Abstract

Electric charge densities and electric current densities in vacuum give rise to the vacuum electromagnetic fields E and B, as described by Maxwell’s equations. In macroscopic media effective charge and current densities produced by microscopic dipole moments also contribute to the total fields, as can be shown from first principles. When the relationships between the field quantities and the dipole moment densities are known the source of the effective density can be ascribed to the material property causing them. We investigate the effective charge densities and current densities caused by electromagnetic chirality. For stationary media chirality generates effective chiral polarization and magnetization current densities that can be combined as an effective chiral current density. Effective chiral charge density contributions are observed for nonstationary observers moving with relativistic velocities. The theory developed here is applicable for perturbation analyses of inhomogeneous structures, such as gratings, in chiral media.

© 1995 Optical Society of America

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References

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  1. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  2. W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1962).
  3. D. L. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1979).
    [CrossRef]
  4. E. J. Post, Formal Structure of Electromagnetics: General Convariance and Electromagnetics (Wiley, New York, 1962).
  5. J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1986).
  6. I. V. Lindell, Methods for Electromagnetic Field Analysis (Oxford U. Press, New York, 1992).
  7. E. Charney, The Molecular Basis of Optical Activity: Optical Rotatory Dispersion and Circular Dichroism (Wiley, New York, 1979).
  8. V. I. Sokolov, Chirality and Optical Activity in Organometallic Compounds (Gordon & Breach, New York, 1990).
  9. V. V. Varadan, A. Lakhtakia, V. K. Varadan, “Equivalent dipole moments of helical arrangements of small, isotropic, point-polarizable scatters: application to chiral polymer design,” J. Appl. Phys. 63, 280–284 (1988).
    [CrossRef]
  10. A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media, Vol. 335 of Lecture Notes in Physics (Springer-Verlag, Berlin, 1989).
  11. C. T. Tai, “A study of the electrodynamics of moving media,” Proc. IEEE 52, 685–689 (1964).
    [CrossRef]
  12. D. K. Cheng, A. Kong, “Covariant descriptions of bianisotropic media,” Proc. IEEE 56, 248–251 (1968).
    [CrossRef]
  13. B. D. H. Tellegen, “The gyrator, a new electric network element,” Philips Res. Rep. 3, 81–101 (1948).
  14. H. Unz, “Electromagnetic radiation in drifting Tellegen anisotropic medium,”IEEE Trans. Antennas Propag. AP-11, 573–578 (1963).
    [CrossRef]
  15. N. Engheta, D. L. Jaggard, M. Kowarz, “Electromagnetic waves in Faraday chiral material,”IEEE Trans. Antennas Propag. 40, 367–374 (1992).
    [CrossRef]
  16. X. Sun, D. L. Jaggard, “Radiation of accelerated particles in chiral media,” J. Appl. Phys. 69, 34–38 (1991).
    [CrossRef]
  17. N. Engheta, M. W. Kowarz, D. L. Jaggard, “Effect of chirality on the Doppler shift and aberration of light waves,” J. Appl. Phys. 66, 2274–2277 (1989).
    [CrossRef]

1992 (1)

N. Engheta, D. L. Jaggard, M. Kowarz, “Electromagnetic waves in Faraday chiral material,”IEEE Trans. Antennas Propag. 40, 367–374 (1992).
[CrossRef]

1991 (1)

X. Sun, D. L. Jaggard, “Radiation of accelerated particles in chiral media,” J. Appl. Phys. 69, 34–38 (1991).
[CrossRef]

1989 (1)

N. Engheta, M. W. Kowarz, D. L. Jaggard, “Effect of chirality on the Doppler shift and aberration of light waves,” J. Appl. Phys. 66, 2274–2277 (1989).
[CrossRef]

1988 (1)

V. V. Varadan, A. Lakhtakia, V. K. Varadan, “Equivalent dipole moments of helical arrangements of small, isotropic, point-polarizable scatters: application to chiral polymer design,” J. Appl. Phys. 63, 280–284 (1988).
[CrossRef]

1979 (1)

D. L. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1979).
[CrossRef]

1968 (1)

D. K. Cheng, A. Kong, “Covariant descriptions of bianisotropic media,” Proc. IEEE 56, 248–251 (1968).
[CrossRef]

1964 (1)

C. T. Tai, “A study of the electrodynamics of moving media,” Proc. IEEE 52, 685–689 (1964).
[CrossRef]

1963 (1)

H. Unz, “Electromagnetic radiation in drifting Tellegen anisotropic medium,”IEEE Trans. Antennas Propag. AP-11, 573–578 (1963).
[CrossRef]

1948 (1)

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

Charney, E.

