Abstract

The field theory of guided waves in optical fibers with step-index profiles and in which both core and cladding are chiral isotropic media is developed. We show that both surface and semileaky modes can propagate in optically active fibers. To shed light on the guidance and leakage properties of chiral isotropic fibers we present a physical interpretation and several numerical results. The new leakage effect associated with semileaky modes is an important property that cannot be neglected in the analysis of chiral optical fibers but that, nevertheless, has been systematically disregarded in the literature.

© 2002 Optical Society of America

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  23. S. K. Sheem, W. K. Burns, and A. F. Milton, “Leaky mode propagation in Ti-diffused LiNbO3 and LiTaO3 waveguides,” Opt. Lett. 3, 76–78 (1978).
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  25. D. Marcuse and I. P. Kaminov, “Modes of a symmetric slab optical waveguide in birefringent media. II. Slab with a coplanar optical axis,” IEEE J. Quantum Electron. QE-15, 92–101 (1979).
    [CrossRef]
  26. W. K. Burns, S. K. Sheem, and A. F. Milton, “Approximate calculation of leaky-mode loss coefficients for Ti-diffused LiNbO3 waveguides,” IEEE J. Quantum Electron. QE-15, 1282–1289 (1979).
    [CrossRef]
  27. J. Čtyroký and M. Čada, “Generalized WKB method for the analysis of light propagation in inhomogeneous anisotropic optical waveguides,” IEEE J. Quantum Electron. QE-17, 1064–1070 (1981).
    [CrossRef]
  28. M. Koshiba, H. Kumagami, and M. Suzuki, “Finite-element solution of planar arbitrary anisotropic diffused optical waveguides,” J. Lightwave Technol. LT-3, 773–778 (1985).
    [CrossRef]
  29. A. Knoesen, T. K. Gaylord, and M. G. Moharam, “Hybrid guided modes in uniaxial dielectric planar waveguides,” J. Lightwave Technol. 6, 1083–1104 (1988).
    [CrossRef]
  30. L. Torner, F. Canal, and J. H. Marco, “Leaky modes in multilayer uniaxial optical waveguides,” Appl. Opt. 29, 2805–2814 (1990).
    [CrossRef] [PubMed]
  31. L. Torner, J. Recolons, and J. P. Torres, “Guided-to-leaky mode transition in uniaxial optical slab waveguides,” J. Lightwave Technol. 11, 1592–1600 (1993).
    [CrossRef]
  32. R. E. Smith and S. N. Houde-Walter, “The migration of bound and leaky solutions to the waveguide dispersion relation,” J. Lightwave Technol. 11, 1760–1768 (1993).
    [CrossRef]
  33. A. D’Orazio, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Leaky wave propagation in planar multilayer birefringent waveguides: longitudinal dielectric tensor configurations,” J. Lightwave Technol. 12, 453–462 (1994).
    [CrossRef]
  34. T. A. Maldonado and T. K. Gaylord, “Hybrid guided modes in biaxial planar waveguides,” J. Lightwave Technol. 14, 486–499 (1996).
    [CrossRef]
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    [CrossRef]
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  39. A. Lakhtakia and W. S. Weiglhofer, “Are linear, nonreciprocal, biisotropic media forbidden?” IEEE Trans. Microwave Theory Tech. 42, 1715–1716 (1994).
    [CrossRef]
  40. A. Lakhtakia and W. S. Weiglhofer, “Constraint on linear, homogeneous constitutive relations,” Phys. Rev. E 50, 5017–5019 (1994).
    [CrossRef]
  41. W. S. Weiglhofer and A. Lakhtakia, “A brief review of a new development for constitutive relations for linear bi-anisotropic media,” IEEE Antennas Propag. Mag. 37, 32–35 (1995).
    [CrossRef]
  42. W. S. Weiglhofer and A. Lakhtakia, “The Post constraint revisited,” Int. J. Electron. Commun. 52, 276–279 (1998).
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    [CrossRef]
  45. S. Tretyakov, “Anything wrong with the naturally non-reciprocal materials?” IEEE Antennas Propag. Mag. 38, 84–85 (1996).
  46. J. C. Monzon, “Author’s reply,” IEEE Trans. Antennas Propag. 45, 749 (1997).
    [CrossRef]
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  48. A. Lakhtakia, “Recent contributions to classical electromagnetic theory of chiral media: what next?” Speculations Sci. Technol. 14, 2–17 (1991).
  49. M. J. Adams, An Introduction to Optical Waveguides (Wiley, Chichester, UK, 1981), pp. 223–228.
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    [CrossRef]

2001

A. L. Topa, C. R. Paiva, and A. M. Barbosa, “Least squares boundary residual method for the analysis of step discontinuities in open chiral waveguides,” Int. J. Electron. Commun. 55, 281–291 (2001).
[CrossRef]

1998

W. S. Weiglhofer and A. Lakhtakia, “The Post constraint revisited,” Int. J. Electron. Commun. 52, 276–279 (1998).

1997

J. C. Monzon, “Author’s reply,” IEEE Trans. Antennas Propag. 45, 749 (1997).
[CrossRef]

1996

S. Tretyakov, “Anything wrong with the naturally non-reciprocal materials?” IEEE Antennas Propag. Mag. 38, 84–85 (1996).

T. A. Maldonado and T. K. Gaylord, “Hybrid guided modes in biaxial planar waveguides,” J. Lightwave Technol. 14, 486–499 (1996).
[CrossRef]

1995

A. H. Sihvola, “Are nonreciprocal bi-isotropic media forbidden indeed?” IEEE Trans. Microwave Theory Tech. 43, 2160–2162 (1995).
[CrossRef]

