellegen anisotropic medium,” IEEE Trans. Antennas Propag. 12, 573–578 (1964).
  24. D. L. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1978).The isotropic Post equations have been derived here by considering the medium to be a suspension of small helices in an achiral host medium.
    [CrossRef]
  25. H. Eyring, J. Walter, G. E. Kimball, Quantum Chemistry (Wiley, New York, 1944), Chap. 17.
  26. S. Bassiri, N. Engheta, C. H. Papas, “Dyadic Green’s function and dipole radiation in chiral media,” Antenna Lab. Rep. no. 118, (California Institute of Technology, Pasadena, Calif., 1985);“Dyadic Green’s function and dipole radiation in chiral media,” Alta Freq. 55, 83–88 (1986).
  27. D. K. Cheng, J. A. Kong, “Covariant descriptions of bianisotropic media,” Proc. IEEE 56, 248–251 (1968).The covariant constitutive equations given here are precisely the same as those of Post.1
    [CrossRef]
  28. J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE 60, 1036–1046 (1972).An infinite-medium Green’s dyadic, expressed as an integral in the three-dimensional spatial-frequency space, for the bianisotropic Tellegen media has been given here.
    [CrossRef]
  29. The transformation of the bianisotropic Tellegen equations into the bianisotropic Post equations involves a redefinition of the permittivity and the permability tensors; this is quite clear from Eq. (5) of Ref. 28.
  30. J. van Bladel, Relativity and Engineering (Springer-Verlag, Berlin, 1984).To a stationary observer, even a moving isotropic medium appears to be bianisotropic. Thus moving media can be described by the bianisotropic Post Eqs. (6a) and (6b), which are Lorentz covariant. This monograph contains an excellent account of the work done in this area since the turn of this century, although it should be noted that the work of Kong and his colleagues has not been cited here.
    [CrossRef]
  31. J. A. Kong, D. K. Cheng, “Wave reflections from a conducting surface with a moving uniaxial sheath,” IEEE Trans. Antennas Propag. 16, 577–583 (1968).
    [CrossRef]
  32. D. K. Cheng, J. A. Kong, “Time-harmonic fields in source-free bianisotropic media,” J. Appl. Phys. 39, 5792–5796 (1968).Normal incidence of plane waves on stationary isotropic or moving uniaxial media has been considered here. The moving uniaxial medium has been modeled by the bianisotropic Post Eqs. (6a) and (6b).
    [CrossRef]
  33. J. A. Kong, “Optics of bianisotropic media,” J. Opt. Soc. Am. 64, 1304–1308 (1974).Plane-wave propagation in and dispersion equations for bianisotropic Tellegen media have been considered here.
    [CrossRef]
  34. J. A. Kong, D. K. Cheng, “Wave behavior at an interface of a semi-infinite moving anisotropic medium,” J. Appl. Phys. 39, 2282–2286 (1968).Plane-wave reflection and refraction characteristics of a plane interface between free space and a bianisotropic Post medium have been derived here.
    [CrossRef]
  35. C. Altman, A. Schatzberg, K. Suchy, “Symmetry transformations and reversal of currents and fields in bounded (bi)anisotropic media,” IEEE Trans. Antennas Propag. AP-32, 1204–1210 (1984).
    [CrossRef]
  36. L. S. Corley, O. Vogl, “Optically active polymers,” Polymer Bull. 3, 211–217(1980).
    [CrossRef]
  37. W. J. Harris, O. Vogl, “Synthesis of optically active polymers,” Polymer Preprints22, 309–310 (1981).
  38. G. Heppke, D. Lötzsch, F. Oestreicher, “Chirale dotier-stoffe mit ausserwöhnlich hohem verdrillungsvermögen,” Z. Naturforsch. Teil A 41, 1214–1218 (1986).
  39. N. Engheta, A. R. Mickelson, “Transition radiation caused by a chiral plate,” IEEE Trans. Antennas Propag. AP-30, 1213–1216 (1982).
    [CrossRef]
  40. H. L. deVries, A. Spoor, R. Jielof, “Properties of the eye with respect to polarized light,” Physica 19, 419–432 (1953).
    [CrossRef]
  41. L. J. Bour, N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21, 1413–1421 (1981).
    [CrossRef] [PubMed]
  42. G. J. Van Blokland, S. C. Verhelst, “Corneal polarization in the living human eye explained with a biaxial model,” J. Opt. Soc. Am. A 4, 82–90 (1987).
    [CrossRef] [PubMed]
  43. H. Shichi, Biochemistry of Vision (Academic, New York, 1983).
  44. T. I. Shaw, “The circular dichroism and optical rotatory dispersion of visual pigments,” in Handbook of Sensory Physiology, H. J. A. Dartnall, ed. (Springer-Verlag, Berlin, 1972), Vol. 7, Part 1.
    [CrossRef]
  45. H. Shichi, “Circular dichroism of bovine rhodopsin,” Photo-chem. Photobiol. 13, 499–506 (1971).
    [CrossRef]
  46. K. A. Piez, “Molecular and aggregate structures of the collagens,” in Extracellular Matrix Biochemistry, K. A. Piez, A. H. Reddi, eds. (Elsevier, New York, 1984), pp. 1–39.
  47. R. L. Trelstad, “Multistep assembly of type I collagen fibrils,” Cell 28, 197–198 (1982).
    [CrossRef] [PubMed]
  48. J. D. Jackson, Classical Electromagnetics (Wiley, New York, 1975), Sec. 6.4.
  49. J. van Bladel, Electromagnetic Fields (Hemisphere, New York, 1985), Chap. 8.
  50. It is easy to derive this result for any of the constitutive equations, provided that the media are homogeneous; for example, it be obtained for the Condon media [Eqs. (3a) and (3b)] from Eqs. (2a) and (2b) of Ref. 9.
  51. Governing differential equations of the type of Eq. (13) were derived for the isotropic Post media [Eqs. (5a) and (5b)] by Bassiri et al.,26 for the bianisotropic Post media by Cheng and Kong,31 for the bianisotropic Tellegen media by Kong,28 and for the isotropic Tellegen media [Eqs. (4a) and (4b)] by Chambers.22
  52. Vector and scalar potentials were also prescribed by Chambers22 for the isotropic Tellegen media [Eqs. (4a) and (4b)].
  53. V. H. Rumsey, “Reaction concept in electromagnetic theory,” Phys. Rev. 94, 1483–1491 (1954).
    [CrossRef]
  54. The satisfaction of reciprocity constraints has been extensively investigated by Krowne21 for the bianisotropic Tellegen media and by Post1 and Kong28 for the bianisotropic Post media [Eqs. (6a) and (6b)].
  55. Losslessness conditions for the isotropic Post media [Eqs. (5a) and (5b)] have been considered by Jaggard et al.24 by Kong28 for the bianisotropic Tellegen and Post media, and by Chambers22 for the isotropic Tellegen media [Eqs. (4a) and (4b)]. Fedorov12 has considered the conservation of energy for the constitutive equations (2a) and (2b) used here.
  56. The conservation of energy and electromagnetic momentum has also been considered by Kong28 for bianisotropic media, using Noether’s theorem.
  57. H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, New York, 1983).
  58. The rotational properties of G were not identified by Bassiri et al.26
  59. R. Kastener, R. Mittra, “A spectral-iteration technique for analyzing scattering from arbitrary bodies. I. Cylindrical scatterers with E-wave incidence,” IEEE Trans. Antennas Propag. AP-31, 499–506 (1983).
    [CrossRef]
  60. R. F. Harrington, Field Computation by Moment Methods (McGraw-Hill, New York, 1968).
  61. P. C. Waterman, “Scattering by dielectric obstacles,” Alta Freq. 38, 348 (1969).
  62. The functions L and R are defined in the spirit of the vector spherical-harmonic representations of the fields QL, and QR introduced by Bohren7 for bounded media.
  63. P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
  64. R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, New York, 1964), Chap. 2.
  65. V. K. Varadan, V. V. Varadan, eds., Acoustic, Electromagnetic and Elastic Scattering—Focus on the T-Matrix Approach (Pergamon, New York, 1980).
  66. A. T. de Hoop, “A reciprocity theorem for the electromagnetic field scattered by an obstacle,” Appl. Sci. Res. B 8, 135–140 (1960).
    [CrossRef]
  67. A. T. de Hoop, “On the plane-wave extinction cross-section of an obstacle,” Appl. Sci. Res. B 7, 463–469 (1959).
    [CrossRef]

