Abstract

The nature of the magneto-optic Kerr effect in a planar dielectric waveguide geometry has been investigated by calculation of the Jones matrix for a planar waveguide structure with a gyrotropic magnetic material as one wall. The intensity of the component of the field that is in the polarization state orthogonal to the input was calculated as a function of length of the gyrotropic material and input polarization state. The degree of polarization rotation depends on the relative orientation of the magnetization in the magnetic material and the direction of propagation. It is found that there exists an optimal waveguide length and input polarization at which the output signal is maximized and that a significant enhancement in polarization rotation is available with respect to free-space reflection. These results indicate that a magnetic-film-bounded planar waveguide can be used for device applications such as magnetic field sensors or magneto-optic modulators.

© 1998 Optical Society of America

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References

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    [CrossRef]
  2. V. M. Gelikonov, D. D. Gusovskii, Yu. N. Konoplev, V. I. Leonov, Yu. A. Mamaev, A. A. Turkin, “Investigation of a fiber-optic polarizer with a metal film and a dielectric buffer layer,” Sov. J. Quantum Electron. 20, 76–78 (1990).
    [CrossRef]
  3. D. A. Todd, G. R. J. Robertson, M. Failes, “Polarization-splitting polished fiber optic couplers,” Opt. Eng. 32, 2077–2082 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1994

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, A. B. Kalè, “Magnetic field measurements using magneto-optic Kerr effect sensors,” Opt. Eng. 33, 3718–3722 (1994).
[CrossRef]

1993

D. A. Todd, G. R. J. Robertson, M. Failes, “Polarization-splitting polished fiber optic couplers,” Opt. Eng. 32, 2077–2082 (1993).
[CrossRef]

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kalè, “Measurement of magnetic fields using the magnetooptic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
[CrossRef]

1990

V. M. Gelikonov, D. D. Gusovskii, Yu. N. Konoplev, V. I. Leonov, Yu. A. Mamaev, A. A. Turkin, “Investigation of a fiber-optic polarizer with a metal film and a dielectric buffer layer,” Sov. J. Quantum Electron. 20, 76–78 (1990).
[CrossRef]

1988

W. Johnstone, G. Stewart, B. Culshaw, T. Hart, “Fiber-optic polarisers and polarising couplers,” Electron. Lett. 24, 866–868 (1988).
[CrossRef]

1976

V. K. Agrawal, Y. Miyazaki, Y. Akao, “Analysis of hybrid modes in an optical waveguide bounded at one side by a gyromagnetic medium,” Opt. Commun. 16, 104–109 (1976).
[CrossRef]

1975

V. K. Agrawal, Y. Miyazaki, Y. Akao, “Waveguide type optical modulator using Kerr magnetooptic effects in Ni-Fe thin films: Experimental study,” Jpn. J. Appl. Phys. 14, 1313–1322 (1975).
[CrossRef]

1974

1967

P. S. Pershan, “Magneto-optical effects,” J. Appl. Phys. 38, 1482–1490 (1967).
[CrossRef]

1964

Agrawal, V. K.

V. K. Agrawal, Y. Miyazaki, Y. Akao, “Analysis of hybrid modes in an optical waveguide bounded at one side by a gyromagnetic medium,” Opt. Commun. 16, 104–109 (1976).
[CrossRef]

V. K. Agrawal, Y. Miyazaki, Y. Akao, “Waveguide type optical modulator using Kerr magnetooptic effects in Ni-Fe thin films: Experimental study,” Jpn. J. Appl. Phys. 14, 1313–1322 (1975).
[CrossRef]

Akao, Y.

V. K. Agrawal, Y. Miyazaki, Y. Akao, “Analysis of hybrid modes in an optical waveguide bounded at one side by a gyromagnetic medium,” Opt. Commun. 16, 104–109 (1976).
[CrossRef]

V. K. Agrawal, Y. Miyazaki, Y. Akao, “Waveguide type optical modulator using Kerr magnetooptic effects in Ni-Fe thin films: Experimental study,” Jpn. J. Appl. Phys. 14, 1313–1322 (1975).
[CrossRef]

Culshaw, B.

W. Johnstone, G. Stewart, B. Culshaw, T. Hart, “Fiber-optic polarisers and polarising couplers,” Electron. Lett. 24, 866–868 (1988).
[CrossRef]

DiMarzio, C. A.