E. Charney, The Molecular Basis of Optical Activity: Optical Rotatory Dispersion and Circular Dichroism (Wiley, New York, 1979).

Cheng, D. K.

D. K. Cheng, A. Kong, “Covariant descriptions of bianisotropic media,” Proc. IEEE 56, 248–251 (1968).
[CrossRef]

Engheta, N.

N. Engheta, D. L. Jaggard, M. Kowarz, “Electromagnetic waves in Faraday chiral material,”IEEE Trans. Antennas Propag. 40, 367–374 (1992).
[CrossRef]

N. Engheta, M. W. Kowarz, D. L. Jaggard, “Effect of chirality on the Doppler shift and aberration of light waves,” J. Appl. Phys. 66, 2274–2277 (1989).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

Jaggard, D. L.

N. Engheta, D. L. Jaggard, M. Kowarz, “Electromagnetic waves in Faraday chiral material,”IEEE Trans. Antennas Propag. 40, 367–374 (1992).
[CrossRef]

X. Sun, D. L. Jaggard, “Radiation of accelerated particles in chiral media,” J. Appl. Phys. 69, 34–38 (1991).
[CrossRef]

N. Engheta, M. W. Kowarz, D. L. Jaggard, “Effect of chirality on the Doppler shift and aberration of light waves,” J. Appl. Phys. 66, 2274–2277 (1989).
[CrossRef]

D. L. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1979).
[CrossRef]

Kong, A.

D. K. Cheng, A. Kong, “Covariant descriptions of bianisotropic media,” Proc. IEEE 56, 248–251 (1968).
[CrossRef]

Kong, J. A.

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

Kowarz, M.

N. Engheta, D. L. Jaggard, M. Kowarz, “Electromagnetic waves in Faraday chiral material,”IEEE Trans. Antennas Propag. 40, 367–374 (1992).
[CrossRef]

Kowarz, M. W.

N. Engheta, M. W. Kowarz, D. L. Jaggard, “Effect of chirality on the Doppler shift and aberration of light waves,” J. Appl. Phys. 66, 2274–2277 (1989).
[CrossRef]

Lakhtakia, A.

V. V. Varadan, A. Lakhtakia, V. K. Varadan, “Equivalent dipole moments of helical arrangements of small, isotropic, point-polarizable scatters: application to chiral polymer design,” J. Appl. Phys. 63, 280–284 (1988).
[CrossRef]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media, Vol. 335 of Lecture Notes in Physics (Springer-Verlag, Berlin, 1989).

Lindell, I. V.

I. V. Lindell, Methods for Electromagnetic Field Analysis (Oxford U. Press, New York, 1992).

Mickelson, A. R.

D. L. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1979).
[CrossRef]

Panofsky, W. K. H.

W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1962).

Papas, C. H.

D. L. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1979).
[CrossRef]

Phillips, M.

W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1962).

Post, E. J.

E. J. Post, Formal Structure of Electromagnetics: General Convariance and Electromagnetics (Wiley, New York, 1962).

Sokolov, V. I.

V. I. Sokolov, Chirality and Optical Activity in Organometallic Compounds (Gordon & Breach, New York, 1990).

Sun, X.

X. Sun, D. L. Jaggard, “Radiation of accelerated particles in chiral media,” J. Appl. Phys. 69, 34–38 (1991).
[CrossRef]

Tai, C. T.

C. T. Tai, “A study of the electrodynamics of moving media,” Proc. IEEE 52, 685–689 (1964).
[CrossRef]

Tellegen, B. D. H.

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

Unz, H.

H. Unz, “Electromagnetic radiation in drifting Tellegen anisotropic medium,”IEEE Trans. Antennas Propag. AP-11, 573–578 (1963).
[CrossRef]

Varadan, V. K.

V. V. Varadan, A. Lakhtakia, V. K. Varadan, “Equivalent dipole moments of helical arrangements of small, isotropic, point-polarizable scatters: application to chiral polymer design,” J. Appl. Phys. 63, 280–284 (1988).
[CrossRef]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media, Vol. 335 of Lecture Notes in Physics (Springer-Verlag, Berlin, 1989).

Varadan, V. V.

V. V. Varadan, A. Lakhtakia, V. K. Varadan, “Equivalent dipole moments of helical arrangements of small, isotropic, point-polarizable scatters: application to chiral polymer design,” J. Appl. Phys. 63, 280–284 (1988).
[CrossRef]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media, Vol. 335 of Lecture Notes in Physics (Springer-Verlag, Berlin, 1989).

