Abstract

The nonlinear (at the second-harmonic frequency of the incident light) optical diffraction by a two-dimensional lattice of magnetic bubbles (cylindrical magnetic domains) is theoretically studied. Because the periods of these structures are comparable with the wavelengths of the fundamental and the second-harmonic radiation, diffraction at the second-harmonic frequency can be expected. We investigate the influence of an external magnetic field on the nonlinear magneto-optical diffraction.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. N. Dadoenkova, I. L. Lyubchanskii, M. I. Lyubchanskii, and Th. Rasing, "Nonlinear magneto-optical diffraction from periodic domain structures in magnetic films," Appl. Phys. Lett. 74, 1880-1882 (1999).
    [CrossRef]
  2. I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, and Th. Rasing, "Nonlinear diffraction by two-dimensional magnetic photonic crystal (magnetic bubble lattice)," Trans. Magn. Soc. Jpn. 2, 160-162 (2002).
    [CrossRef]
  3. I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, K. Y. Guslienko, and Th. Rasing, "Nonlinear magneto-optical diffraction by two-dimensional magnetic structures," Appl. Phys. B 74, 711-714 (2002).
    [CrossRef]
  4. J. Hamrle, L. Polerecky, and J. Ferré, "Theory of SHG from multilayer systems based on electric point-dipole radiation - application to magnetic multilayers," Phys. Rev. B 68, 144401-1-144401-28 (2003).
    [CrossRef]
  5. S. V. Lazarenko, A. Kirilyuk, Th. Rasing, and J. C. Lodder, "Linear and nonlinear magneto-optical diffraction from one-dimensional periodic structures," J. Appl. Phys. 93, 7903-7905 (2003).
    [CrossRef]
  6. A. Hubert and R. Schäfer, Magnetic Domains (Springer, Berlin, 1998).
  7. V. G. Bar'yakhtar, I. L. Lyubchanskii, Yu. V. Melikhov, and L. N. Ovander, "Raman and Brillouin scattering of light by magnetic-bubble lattice fluctuations," Sov. Phys. Solid State 24, 1021-1024 (1982).
  8. Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, New York, 1984).
  9. A. V. Petukhov, I. L. Lyubchanskii, and Th. Rasing, "Theory of nonlinear magneto-optical imaging of magnetic domains and domain walls," Phys. Rev. B 56, 2680-2687 (1997).
    [CrossRef]
  10. W. F. Druyvesteyn and J. W. F. Dorleijn, "Calculations on periodic magnetic domain structures," Philips Res. Rep. 26, 11-28 (1971).
  11. K.-H. Hellewege and A. M. Hellewege, eds., Landolt-Bornstein, Numerical Data and Functional Relationships in Science and Technology, New Series. Group III: Crystal and Solid State Physics, Vol. 12: Magnetic and Another Properties of Oxides and Related Compounds (Springer, Berlin, 1978).
  12. A. K. Zvezdin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (Institute of Physics, Bristol, UK, 1997).
  13. O. A. Aktsipetrov, O. V. Braginskii, and D. A. Esikov, "Nonlinear optics of gyrotropic media: second harmonic generation in rare-earth iron garnets," Sov. J. Quantum Electron. 20, 259-263 (1990).
    [CrossRef]
  14. R. V. Pisarev, B. B. Krichevtsov, V. N. Gridnev, V. P. Klin, D. Frölich, and Ch. Pahlke-Lerch, "Optical second-harmonic generation in magnetic garnet thin film," J. Phys.: Condens. Matter 5, 8621-8628 (1993).
  15. V. N. Gridnev, V. V. Pavlov, R. V. Pisarev, A. Kirilyuk, and Th. Rasing, "Second harmonic generation in anisotropic magnetic films," Phys. Rev. B 63, 184407 (2001).
    [CrossRef]
  16. V. Kirilyuk, A. Kirilyuk, and Th. Rasing, "A combined nonlinear and linear magneto-optical microscopy," Appl. Phys. Lett. 70, 2306-2308 (1997).
    [CrossRef]

2003 (2)

J. Hamrle, L. Polerecky, and J. Ferré, "Theory of SHG from multilayer systems based on electric point-dipole radiation - application to magnetic multilayers," Phys. Rev. B 68, 144401-1-144401-28 (2003).
[CrossRef]

S. V. Lazarenko, A. Kirilyuk, Th. Rasing, and J. C. Lodder, "Linear and nonlinear magneto-optical diffraction from one-dimensional periodic structures," J. Appl. Phys. 93, 7903-7905 (2003).
[CrossRef]

2002 (2)

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, and Th. Rasing, "Nonlinear diffraction by two-dimensional magnetic photonic crystal (magnetic bubble lattice)," Trans. Magn. Soc. Jpn. 2, 160-162 (2002).
[CrossRef]