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, A. B. Kalè, “Magnetic field measurements using magneto-optic Kerr effect sensors,” Opt. Eng. 33, 3718–3722 (1994).
[CrossRef]

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kalè, “Measurement of magnetic fields using the magnetooptic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
[CrossRef]

Failes, M.

D. A. Todd, G. R. J. Robertson, M. Failes, “Polarization-splitting polished fiber optic couplers,” Opt. Eng. 32, 2077–2082 (1993).
[CrossRef]

Gelikonov, V. M.

V. M. Gelikonov, D. D. Gusovskii, Yu. N. Konoplev, V. I. Leonov, Yu. A. Mamaev, A. A. Turkin, “Investigation of a fiber-optic polarizer with a metal film and a dielectric buffer layer,” Sov. J. Quantum Electron. 20, 76–78 (1990).
[CrossRef]

Gusovskii, D. D.

V. M. Gelikonov, D. D. Gusovskii, Yu. N. Konoplev, V. I. Leonov, Yu. A. Mamaev, A. A. Turkin, “Investigation of a fiber-optic polarizer with a metal film and a dielectric buffer layer,” Sov. J. Quantum Electron. 20, 76–78 (1990).
[CrossRef]

Hart, T.

W. Johnstone, G. Stewart, B. Culshaw, T. Hart, “Fiber-optic polarisers and polarising couplers,” Electron. Lett. 24, 866–868 (1988).
[CrossRef]

Johnstone, W.

W. Johnstone, G. Stewart, B. Culshaw, T. Hart, “Fiber-optic polarisers and polarising couplers,” Electron. Lett. 24, 866–868 (1988).
[CrossRef]

Kalè, A. B.

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, A. B. Kalè, “Magnetic field measurements using magneto-optic Kerr effect sensors,” Opt. Eng. 33, 3718–3722 (1994).
[CrossRef]

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kalè, “Measurement of magnetic fields using the magnetooptic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
[CrossRef]

Konoplev, Yu. N.

V. M. Gelikonov, D. D. Gusovskii, Yu. N. Konoplev, V. I. Leonov, Yu. A. Mamaev, A. A. Turkin, “Investigation of a fiber-optic polarizer with a metal film and a dielectric buffer layer,” Sov. J. Quantum Electron. 20, 76–78 (1990).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifschitz, L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1980), p. 269.

Leonov, V. I.

V. M. Gelikonov, D. D. Gusovskii, Yu. N. Konoplev, V. I. Leonov, Yu. A. Mamaev, A. A. Turkin, “Investigation of a fiber-optic polarizer with a metal film and a dielectric buffer layer,” Sov. J. Quantum Electron. 20, 76–78 (1990).
[CrossRef]

Lifschitz, E. M.

L. D. Landau, E. M. Lifschitz, L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1980), p. 269.

Lindberg, S. C.

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, A. B. Kalè, “Magnetic field measurements using magneto-optic Kerr effect sensors,” Opt. Eng. 33, 3718–3722 (1994).
[CrossRef]

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kalè, “Measurement of magnetic fields using the magnetooptic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
[CrossRef]

Mamaev, Yu. A.

V. M. Gelikonov, D. D. Gusovskii, Yu. N. Konoplev, V. I. Leonov, Yu. A. Mamaev, A. A. Turkin, “Investigation of a fiber-optic polarizer with a metal film and a dielectric buffer layer,” Sov. J. Quantum Electron. 20, 76–78 (1990).
[CrossRef]

McKnight, S. W.

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kalè, “Measurement of magnetic fields using the magnetooptic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
[CrossRef]

Miyazaki, Y.

V. K. Agrawal, Y. Miyazaki, Y. Akao, “Analysis of hybrid modes in an optical waveguide bounded at one side by a gyromagnetic medium,” Opt. Commun. 16, 104–109 (1976).
[CrossRef]

V. K. Agrawal, Y. Miyazaki, Y. Akao, “Waveguide type optical modulator using Kerr magnetooptic effects in Ni-Fe thin films: Experimental study,” Jpn. J. Appl. Phys. 14, 1313–1322 (1975).
[CrossRef]

Oliver, S. A.

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, A. B. Kalè, “Magnetic field measurements using magneto-optic Kerr effect sensors,” Opt. Eng. 33, 3718–3722 (1994).
[CrossRef]

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kalè, “Measurement of magnetic fields using the magnetooptic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
[CrossRef]

Pershan, P. S.

P. S. Pershan, “Magneto-optical effects,” J. Appl. Phys. 38, 1482–1490 (1967).
[CrossRef]

Pitaevskii, L. P.