W. S. Weiglhofer and A. Lakhtakia, “A brief review of a new development for constitutive relations for linear bi-anisotropic media,” IEEE Antennas Propag. Mag. 37, 32–35 (1995).
[CrossRef]

H. Cory, “Chiral devices—an overview of canonical problems,” J. Electromagn. Waves Appl. 9, 805–829 (1995).
[CrossRef]

S. F. Mahmoud, “Guided modes on open chirowaveguides,” IEEE Trans. Microwave Theory Tech. 43, 205–209 (1995).
[CrossRef]

1994

A. Lakhtakia and W. S. Weiglhofer, “Are linear, nonreciprocal, biisotropic media forbidden?” IEEE Trans. Microwave Theory Tech. 42, 1715–1716 (1994).
[CrossRef]

A. Lakhtakia and W. S. Weiglhofer, “Constraint on linear, homogeneous constitutive relations,” Phys. Rev. E 50, 5017–5019 (1994).
[CrossRef]

A. D’Orazio, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Leaky wave propagation in planar multilayer birefringent waveguides: longitudinal dielectric tensor configurations,” J. Lightwave Technol. 12, 453–462 (1994).
[CrossRef]

R. C. Qiu and I-T. Lu, “Guided waves in chiral optical fibers,” J. Opt. Soc. Am. A 11, 3212–3219 (1994).
[CrossRef]

A. K. Singh, Kh. S. Singh, P. Khastgir, S. P. Ojha, and O. N. Singh, “Modal cutoff condition of an optical chiral fiber with different chiralities in the core and the cladding,” J. Opt. Soc. Am. B 11, 1283–1287 (1994).
[CrossRef]

1993

H. Cory and S. Gov, “Mode energy transfer along a circular open chirowaveguide,” Microwave Opt. Technol. Lett. 6, 536–541 (1993).
[CrossRef]

L. Torner, J. Recolons, and J. P. Torres, “Guided-to-leaky mode transition in uniaxial optical slab waveguides,” J. Lightwave Technol. 11, 1592–1600 (1993).
[CrossRef]

R. E. Smith and S. N. Houde-Walter, “The migration of bound and leaky solutions to the waveguide dispersion relation,” J. Lightwave Technol. 11, 1760–1768 (1993).
[CrossRef]

1992

H. Cory and T. Tamir, “Coupling processes in circular open chirowaveguides,” IEE Proc. H 139, 165–170 (1992).

I. V. Lindell, A. H. Sihvola, and J. Kurkijärvi, “Karl F. Lindman—the last Hertzian and a harbinger of electromagnetic chirality,” IEEE Antennas Propag. Mag. 34, 24–30 (1992).
[CrossRef]

C. R. Paiva, A. L. Topa, and A. M. Barbosa, “Semileaky waves in dielectric chirowaveguides,” Opt. Lett. 17, 1670–1672 (1992).
[CrossRef] [PubMed]

1991

N. Engheta and P. Pelet, “Surface waves in chiral layers,” Opt. Lett. 16, 723–725 (1991).
[CrossRef] [PubMed]

C. R. Paiva and A. M. Barbosa, “A method for the analysis of biisotropic planar waveguides—application to a grounded chiroslabguide,” Electromagnetics 11, 209–221 (1991).
[CrossRef]

H. Cory and I. Rosenhouse, “Electromagnetic wave propagation along a chiral slab,” IEE Proc. H 138, 51–54 (1991).

M. I. Oksanen, P. K. Koivisto, and I. V. Lindell, “Dispersion curves and fields for a chiral slab waveguide,” IEE Proc. H 138, 327–334 (1991).

A. H. Sihvola and I. V. Lindell, “Bi-isotropic constitutive relations,” Microwave Opt. Technol. Lett. 4, 295–297 (1991).
[CrossRef]

A. Lakhtakia, “Recent contributions to classical electromagnetic theory of chiral media: what next?” Speculations Sci. Technol. 14, 2–17 (1991).

1990

J. A. M. Svedin, “Propagation analysis of chirowaveguides using the finite-element method,” IEEE Trans. Microwave Theory Tech. 38, 1488–1496 (1990).
[CrossRef]

L. Torner, F. Canal, and J. H. Marco, “Leaky modes in multilayer uniaxial optical waveguides,” Appl. Opt. 29, 2805–2814 (1990).
[CrossRef] [PubMed]

1988

A. Knoesen, T. K. Gaylord, and M. G. Moharam, “Hybrid guided modes in uniaxial dielectric planar waveguides,” J. Lightwave Technol. 6, 1083–1104 (1988).
[CrossRef]

1985

M. Koshiba, H. Kumagami, and M. Suzuki, “Finite-element solution of planar arbitrary anisotropic diffused optical waveguides,” J. Lightwave Technol. LT-3, 773–778 (1985).
[CrossRef]

1982

M. P. Carpentier and A. F. dos Santos, “Solution of equations involving analytic functions,” J. Comput. Phys. 45, 210–220 (1982).
[CrossRef]

1981

S. T. Peng and A. A. Oliner, “Guidance and leakage properties of a class of open dielectric waveguides. I. Mathematical formulations,” IEEE Trans. Microwave Theory Tech. MTT-29, 843–855 (1981).
[CrossRef]

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides. II. New physical effects,” IEEE Trans. Microwave Theory Tech. MTT-29, 855–869 (1981).
[CrossRef]

J. Čtyroký and M. Čada, “Generalized WKB method for the analysis of light propagation in inhomogeneous anisotropic optical waveguides,” IEEE J. Quantum Electron. QE-17, 1064–1070 (1981).
[CrossRef]