1987 (1)

1986 (4)

M. P. Silverman, “Reflection and refraction at the surface of a chiral medium: comparison of gyrotropic constitutive relations invariant or noninvariant under a duality transformation,” J. Opt. Soc. Am. A 3, 830–837 (1986).
[CrossRef]

G. Heppke, D. Lötzsch, F. Oestreicher, “Chirale dotier-stoffe mit ausserwöhnlich hohem verdrillungsvermögen,” Z. Naturforsch. Teil A 41, 1214–1218 (1986).

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral-chiral interface,” IEEE Trans. Electromag. Compat. EC-28, 90–95 (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 (2)

M. P. Silverman, “Specular light scattering from a chiral medium: unambiguous test of gyrotropic constitutive equations,” Lett. Nuovo Cimento 43, 378–382 (1985).
[CrossRef]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Scattering and absorption characteristics of lossy dielectric, chiral, non-spherical objects,” Appl. Opt. 24, 4146–4154 (1985).
[CrossRef] [PubMed]

1984 (2)

C. M. Krowne, “Electromagnetic theorems for complex anisotropic medium,” IEEE Trans. Antennas Propag. AP-32, 1224–1230 (1984).
[CrossRef]

C. Altman, A. Schatzberg, K. Suchy, “Symmetry transformations and reversal of currents and fields in bounded (bi)anisotropic media,” IEEE Trans. Antennas Propag. AP-32, 1204–1210 (1984).
[CrossRef]

1983 (1)

R. Kastener, R. Mittra, “A spectral-iteration technique for analyzing scattering from arbitrary bodies. I. Cylindrical scatterers with E-wave incidence,” IEEE Trans. Antennas Propag. AP-31, 499–506 (1983).
[CrossRef]

1982 (2)

R. L. Trelstad, “Multistep assembly of type I collagen fibrils,” Cell 28, 197–198 (1982).
[CrossRef] [PubMed]

N. Engheta, A. R. Mickelson, “Transition radiation caused by a chiral plate,” IEEE Trans. Antennas Propag. AP-30, 1213–1216 (1982).
[CrossRef]

1981 (1)

L. J. Bour, N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21, 1413–1421 (1981).
[CrossRef] [PubMed]

1980 (1)

L. S. Corley, O. Vogl, “Optically active polymers,” Polymer Bull. 3, 211–217(1980).
[CrossRef]

1978 (2)

D. L. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1978).The isotropic Post equations have been derived here by considering the medium to be a suspension of small helices in an achiral host medium.
[CrossRef]

C. F. Bohren, “Scattering of electromagnetic waves by an optically active cylinder,” J. Colloid Interface Sci. 66, 105–109 (1978).
[CrossRef]

1976 (1)

C. F. Bohren, “Angular dependence of the scattering contribution to circular dichroism,” Chem. Phys. Lett. 40, 391–396 (1976).
[CrossRef]

1975 (1)

C. F. Bohren, “Scattering of electromagnetic waves by an optically active spherical shell,” J. Chem. Phys. 62, 1566–1571 (1975).
[CrossRef]

1974 (2)

1972 (1)

J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE 60, 1036–1046 (1972).An infinite-medium Green’s dyadic, expressed as an integral in the three-dimensional spatial-frequency space, for the bianisotropic Tellegen media has been given here.
[CrossRef]

1971 (1)

H. Shichi, “Circular dichroism of bovine rhodopsin,” Photo-chem. Photobiol. 13, 499–506 (1971).
[CrossRef]

1969 (1)

P. C. Waterman, “Scattering by dielectric obstacles,” Alta Freq. 38, 348 (1969).

1968 (4)

D. K. Cheng, J. A. Kong, “Covariant descriptions of bianisotropic media,” Proc. IEEE 56, 248–251 (1968).The covariant constitutive equations given here are precisely the same as those of Post.1
[CrossRef]

J. A. Kong, D. K. Cheng, “Wave reflections from a conducting surface with a moving uniaxial sheath,” IEEE Trans. Antennas Propag. 16, 577–583 (1968).
[CrossRef]

D. K. Cheng, J. A. Kong, “Time-harmonic fields in source-free bianisotropic media,” J. Appl. Phys. 39, 5792–5796 (1968).Normal incidence of plane waves on stationary isotropic or moving uniaxial media has been considered here. The moving uniaxial medium has been modeled by the bianisotropic Post Eqs. (6a) and (6b).
[CrossRef]

J. A. Kong, D. K. Cheng, “Wave behavior at an interface of a semi-infinite moving anisotropic medium,” J. Appl. Phys. 39, 2282–2286 (1968).Plane-wave reflection and refraction characteristics of a plane interface between free space and a bianisotropic Post medium have been derived here.
[CrossRef]

1964 (1)

H. Unz, “Electromagnetic radiation in drifting Tellegen anisotropic medium,” IEEE Trans. Antennas Propag. 12, 573–578 (1964).

1960 (1)

A. T. de Hoop, “A reciprocity theorem for the electromagnetic field scattered by an obstacle,” Appl. Sci. Res. B 8, 135–140 (1960).
[CrossRef]

1959 (4)

A. T. de Hoop, “On the plane-wave extinction cross-section of an obstacle,” Appl. Sci. Res. B 7, 463–469 (1959).
[CrossRef]

F. I. Fedorov, “On the theory of optical activity in crystals. I. The law of conservation of energy and the optical activity tensors,” Opt. Spectrosc. (USSR) 6, 49–53 (1959).

F. I. Fedorov, “On the theory of optical activity in crystals. II. Crystals of cubic symmetry and plane classes of central symmetry,” Opt. Spectrosc. (USSR) 6, 237–240 (1959).

B. V. Bokut’, F. I. Fedorov, “On the theory of optical activity in crystals. III. General equations of normals,” Opt. Spectrosc. (USSR) 6, 342–344 (1959).

