Abstract

We investigate reflection from and transmission through chiral multilayers with discrete and continuous variations in material characteristics. Both boundary-value and initial-value approaches are used. The S-parameter matrix and associated copolarized and cross-polarized reflection and transmission coefficients are derived from the chiral constitutive relations, Maxwell’s equations, and boundary conditions. A generalized matrix Riccati equation is found for the reflection and transmission coefficients of arbitrary chiral multilayers by using an initial-value approach and Ambarzumian’s principle of invariant embedding. All results are exact and applicable to both normal and oblique incidence. Special emphasis is given to the physical principles involved, to special cases, and to salient features.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. L. Jaggard, A. R. Mickelson, C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. 18, 211–216 (1979).
    [Crossref]
  2. D. L. Jaggard, N. Engheta, “Chirality in electrodynamics: modelling and applications,” in Directions in Electromagnetic Wave Modelling, H. L. Bertoni, L. B. Felsen, eds. (Plenum, New York, 1992), pp. 435–466.
  3. A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Scattering and absorption characteristics of lossy dielectric, chiral, nonspherical objects,” Appl. Opt. 24, 4146–4154 (1985).
    [Crossref] [PubMed]
  4. M. P. Silverman, “Reflection and refraction at a 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]
  5. I. V. Lindell, A. H. Sihvola, “Quasi-static analysis of scattering from a chiral sphere,”J. Electromag. Waves Appl. 4, 1223–1231 (1990).
    [Crossref]
  6. M. S. Kluskens, E. H. Newman, “Scattering by a multilayer chiral cylinder,”IEEE Trans. Antennas Propag. 39, 91–96 (1991).
    [Crossref]
  7. D. L. Jaggard, J. C. Liu, “Chiral layers on curved surfaces,”J. Electromag. Waves Applic.6 (to be published).
  8. D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire scatterers in chiral media,” Opt. Lett. 16, 781–783 (1991).
    [Crossref] [PubMed]
  9. N. Engheta, S. Bassiri, “Cerenkov radiation in chiral media,” J. Appl. Phys. 68, 4393–4398 (1990).
    [Crossref]
  10. X. Sun, D. L. Jaggard, “Accelerated particle radiation in chiral media,” J. Appl. Phys. 69, 34–38 (1991).
    [Crossref]
  11. N. Engheta, P. Pelet, “Modes in chirowaveguides,” Opt. Lett. 14, 593–595 (1989).
    [Crossref] [PubMed]
  12. P. Pelet, N. Engheta, “Coupled-mode theory in chirowaveguides,” J. Appl. Phys. 67, 2742 (1990).
    [Crossref]
  13. D. L. Jaggard, X. Sun, N. Engheta, “Canonical sources and duality in chiral media,”IEEE Trans. Antennas Propag. 36, 1007–1013 (1988).
    [Crossref]
  14. N. Engheta, M. W. Kowarz, “Antenna radiation in the presence of a chiral sphere,” J. Appl. Phys. 67, 639–647 (1990).
    [Crossref]
  15. D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire antennas in chiral media,” Electron. Lett. 27, 243–244 (1991).
    [Crossref]
  16. S. Bassiri, C. H. Papas, N. Engheta, “Electromagnetic wave propagation through a dielectric-chiral interface and through a chiral slab,” J. Opt. Soc. Am. A 5, 1450–1459 (1988).
    [Crossref]
  17. D. L. Jaggard, N. Engheta, “ChirosorbTMas an invisible medium,” Electron. Lett. 25, 173–174 (1989).
    [Crossref]
  18. D. L. Jaggard, N. Engheta, “Electromagnetic chirality: past, present and future,” presented at the 1989 IEEE Antennas and Propagation Society–International Union of Radio Science Meeting, San Jose, Calif., June 1989.
  19. P. Tamirisa, P. L. E. Uslenghi, C. Long Yu, “Evaluation of reflection and transmission coefficients for multilayered chiral structures,” presented at the 1989 International Symposium on Antennas and Propagation, Tokyo, August 1989.
  20. D. L. Jaggard, N. Engheta, J. C. Liu, “ChiroshieldTM: a Salisbury/Dallenbach shield alternative,” Electron. Lett. 26, 1332–1334 (1990).
    [Crossref]
  21. A. J. Viitanen, I. V. Lindell, A. H. Sihvola, “Eigensolutions for the reflection problem involving the interface of two chiral half-spaces,” J. Opt. Soc. Am. A 7, 683–692 (1990).
    [Crossref]
  22. M. I. Oksanen, S. A. Tretyakov, I. V. Lindell, “Vector circuit theory for isotropic and chiral slabs,”J. Electromag. Waves Applic. 4, 613–643 (1990).
  23. T. Guire, V. V. Varadan, V. K. Varadan, “Influence of chirality on the reflection of em waves by planar dielectric slabs,”IEEE Trans. Electromag. Compat. 32, 300–303 (1990).
    [Crossref]
  24. D. L. Jaggard, J. C. Liu, X. Sun, “Spherical ChiroshieldTM,” Electron. Lett. 27, 77–79 (1991).
    [Crossref]
  25. V. A. Ambarzumian, “Diffuse reflection of light by a foggy medium,” C. R. (Dokl.) Acad. Sci. URSS 38, 229–232 (1943).
  26. By copolarization, we mean here that the polarizations of the waves before and after a transition are the same. In particular, RCP → RCP and LCP → LCP are copolarized transitions. The copolarized coefficients include r++, r−−, t++, and t−−. In contrast, RCP → LCP and LCP → RCP transitions are called cross-polarized transitions. The cross-polarized coefficients used in this paper include r+−, r−+, t+−, and t−+.
  27. D. L. Jaggard, A. R. Mickelson, “The reflection of electromagnetic waves from almost periodic structures,” Appl. Phys. 18, 211–216 (1979).
    [Crossref]
  28. P. J. Lin-Chung, S. Teitler, “4 × 4 matrix formalism for optics in stratified anisotropic media,” J. Opt. Soc. Am. A 1, 703–706 (1984).
    [Crossref]
  29. O. Schwelb, “Reflection coefficient and input admittance for nonuniform anisotropic layered waveguides,” Arch. Elektron. Übertragungstech. (Germany) 39, 199–202 (1985).
  30. J. B. Titchener, J. R. Wills, “The reflection of waves from stratified anisotropic media,”IEEE Trans. Antennas Propag. 39, 35–39 (1991).
    [Crossref]
  31. R. D. Graglia, P. L. E. Uslenghi, R. E. Zich, “Dispersion relation for bianisotropic materials and its symmetry properties,”IEEE Trans. Antennas Propag. 39, 83–90 (1991).
    [Crossref]
  32. D. L. Jaggard, N. Engheta, J. C. Liu: “ChiroshieldTM: the chiral Salisbury shield,” presented at the 1990 International Union of Radio Science Meeting, Dallas, May 7–11, 1990; D. L. Jaggard, X. Sun, J. Liu, “Chiral Riccati equation for inhomogeneous chiral material,” presented at the Progress in Electromagnetics Research Symposium, Cambridge, Mass., July 1–5, 1991.
  33. D. L. Jaggard, X. Sun, J. C. Liu, “On the chiral Riccati equation,” Microwave Opt. Technol. Lett. 5, 107–112 (1992).
    [Crossref]