1979

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

D. Marcuse and I. P. Kaminov, “Modes of a symmetric slab optical waveguide in birefringent media. II. Slab with a coplanar optical axis,” IEEE J. Quantum Electron. QE-15, 92–101 (1979).
[CrossRef]

W. K. Burns, S. K. Sheem, and A. F. Milton, “Approximate calculation of leaky-mode loss coefficients for Ti-diffused LiNbO3 waveguides,” IEEE J. Quantum Electron. QE-15, 1282–1289 (1979).
[CrossRef]

1978

J. Čtyroký and M. Čada, “Guidance and semileaky modes in anisotropic optical waveguides of LiNbO3 type,” Opt. Commun. 27, 353–357 (1978).
[CrossRef]

K. Yamanouchi, T. Kamiya, and K. Shibayama, “New leaky surface waves in anisotropic metal-diffused optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-26, 298–305 (1978).
[CrossRef]

S. K. Sheem, W. K. Burns, and A. F. Milton, “Leaky mode propagation in Ti-diffused LiNbO3 and LiTaO3 waveguides,” Opt. Lett. 3, 76–78 (1978).
[CrossRef]

1937

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

Barbosa, A. M.

A. L. Topa, C. R. Paiva, and A. M. Barbosa, “Least squares boundary residual method for the analysis of step discontinuities in open chiral waveguides,” Int. J. Electron. Commun. 55, 281–291 (2001).
[CrossRef]

C. R. Paiva, A. L. Topa, and A. M. Barbosa, “Semileaky waves in dielectric chirowaveguides,” Opt. Lett. 17, 1670–1672 (1992).
[CrossRef] [PubMed]

C. R. Paiva and A. M. Barbosa, “A method for the analysis of biisotropic planar waveguides—application to a grounded chiroslabguide,” Electromagnetics 11, 209–221 (1991).
[CrossRef]

Burns, W. K.

W. K. Burns, S. K. Sheem, and A. F. Milton, “Approximate calculation of leaky-mode loss coefficients for Ti-diffused LiNbO3 waveguides,” IEEE J. Quantum Electron. QE-15, 1282–1289 (1979).
[CrossRef]

S. K. Sheem, W. K. Burns, and A. F. Milton, “Leaky mode propagation in Ti-diffused LiNbO3 and LiTaO3 waveguides,” Opt. Lett. 3, 76–78 (1978).
[CrossRef]

Cada, M.

J. Čtyroký and M. Čada, “Generalized WKB method for the analysis of light propagation in inhomogeneous anisotropic optical waveguides,” IEEE J. Quantum Electron. QE-17, 1064–1070 (1981).
[CrossRef]

J. Čtyroký and M. Čada, “Guidance and semileaky modes in anisotropic optical waveguides of LiNbO3 type,” Opt. Commun. 27, 353–357 (1978).
[CrossRef]

Canal, F.

Carpentier, M. P.

M. P. Carpentier and A. F. dos Santos, “Solution of equations involving analytic functions,” J. Comput. Phys. 45, 210–220 (1982).
[CrossRef]

Condon, E. U.

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

Cory, H.

H. Cory, “Chiral devices—an overview of canonical problems,” J. Electromagn. Waves Appl. 9, 805–829 (1995).
[CrossRef]

H. Cory and S. Gov, “Mode energy transfer along a circular open chirowaveguide,” Microwave Opt. Technol. Lett. 6, 536–541 (1993).
[CrossRef]

H. Cory and T. Tamir, “Coupling processes in circular open chirowaveguides,” IEE Proc. H 139, 165–170 (1992).

H. Cory and I. Rosenhouse, “Electromagnetic wave propagation along a chiral slab,” IEE Proc. H 138, 51–54 (1991).

Ctyroký, J.

J. Čtyroký and M. Čada, “Generalized WKB method for the analysis of light propagation in inhomogeneous anisotropic optical waveguides,” IEEE J. Quantum Electron. QE-17, 1064–1070 (1981).
[CrossRef]

J. Čtyroký and M. Čada, “Guidance and semileaky modes in anisotropic optical waveguides of LiNbO3 type,” Opt. Commun. 27, 353–357 (1978).
[CrossRef]

D’Orazio, A.

A. D’Orazio, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Leaky wave propagation in planar multilayer birefringent waveguides: longitudinal dielectric tensor configurations,” J. Lightwave Technol. 12, 453–462 (1994).
[CrossRef]

De Sario, M.

A. D’Orazio, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Leaky wave propagation in planar multilayer birefringent waveguides: longitudinal dielectric tensor configurations,” J. Lightwave Technol. 12, 453–462 (1994).
[CrossRef]

dos Santos, A. F.

M. P. Carpentier and A. F. dos Santos, “Solution of equations involving analytic functions,” J. Comput. Phys. 45, 210–220 (1982).
[CrossRef]

Engheta, N.

Gaylord, T. K.

T. A. Maldonado and T. K. Gaylord, “Hybrid guided modes in biaxial planar waveguides,” J. Lightwave Technol. 14, 486–499 (1996).
[CrossRef]

A. Knoesen, T. K. Gaylord, and M. G. Moharam, “Hybrid guided modes in uniaxial dielectric planar waveguides,” J. Lightwave Technol. 6, 1083–1104 (1988).
[CrossRef]

Gov, S.

H. Cory and S. Gov, “Mode energy transfer along a circular open chirowaveguide,” Microwave Opt. Technol. Lett. 6, 536–541 (1993).
[CrossRef]

Houde-Walter, S. N.