1958 (1)

R. A. Satten, “Time-reversal symmetry and electromagnetic polarization fields,” J. Chem. Phys. 28, 742–743 (1958).
[CrossRef]

1956 (1)

LI. G. Chambers, “Propagation in a gyrational medium,” Q. J. Mech. Appl. Math. 9, 360–370 (1956).This paper contains several errors, chiefly as follows: Eqs. (4.6) are not a necessary consequence of Eqs. (4.5), and Sec. 8 appears to imply a Green’s function of the kind Fexp(ikr)/R, which is incorrect.
[CrossRef]

1954 (1)

V. H. Rumsey, “Reaction concept in electromagnetic theory,” Phys. Rev. 94, 1483–1491 (1954).
[CrossRef]

1953 (1)

H. L. deVries, A. Spoor, R. Jielof, “Properties of the eye with respect to polarized light,” Physica 19, 419–432 (1953).
[CrossRef]

1948 (1)

B. D. H. Tellegen, “The gyrator: a new electric network element,” Phillips Res. Rep. 3, 81–101 (1948).

1937 (1)

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
[CrossRef]

Altman, C.

C. Altman, A. Schatzberg, K. Suchy, “Symmetry transformations and reversal of currents and fields in bounded (bi)anisotropic media,” IEEE Trans. Antennas Propag. AP-32, 1204–1210 (1984).
[CrossRef]

Barron, L. D.

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, Cambridge, 1982).

Bassiri, S.

S. Bassiri, N. Engheta, C. H. Papas, “Dyadic Green’s function and dipole radiation in chiral media,” Antenna Lab. Rep. no. 118, (California Institute of Technology, Pasadena, Calif., 1985);“Dyadic Green’s function and dipole radiation in chiral media,” Alta Freq. 55, 83–88 (1986).

Bohren, C. F.

C. F. Bohren, “Scattering of electromagnetic waves by an optically active cylinder,” J. Colloid Interface Sci. 66, 105–109 (1978).
[CrossRef]

C. F. Bohren, “Angular dependence of the scattering contribution to circular dichroism,” Chem. Phys. Lett. 40, 391–396 (1976).
[CrossRef]

C. F. Bohren, “Scattering of electromagnetic waves by an optically active spherical shell,” J. Chem. Phys. 62, 1566–1571 (1975).
[CrossRef]

C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
[CrossRef]

C. F. Bohren, “Light scattering by optically active particles,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1975).

Bokut’, B. V.

B. V. Bokut’, F. I. Fedorov, “On the theory of optical activity in crystals. III. General equations of normals,” Opt. Spectrosc. (USSR) 6, 342–344 (1959).

Born, M.

M. Born, Optik (Springer-Verlag, Heidelberg, 1972), p. 412.

Bour, L. J.

L. J. Bour, N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21, 1413–1421 (1981).
[CrossRef] [PubMed]

Chambers, LI. G.

LI. G. Chambers, “Propagation in a gyrational medium,” Q. J. Mech. Appl. Math. 9, 360–370 (1956).This paper contains several errors, chiefly as follows: Eqs. (4.6) are not a necessary consequence of Eqs. (4.5), and Sec. 8 appears to imply a Green’s function of the kind Fexp(ikr)/R, which is incorrect.
[CrossRef]

Charney, E.

E. Charney, The Molecular Basis of Optical Activity (Krieger, Tampa, Fla., 1979).

Chen, H. C.

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

Cheng, D. K.

J. A. Kong, D. K. Cheng, “Wave behavior at an interface of a semi-infinite moving anisotropic medium,” J. Appl. Phys. 39, 2282–2286 (1968).Plane-wave reflection and refraction characteristics of a plane interface between free space and a bianisotropic Post medium have been derived here.
[CrossRef]

J. A. Kong, D. K. Cheng, “Wave reflections from a conducting surface with a moving uniaxial sheath,” IEEE Trans. Antennas Propag. 16, 577–583 (1968).
[CrossRef]

D. K. Cheng, J. A. Kong, “Time-harmonic fields in source-free bianisotropic media,” J. Appl. Phys. 39, 5792–5796 (1968).Normal incidence of plane waves on stationary isotropic or moving uniaxial media has been considered here. The moving uniaxial medium has been modeled by the bianisotropic Post Eqs. (6a) and (6b).
[CrossRef]

D. K. Cheng, J. A. Kong, “Covariant descriptions of bianisotropic media,” Proc. IEEE 56, 248–251 (1968).The covariant constitutive equations given here are precisely the same as those of Post.1
[CrossRef]

Condon, E. U.

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
[CrossRef]

Corley, L. S.

L. S. Corley, O. Vogl, “Optically active polymers,” Polymer Bull. 3, 211–217(1980).
[CrossRef]

de Hoop, A. T.

A. T. de Hoop, “A reciprocity theorem for the electromagnetic field scattered by an obstacle,” Appl. Sci. Res. B 8, 135–140 (1960).
[CrossRef]

A. T. de Hoop, “On the plane-wave extinction cross-section of an obstacle,” Appl. Sci. Res. B 7, 463–469 (1959).
[CrossRef]

deVries, H. L.

H. L. deVries, A. Spoor, R. Jielof, “Properties of the eye with respect to polarized light,” Physica 19, 419–432 (1953).
[CrossRef]

Engheta, N.

N. Engheta, A. R. Mickelson, “Transition radiation caused by a chiral plate,” IEEE Trans. Antennas Propag. AP-30, 1213–1216 (1982).
[CrossRef]

S. Bassiri, N. Engheta, C. H. Papas, “Dyadic Green’s function and dipole radiation in chiral media,” Antenna Lab. Rep. no. 118, (California Institute of Technology, Pasadena, Calif., 1985);“Dyadic Green’s function and dipole radiation in chiral media,” Alta Freq. 55, 83–88 (1986).

Eyring, H.

H. Eyring, J. Walter, G. E. Kimball, Quantum Chemistry (Wiley, New York, 1944), Chap. 17.

Fedorov, F. I.

B. V. Bokut’, F. I. Fedorov, “On the theory of optical activity in crystals. III. General equations of normals,” Opt. Spectrosc. (USSR) 6, 342–344 (1959).

F. I. Fedorov, “On the theory of optical activity in crystals. I. The law of conservation of energy and the optical activity tensors,” Opt. Spectrosc. (USSR) 6, 49–53 (1959).

F. I. Fedorov, “On the theory of optical activity in crystals. II. Crystals of cubic symmetry and plane classes of central symmetry,” Opt. Spectrosc. (USSR) 6, 237–240 (1959).

Feshbach, H.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Harrington, R. F.

R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, New York, 1964), Chap. 2.

R. F. Harrington, Field Computation by Moment Methods (McGraw-Hill, New York, 1968).

Harris, W. J.

W. J. Harris, O. Vogl, “Synthesis of optically active polymers,” Polymer Preprints22, 309–310 (1981).

Heppke, G.

G. Heppke, D. Lötzsch, F. Oestreicher, “Chirale dotier-stoffe mit ausserwöhnlich hohem verdrillungsvermögen,” Z. Naturforsch. Teil A 41, 1214–1218 (1986).

Jackson, J. D.

J. D. Jackson, Classical Electromagnetics (Wiley, New York, 1975), Sec. 6.4.

Jaggard, D. L.

D. L. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1978).The isotropic Post equations have been derived here by considering the medium to be a suspension of small helices in an achiral host medium.
[CrossRef]

Jielof, R.

H. L. deVries, A. Spoor, R. Jielof, “Properties of the eye with respect to polarized light,” Physica 19, 419–432 (1953).
[CrossRef]

Kastener, R.