1992 (1)

D. L. Jaggard, X. Sun, J. C. Liu, “On the chiral Riccati equation,” Microwave Opt. Technol. Lett. 5, 107–112 (1992).
[Crossref]

1991 (7)

D. L. Jaggard, J. C. Liu, X. Sun, “Spherical ChiroshieldTM,” Electron. Lett. 27, 77–79 (1991).
[Crossref]

J. B. Titchener, J. R. Wills, “The reflection of waves from stratified anisotropic media,”IEEE Trans. Antennas Propag. 39, 35–39 (1991).
[Crossref]

R. D. Graglia, P. L. E. Uslenghi, R. E. Zich, “Dispersion relation for bianisotropic materials and its symmetry properties,”IEEE Trans. Antennas Propag. 39, 83–90 (1991).
[Crossref]

M. S. Kluskens, E. H. Newman, “Scattering by a multilayer chiral cylinder,”IEEE Trans. Antennas Propag. 39, 91–96 (1991).
[Crossref]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire scatterers in chiral media,” Opt. Lett. 16, 781–783 (1991).
[Crossref] [PubMed]

X. Sun, D. L. Jaggard, “Accelerated particle radiation in chiral media,” J. Appl. Phys. 69, 34–38 (1991).
[Crossref]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire antennas in chiral media,” Electron. Lett. 27, 243–244 (1991).
[Crossref]

1990 (8)

P. Pelet, N. Engheta, “Coupled-mode theory in chirowaveguides,” J. Appl. Phys. 67, 2742 (1990).
[Crossref]

D. L. Jaggard, N. Engheta, J. C. Liu, “ChiroshieldTM: a Salisbury/Dallenbach shield alternative,” Electron. Lett. 26, 1332–1334 (1990).
[Crossref]

A. J. Viitanen, I. V. Lindell, A. H. Sihvola, “Eigensolutions for the reflection problem involving the interface of two chiral half-spaces,” J. Opt. Soc. Am. A 7, 683–692 (1990).
[Crossref]

M. I. Oksanen, S. A. Tretyakov, I. V. Lindell, “Vector circuit theory for isotropic and chiral slabs,”J. Electromag. Waves Applic. 4, 613–643 (1990).

T. Guire, V. V. Varadan, V. K. Varadan, “Influence of chirality on the reflection of em waves by planar dielectric slabs,”IEEE Trans. Electromag. Compat. 32, 300–303 (1990).
[Crossref]

N. Engheta, S. Bassiri, “Cerenkov radiation in chiral media,” J. Appl. Phys. 68, 4393–4398 (1990).
[Crossref]

I. V. Lindell, A. H. Sihvola, “Quasi-static analysis of scattering from a chiral sphere,”J. Electromag. Waves Appl. 4, 1223–1231 (1990).
[Crossref]

N. Engheta, M. W. Kowarz, “Antenna radiation in the presence of a chiral sphere,” J. Appl. Phys. 67, 639–647 (1990).
[Crossref]

1989 (2)

D. L. Jaggard, N. Engheta, “ChirosorbTMas an invisible medium,” Electron. Lett. 25, 173–174 (1989).
[Crossref]

N. Engheta, P. Pelet, “Modes in chirowaveguides,” Opt. Lett. 14, 593–595 (1989).
[Crossref] [PubMed]

1988 (2)

D. L. Jaggard, X. Sun, N. Engheta, “Canonical sources and duality in chiral media,”IEEE Trans. Antennas Propag. 36, 1007–1013 (1988).
[Crossref]

S. Bassiri, C. H. Papas, N. Engheta, “Electromagnetic wave propagation through a dielectric-chiral interface and through a chiral slab,” J. Opt. Soc. Am. A 5, 1450–1459 (1988).
[Crossref]

1986 (1)

1985 (2)

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

O. Schwelb, “Reflection coefficient and input admittance for nonuniform anisotropic layered waveguides,” Arch. Elektron. Übertragungstech. (Germany) 39, 199–202 (1985).