R. E. Smith and S. N. Houde-Walter, “The migration of bound and leaky solutions to the waveguide dispersion relation,” J. Lightwave Technol. 11, 1760–1768 (1993).
[CrossRef]

Hsu, T. I.

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides. II. New physical effects,” IEEE Trans. Microwave Theory Tech. MTT-29, 855–869 (1981).
[CrossRef]

Jaggard, D. L.

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

Kaminov, I. P.

D. Marcuse and I. P. Kaminov, “Modes of a symmetric slab optical waveguide in birefringent media. II. Slab with a coplanar optical axis,” IEEE J. Quantum Electron. QE-15, 92–101 (1979).
[CrossRef]

Kamiya, T.

K. Yamanouchi, T. Kamiya, and K. Shibayama, “New leaky surface waves in anisotropic metal-diffused optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-26, 298–305 (1978).
[CrossRef]

Khastgir, P.

Knoesen, A.

A. Knoesen, T. K. Gaylord, and M. G. Moharam, “Hybrid guided modes in uniaxial dielectric planar waveguides,” J. Lightwave Technol. 6, 1083–1104 (1988).
[CrossRef]

Koivisto, P. K.

M. I. Oksanen, P. K. Koivisto, and I. V. Lindell, “Dispersion curves and fields for a chiral slab waveguide,” IEE Proc. H 138, 327–334 (1991).

Koshiba, M.

M. Koshiba, H. Kumagami, and M. Suzuki, “Finite-element solution of planar arbitrary anisotropic diffused optical waveguides,” J. Lightwave Technol. LT-3, 773–778 (1985).
[CrossRef]

Kumagami, H.

M. Koshiba, H. Kumagami, and M. Suzuki, “Finite-element solution of planar arbitrary anisotropic diffused optical waveguides,” J. Lightwave Technol. LT-3, 773–778 (1985).
[CrossRef]

Kurkijärvi, J.

I. V. Lindell, A. H. Sihvola, and J. Kurkijärvi, “Karl F. Lindman—the last Hertzian and a harbinger of electromagnetic chirality,” IEEE Antennas Propag. Mag. 34, 24–30 (1992).
[CrossRef]

Lakhtakia, A.

W. S. Weiglhofer and A. Lakhtakia, “The Post constraint revisited,” Int. J. Electron. Commun. 52, 276–279 (1998).

W. S. Weiglhofer and A. Lakhtakia, “A brief review of a new development for constitutive relations for linear bi-anisotropic media,” IEEE Antennas Propag. Mag. 37, 32–35 (1995).
[CrossRef]

A. Lakhtakia and W. S. Weiglhofer, “Are linear, nonreciprocal, biisotropic media forbidden?” IEEE Trans. Microwave Theory Tech. 42, 1715–1716 (1994).
[CrossRef]

A. Lakhtakia and W. S. Weiglhofer, “Constraint on linear, homogeneous constitutive relations,” Phys. Rev. E 50, 5017–5019 (1994).
[CrossRef]

A. Lakhtakia, “Recent contributions to classical electromagnetic theory of chiral media: what next?” Speculations Sci. Technol. 14, 2–17 (1991).

Lindell, I. V.

I. V. Lindell, A. H. Sihvola, and J. Kurkijärvi, “Karl F. Lindman—the last Hertzian and a harbinger of electromagnetic chirality,” IEEE Antennas Propag. Mag. 34, 24–30 (1992).
[CrossRef]

A. H. Sihvola and I. V. Lindell, “Bi-isotropic constitutive relations,” Microwave Opt. Technol. Lett. 4, 295–297 (1991).
[CrossRef]

M. I. Oksanen, P. K. Koivisto, and I. V. Lindell, “Dispersion curves and fields for a chiral slab waveguide,” IEE Proc. H 138, 327–334 (1991).

Lu, I-T.

Mahmoud, S. F.

S. F. Mahmoud, “Guided modes on open chirowaveguides,” IEEE Trans. Microwave Theory Tech. 43, 205–209 (1995).
[CrossRef]

Maldonado, T. A.

T. A. Maldonado and T. K. Gaylord, “Hybrid guided modes in biaxial planar waveguides,” J. Lightwave Technol. 14, 486–499 (1996).
[CrossRef]

Marco, J. H.

Marcuse, D.

D. Marcuse and I. P. Kaminov, “Modes of a symmetric slab optical waveguide in birefringent media. II. Slab with a coplanar optical axis,” IEEE J. Quantum Electron. QE-15, 92–101 (1979).
[CrossRef]

Mickelson, A. R.

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

Milton, A. F.

W. K. Burns, S. K. Sheem, and A. F. Milton, “Approximate calculation of leaky-mode loss coefficients for Ti-diffused LiNbO3 waveguides,” IEEE J. Quantum Electron. QE-15, 1282–1289 (1979).
[CrossRef]

S. K. Sheem, W. K. Burns, and A. F. Milton, “Leaky mode propagation in Ti-diffused LiNbO3 and LiTaO3 waveguides,” Opt. Lett. 3, 76–78 (1978).
[CrossRef]

Moharam, M. G.

A. Knoesen, T. K. Gaylord, and M. G. Moharam, “Hybrid guided modes in uniaxial dielectric planar waveguides,” J. Lightwave Technol. 6, 1083–1104 (1988).
[CrossRef]

Monzon, J. C.

J. C. Monzon, “Author’s reply,” IEEE Trans. Antennas Propag. 45, 749 (1997).
[CrossRef]

Ojha, S. P.

Oksanen, M. I.