Appl. Phys. (1)

D. L. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1979).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

H. Unz, “Electromagnetic radiation in drifting Tellegen anisotropic medium,”IEEE Trans. Antennas Propag. AP-11, 573–578 (1963).
[CrossRef]

N. Engheta, D. L. Jaggard, M. Kowarz, “Electromagnetic waves in Faraday chiral material,”IEEE Trans. Antennas Propag. 40, 367–374 (1992).
[CrossRef]

J. Appl. Phys. (3)

X. Sun, D. L. Jaggard, “Radiation of accelerated particles in chiral media,” J. Appl. Phys. 69, 34–38 (1991).
[CrossRef]

N. Engheta, M. W. Kowarz, D. L. Jaggard, “Effect of chirality on the Doppler shift and aberration of light waves,” J. Appl. Phys. 66, 2274–2277 (1989).
[CrossRef]

V. V. Varadan, A. Lakhtakia, V. K. Varadan, “Equivalent dipole moments of helical arrangements of small, isotropic, point-polarizable scatters: application to chiral polymer design,” J. Appl. Phys. 63, 280–284 (1988).
[CrossRef]

Philips Res. Rep. (1)

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

Proc. IEEE (2)

C. T. Tai, “A study of the electrodynamics of moving media,” Proc. IEEE 52, 685–689 (1964).
[CrossRef]

D. K. Cheng, A. Kong, “Covariant descriptions of bianisotropic media,” Proc. IEEE 56, 248–251 (1968).
[CrossRef]

Other (8)

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media, Vol. 335 of Lecture Notes in Physics (Springer-Verlag, Berlin, 1989).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1962).

E. J. Post, Formal Structure of Electromagnetics: General Convariance and Electromagnetics (Wiley, New York, 1962).

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

I. V. Lindell, Methods for Electromagnetic Field Analysis (Oxford U. Press, New York, 1992).

E. Charney, The Molecular Basis of Optical Activity: Optical Rotatory Dispersion and Circular Dichroism (Wiley, New York, 1979).

V. I. Sokolov, Chirality and Optical Activity in Organometallic Compounds (Gordon & Breach, New York, 1990).

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Figures (3)

Fig. 1
Fig. 1

Illustration of induced currents in a right-handed chiral scatterer. The induced currents are the sources of the chiral current density in media composed of a random distribution of chiral scatterers with a common handedness.

Fig. 2
Fig. 2

Illustration of a moving observer’s reference frame in a stationary chiral medium. The material parameters, χe, χm, and ξc, are measured in the stationary reference frame, and the effective polarization current density Jp, the effective magnetization current density JM, and the chiral current density Jc are shown. The primes denote quantities measured in the moving reference frame.

Fig. 3
Fig. 3

Variation in the propagation constants measured by a moving observer in a stationary, right-handed chiral medium.

Equations (23)