1984 (1)

1979 (2)

D. L. Jaggard, A. R. Mickelson, “The reflection of electromagnetic waves from almost periodic structures,” Appl. Phys. 18, 211–216 (1979).
[Crossref]

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

1943 (1)

V. A. Ambarzumian, “Diffuse reflection of light by a foggy medium,” C. R. (Dokl.) Acad. Sci. URSS 38, 229–232 (1943).

Ambarzumian, V. A.

V. A. Ambarzumian, “Diffuse reflection of light by a foggy medium,” C. R. (Dokl.) Acad. Sci. URSS 38, 229–232 (1943).

Bassiri, S.

Engheta, N.

N. Engheta, S. Bassiri, “Cerenkov radiation in chiral media,” J. Appl. Phys. 68, 4393–4398 (1990).
[Crossref]

P. Pelet, N. Engheta, “Coupled-mode theory in chirowaveguides,” J. Appl. Phys. 67, 2742 (1990).
[Crossref]

N. Engheta, M. W. Kowarz, “Antenna radiation in the presence of a chiral sphere,” J. Appl. Phys. 67, 639–647 (1990).
[Crossref]

D. L. Jaggard, N. Engheta, J. C. Liu, “ChiroshieldTM: a Salisbury/Dallenbach shield alternative,” Electron. Lett. 26, 1332–1334 (1990).
[Crossref]

D. L. Jaggard, N. Engheta, “ChirosorbTMas an invisible medium,” Electron. Lett. 25, 173–174 (1989).
[Crossref]

N. Engheta, P. Pelet, “Modes in chirowaveguides,” Opt. Lett. 14, 593–595 (1989).
[Crossref] [PubMed]

S. Bassiri, C. H. Papas, N. Engheta, “Electromagnetic wave propagation through a dielectric-chiral interface and through a chiral slab,” J. Opt. Soc. Am. A 5, 1450–1459 (1988).
[Crossref]

D. L. Jaggard, X. Sun, N. Engheta, “Canonical sources and duality in chiral media,”IEEE Trans. Antennas Propag. 36, 1007–1013 (1988).
[Crossref]

D. L. Jaggard, N. Engheta, “Chirality in electrodynamics: modelling and applications,” in Directions in Electromagnetic Wave Modelling, H. L. Bertoni, L. B. Felsen, eds. (Plenum, New York, 1992), pp. 435–466.

D. L. Jaggard, N. Engheta, “Electromagnetic chirality: past, present and future,” presented at the 1989 IEEE Antennas and Propagation Society–International Union of Radio Science Meeting, San Jose, Calif., June 1989.

D. L. Jaggard, N. Engheta, J. C. Liu: “ChiroshieldTM: the chiral Salisbury shield,” presented at the 1990 International Union of Radio Science Meeting, Dallas, May 7–11, 1990; D. L. Jaggard, X. Sun, J. Liu, “Chiral Riccati equation for inhomogeneous chiral material,” presented at the Progress in Electromagnetics Research Symposium, Cambridge, Mass., July 1–5, 1991.

Graglia, R. D.

R. D. Graglia, P. L. E. Uslenghi, R. E. Zich, “Dispersion relation for bianisotropic materials and its symmetry properties,”IEEE Trans. Antennas Propag. 39, 83–90 (1991).
[Crossref]

Grot, A.

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire scatterers in chiral media,” Opt. Lett. 16, 781–783 (1991).
[Crossref] [PubMed]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire antennas in chiral media,” Electron. Lett. 27, 243–244 (1991).
[Crossref]

Guire, T.

T. Guire, V. V. Varadan, V. K. Varadan, “Influence of chirality on the reflection of em waves by planar dielectric slabs,”IEEE Trans. Electromag. Compat. 32, 300–303 (1990).
[Crossref]

Jaggard, D. L.

D. L. Jaggard, X. Sun, J. C. Liu, “On the chiral Riccati equation,” Microwave Opt. Technol. Lett. 5, 107–112 (1992).
[Crossref]

D. L. Jaggard, J. C. Liu, X. Sun, “Spherical ChiroshieldTM,” Electron. Lett. 27, 77–79 (1991).
[Crossref]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire scatterers in chiral media,” Opt. Lett. 16, 781–783 (1991).
[Crossref] [PubMed]

X. Sun, D. L. Jaggard, “Accelerated particle radiation in chiral media,” J. Appl. Phys. 69, 34–38 (1991).
[Crossref]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire antennas in chiral media,” Electron. Lett. 27, 243–244 (1991).
[Crossref]

D. L. Jaggard, N. Engheta, J. C. Liu, “ChiroshieldTM: a Salisbury/Dallenbach shield alternative,” Electron. Lett. 26, 1332–1334 (1990).
[Crossref]