M. I. Oksanen, P. K. Koivisto, and I. V. Lindell, “Dispersion curves and fields for a chiral slab waveguide,” IEE Proc. H 138, 327–334 (1991).

Oliner, A. A.

S. T. Peng and A. A. Oliner, “Guidance and leakage properties of a class of open dielectric waveguides. I. Mathematical formulations,” IEEE Trans. Microwave Theory Tech. MTT-29, 843–855 (1981).
[CrossRef]

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides. II. New physical effects,” IEEE Trans. Microwave Theory Tech. MTT-29, 855–869 (1981).
[CrossRef]

Paiva, C. R.

A. L. Topa, C. R. Paiva, and A. M. Barbosa, “Least squares boundary residual method for the analysis of step discontinuities in open chiral waveguides,” Int. J. Electron. Commun. 55, 281–291 (2001).
[CrossRef]

C. R. Paiva, A. L. Topa, and A. M. Barbosa, “Semileaky waves in dielectric chirowaveguides,” Opt. Lett. 17, 1670–1672 (1992).
[CrossRef] [PubMed]

C. R. Paiva and A. M. Barbosa, “A method for the analysis of biisotropic planar waveguides—application to a grounded chiroslabguide,” Electromagnetics 11, 209–221 (1991).
[CrossRef]

Papas, C. H.

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

Pelet, P.

Peng, S. T.

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides. II. New physical effects,” IEEE Trans. Microwave Theory Tech. MTT-29, 855–869 (1981).
[CrossRef]

S. T. Peng and A. A. Oliner, “Guidance and leakage properties of a class of open dielectric waveguides. I. Mathematical formulations,” IEEE Trans. Microwave Theory Tech. MTT-29, 843–855 (1981).
[CrossRef]

Petruzzelli, V.

A. D’Orazio, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Leaky wave propagation in planar multilayer birefringent waveguides: longitudinal dielectric tensor configurations,” J. Lightwave Technol. 12, 453–462 (1994).
[CrossRef]

Prudenzano, F.

A. D’Orazio, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Leaky wave propagation in planar multilayer birefringent waveguides: longitudinal dielectric tensor configurations,” J. Lightwave Technol. 12, 453–462 (1994).
[CrossRef]

Qiu, R. C.

Recolons, J.

L. Torner, J. Recolons, and J. P. Torres, “Guided-to-leaky mode transition in uniaxial optical slab waveguides,” J. Lightwave Technol. 11, 1592–1600 (1993).
[CrossRef]

Rosenhouse, I.

H. Cory and I. Rosenhouse, “Electromagnetic wave propagation along a chiral slab,” IEE Proc. H 138, 51–54 (1991).

Sanchez, A.

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides. II. New physical effects,” IEEE Trans. Microwave Theory Tech. MTT-29, 855–869 (1981).
[CrossRef]

Sheem, S. K.

W. K. Burns, S. K. Sheem, and A. F. Milton, “Approximate calculation of leaky-mode loss coefficients for Ti-diffused LiNbO3 waveguides,” IEEE J. Quantum Electron. QE-15, 1282–1289 (1979).
[CrossRef]

S. K. Sheem, W. K. Burns, and A. F. Milton, “Leaky mode propagation in Ti-diffused LiNbO3 and LiTaO3 waveguides,” Opt. Lett. 3, 76–78 (1978).
[CrossRef]

Shibayama, K.

K. Yamanouchi, T. Kamiya, and K. Shibayama, “New leaky surface waves in anisotropic metal-diffused optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-26, 298–305 (1978).
[CrossRef]

Sihvola, A. H.

A. H. Sihvola, “Are nonreciprocal bi-isotropic media forbidden indeed?” IEEE Trans. Microwave Theory Tech. 43, 2160–2162 (1995).
[CrossRef]

I. V. Lindell, A. H. Sihvola, and J. Kurkijärvi, “Karl F. Lindman—the last Hertzian and a harbinger of electromagnetic chirality,” IEEE Antennas Propag. Mag. 34, 24–30 (1992).
[CrossRef]

A. H. Sihvola and I. V. Lindell, “Bi-isotropic constitutive relations,” Microwave Opt. Technol. Lett. 4, 295–297 (1991).
[CrossRef]

Singh, A. K.

Singh, Kh. S.

Singh, O. N.

Smith, R. E.

R. E. Smith and S. N. Houde-Walter, “The migration of bound and leaky solutions to the waveguide dispersion relation,” J. Lightwave Technol. 11, 1760–1768 (1993).
[CrossRef]

Suzuki, M.

M. Koshiba, H. Kumagami, and M. Suzuki, “Finite-element solution of planar arbitrary anisotropic diffused optical waveguides,” J. Lightwave Technol. LT-3, 773–778 (1985).
[CrossRef]

Svedin, J. A. M.

J. A. M. Svedin, “Propagation analysis of chirowaveguides using the finite-element method,” IEEE Trans. Microwave Theory Tech. 38, 1488–1496 (1990).
[CrossRef]

Tamir, T.

H. Cory and T. Tamir, “Coupling processes in circular open chirowaveguides,” IEE Proc. H 139, 165–170 (1992).

Topa, A. L.

A. L. Topa, C. R. Paiva, and A. M. Barbosa, “Least squares boundary residual method for the analysis of step discontinuities in open chiral waveguides,” Int. J. Electron. Commun. 55, 281–291 (2001).
[CrossRef]

C. R. Paiva, A. L. Topa, and A. M. Barbosa, “Semileaky waves in dielectric chirowaveguides,” Opt. Lett. 17, 1670–1672 (1992).
[CrossRef] [PubMed]

Torner, L.