R. Kastener, R. Mittra, “A spectral-iteration technique for analyzing scattering from arbitrary bodies. I. Cylindrical scatterers with E-wave incidence,” IEEE Trans. Antennas Propag. AP-31, 499–506 (1983).
[CrossRef]

Kimball, G. E.

H. Eyring, J. Walter, G. E. Kimball, Quantum Chemistry (Wiley, New York, 1944), Chap. 17.

Kong, J. A.

J. A. Kong, “Optics of bianisotropic media,” J. Opt. Soc. Am. 64, 1304–1308 (1974).Plane-wave propagation in and dispersion equations for bianisotropic Tellegen media have been considered here.
[CrossRef]

J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE 60, 1036–1046 (1972).An infinite-medium Green’s dyadic, expressed as an integral in the three-dimensional spatial-frequency space, for the bianisotropic Tellegen media has been given here.
[CrossRef]

D. K. Cheng, J. A. Kong, “Covariant descriptions of bianisotropic media,” Proc. IEEE 56, 248–251 (1968).The covariant constitutive equations given here are precisely the same as those of Post.1
[CrossRef]

J. A. Kong, D. K. Cheng, “Wave reflections from a conducting surface with a moving uniaxial sheath,” IEEE Trans. Antennas Propag. 16, 577–583 (1968).
[CrossRef]

D. K. Cheng, J. A. Kong, “Time-harmonic fields in source-free bianisotropic media,” J. Appl. Phys. 39, 5792–5796 (1968).Normal incidence of plane waves on stationary isotropic or moving uniaxial media has been considered here. The moving uniaxial medium has been modeled by the bianisotropic Post Eqs. (6a) and (6b).
[CrossRef]

J. A. Kong, D. K. Cheng, “Wave behavior at an interface of a semi-infinite moving anisotropic medium,” J. Appl. Phys. 39, 2282–2286 (1968).Plane-wave reflection and refraction characteristics of a plane interface between free space and a bianisotropic Post medium have been derived here.
[CrossRef]

Krowne, C. M.

C. M. Krowne, “Electromagnetic theorems for complex anisotropic medium,” IEEE Trans. Antennas Propag. AP-32, 1224–1230 (1984).
[CrossRef]

Lakhtakia, A.

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral-chiral interface,” IEEE Trans. Electromag. Compat. EC-28, 90–95 (1986).
[CrossRef]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Scattering and absorption characteristics of lossy dielectric, chiral, non-spherical objects,” Appl. Opt. 24, 4146–4154 (1985).
[CrossRef] [PubMed]

Lopes Cardozo, N. J.

L. J. Bour, N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21, 1413–1421 (1981).
[CrossRef] [PubMed]

Lötzsch, D.

G. Heppke, D. Lötzsch, F. Oestreicher, “Chirale dotier-stoffe mit ausserwöhnlich hohem verdrillungsvermögen,” Z. Naturforsch. Teil A 41, 1214–1218 (1986).

Mickelson, A. R.

N. Engheta, A. R. Mickelson, “Transition radiation caused by a chiral plate,” IEEE Trans. Antennas Propag. AP-30, 1213–1216 (1982).
[CrossRef]

D. L. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1978).The isotropic Post equations have been derived here by considering the medium to be a suspension of small helices in an achiral host medium.
[CrossRef]

Mittra, R.

R. Kastener, R. Mittra, “A spectral-iteration technique for analyzing scattering from arbitrary bodies. I. Cylindrical scatterers with E-wave incidence,” IEEE Trans. Antennas Propag. AP-31, 499–506 (1983).
[CrossRef]

Morse, P. M.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Oestreicher, F.

G. Heppke, D. Lötzsch, F. Oestreicher, “Chirale dotier-stoffe mit ausserwöhnlich hohem verdrillungsvermögen,” Z. Naturforsch. Teil A 41, 1214–1218 (1986).

Papas, C. H.

D. L. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1978).The isotropic Post equations have been derived here by considering the medium to be a suspension of small helices in an achiral host medium.
[CrossRef]

S. Bassiri, N. Engheta, C. H. Papas, “Dyadic Green’s function and dipole radiation in chiral media,” Antenna Lab. Rep. no. 118, (California Institute of Technology, Pasadena, Calif., 1985);“Dyadic Green’s function and dipole radiation in chiral media,” Alta Freq. 55, 83–88 (1986).

Piez, K. A.

K. A. Piez, “Molecular and aggregate structures of the collagens,” in Extracellular Matrix Biochemistry, K. A. Piez, A. H. Reddi, eds. (Elsevier, New York, 1984), pp. 1–39.

Post, E. J.

E. J. Post, Formal Structure of Electromagnetics (North-Holland, Amsterdam, 1962), Chap. 8.

Rumsey, V. H.

V. H. Rumsey, “Reaction concept in electromagnetic theory,” Phys. Rev. 94, 1483–1491 (1954).
[CrossRef]

Satten, R. A.

R. A. Satten, “Time-reversal symmetry and electromagnetic polarization fields,” J. Chem. Phys. 28, 742–743 (1958).
[CrossRef]

Schatzberg, A.

C. Altman, A. Schatzberg, K. Suchy, “Symmetry transformations and reversal of currents and fields in bounded (bi)anisotropic media,” IEEE Trans. Antennas Propag. AP-32, 1204–1210 (1984).
[CrossRef]

Shaw, T. I.

T. I. Shaw, “The circular dichroism and optical rotatory dispersion of visual pigments,” in Handbook of Sensory Physiology, H. J. A. Dartnall, ed. (Springer-Verlag, Berlin, 1972), Vol. 7, Part 1.
[CrossRef]

Shichi, H.

H. Shichi, “Circular dichroism of bovine rhodopsin,” Photo-chem. Photobiol. 13, 499–506 (1971).
[CrossRef]

H. Shichi, Biochemistry of Vision (Academic, New York, 1983).

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]

M. P. Silverman, “Reflection and refraction at the surface of a chiral medium: comparison of gyrotropic constitutive relations invariant or noninvariant under a duality transformation,” J. Opt. Soc. Am. A 3, 830–837 (1986).
[CrossRef]

M. P. Silverman, “Specular light scattering from a chiral medium: unambiguous test of gyrotropic constitutive equations,” Lett. Nuovo Cimento 43, 378–382 (1985).
[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]

Spoor, A.

H. L. deVries, A. Spoor, R. Jielof, “Properties of the eye with respect to polarized light,” Physica 19, 419–432 (1953).
[CrossRef]

Suchy, K.

C. Altman, A. Schatzberg, K. Suchy, “Symmetry transformations and reversal of currents and fields in bounded (bi)anisotropic media,” IEEE Trans. Antennas Propag. AP-32, 1204–1210 (1984).
[CrossRef]

Tellegen, B. D. H.

B. D. H. Tellegen, “The gyrator: a new electric network element,” Phillips Res. Rep. 3, 81–101 (1948).

Trelstad, R. L.

R. L. Trelstad, “Multistep assembly of type I collagen fibrils,” Cell 28, 197–198 (1982).
[CrossRef] [PubMed]

Unz, H.

H. Unz, “Electromagnetic radiation in drifting Tellegen anisotropic medium,” IEEE Trans. Antennas Propag. 12, 573–578 (1964).

van Bladel, J.