D. L. Jaggard, N. Engheta, “ChirosorbTMas an invisible medium,” Electron. Lett. 25, 173–174 (1989).
[Crossref]

D. L. Jaggard, X. Sun, N. Engheta, “Canonical sources and duality in chiral media,”IEEE Trans. Antennas Propag. 36, 1007–1013 (1988).
[Crossref]

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

D. L. Jaggard, A. R. Mickelson, “The reflection of electromagnetic waves from almost periodic structures,” Appl. Phys. 18, 211–216 (1979).
[Crossref]

D. L. Jaggard, N. Engheta, J. C. Liu: “ChiroshieldTM: the chiral Salisbury shield,” presented at the 1990 International Union of Radio Science Meeting, Dallas, May 7–11, 1990; D. L. Jaggard, X. Sun, J. Liu, “Chiral Riccati equation for inhomogeneous chiral material,” presented at the Progress in Electromagnetics Research Symposium, Cambridge, Mass., July 1–5, 1991.

D. L. Jaggard, J. C. Liu, “Chiral layers on curved surfaces,”J. Electromag. Waves Applic.6 (to be published).

D. L. Jaggard, N. Engheta, “Chirality in electrodynamics: modelling and applications,” in Directions in Electromagnetic Wave Modelling, H. L. Bertoni, L. B. Felsen, eds. (Plenum, New York, 1992), pp. 435–466.

D. L. Jaggard, N. Engheta, “Electromagnetic chirality: past, present and future,” presented at the 1989 IEEE Antennas and Propagation Society–International Union of Radio Science Meeting, San Jose, Calif., June 1989.

Kluskens, M. S.

M. S. Kluskens, E. H. Newman, “Scattering by a multilayer chiral cylinder,”IEEE Trans. Antennas Propag. 39, 91–96 (1991).
[Crossref]

Kowarz, M. W.

N. Engheta, M. W. Kowarz, “Antenna radiation in the presence of a chiral sphere,” J. Appl. Phys. 67, 639–647 (1990).
[Crossref]

Lakhtakia, A.

Lin-Chung, P. J.

Lindell, I. V.

A. J. Viitanen, I. V. Lindell, A. H. Sihvola, “Eigensolutions for the reflection problem involving the interface of two chiral half-spaces,” J. Opt. Soc. Am. A 7, 683–692 (1990).
[Crossref]

I. V. Lindell, A. H. Sihvola, “Quasi-static analysis of scattering from a chiral sphere,”J. Electromag. Waves Appl. 4, 1223–1231 (1990).
[Crossref]

M. I. Oksanen, S. A. Tretyakov, I. V. Lindell, “Vector circuit theory for isotropic and chiral slabs,”J. Electromag. Waves Applic. 4, 613–643 (1990).

Liu, J. C.

D. L. Jaggard, X. Sun, J. C. Liu, “On the chiral Riccati equation,” Microwave Opt. Technol. Lett. 5, 107–112 (1992).
[Crossref]

D. L. Jaggard, J. C. Liu, X. Sun, “Spherical ChiroshieldTM,” Electron. Lett. 27, 77–79 (1991).
[Crossref]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire scatterers in chiral media,” Opt. Lett. 16, 781–783 (1991).
[Crossref] [PubMed]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire antennas in chiral media,” Electron. Lett. 27, 243–244 (1991).
[Crossref]

D. L. Jaggard, N. Engheta, J. C. Liu, “ChiroshieldTM: a Salisbury/Dallenbach shield alternative,” Electron. Lett. 26, 1332–1334 (1990).
[Crossref]

D. L. Jaggard, J. C. Liu, “Chiral layers on curved surfaces,”J. Electromag. Waves Applic.6 (to be published).

D. L. Jaggard, N. Engheta, J. C. Liu: “ChiroshieldTM: the chiral Salisbury shield,” presented at the 1990 International Union of Radio Science Meeting, Dallas, May 7–11, 1990; D. L. Jaggard, X. Sun, J. Liu, “Chiral Riccati equation for inhomogeneous chiral material,” presented at the Progress in Electromagnetics Research Symposium, Cambridge, Mass., July 1–5, 1991.

Long Yu, C.

P. Tamirisa, P. L. E. Uslenghi, C. Long Yu, “Evaluation of reflection and transmission coefficients for multilayered chiral structures,” presented at the 1989 International Symposium on Antennas and Propagation, Tokyo, August 1989.

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]

D. L. Jaggard, A. R. Mickelson, “The reflection of electromagnetic waves from almost periodic structures,” Appl. Phys. 18, 211–216 (1979).
[Crossref]

Newman, E. H.

M. S. Kluskens, E. H. Newman, “Scattering by a multilayer chiral cylinder,”IEEE Trans. Antennas Propag. 39, 91–96 (1991).
[Crossref]

Oksanen, M. I.

M. I. Oksanen, S. A. Tretyakov, I. V. Lindell, “Vector circuit theory for isotropic and chiral slabs,”J. Electromag. Waves Applic. 4, 613–643 (1990).

Papas, C. H.

Pelet, P.

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire antennas in chiral media,” Electron. Lett. 27, 243–244 (1991).
[Crossref]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire scatterers in chiral media,” Opt. Lett. 16, 781–783 (1991).
[Crossref] [PubMed]

P. Pelet, N. Engheta, “Coupled-mode theory in chirowaveguides,” J. Appl. Phys. 67, 2742 (1990).
[Crossref]

N. Engheta, P. Pelet, “Modes in chirowaveguides,” Opt. Lett. 14, 593–595 (1989).
[Crossref] [PubMed]

Schwelb, O.