L. Torner, J. Recolons, and J. P. Torres, “Guided-to-leaky mode transition in uniaxial optical slab waveguides,” J. Lightwave Technol. 11, 1592–1600 (1993).
[CrossRef]

L. Torner, F. Canal, and J. H. Marco, “Leaky modes in multilayer uniaxial optical waveguides,” Appl. Opt. 29, 2805–2814 (1990).
[CrossRef] [PubMed]

Torres, J. P.

L. Torner, J. Recolons, and J. P. Torres, “Guided-to-leaky mode transition in uniaxial optical slab waveguides,” J. Lightwave Technol. 11, 1592–1600 (1993).
[CrossRef]

Tretyakov, S.

S. Tretyakov, “Anything wrong with the naturally non-reciprocal materials?” IEEE Antennas Propag. Mag. 38, 84–85 (1996).

Weiglhofer, W. S.

W. S. Weiglhofer and A. Lakhtakia, “The Post constraint revisited,” Int. J. Electron. Commun. 52, 276–279 (1998).

W. S. Weiglhofer and A. Lakhtakia, “A brief review of a new development for constitutive relations for linear bi-anisotropic media,” IEEE Antennas Propag. Mag. 37, 32–35 (1995).
[CrossRef]

A. Lakhtakia and W. S. Weiglhofer, “Are linear, nonreciprocal, biisotropic media forbidden?” IEEE Trans. Microwave Theory Tech. 42, 1715–1716 (1994).
[CrossRef]

A. Lakhtakia and W. S. Weiglhofer, “Constraint on linear, homogeneous constitutive relations,” Phys. Rev. E 50, 5017–5019 (1994).
[CrossRef]

Yamanouchi, K.

K. Yamanouchi, T. Kamiya, and K. Shibayama, “New leaky surface waves in anisotropic metal-diffused optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-26, 298–305 (1978).
[CrossRef]

Appl. Opt.

Electromagnetics

C. R. Paiva and A. M. Barbosa, “A method for the analysis of biisotropic planar waveguides—application to a grounded chiroslabguide,” Electromagnetics 11, 209–221 (1991).
[CrossRef]

IEE Proc. H

H. Cory and I. Rosenhouse, “Electromagnetic wave propagation along a chiral slab,” IEE Proc. H 138, 51–54 (1991).

M. I. Oksanen, P. K. Koivisto, and I. V. Lindell, “Dispersion curves and fields for a chiral slab waveguide,” IEE Proc. H 138, 327–334 (1991).

H. Cory and T. Tamir, “Coupling processes in circular open chirowaveguides,” IEE Proc. H 139, 165–170 (1992).

IEEE Antennas Propag. Mag.

W. S. Weiglhofer and A. Lakhtakia, “A brief review of a new development for constitutive relations for linear bi-anisotropic media,” IEEE Antennas Propag. Mag. 37, 32–35 (1995).
[CrossRef]

S. Tretyakov, “Anything wrong with the naturally non-reciprocal materials?” IEEE Antennas Propag. Mag. 38, 84–85 (1996).

I. V. Lindell, A. H. Sihvola, and J. Kurkijärvi, “Karl F. Lindman—the last Hertzian and a harbinger of electromagnetic chirality,” IEEE Antennas Propag. Mag. 34, 24–30 (1992).
[CrossRef]

IEEE J. Quantum Electron.

D. Marcuse and I. P. Kaminov, “Modes of a symmetric slab optical waveguide in birefringent media. II. Slab with a coplanar optical axis,” IEEE J. Quantum Electron. QE-15, 92–101 (1979).
[CrossRef]

W. K. Burns, S. K. Sheem, and A. F. Milton, “Approximate calculation of leaky-mode loss coefficients for Ti-diffused LiNbO3 waveguides,” IEEE J. Quantum Electron. QE-15, 1282–1289 (1979).
[CrossRef]

J. Čtyroký and M. Čada, “Generalized WKB method for the analysis of light propagation in inhomogeneous anisotropic optical waveguides,” IEEE J. Quantum Electron. QE-17, 1064–1070 (1981).
[CrossRef]

IEEE Trans. Antennas Propag.

J. C. Monzon, “Author’s reply,” IEEE Trans. Antennas Propag. 45, 749 (1997).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

A. H. Sihvola, “Are nonreciprocal bi-isotropic media forbidden indeed?” IEEE Trans. Microwave Theory Tech. 43, 2160–2162 (1995).
[CrossRef]

A. Lakhtakia and W. S. Weiglhofer, “Are linear, nonreciprocal, biisotropic media forbidden?” IEEE Trans. Microwave Theory Tech. 42, 1715–1716 (1994).
[CrossRef]

J. A. M. Svedin, “Propagation analysis of chirowaveguides using the finite-element method,” IEEE Trans. Microwave Theory Tech. 38, 1488–1496 (1990).
[CrossRef]

S. F. Mahmoud, “Guided modes on open chirowaveguides,” IEEE Trans. Microwave Theory Tech. 43, 205–209 (1995).
[CrossRef]

S. T. Peng and A. A. Oliner, “Guidance and leakage properties of a class of open dielectric waveguides. I. Mathematical formulations,” IEEE Trans. Microwave Theory Tech. MTT-29, 843–855 (1981).
[CrossRef]

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, “Guidance and leakage properties of a class of open dielectric waveguides. II. New physical effects,” IEEE Trans. Microwave Theory Tech. MTT-29, 855–869 (1981).
[CrossRef]

K. Yamanouchi, T. Kamiya, and K. Shibayama, “New leaky surface waves in anisotropic metal-diffused optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-26, 298–305 (1978).
[CrossRef]

Int. J. Electron. Commun.