J. van Bladel, Relativity and Engineering (Springer-Verlag, Berlin, 1984).To a stationary observer, even a moving isotropic medium appears to be bianisotropic. Thus moving media can be described by the bianisotropic Post Eqs. (6a) and (6b), which are Lorentz covariant. This monograph contains an excellent account of the work done in this area since the turn of this century, although it should be noted that the work of Kong and his colleagues has not been cited here.
[CrossRef]

J. van Bladel, Electromagnetic Fields (Hemisphere, New York, 1985), Chap. 8.

Van Blokland, G. J.

Varadan, V. K.

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral-chiral interface,” IEEE Trans. Electromag. Compat. EC-28, 90–95 (1986).
[CrossRef]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Scattering and absorption characteristics of lossy dielectric, chiral, non-spherical objects,” Appl. Opt. 24, 4146–4154 (1985).
[CrossRef] [PubMed]

Varadan, V. V.

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral-chiral interface,” IEEE Trans. Electromag. Compat. EC-28, 90–95 (1986).
[CrossRef]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Scattering and absorption characteristics of lossy dielectric, chiral, non-spherical objects,” Appl. Opt. 24, 4146–4154 (1985).
[CrossRef] [PubMed]

Verhelst, S. C.

Vogl, O.

L. S. Corley, O. Vogl, “Optically active polymers,” Polymer Bull. 3, 211–217(1980).
[CrossRef]

W. J. Harris, O. Vogl, “Synthesis of optically active polymers,” Polymer Preprints22, 309–310 (1981).

Walter, J.

H. Eyring, J. Walter, G. E. Kimball, Quantum Chemistry (Wiley, New York, 1944), Chap. 17.

Waterman, P. C.

P. C. Waterman, “Scattering by dielectric obstacles,” Alta Freq. 38, 348 (1969).

Alta Freq. (1)

P. C. Waterman, “Scattering by dielectric obstacles,” Alta Freq. 38, 348 (1969).

Am. J. Phys. (1)

M. P. Silverman, R. B. Sohn, “Effects of circular birefringence on light propagation and reflection,” Am. J. Phys. 54, 69–76 (1986).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. (1)

D. L. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1978).The isotropic Post equations have been derived here by considering the medium to be a suspension of small helices in an achiral host medium.
[CrossRef]

Appl. Sci. Res. B (2)

A. T. de Hoop, “A reciprocity theorem for the electromagnetic field scattered by an obstacle,” Appl. Sci. Res. B 8, 135–140 (1960).
[CrossRef]

A. T. de Hoop, “On the plane-wave extinction cross-section of an obstacle,” Appl. Sci. Res. B 7, 463–469 (1959).
[CrossRef]

Cell (1)

R. L. Trelstad, “Multistep assembly of type I collagen fibrils,” Cell 28, 197–198 (1982).
[CrossRef] [PubMed]

Chem. Phys. Lett. (2)

C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
[CrossRef]

C. F. Bohren, “Angular dependence of the scattering contribution to circular dichroism,” Chem. Phys. Lett. 40, 391–396 (1976).
[CrossRef]

IEEE Trans. Antennas Propag. (6)

J. A. Kong, D. K. Cheng, “Wave reflections from a conducting surface with a moving uniaxial sheath,” IEEE Trans. Antennas Propag. 16, 577–583 (1968).
[CrossRef]

C. Altman, A. Schatzberg, K. Suchy, “Symmetry transformations and reversal of currents and fields in bounded (bi)anisotropic media,” IEEE Trans. Antennas Propag. AP-32, 1204–1210 (1984).
[CrossRef]

C. M. Krowne, “Electromagnetic theorems for complex anisotropic medium,” IEEE Trans. Antennas Propag. AP-32, 1224–1230 (1984).
[CrossRef]

H. Unz, “Electromagnetic radiation in drifting Tellegen anisotropic medium,” IEEE Trans. Antennas Propag. 12, 573–578 (1964).

N. Engheta, A. R. Mickelson, “Transition radiation caused by a chiral plate,” IEEE Trans. Antennas Propag. AP-30, 1213–1216 (1982).
[CrossRef]

R. Kastener, R. Mittra, “A spectral-iteration technique for analyzing scattering from arbitrary bodies. I. Cylindrical scatterers with E-wave incidence,” IEEE Trans. Antennas Propag. AP-31, 499–506 (1983).
[CrossRef]

IEEE Trans. Electromag. Compat. (1)

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “A parametric study of microwave reflection characteristics of a planar achiral-chiral interface,” IEEE Trans. Electromag. Compat. EC-28, 90–95 (1986).
[CrossRef]

J. Appl. Phys. (2)

J. A. Kong, D. K. Cheng, “Wave behavior at an interface of a semi-infinite moving anisotropic medium,” J. Appl. Phys. 39, 2282–2286 (1968).Plane-wave reflection and refraction characteristics of a plane interface between free space and a bianisotropic Post medium have been derived here.
[CrossRef]

D. K. Cheng, J. A. Kong, “Time-harmonic fields in source-free bianisotropic media,” J. Appl. Phys. 39, 5792–5796 (1968).Normal incidence of plane waves on stationary isotropic or moving uniaxial media has been considered here. The moving uniaxial medium has been modeled by the bianisotropic Post Eqs. (6a) and (6b).
[CrossRef]

J. Chem. Phys. (2)

R. A. Satten, “Time-reversal symmetry and electromagnetic polarization fields,” J. Chem. Phys. 28, 742–743 (1958).
[CrossRef]

C. F. Bohren, “Scattering of electromagnetic waves by an optically active spherical shell,” J. Chem. Phys. 62, 1566–1571 (1975).
[CrossRef]

J. Colloid Interface Sci. (1)

C. F. Bohren, “Scattering of electromagnetic waves by an optically active cylinder,” J. Colloid Interface Sci. 66, 105–109 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Lett. Nuovo Cimento (1)

M. P. Silverman, “Specular light scattering from a chiral medium: unambiguous test of gyrotropic constitutive equations,” Lett. Nuovo Cimento 43, 378–382 (1985).
[CrossRef]

Opt. Spectrosc. (USSR) (3)

F. I. Fedorov, “On the theory of optical activity in crystals. I. The law of conservation of energy and the optical activity tensors,” Opt. Spectrosc. (USSR) 6, 49–53 (1959).

F. I. Fedorov, “On the theory of optical activity in crystals. II. Crystals of cubic symmetry and plane classes of central symmetry,” Opt. Spectrosc. (USSR) 6, 237–240 (1959).

B. V. Bokut’, F. I. Fedorov, “On the theory of optical activity in crystals. III. General equations of normals,” Opt. Spectrosc. (USSR) 6, 342–344 (1959).