O. Schwelb, “Reflection coefficient and input admittance for nonuniform anisotropic layered waveguides,” Arch. Elektron. Übertragungstech. (Germany) 39, 199–202 (1985).

Sihvola, A. H.

A. J. Viitanen, I. V. Lindell, A. H. Sihvola, “Eigensolutions for the reflection problem involving the interface of two chiral half-spaces,” J. Opt. Soc. Am. A 7, 683–692 (1990).
[Crossref]

I. V. Lindell, A. H. Sihvola, “Quasi-static analysis of scattering from a chiral sphere,”J. Electromag. Waves Appl. 4, 1223–1231 (1990).
[Crossref]

Silverman, M. P.

Sun, X.

D. L. Jaggard, X. Sun, J. C. Liu, “On the chiral Riccati equation,” Microwave Opt. Technol. Lett. 5, 107–112 (1992).
[Crossref]

D. L. Jaggard, J. C. Liu, X. Sun, “Spherical ChiroshieldTM,” Electron. Lett. 27, 77–79 (1991).
[Crossref]

X. Sun, D. L. Jaggard, “Accelerated particle radiation in chiral media,” J. Appl. Phys. 69, 34–38 (1991).
[Crossref]

D. L. Jaggard, X. Sun, N. Engheta, “Canonical sources and duality in chiral media,”IEEE Trans. Antennas Propag. 36, 1007–1013 (1988).
[Crossref]

Tamirisa, P.

P. Tamirisa, P. L. E. Uslenghi, C. Long Yu, “Evaluation of reflection and transmission coefficients for multilayered chiral structures,” presented at the 1989 International Symposium on Antennas and Propagation, Tokyo, August 1989.

Teitler, S.

Titchener, J. B.

J. B. Titchener, J. R. Wills, “The reflection of waves from stratified anisotropic media,”IEEE Trans. Antennas Propag. 39, 35–39 (1991).
[Crossref]

Tretyakov, S. A.

M. I. Oksanen, S. A. Tretyakov, I. V. Lindell, “Vector circuit theory for isotropic and chiral slabs,”J. Electromag. Waves Applic. 4, 613–643 (1990).

Uslenghi, P. L. E.

R. D. Graglia, P. L. E. Uslenghi, R. E. Zich, “Dispersion relation for bianisotropic materials and its symmetry properties,”IEEE Trans. Antennas Propag. 39, 83–90 (1991).
[Crossref]

P. Tamirisa, P. L. E. Uslenghi, C. Long Yu, “Evaluation of reflection and transmission coefficients for multilayered chiral structures,” presented at the 1989 International Symposium on Antennas and Propagation, Tokyo, August 1989.

Varadan, V. K.

T. Guire, V. V. Varadan, V. K. Varadan, “Influence of chirality on the reflection of em waves by planar dielectric slabs,”IEEE Trans. Electromag. Compat. 32, 300–303 (1990).
[Crossref]

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

Varadan, V. V.

T. Guire, V. V. Varadan, V. K. Varadan, “Influence of chirality on the reflection of em waves by planar dielectric slabs,”IEEE Trans. Electromag. Compat. 32, 300–303 (1990).
[Crossref]

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

Viitanen, A. J.

Wills, J. R.

J. B. Titchener, J. R. Wills, “The reflection of waves from stratified anisotropic media,”IEEE Trans. Antennas Propag. 39, 35–39 (1991).
[Crossref]

Zich, R. E.

R. D. Graglia, P. L. E. Uslenghi, R. E. Zich, “Dispersion relation for bianisotropic materials and its symmetry properties,”IEEE Trans. Antennas Propag. 39, 83–90 (1991).
[Crossref]

Appl. Opt. (1)

Appl. Phys. (2)

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

D. L. Jaggard, A. R. Mickelson, “The reflection of electromagnetic waves from almost periodic structures,” Appl. Phys. 18, 211–216 (1979).
[Crossref]

Arch. Elektron. Übertragungstech. (Germany) (1)

O. Schwelb, “Reflection coefficient and input admittance for nonuniform anisotropic layered waveguides,” Arch. Elektron. Übertragungstech. (Germany) 39, 199–202 (1985).

C. R. (Dokl.) Acad. Sci. URSS (1)

V. A. Ambarzumian, “Diffuse reflection of light by a foggy medium,” C. R. (Dokl.) Acad. Sci. URSS 38, 229–232 (1943).

Electron. Lett. (4)

D. L. Jaggard, J. C. Liu, X. Sun, “Spherical ChiroshieldTM,” Electron. Lett. 27, 77–79 (1991).
[Crossref]

D. L. Jaggard, N. Engheta, J. C. Liu, “ChiroshieldTM: a Salisbury/Dallenbach shield alternative,” Electron. Lett. 26, 1332–1334 (1990).
[Crossref]

D. L. Jaggard, J. C. Liu, A. Grot, P. Pelet, “Thin wire antennas in chiral media,” Electron. Lett. 27, 243–244 (1991).
[Crossref]

D. L. Jaggard, N. Engheta, “ChirosorbTMas an invisible medium,” Electron. Lett. 25, 173–174 (1989).
[Crossref]

IEEE Trans. Antennas Propag. (4)