L. D. Landau, E. M. Lifschitz, L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1980), p. 269.

Robertson, G. R. J.

D. A. Todd, G. R. J. Robertson, M. Failes, “Polarization-splitting polished fiber optic couplers,” Opt. Eng. 32, 2077–2082 (1993).
[CrossRef]

Robinson, C. C.

Stewart, G.

W. Johnstone, G. Stewart, B. Culshaw, T. Hart, “Fiber-optic polarisers and polarising couplers,” Electron. Lett. 24, 866–868 (1988).
[CrossRef]

Todd, D. A.

D. A. Todd, G. R. J. Robertson, M. Failes, “Polarization-splitting polished fiber optic couplers,” Opt. Eng. 32, 2077–2082 (1993).
[CrossRef]

Turkin, A. A.

V. M. Gelikonov, D. D. Gusovskii, Yu. N. Konoplev, V. I. Leonov, Yu. A. Mamaev, A. A. Turkin, “Investigation of a fiber-optic polarizer with a metal film and a dielectric buffer layer,” Sov. J. Quantum Electron. 20, 76–78 (1990).
[CrossRef]

Vassell, M. O.

Appl. Phys. Lett.

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kalè, “Measurement of magnetic fields using the magnetooptic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
[CrossRef]

Electron. Lett.

W. Johnstone, G. Stewart, B. Culshaw, T. Hart, “Fiber-optic polarisers and polarising couplers,” Electron. Lett. 24, 866–868 (1988).
[CrossRef]

J. Appl. Phys.

P. S. Pershan, “Magneto-optical effects,” J. Appl. Phys. 38, 1482–1490 (1967).
[CrossRef]

J. Opt. Soc. Am.

Jpn. J. Appl. Phys.

V. K. Agrawal, Y. Miyazaki, Y. Akao, “Waveguide type optical modulator using Kerr magnetooptic effects in Ni-Fe thin films: Experimental study,” Jpn. J. Appl. Phys. 14, 1313–1322 (1975).
[CrossRef]

Opt. Commun.

V. K. Agrawal, Y. Miyazaki, Y. Akao, “Analysis of hybrid modes in an optical waveguide bounded at one side by a gyromagnetic medium,” Opt. Commun. 16, 104–109 (1976).
[CrossRef]

Opt. Eng.

D. A. Todd, G. R. J. Robertson, M. Failes, “Polarization-splitting polished fiber optic couplers,” Opt. Eng. 32, 2077–2082 (1993).
[CrossRef]

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, A. B. Kalè, “Magnetic field measurements using magneto-optic Kerr effect sensors,” Opt. Eng. 33, 3718–3722 (1994).
[CrossRef]

Sov. J. Quantum Electron.

V. M. Gelikonov, D. D. Gusovskii, Yu. N. Konoplev, V. I. Leonov, Yu. A. Mamaev, A. A. Turkin, “Investigation of a fiber-optic polarizer with a metal film and a dielectric buffer layer,” Sov. J. Quantum Electron. 20, 76–78 (1990).
[CrossRef]

Other

L. D. Landau, E. M. Lifschitz, L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1980), p. 269.

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Figures (3)

Fig. 1
Fig. 1

Layer structure and coordinate system.

Fig. 2
Fig. 2

Intensity of cross-polarized light in the two pairs of modes that can propagate in the structure: (a) lowest order and (b) second order. Note the differences in signal strength and optimal waveguide length.

Fig. 3
Fig. 3

Intensity of maximum cross-polarized signal as a function of the magnetization angle θ. In our geometry, the ratio of the magnetic field to the saturation field is equal to the cosine of the angle that the magnetization makes with the direction of propagation.

Equations (4)

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

ε ˆ 3 = ε ˆ 3 0 - iQ ε ˆ 3   sin   θ * 0 ε ˆ 3 iQ ε ˆ 3   cos   θ * - iQ ε ˆ 3   sin   θ iQ ε ˆ 3   cos   θ ε ˆ 3 ,
J = V GDG - 1 V ,
V = E TM | E 1 E TE | E 1 E TM | E 2 E TE | E 2 , D = exp i β 1 l 0 0 exp i β 2 l , G = 1 / N 1 -   E 1 * E 2 w d z N 1 2 N 2 0 1 / N 2 .
sin 2   φ - sin   φ   cos   φ - sin   φ   cos   φ cos 2   φ ,

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