Phillips Res. Rep. (1)

B. D. H. Tellegen, “The gyrator: a new electric network element,” Phillips Res. Rep. 3, 81–101 (1948).

Photo-chem. Photobiol. (1)

H. Shichi, “Circular dichroism of bovine rhodopsin,” Photo-chem. Photobiol. 13, 499–506 (1971).
[CrossRef]

Phys. Rev. (1)

V. H. Rumsey, “Reaction concept in electromagnetic theory,” Phys. Rev. 94, 1483–1491 (1954).
[CrossRef]

Physica (1)

H. L. deVries, A. Spoor, R. Jielof, “Properties of the eye with respect to polarized light,” Physica 19, 419–432 (1953).
[CrossRef]

Polymer Bull. (1)

L. S. Corley, O. Vogl, “Optically active polymers,” Polymer Bull. 3, 211–217(1980).
[CrossRef]

Proc. IEEE (2)

D. K. Cheng, J. A. Kong, “Covariant descriptions of bianisotropic media,” Proc. IEEE 56, 248–251 (1968).The covariant constitutive equations given here are precisely the same as those of Post.1
[CrossRef]

J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE 60, 1036–1046 (1972).An infinite-medium Green’s dyadic, expressed as an integral in the three-dimensional spatial-frequency space, for the bianisotropic Tellegen media has been given here.
[CrossRef]

Q. J. Mech. Appl. Math. (1)

LI. G. Chambers, “Propagation in a gyrational medium,” Q. J. Mech. Appl. Math. 9, 360–370 (1956).This paper contains several errors, chiefly as follows: Eqs. (4.6) are not a necessary consequence of Eqs. (4.5), and Sec. 8 appears to imply a Green’s function of the kind Fexp(ikr)/R, which is incorrect.
[CrossRef]

Rev. Mod. Phys. (1)

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
[CrossRef]

Vision Res. (1)

L. J. Bour, N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21, 1413–1421 (1981).
[CrossRef] [PubMed]

Z. Naturforsch. Teil A (1)

G. Heppke, D. Lötzsch, F. Oestreicher, “Chirale dotier-stoffe mit ausserwöhnlich hohem verdrillungsvermögen,” Z. Naturforsch. Teil A 41, 1214–1218 (1986).

Other (28)

W. J. Harris, O. Vogl, “Synthesis of optically active polymers,” Polymer Preprints22, 309–310 (1981).

H. Eyring, J. Walter, G. E. Kimball, Quantum Chemistry (Wiley, New York, 1944), Chap. 17.

S. Bassiri, N. Engheta, C. H. Papas, “Dyadic Green’s function and dipole radiation in chiral media,” Antenna Lab. Rep. no. 118, (California Institute of Technology, Pasadena, Calif., 1985);“Dyadic Green’s function and dipole radiation in chiral media,” Alta Freq. 55, 83–88 (1986).

The transformation of the bianisotropic Tellegen equations into the bianisotropic Post equations involves a redefinition of the permittivity and the permability tensors; this is quite clear from Eq. (5) of Ref. 28.

J. van Bladel, Relativity and Engineering (Springer-Verlag, Berlin, 1984).To a stationary observer, even a moving isotropic medium appears to be bianisotropic. Thus moving media can be described by the bianisotropic Post Eqs. (6a) and (6b), which are Lorentz covariant. This monograph contains an excellent account of the work done in this area since the turn of this century, although it should be noted that the work of Kong and his colleagues has not been cited here.
[CrossRef]

E. J. Post, Formal Structure of Electromagnetics (North-Holland, Amsterdam, 1962), Chap. 8.

E. Charney, The Molecular Basis of Optical Activity (Krieger, Tampa, Fla., 1979).

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, Cambridge, 1982).

M. Born, Optik (Springer-Verlag, Heidelberg, 1972), p. 412.

C. F. Bohren, “Light scattering by optically active particles,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1975).

H. Shichi, Biochemistry of Vision (Academic, New York, 1983).

T. I. Shaw, “The circular dichroism and optical rotatory dispersion of visual pigments,” in Handbook of Sensory Physiology, H. J. A. Dartnall, ed. (Springer-Verlag, Berlin, 1972), Vol. 7, Part 1.
[CrossRef]

J. D. Jackson, Classical Electromagnetics (Wiley, New York, 1975), Sec. 6.4.

J. van Bladel, Electromagnetic Fields (Hemisphere, New York, 1985), Chap. 8.

It is easy to derive this result for any of the constitutive equations, provided that the media are homogeneous; for example, it be obtained for the Condon media [Eqs. (3a) and (3b)] from Eqs. (2a) and (2b) of Ref. 9.

Governing differential equations of the type of Eq. (13) were derived for the isotropic Post media [Eqs. (5a) and (5b)] by Bassiri et al.,26 for the bianisotropic Post media by Cheng and Kong,31 for the bianisotropic Tellegen media by Kong,28 and for the isotropic Tellegen media [Eqs. (4a) and (4b)] by Chambers.22

Vector and scalar potentials were also prescribed by Chambers22 for the isotropic Tellegen media [Eqs. (4a) and (4b)].

The satisfaction of reciprocity constraints has been extensively investigated by Krowne21 for the bianisotropic Tellegen media and by Post1 and Kong28 for the bianisotropic Post media [Eqs. (6a) and (6b)].

Losslessness conditions for the isotropic Post media [Eqs. (5a) and (5b)] have been considered by Jaggard et al.24 by Kong28 for the bianisotropic Tellegen and Post media, and by Chambers22 for the isotropic Tellegen media [Eqs. (4a) and (4b)]. Fedorov12 has considered the conservation of energy for the constitutive equations (2a) and (2b) used here.

The conservation of energy and electromagnetic momentum has also been considered by Kong28 for bianisotropic media, using Noether’s theorem.

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

The rotational properties of G were not identified by Bassiri et al.26

K. A. Piez, “Molecular and aggregate structures of the collagens,” in Extracellular Matrix Biochemistry, K. A. Piez, A. H. Reddi, eds. (Elsevier, New York, 1984), pp. 1–39.

R. F. Harrington, Field Computation by Moment Methods (McGraw-Hill, New York, 1968).

The functions L and R are defined in the spirit of the vector spherical-harmonic representations of the fields QL, and QR introduced by Bohren7 for bounded media.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, New York, 1964), Chap. 2.

V. K. Varadan, V. V. Varadan, eds., Acoustic, Electromagnetic and Elastic Scattering—Focus on the T-Matrix Approach (Pergamon, New York, 1980).

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Figures (2)

Fig. 1
Fig. 1

Relevant to Huygens’s principle.

Fig. 2
Fig. 2

For the far-zone scattering amplitude.

Equations (123)