D. L. Jaggard, X. Sun, N. Engheta, “Canonical sources and duality in chiral media,”IEEE Trans. Antennas Propag. 36, 1007–1013 (1988).
[Crossref]

M. S. Kluskens, E. H. Newman, “Scattering by a multilayer chiral cylinder,”IEEE Trans. Antennas Propag. 39, 91–96 (1991).
[Crossref]

J. B. Titchener, J. R. Wills, “The reflection of waves from stratified anisotropic media,”IEEE Trans. Antennas Propag. 39, 35–39 (1991).
[Crossref]

R. D. Graglia, P. L. E. Uslenghi, R. E. Zich, “Dispersion relation for bianisotropic materials and its symmetry properties,”IEEE Trans. Antennas Propag. 39, 83–90 (1991).
[Crossref]

IEEE Trans. Electromag. Compat. (1)

T. Guire, V. V. Varadan, V. K. Varadan, “Influence of chirality on the reflection of em waves by planar dielectric slabs,”IEEE Trans. Electromag. Compat. 32, 300–303 (1990).
[Crossref]

J. Appl. Phys. (4)

P. Pelet, N. Engheta, “Coupled-mode theory in chirowaveguides,” J. Appl. Phys. 67, 2742 (1990).
[Crossref]

N. Engheta, M. W. Kowarz, “Antenna radiation in the presence of a chiral sphere,” J. Appl. Phys. 67, 639–647 (1990).
[Crossref]

N. Engheta, S. Bassiri, “Cerenkov radiation in chiral media,” J. Appl. Phys. 68, 4393–4398 (1990).
[Crossref]

X. Sun, D. L. Jaggard, “Accelerated particle radiation in chiral media,” J. Appl. Phys. 69, 34–38 (1991).
[Crossref]

J. Electromag. Waves Appl. (1)

I. V. Lindell, A. H. Sihvola, “Quasi-static analysis of scattering from a chiral sphere,”J. Electromag. Waves Appl. 4, 1223–1231 (1990).
[Crossref]

J. Electromag. Waves Applic. (1)

M. I. Oksanen, S. A. Tretyakov, I. V. Lindell, “Vector circuit theory for isotropic and chiral slabs,”J. Electromag. Waves Applic. 4, 613–643 (1990).

J. Opt. Soc. Am. A (4)

Microwave Opt. Technol. Lett. (1)

D. L. Jaggard, X. Sun, J. C. Liu, “On the chiral Riccati equation,” Microwave Opt. Technol. Lett. 5, 107–112 (1992).
[Crossref]

Opt. Lett. (2)

Other (6)

D. L. Jaggard, J. C. Liu, “Chiral layers on curved surfaces,”J. Electromag. Waves Applic.6 (to be published).

D. L. Jaggard, N. Engheta, “Chirality in electrodynamics: modelling and applications,” in Directions in Electromagnetic Wave Modelling, H. L. Bertoni, L. B. Felsen, eds. (Plenum, New York, 1992), pp. 435–466.

D. L. Jaggard, N. Engheta, “Electromagnetic chirality: past, present and future,” presented at the 1989 IEEE Antennas and Propagation Society–International Union of Radio Science Meeting, San Jose, Calif., June 1989.

P. Tamirisa, P. L. E. Uslenghi, C. Long Yu, “Evaluation of reflection and transmission coefficients for multilayered chiral structures,” presented at the 1989 International Symposium on Antennas and Propagation, Tokyo, August 1989.

D. L. Jaggard, N. Engheta, J. C. Liu: “ChiroshieldTM: the chiral Salisbury shield,” presented at the 1990 International Union of Radio Science Meeting, Dallas, May 7–11, 1990; D. L. Jaggard, X. Sun, J. Liu, “Chiral Riccati equation for inhomogeneous chiral material,” presented at the Progress in Electromagnetics Research Symposium, Cambridge, Mass., July 1–5, 1991.

By copolarization, we mean here that the polarizations of the waves before and after a transition are the same. In particular, RCP → RCP and LCP → LCP are copolarized transitions. The copolarized coefficients include r++, r−−, t++, and t−−. In contrast, RCP → LCP and LCP → RCP transitions are called cross-polarized transitions. The cross-polarized coefficients used in this paper include r+−, r−+, t+−, and t−+.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Wave interaction with a family of N chiral slabs of infinite transverse extent. For the nth layer, there are three material parameters, ηn,kn+, and kn, and two distinct angles, θn+ and θn, one for each mode determined from the initial incident angle θ0 and material parameters through chiro-Snell’s law.

Fig. 2
Fig. 2

Typical chiral–chiral interface embedded in the chiral multilayer problem shown in Fig. 1. The subscripts + and − indicate, respectively, the positive (RCP) and negative (LCP) modes, while subscripts L and R denote the left-going and right-going waves, respectively. Polarizations are composed of components perpendicular and parallel to the incident plane, defined by the incident wave vector and the normal of the interface, in the convention shown in this figure.

Fig. 3
Fig. 3

Illustration of the multireflection and multitransmission mechanism at point z with an infinitesimal increment Δz. The reflection and transmission Riccati equations are derived from this figure by summing, respectively, the reflected and transmitted terms to first order in Δz.