A. L. Topa, C. R. Paiva, and A. M. Barbosa, “Least squares boundary residual method for the analysis of step discontinuities in open chiral waveguides,” Int. J. Electron. Commun. 55, 281–291 (2001).
[CrossRef]

W. S. Weiglhofer and A. Lakhtakia, “The Post constraint revisited,” Int. J. Electron. Commun. 52, 276–279 (1998).

J. Appl. Phys.

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

J. Comput. Phys.

M. P. Carpentier and A. F. dos Santos, “Solution of equations involving analytic functions,” J. Comput. Phys. 45, 210–220 (1982).
[CrossRef]

J. Electromagn. Waves Appl.

H. Cory, “Chiral devices—an overview of canonical problems,” J. Electromagn. Waves Appl. 9, 805–829 (1995).
[CrossRef]

J. Lightwave Technol.

L. Torner, J. Recolons, and J. P. Torres, “Guided-to-leaky mode transition in uniaxial optical slab waveguides,” J. Lightwave Technol. 11, 1592–1600 (1993).
[CrossRef]

R. E. Smith and S. N. Houde-Walter, “The migration of bound and leaky solutions to the waveguide dispersion relation,” J. Lightwave Technol. 11, 1760–1768 (1993).
[CrossRef]

A. D’Orazio, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Leaky wave propagation in planar multilayer birefringent waveguides: longitudinal dielectric tensor configurations,” J. Lightwave Technol. 12, 453–462 (1994).
[CrossRef]

T. A. Maldonado and T. K. Gaylord, “Hybrid guided modes in biaxial planar waveguides,” J. Lightwave Technol. 14, 486–499 (1996).
[CrossRef]

M. Koshiba, H. Kumagami, and M. Suzuki, “Finite-element solution of planar arbitrary anisotropic diffused optical waveguides,” J. Lightwave Technol. LT-3, 773–778 (1985).
[CrossRef]

A. Knoesen, T. K. Gaylord, and M. G. Moharam, “Hybrid guided modes in uniaxial dielectric planar waveguides,” J. Lightwave Technol. 6, 1083–1104 (1988).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Microwave Opt. Technol. Lett.

A. H. Sihvola and I. V. Lindell, “Bi-isotropic constitutive relations,” Microwave Opt. Technol. Lett. 4, 295–297 (1991).
[CrossRef]

H. Cory and S. Gov, “Mode energy transfer along a circular open chirowaveguide,” Microwave Opt. Technol. Lett. 6, 536–541 (1993).
[CrossRef]

Opt. Commun.

J. Čtyroký and M. Čada, “Guidance and semileaky modes in anisotropic optical waveguides of LiNbO3 type,” Opt. Commun. 27, 353–357 (1978).
[CrossRef]

Opt. Lett.

Phys. Rev. E

A. Lakhtakia and W. S. Weiglhofer, “Constraint on linear, homogeneous constitutive relations,” Phys. Rev. E 50, 5017–5019 (1994).
[CrossRef]

Rev. Mod. Phys.

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

Speculations Sci. Technol.

A. Lakhtakia, “Recent contributions to classical electromagnetic theory of chiral media: what next?” Speculations Sci. Technol. 14, 2–17 (1991).

Other

M. J. Adams, An Introduction to Optical Waveguides (Wiley, Chichester, UK, 1981), pp. 223–228.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 248–259.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965), Eq. (9.7.2).

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Boston, Mass., 1994), pp. 23–58.

E. J. Post, Formal Structure of Electromagnetics—General Covariance and Electromagnetics (Dover, Mineola, N.Y., 1997), pp. 129, 168–171.

A. Lakhtakia, ed., Selected Papers on Natural Optical Activity, Vol. MS15 of SPIE Milestone Series (SPIE Optical Engineering Press, Bellingham, Wash. 1990).

A. Lakhtakia, Beltrami Fields in Chiral Media (World Scientific, Singapore, 1994).

F. M. Janeiro, A. L. Topa, and C. R. Paiva, “Semi-leaky modes in chiral optical fibers,” presented at LEOS 2001, 14th Annual Meeting, San Diego, Calif., 2001.

R. E. Collin, Field Theory of Guided Waves, 2nd ed., (IEEE Press, New York, 1991), pp. 725–744.

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Boston, Mass., 1994), pp. 119–151.

S. A. Kuehl, S. S. Grové, E. Kuehl, M. Bingle, and J. H. Cloete, “Manufacture of microwave chiral materials and their electromagnetic properties,” in Advances in Complex Electromagnetic Materials, A. Priou, A. Sihvola, S. Tretyakov, and A. Vinogradov, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1997), pp. 317–332.

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Figures (8)

Fig. 1
Fig. 1

(a) Chiral optical fiber. The cladding has an infinite radius. (b) Longitudinal cross section.

Fig. 2
Fig. 2

Trajectories of rays at a planar interface between different chiral media when the incident wave is (a) a RCP wave and (b) a LCP wave.

Fig. 3
Fig. 3

Effective refractive index neff versus chirality χ. In region 1, only surface modes may propagate, whereas in region 2 only semileaky modes may exist.

Fig. 4
Fig. 4

Effective refractive index versus the fiber’s normalized chirality parameter for all modes propagating at v=4.5. Arrows represent the normalized propagation constants for unbounded media. Solid lines, surface modes; dashed lines, semileaky modes. Modes HE12 and EH11 couple in region A, whereas modes EH-11 and HE-11 couple in region B (see Figs. 5 and 6 below).