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ɛ 0 · E = ρ total = ρ e - · P ,
1 μ 0 × B = J total = J e + × M + P t + ɛ 0 E t ,
P = ɛ 0 χ e E + i ξ c B ,
M = χ m μ 0 B - i ξ c E ,
ɛ 0 · E = ρ e - ɛ 0 χ e · E - i ξ c · B
= ρ e - i ξ c ρ m - ɛ 0 χ e · E ,
1 μ 0 × B = J e + χ m μ 0 × B - i ξ c × E + ɛ 0 χ e E t + i ξ c B t + ɛ 0 E t
= J e + i ξ c J m + χ m μ 0 × B + ɛ 0 χ e E t + ɛ 0 E t + i 2 ξ c B t ,
= J e - i ξ c J m + χ m μ 0 × B + ɛ 0 χ e E t + ɛ 0 E t - i 2 ξ c × E ,
P = γ ( P - v × M c 2 ) + ( 1 - γ ) ( P · v ) v v 2 = ɛ 0 χ e E ( achiral terms ) + i ξ c B ( chiral terms ) ( stationary terms ) - 1 η 0 ( χ e + χ m ) γ 2 c v × B ( nonstationary terms ) + ɛ 0 ( χ e + χ m ) ( γ v c ) 2 E + 2 i ξ c γ 2 c 2 ( v 2 B + v × E ) ( relativistic terms ) ,
M = γ ( M + v × P ) + ( 1 - γ ) ( M · v ) v v 2 = χ m μ 0 B ( achiral terms ) - i ξ c E ( chiral terms ) ( stationary terms ) + 1 η 0 ( χ e + χ m ) γ 2 c v × E + 2 i ξ c γ 2 v × B ( nonstationary terms ) + 1 μ 0 ( χ e + χ m ) ( γ v c ) 2 B - 2 i ξ c ( γ v c ) 2 E ( relativistic terms ) .
P = [ ɛ 0 χ e 0 0 0 ɛ 0 γ 2 [ χ e + χ m ( v c ) 2 ] - 2 i ξ c v ( γ c ) 2 0 2 i ξ c v ( γ c ) 2 ɛ 0 γ 2 [ χ e + χ m ( v c ) 2 ] ] [ E 1 E 2 E 3 ] + i [ ξ c 0 0 0 ξ c γ 2 [ 1 + ( v c ) 2 ] - i χ e + χ m η 0 γ 2 γ c 0 i χ e + χ m η 0 γ 2 γ c ξ c γ 2 [ 1 + ( v c ) 2 ] ] × [ B 1 B 2 B 3 ] ,
M = [ χ m μ 0 0 0 0 γ 2 μ 0 [ χ m + χ e ( v c ) 2 ] - 2 i ξ c γ 2 v 0 2 i ξ c γ 2 v γ 2 μ 0 [ χ m + χ e ( v c 2 ) ] ] [ B 1 B 2 B 3 ] - i [ ξ c 0 0 0 ξ c γ 2 [ 1 + ( v c ) 2 ] - i χ e + χ m η 0 γ 2 γ c 0 i χ e + χ m η 0 γ 2 γ c ξ c γ 2 [ 1 + ( v c ) 2 ] ] × [ E 1 E 2 E 3 ] .
P = [ ɛ 0 χ e 0 0 0 ɛ 0 γ 2 [ χ e + χ m ( v c ) 2 ] + 2 ξ c v ( γ c ) 2 0 0 0 ɛ 0 γ 2 [ χ e + χ m ( v c ) 2 ] - 2 ξ c v ( γ c ) 2 ] [ E 1 E + E - ] + i [ ξ c 0 0 0 ξ c γ 2 [ 1 + ( v c ) 2 ] + χ e + χ m η 0 γ 2 v c 0 0 0 ξ c γ 2 [ 1 + ( v c ) 2 ] - χ e + χ m η 0 γ 2 v c ] [ B 1 B + B - ] ,
M = [ χ m μ 0 0 0 0 γ 2 μ 0 [ χ m + χ e ( v c ) 2 ] + 2 ξ c γ 2 v 0 0 0 γ 2 μ 0 [ χ m + χ e ( v c ) 2 ] - 2 ξ c γ 2 v ] [ B 1 B + B - ] - i [ ξ c 0 0 0 ξ c γ 2 [ 1 + ( v c ) 2 ] + χ e + χ m η 0 γ 2 v c 0 0 0 ξ c γ 2 [ 1 + ( v c ) 2 ] - χ e + χ m η 0 γ 2 v c ] [ E 1 E + E - ] .
ɛ 0 · E = ρ e - ɛ 0 χ e · E ( achiral stationary terms ) - i ξ c ρ m ( chiral stationary term ) + 1 η 0 ( χ e + χ m ) γ 2 c ( · v × B ) ( achiral nonstationary term ) - ɛ 0 ( χ e + χ m ) ( v c γ ) 2 · E ( achiral relativistic terms ) - 2 i ξ c ( γ c ) 2 ( v 2 · B · v × E ) ( chiral relativistic terms ) ,
1 μ 0 × B = J e + χ m μ 0 × B + ɛ 0 E t + ɛ 0 χ e E t ( achiral stationary terms ) - i ξ c J m - i 2 ξ c × E ( or i ξ c J m + i 2 ξ c B t ) ( chiral stationary term ) + 1 η 0 ( χ e + χ m ) γ 2 c ( × v × E - v × B t ) ( achiral nonstationary term ) + 2 i ξ c γ 2 × v × B ( chiral nonstationary term ) + ( χ e + χ m ) ( γ v c ) 2 ( ɛ 0 E t + 1 μ 0 × B ) ( achiral relativistic terms ) + 2 i ξ c ( γ c ) 2 ( v × E t + v 2 B t - v 2 × E ) ( chiral relativistic terms ) ,
ρ = γ [ ρ - ( J · v ) 1 c 2 ] ,
J = γ [ ( J · v ) v v 2 - ρ v ] + J ,
J c = i ξ c J m + i 2 ξ c B t + 2 i ξ c γ 2 [ × v × B + v c × E t ] + ( v c ) 2 B t - ( v c ) 2 × E ] .
( 1 - χ m ) ( β ± + v c k 0 ) 2 - ( 1 + χ e ) ( v c β ± + k 0 ) 2 ± 2 η ξ c ( β ± + v c k 0 ) ( v c β ± + k 0 ) = 0 ,
β ± ω = k ± ω - k 0 ω v c 1 - k ± ω v c ,
k ± = ± ω μ 0 1 - χ m ξ c + [ ( ω μ 0 1 - χ m ξ c ) 2 + ω 2 μ 0 ɛ 0 1 + χ e 1 - χ m ] 1 / 2 .

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