Equations (79)

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

D = E + i ξ c B ,             H = B / μ + i ξ c E .
{ × × - 2 ω μ ξ c × - ω 2 μ } Q = 0 ,
k ± = ω [ ( μ + μ 2 ξ c 2 ) 1 / 2 ± μ ξ c ] .
k + + k - 2 = ω ( μ + μ 2 ξ c 2 ) 1 / 2
( k + k - ) 1 / 2 = ω ( μ ) 1 / 2 ,
η = 1 ( μ + ξ c 2 ) 1 / 2 .
k 0 sin θ 0 = k n + sin θ n + = k n - sin θ n -             ( n = 0 , 1 , N + 1 ) ,
k + sin θ + = k - sin θ - = k + sin θ + = k - sin θ - = k 0 sin θ 0 .
E + R - E - R + E + L - E - L = E + R - E - R + E + L - E - L ,
E + R cos θ + + E - R cos θ - - E + L cos θ + - E - L cos θ - = E + R cos θ + + E - R cos θ - - E + L cos θ + - E - L × cos θ - .
1 η ( E + R + E - R + E + L + E - L ) = 1 η ( E + R + E - R + E + L + E - L ) ,
1 η ( E + R cos θ + - E - R cos θ - - E + L cos θ + + E - L cos θ - ) = 1 η ( E + R cos θ + - E - R cos θ - - E + L × cos θ + + E - L cos θ - ) .
[ E + R E - R E + L E - L ] = [ m 11 m 12 m 12 m 14 m 21 m 22 m 23 m 24 m 31 m 32 m 33 m 34 m 41 m 42 m 43 m 44 ] [ E + R E - R E + L E - L ]
E = M E .
M = [ M T M R M R M T ] .
M T = [ η r + 1 4 ( 1 + cos θ + cos θ + ) η r - 1 4 ( 1 - cos θ - cos θ + ) η r - 1 4 ( 1 - cos θ + cos θ - ) η r + 1 4 ( 1 + cos θ - cos θ - ) ] ,
M R = [ η r + 1 4 ( 1 - cos θ + cos θ + ) η r - 1 4 ( 1 + cos θ - cos θ + ) η r - 1 4 ( 1 + cos θ + cos θ - ) η r + 1 4 ( 1 - cos θ - cos θ - ) ] ,
M = η r 2 cos θ + cos θ - cos θ + cos θ - .
M T = ( η r + 1 ) 2 16 ( 1 + cos θ + cos θ + ) ( 1 + cos θ - cos θ - ) - ( η r - 1 ) 2 16 ( 1 - cos θ + cos θ - ) ( 1 - cos θ - cos θ + ) ,
M R = ( η r + 1 ) 2 16 ( 1 - cos θ + cos θ + ) ( 1 - cos θ + cos θ - ) - ( η r - 1 ) 2 16 ( 1 + cos θ + cos θ - ) ( 1 + cos θ - cos θ + ) .
M 0 = [ η r + 1 2 0 0 η r - 1 2 0 η r + 1 2 η r - 1 2 0 0 η r - 1 2 η r + 1 2 0 η r - 1 2 0 0 η r + 1 2 ] ,
[ E + R E - R ] = [ t + + t - + t + - t - - ] [ E + R E - R ]
E R = T E R .
T = M T - 1 = 1 M T × [ η r + 1 4 ( 1 + cos θ - cos θ - ) - η r - 1 4 ( 1 - cos θ - cos θ + ) η r - 1 4 ( 1 - cos θ + cos θ - ) η r + 1 4 ( 1 + cos θ + cos θ + ) ] .
T 0 = [ 2 η r + 1 0 0 2 η r + 1 ] .
[ E + L E - L ] = [ r + + r - + r + - r - - ] [ E + R R - R ]
E L = R E R .
R = M R M T - 1 = 1 M T × [ ( η r + 1 ) 2 16 ( 1 - cos θ + cos θ + ) ( 1 + cos θ - cos θ - ) - ( η r - 1 ) 2 16 ( 1 - cos θ + cos θ - ) ( 1 + cos θ - cos θ + )             η r 2 - 1 8 cos θ + + cos θ - cos θ + η r 2 - 1 8 cos θ + + cos θ - cos θ -             ( η r + 1 ) 2 16 ( 1 + cos θ + cos θ + ) ( 1 - cos θ - cos θ - ) - ( η r - 1 ) 2 16 ( 1 + cos θ + cos θ - ) ( 1 - cos θ - cos θ + ) ] .
R 0 = [ 0 η r - 1 η r + 1 η r - 1 η r + 1 0 ] .
R = - M T - 1 M R ,
T = M T - M R M T - 1 M R .
R = - 1 M T × [ ( η r + 1 ) 2 16 ( 1 - cos θ + cos θ + ) ( 1 + cos θ - cos θ - ) - ( η r - 1 ) 2 16 ( 1 + cos θ + cos θ - ) ( 1 - cos θ - cos θ + )             η r 2 - 1 8 ( cos θ - cos θ + + cos θ - cos θ - ) η r 2 - 1 8 ( cos θ + cos θ + + cos θ + cos θ - )             ( η r + 1 ) 2 16 ( 1 + cos θ + cos θ + ) ( 1 - cos θ - cos θ - ) - ( η r - 1 ) 2 16 ( 1 - cos θ + cos θ - ) ( 1 + cos θ - cos θ + ) ] ,