Fig. 5
Fig. 5

Coupling between EH11 and HE12 modes.

Fig. 6
Fig. 6

Coupling between EH-11 and HE-11 modes.

Fig. 7
Fig. 7

Leakage loss versus chirality for the semileaky modes in Fig. 4. Surface modes become semileaky modes when the fiber’s normalized chirality parameter is above a certain critical value that depends on each individual mode.

Fig. 8
Fig. 8

Root loci of normalized variable w+ for HE-31 and HE-12 modes in terms of normalized parameter g¯.

Tables (1)

Tables Icon

Table 1 Critical Angles at the Core–Cladding Interface (Fig. 2)

Equations (67)

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

D=0E-gHt,
B=μ0μH+gEt.
A(r, ω)=-A(r, t)exp(iωt)dt,
A(r, t)=12π-A(r, ω)exp(-iωt)dω,
DB=0i0μ0χ-i0μ0χμ0μEH,
0Z0=μ0Y0=0μ0=1/c,
χ(ω)=ωg0μ0=k0c2g=2πc2λg,
×I¯0¯0¯-×I¯EH=iωBD.
Er=-iβEzr+k0βD[Z0μ(k+k--β2)g+iχ(k+k-+β2)f],
Hr=-iβHzr-k0βD[Y0(k+k--β2)f-iχ(k+k-+β2)g],
Eϕ=1D(Sf-2ik02Z0μχg),
Hϕ=1D(Sg+2ik02Y0χf),
k±=(μ±χ)k0,
S=(μ+χ2)k02-β2,
D=(k+2-β2)(k-2-β2),
f=-mβrEz-ik0Z0μHzr-k0χEzr,
g=-mβrHz+ik0Y0Ezr-k0χHzr.
κ±2=k±2-β2,
EzHz=M¯Ez(+)Ez(-),M¯=11-iYciYc,
2ψ±r2+1rψ±r+κ±2-m2r2ψ±=0.
h±2=β±2-β2,α±2=β2-γ±2,
β±=p±k0,p±=n1±χ1,
γ±=q±k0,q±=n2±χ2,
n1=1μ1,n2=2μ2,
2ψ±r2+1rψ±r+h±2-m2r2ψ±=0,
2ψ±r2+1rψ±r-α±2+m2r2ψ±=0,
Ez(r, ϕ, z, t)Hz(r, ϕ, z, t)=F(r)G(r)exp(imϕ)exp[i(βz-ωt)],
F(r)G(r)=M¯ψ+(r)ψ-(r),ψ±(r)=A±Jm(h±r)raB±Km(α±r)r>a.
F(r)G(r)=M¯A+Jm(h+r)A-Jm(h-r),
F(r)G(r)=M¯B+Km(α+r)B-Km(α-r),
u±=h±a,w±=α±a.
η=Y2Y1=y2y1=μ1n2μ2n1,
(1+η)Km(w+)(1-η)Km(w-)(1-η)Km(w+)(1+η)Km(w-)B+B-
=2A+Jm(u+)2A-Jm(u-),
B+=Q+A++Q-A-,B-=R+A++R-A-,
Q±=(η±1)Jm(u±)2ηKm(w+),R±=(η1)Jm(u±)2ηKm(w-).
Λ11Λ12Λ21Λ22A+A-=00,
Λ11=Γ+-Δ+,Λ12=Γ--Δ-,
Λ21=iΓ+-Ω+,Λ22=-iΓ--Ω-.
Γ±=2(a1iy1a2)ρ±+2(a3iy1a4)σ±,
Δ±=2(b1iy1b2)ρ±-(b3ζ±-iy2b4ξ±),
Ω±=2(ηy2b2±ib1)ρ±-η(y2b4ζ±+ib3ξ±),
ρ±=Jm(u±),σ±=u±Jm(u±),
τ±=w± Km(w±)Km(w±),
ζ±=-(τ++τ-)±1η(τ+-τ-)ρ±,
ξ±=-(τ+-τ-)±1η(τ++τ-)ρ±.
a1=-m(βa)21u+2+1u-2,
b1=m(βa)21w+2+1w-2,
a2=2imμ1χ1 (βa)(k0a)2u+2u-2,
b2=2imμ2χ2 (βa)(k0a)2w+2w-2,
a3=χ1(k0a)(β+β-+β2)a2u+2u-2,
b3=χ2(k0a)(γ+γ-+β2)a2w+2w-2,
a4=-iμ1(k0a)(β+β--β2)a2u+2u-2,
b4=-iμ2(k0a)(γ+γ--β2)a2w+2w-2.
Λ11Λ22-Λ12Λ21=0.
n1=1μ1>n2=2μ2.
β=neffk0+i(α/2),
β=β+ sin θ1(+)=β- sin θ1(+, -)=γ+ sin θ2(+,+)=γ- sin θ2(+, -),
β=β- sin θ1(-)=β+ sin θ1(-,+)=γ+ sin θ2(-,+)=γ- sin θ2(-, -).
θ1c(-,+)>θ1c(+,+)>θ1c(-, -)>θ1c(+, -).
R(α+)I(α+)=R(α-)I(α-),
R2(α+)-I2(α+)=R2(α-)-I2(α-)-4n2χk02.
F(r)π2 B+α+r exp(-α+r)+B-α-r exp(-α-r).
R(w+)<0,I(w+)<0,
R(w-)>0,I(w-)>0.
w±=2πaλneff+iαλ4π2-q±21/2
χ=g¯v,g¯=gc2an12-n22,

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