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

D = ( E + η × E ) ,
B = μ H ,
D = [ E + β × E ] ,
B = μ [ H + β × H ] ,
D = C E χ H / t ,
B = μ C H + χ E / t ,
D = T E + ζ H ,
B = μ T H ζ E .
D = P E + i ξ B ,
B = μ P [ H i ξ E ] ,
c D = B · E + c L · B ,
H = m · E + c D · B ,
( 1 k 2 β 2 ) D = E + i ( β / ω ) k 2 H ,
( 1 k 2 β 2 ) B = μ H i ( β / ω ) k 2 E ,
× E = γ 2 β E + i ω μ ( γ / k ) 2 H ,
× H = γ 2 β H i ω ( γ / k ) 2 E ,
× D = γ 2 β D + i ω ( γ k ) 2 B ,
× B = γ 2 β B i ω μ ( γ / k ) 2 D .
γ 2 = k 2 [ 1 k 2 β 2 ] 1 = ω 2 μ [ 1 ω 2 β 2 μ ] 1 .
2 E + γ 2 β × E + i ω μ ( γ / k ) 2 × H = 0
2 E + 2 γ 2 β × E + γ 2 E = 0 .
2 U + 2 γ 2 β × U + γ 2 U = 0 , U = E , H , D , B .
B = × [ A + β × A ] ,
E = i ω [ A + β × A ] V ,
D = i ω [ A + 2 β × A + β 2 × × A ] V ,
H = μ 1 × A .
( k / γ ) 2 2 A + 2 k 2 β × A + k 2 A + [ i ω μ V ( k / γ ) 2 · A ] = 0 .
i ω μ V ( k / γ ) 2 · A = 0 ,
[ 2 + γ 2 ] V = 0 .
E = 1 × F ,
H = i ω [ F + β × F ] + W .
× E a , b = γ 2 β E a , b + i ω μ ( γ / k ) 2 H a , b + K a , b ,
× H a , b = γ 2 β H a , b + i ω ( γ / k ) 2 E a , b + J a , b .
× E a , b = γ 2 β E a , b + i ω μ ( γ / k ) 2 H a , b + K a , b ,
× H a , b = γ 2 β H a , b + i ω ( γ / k ) 2 E a , b + J a , b .
· ( H a × E b ) = [ i ω ( γ / k ) 2 E a · E b + i ω μ ( γ / k ) 2 H a · H b + ( γ 2 β γ 2 β ) H a · E b ] + J a · E b + K b · H a ,
· ( H b × E a ) = [ i ω ( γ / k ) 2 E a · E b + i ω μ ( γ / k ) 2 H a · H b ( γ 2 β γ 2 β ) E a · H b ] + J b · E a + K a · H b .
all space d 3 x ( J b · E a K b · H a ) = all space d 3 x ( J a · E b K a · H b ) .
. B + W / t + P mech = 0 ,
= E × H ,
W = ( 1 / 2 ) [ E · D + H · B ] = ( 1 / 2 ) [ D · D / + B · B / μ ] ,
P mech = J · E = J · D / ,
· ( E × H ) + H · ( B / t ) + E . ( D / t ) + J · E = 0 .
H · ( B / t ) = ( 1 / 2 ) { / t } [ H · B ] + ( 1 / 2 ) μ β · [ { H / t } × H ] ,
E · ( D / t ) = ( 1 / 2 ) { / t } [ E · D ] + ( 1 / 2 ) β · [ { E / t } × E ] ,
· [ E × H ( β / 2 ) ( μ { H / t } × H + { E / t } × E ) ] + ( / t ) [ ( 1 / 2 ) { E D + H · B } ] + [ J · E ] = 0 .
· [ E × H ] + ( / t ) [ ( 1 / 2 ) { D · D / + B · B / μ } ] + [ J · D / ] = 0 .
· P + ( 1 / 2 ) Re { i ω ( E · D * H · B * ) } + ( 1 / 2 ) Re { E · J * } = 0 ,
· P + ( 1 / 2 ) Re { i ω ( D · D * / B · B * / μ ) } + ( 1 / 2 ) Re { D · J * / } = 0 ,
J × B + ( · D ) E + ( / t ) [ D × B ] = [ E ( · E ) E × ( × E ) ] + μ [ H ( · H ) H × ( × H ) ] .
J × B + ( · D ) E = ρ v [ E + v × B ] ,
( / t ) G mech = V d 3 x ρ ν [ E + v × B ] .
G em = V d 3 x [ D × B ] .
( T ) n m = [ E n E m ( 1 / 2 ) E · E δ n m ] + μ [ H n H m ( 1 / 2 ) H · H δ n m ] , n , m = 1 , 2 , 3 ,
( / t ) [ G mech + G em ] n = m = 1 , 2 , 3 V d 3 x ( / x m ) ( T ) n m , n = 1 , 2 , 3 ,
G 1 ( r , r ) = G 1 ( r , r ) + G 2 ( r , r ) ,
G 1 ( r , r ) = ( k / 8 π γ 2 ) [ γ 1 F + γ 1 1 + × F ] g ( γ 1 ; R ) ,
G 2 ( r , r ) = ( k / 8 π γ 2 ) [ γ 2 F + γ 2 1 × F ] g ( γ 2 ; R ) ,
g ( σ ; R ) = exp [ i σ R ] / R ,
γ 1 = k [ 1 k β ] 1 ,
γ 2 = k [ 1 + k β ] 1 ,
G ( r , r ) | k β = ± 1 = ( 1 / 8 π k ) [ ( k / 2 ) F ( k / 2 ) 1 ± × F ] × g ( k / 2 ; R ) .
G ( r , r ) = [ G ( r , r ) ] T ,
× G ( r , r ) = [ × G ( r , r ) ] T ,
× G 1 ( r , r ) = γ 1 G 1 ( r , r ) ,
× G 2 ( r , r ) = γ 2 G 2 ( r , r ) ,
G ( r , r ) = Γ 1 ( r , r ) + Γ 2 ( r , r ) ,
Γ 1 ( r , r ) = ( 1 / 8 π ) [ F + γ 1 2 ] g ( γ 1 ; R ) ,
Γ 2 ( r , r ) = ( 1 / 8 π ) [ F + γ 2 2 ] g ( γ 2 ; R ) ;
× Γ 1 ( r , r ) = γ 1 Γ 1 ( r , r ) ,
× Γ 2 ( r , r ) = γ 2 Γ 2 ( r , r ) ,
G ( r , r ) = ( 1 / 4 π ) [ F + k 2 ] g ( k ; R ) ,
U 1 = ( ê x + i ê y ) exp ( i γ 1 z ) ,
U 2 = ( ê x i ê y ) exp ( i γ 2 z ) .
g ( σ ; R ) = [ { i σ R 1 R 2 } ( 3 RR R 2 ) ( σ / R ) 2 RR ] g ( σ ; R ) ,
× [ F g ( σ ; R ) ] = { i σ R 1 R 2 } g ( σ ; R ) R × F
Γ 1 ( r , r ) = ( i γ 1 / 2 π ) v D n m L ν ( 3 ) ( r > ) L ν ( 1 ) ( r < ) ,
Γ 2 ( r , r ) = ( i γ 2 / 2 π ) v D n m R ν ( 3 ) ( r > ) R ν ( 1 ) ( r < ) ,
L ν ( j ) ( r ) = M ν ( j ) ( γ 1 r ) + N ν ( j ) ( γ 1 r ) ,
R ν ( j ) ( r ) = M ν ( j ) ( γ 2 r ) N ν ( j ) ( γ 2 r ) ,
V e d 3 x { U · ( × × W ) ( × × U ) · W } = S + S d 2 x { ê n × ( × U ) · W + ( ê n × U ) · ( × W ) } ,