T = 1 M T [ η r cos θ + cos θ + η r + 1 4 ( 1 + cos θ - cos θ - ) - η r cos θ - cos θ + η r - 1 4 ( 1 - cos θ + cos θ - ) - η r cos θ + cos θ - η r - 1 4 ( 1 - cos θ - cos θ + ) η r cos θ - cos θ - η r + 1 4 ( 1 + cos θ + cos θ + ) ] .
R 0 = [ 0 1 - η r 1 + η r 1 - η r 1 + η r 0 ] ,
T 0 = [ 2 η r η r + 1 0 0 2 η r η r + 1 ] ,
M T = η r 2 + 1 8 cos θ + + cos θ - cos θ + η r 4 ( 1 + cos θ + cos θ - cos 2 θ ) ,
R = 1 M T × [ η r 4 ( 1 - cos θ + cos θ ) ( 1 + cos θ - cos θ ) η r 2 - 1 8 cos θ + + cos θ - cos θ η r 2 - 1 8 cos θ + + cos θ - cos θ η r 4 ( 1 + cos θ + cos θ ) ( 1 - cos θ - cos θ ) ] .
T = [ 2 cos θ + cos θ + + cos θ + 0 0 2 cos θ - cos θ - + cos θ - ] ,
R = [ cos θ + - cos θ + cos θ + + cos θ + 0 0 cos θ - - cos θ - cos θ - + cos θ - ] .
E + L E - L = r + + E + R + r - + E - R r + - E + R + r - - E - R
r + + r - - - r - + r + - = R = M R M T = 0.
( η r - 1 η r + 1 ) 2 = ( cos θ + p - cos θ + p ) ( cos θ - p - cos θ - p ) ( cos θ + p + cos θ - p ) ( cos θ - p + cos θ + p ) .
2 η r η r 2 + 1 = cos θ p ( cos θ + p + cos θ - p ) cos 2 θ p + cos θ + p cos θ - p .
η r = cos θ p cos θ p             or             η r = cos θ p cos θ p ,
k n ± < k 0 sin θ 0
E - R = t + - E + R + t - - E - R = 0.
E - R E + R = η r - 1 η r + 1 ( 1 - cos θ + cos θ - ) ( 1 + cos θ + cos θ + ) - 1 .
E + R E - R = η r - 1 η r + 1 ( 1 - cos θ - cos θ + ) ( 1 + cos θ - cos θ - ) - 1 .
E - R E + R = η r - 1 η r + 1 cos θ - cos θ + cos θ + cos θ + ,
E + R E - R = η r - 1 η r + 1 cos θ - cos θ - cos θ + cos θ - .
r = E + L + E - L E + R + E - R = η r cos θ - cos θ + η r cos θ + cos θ + ,
r = E + L - E - L E + R - E - R = cos θ - η r cos θ + cos θ + η r cos θ + ,
t = E + R E + R + E - R = 2 cos θ η r cos θ + cos θ + ,
t = E + R E + R - E - R = 2 cos θ cos θ + η r cos θ + ,
[ E n - 1 + R E n - 1 - R E n - 1 + L E n - 1 - L ] = [ e - i φ n + 0 0 0 0 e - i φ n - 0 0 0 0 e i φ n + 0 0 0 0 e i φ n - ] [ E n + R E n - R E n + L E n - L ]
E n - 1 = P n n E ,
φ n ± = k n ± d n cos θ n ± .
E n = M n n E .
S = M 0 P 1 M 1 P n M n P N M N .
S = [ S T S R S R S T ] .
R S = S R S T - 1 ,
T S = S T - 1 .
R S = - S T - 1 S R ,
T S = S T - S R S T - 1 S R .
S = η 0 2 η N + 1 2 cos 2 θ N + 1 cos 2 θ 0 .
d r d z = 1 2 k d k d z ( 1 - r 2 ) - i 2 k r ,
d d z R = χ - R χ R - i K R - i R K ,
χ = [ 1 2 k + d k + d z tan 2 θ + 1 2 η d η d z 1 2 η d η d z 1 2 k - d k - d z tan 2 θ - ] ,
K = [ k + cos θ + 0 0 k - cos θ - ]
[ a 1 a 2 a 3 a 4 ] [ b 1 b 2 b 3 b 4 ] = [ a 1 b 1 a 2 b 2 a 3 b 3 a 4 b 4 ] .
d d z R = χ - R χ R - i 2 κ R ,
κ = [ k + cos θ + k + cos θ + + k - cos θ - 2 k + cos θ + + k - cos θ - 2 k - cos θ - ] .
d r d z = 1 2 η d η d z ( 1 - r 2 ) - i ( k + + k - ) r ,
R ( u + ) = [ R ( u - ) - R int ] [ I - R int R ( u - ) ] - 1 ,
r ( u + ) = r ( u - ) + r 0 1 + r 0 r ( u - ) ,
d d z T = T ( γ - χ R - i K ) ,
γ = [ 1 2 k + d k + d z tan 2 θ + - 1 2 η d η d z - 1 4 η d η d z ( 1 - cos θ - cos θ + ) - 1 4 η d η d z ( 1 - cos θ + cos θ - ) 1 2 k - d k - d z tan 2 θ - - 1 2 η d η d z ] .
d t ± ± d z = - 1 2 η d η d z t ± ± ( 1 + r ± ) - i k ± t ± ±
d d z ln ( t ± ± ) = - 1 2 η d η d z ( 1 + r ± ) - i k ± ,

Metrics