V e d 3 x { U · ( × × G ) ( × × U ) . G } = S + S d 2 x { ê n × ( × U ) · G + ( ê n × U ) · ( × G ) } .
V d 3 x { U ( r ) · ( F ) δ ( r r ) } = 2 γ 2 β S + S d 2 x ê n d 2 x ê n · [ U ( r ) × G ( r r ) ] + S + S d 2 x { ê n × ( × U ) ( r ) ] · G ( r r ) d 2 x { ê n × ( × U ) ( r ) ] G ( r r ) + [ ê n × U ( r ) · [ × ] G ( r r ) ] } .
U ( r ) = 2 γ 2 β S d 2 x G ( r , r ) d 2 x G ( r , r ) · [ ê n × U ( r ) ] + S d 2 x { G ( r , r ) d 2 x { G ( r , r ) · ( ê n × [ × U ( r ) ] ) + [ × G ( r , r ) ] · [ ê n × U ( r ) ] } , r V e ,
0 = 2 γ 2 β S d 2 x G ( r , r ) · [ ê n × U ( r ) ] d 2 x G ( r , r ) · [ ê n × U ( r ) ] + S d 2 x { G ( r , r ) · ( ê n × [ × U ( r ) ] ) d 2 x { G ( r , r ) · ( ê n × [ × U ( r ) ] ) + [ × G ( r , r ) ] · [ ê n × U ( r ) ] } , r V i .
U inc ( r ) = 2 γ 2 β S d 2 x G ( r , r ) · [ ê n × U + ( r ) ] d 2 x G ( r , r ) · [ ê n × U + ( r ) ] + S d 2 x ( G ( r , r ) · { ê n × [ + × U ( r ) ] } + [ × G ( r , r ) ] · [ e n × U + ( r ) ] ) , r V i ,
U sc ( r ) = 2 γ 2 β S d 2 x G ( r , r ) · [ ê n × U + ( r ) ] + S d 2 x ( G ( r , r ) · { ê n × [ + × U ( r ) ] } + [ × G ( r , r ) ] · [ ê n × U + ( r ) ] ) , r V i .
ê n × [ + × U ( r ) ] = ê n × [ × U int ( r ) ] ,
ê n × U + ( r ) = ê n × U int ( r ) ] , r S
E sc ( r ) = ( γ 2 / k ) S d 2 x { Γ 1 ( r , r ) Γ 2 ( r , r ) } · [ ê n × E sc ( r ) ] + ( i ω μ γ 2 / k 2 ) S d 2 x { Γ 1 ( r , r ) + Γ 2 ( r , r ) } · [ ê n × H sc ( r ) ] , r V e .
Γ 1 ( r , r ) F ( 1 / 8 π ) { exp [ i γ 1 r ] / r } exp ( i γ 1 η ̂ · r ) ,
Γ 2 ( r , r ) F ( 1 / 8 π ) { exp ( i γ 2 r ) / r } exp ( i γ 2 η ̂ · r ) ,
E sc ( r ) = { exp ( i γ 1 r ) / r } F t 1 ( η ̂ ) + { exp ( i γ 2 r ) / r } F t 2 ( η ̂ ) ,
F t 1 ( η ̂ ) = ( i γ 2 / 8 ω π ) S d 2 x ê n d 2 x ê n × { H sc ( r ) ( i ω / k ) E sc ( r ) } × exp ( i γ 1 η ̂ · r ) ,
F t 2 ( η ̂ ) = ( i γ 2 / 8 ω π ) S d 2 x ê n d 2 x ê n × { H sc ( r ) + ( i ω / k ) E sc ( r ) } × exp ( i γ 2 η ̂ · r ) ,
E 1 inc ( r ) = ê 1 exp [ i γ 1 η ̂ 1 · r ] ,
H 1 inc ( r ) = ( i ω / k ) ê 1 exp ( i γ 1 η ̂ 1 · r ) ,
ê 1 · η ̂ 1 = 0 ,
η ̂ 1 × ê 1 = i ê 1 ,
E 2 inc ( r ) = ê 2 exp [ i γ 2 η ̂ 2 · r ] ,
H 2 inc ( r ) = ( i ω / k ) ê 2 exp ( i γ 2 η ̂ 2 · r ) ,
ê 2 · η ̂ 2 = 0 ,
η ̂ 2 × ê 2 = i ê 2 ,
F t 1 ( η ̂ ) = S 11 ( η ̂ η ̂ 1 ) · ê 1 + S 12 ( η ̂ η ̂ 2 ) · ê 2 ,
F t 2 ( η ̂ ) = S 21 ( η ̂ η ̂ 1 ) · ê 1 + S 22 ( η ̂ η ̂ 2 ) · ê 2 .
m = 1 , 2 S d 2 x [ { ê n × H sc ( r ) } · E m inc ( r ) + { ê n × E sc ( r ) } · H m inc ( r ) ] = m = 1 , 2 S d 2 x [ { ê n × H sc ( r ) } · E m inc ( r ) + { ê n × E sc ( r ) } · H m inc ( r ) ] .
[ ê 1 S 11 ( η ̂ 1 η ̂ 1 ) ê 1 ê 1 S 11 ( η ̂ 1 η ̂ 1 ) ê 1 ] + [ ê 1 S 12 ( η ̂ 1 η ̂ 2 ) ê 2 ê 2 S 21 ( η ̂ 2 η ̂ 1 ) ê 1 ] + [ ê 2 S 21 ( η ̂ 2 η ̂ 1 ) ê 1 ê 1 S 12 ( η ̂ 1 η ̂ 2 ) ê 2 ] + [ ê 2 S 22 ( η ̂ 2 η ̂ 2 ) ê 2 ê 1 S 22 ( η ̂ 2 η ̂ 2 ) ê 2 ] = 0 ,
S 11 ( η ̂ 1 η ̂ 1 ) = [ S 11 ( η ̂ 1 η ̂ 1 ) ] T ,
S 22 ( η ̂ 2 η ̂ 2 ) = [ S 22 ( η ̂ 2 η ̂ 2 ) ] T ,
S 12 ( η ̂ 1 η ̂ 2 ) = [ S 21 ( η ̂ 2 η ̂ 1 ) ] T ,
S 21 ( η ̂ 2 η ̂ 1 ) = [ S 12 ( η ̂ 1 η ̂ 2 ) ] T .
S = [ S 11 S 12 S 21 S 22 ] ,
P sc = ( 1 / 2 ) Re { S d 2 x ê n · E sc × H sc * } ,
P abs = ( 1 / 2 ) Re { S d 2 x ê n · E sc + E inc ] × [ H sc * + H inc * ] } ;
P ext = ( 1 / 2 ) Re { S d 2 x ê n · E inc × H sc * + E sc × H inc * ] } ,
P 1 ext = ( 1 / 2 ) Re { ê 1 * · S d 2 x ê n × { H sc ( r ) ( i ω / k ) E sc ( r ) } exp [ i γ 1 η ̂ 1 · r ] } ,
C 1 ext = ( 2 k / ω ) | ê 1 | 2 P 1 ext .
C 1 ext = ( 8 π k / γ 2 ) Im { ê 1 * · F t 1 ( η ̂ 1 ) | ê 1 | 2 } .
P 2 ext = ( 1 / 2 ) Re { ê 2 * · S d 2 x ê n × { H sc ( r ) + ( i ω / k ) E sc ( r ) } exp [ i γ 2 η ̂ 2 · r ] } ,
C 2 ext = ( 8 π k / γ 2 ) Im { ê 2 * · F t 2 ( η ̂ 2 ) | ê 2 | 2 } .
G ( ρ , ρ ) = ( i k / 8 γ 2 ) [ γ 1 F + γ 1 1 + × F ] H 0 ( γ 2 | ρ ρ | ) + ( i k / 8 γ 2 ) [ γ 2 F + γ 2 1 × F ] H 0 ( γ 2 | ρ ρ | ) ,
G ( x , x ) = ( i k / 4 γ 1 γ 2 ) [ γ 1 F + γ 1 1 + × F ] × exp ( i γ 1 x x ) + ( i k / 4 γ 2 γ 2 ) [ γ 2 F + γ 2 1 × F ] exp ( i γ 2 x x ) .
[ 2 F γ 2 F 2 γ 2 β × F ] · U ( r ) = × U 0 ( r )

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