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, K. Y. Guslienko, and Th. Rasing, "Nonlinear magneto-optical diffraction by two-dimensional magnetic structures," Appl. Phys. B 74, 711-714 (2002).
[CrossRef]

2001 (1)

V. N. Gridnev, V. V. Pavlov, R. V. Pisarev, A. Kirilyuk, and Th. Rasing, "Second harmonic generation in anisotropic magnetic films," Phys. Rev. B 63, 184407 (2001).
[CrossRef]

1999 (1)

N. N. Dadoenkova, I. L. Lyubchanskii, M. I. Lyubchanskii, and Th. Rasing, "Nonlinear magneto-optical diffraction from periodic domain structures in magnetic films," Appl. Phys. Lett. 74, 1880-1882 (1999).
[CrossRef]

1997 (2)

A. V. Petukhov, I. L. Lyubchanskii, and Th. Rasing, "Theory of nonlinear magneto-optical imaging of magnetic domains and domain walls," Phys. Rev. B 56, 2680-2687 (1997).
[CrossRef]

V. Kirilyuk, A. Kirilyuk, and Th. Rasing, "A combined nonlinear and linear magneto-optical microscopy," Appl. Phys. Lett. 70, 2306-2308 (1997).
[CrossRef]

1993 (1)

R. V. Pisarev, B. B. Krichevtsov, V. N. Gridnev, V. P. Klin, D. Frölich, and Ch. Pahlke-Lerch, "Optical second-harmonic generation in magnetic garnet thin film," J. Phys.: Condens. Matter 5, 8621-8628 (1993).

1990 (1)

O. A. Aktsipetrov, O. V. Braginskii, and D. A. Esikov, "Nonlinear optics of gyrotropic media: second harmonic generation in rare-earth iron garnets," Sov. J. Quantum Electron. 20, 259-263 (1990).
[CrossRef]

1982 (1)

V. G. Bar'yakhtar, I. L. Lyubchanskii, Yu. V. Melikhov, and L. N. Ovander, "Raman and Brillouin scattering of light by magnetic-bubble lattice fluctuations," Sov. Phys. Solid State 24, 1021-1024 (1982).

1971 (1)

W. F. Druyvesteyn and J. W. F. Dorleijn, "Calculations on periodic magnetic domain structures," Philips Res. Rep. 26, 11-28 (1971).

Aktsipetrov, O. A.

O. A. Aktsipetrov, O. V. Braginskii, and D. A. Esikov, "Nonlinear optics of gyrotropic media: second harmonic generation in rare-earth iron garnets," Sov. J. Quantum Electron. 20, 259-263 (1990).
[CrossRef]

Bar'yakhtar, V. G.

V. G. Bar'yakhtar, I. L. Lyubchanskii, Yu. V. Melikhov, and L. N. Ovander, "Raman and Brillouin scattering of light by magnetic-bubble lattice fluctuations," Sov. Phys. Solid State 24, 1021-1024 (1982).

Braginskii, O. V.

O. A. Aktsipetrov, O. V. Braginskii, and D. A. Esikov, "Nonlinear optics of gyrotropic media: second harmonic generation in rare-earth iron garnets," Sov. J. Quantum Electron. 20, 259-263 (1990).
[CrossRef]

Dadoenkova, N. N.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, and Th. Rasing, "Nonlinear diffraction by two-dimensional magnetic photonic crystal (magnetic bubble lattice)," Trans. Magn. Soc. Jpn. 2, 160-162 (2002).
[CrossRef]

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, K. Y. Guslienko, and Th. Rasing, "Nonlinear magneto-optical diffraction by two-dimensional magnetic structures," Appl. Phys. B 74, 711-714 (2002).
[CrossRef]

N. N. Dadoenkova, I. L. Lyubchanskii, M. I. Lyubchanskii, and Th. Rasing, "Nonlinear magneto-optical diffraction from periodic domain structures in magnetic films," Appl. Phys. Lett. 74, 1880-1882 (1999).
[CrossRef]

Dorleijn, J. W. F.

W. F. Druyvesteyn and J. W. F. Dorleijn, "Calculations on periodic magnetic domain structures," Philips Res. Rep. 26, 11-28 (1971).

Druyvesteyn , W. F.

W. F. Druyvesteyn and J. W. F. Dorleijn, "Calculations on periodic magnetic domain structures," Philips Res. Rep. 26, 11-28 (1971).

Esikov, D. A.

O. A. Aktsipetrov, O. V. Braginskii, and D. A. Esikov, "Nonlinear optics of gyrotropic media: second harmonic generation in rare-earth iron garnets," Sov. J. Quantum Electron. 20, 259-263 (1990).
[CrossRef]

Ferré, J.

J. Hamrle, L. Polerecky, and J. Ferré, "Theory of SHG from multilayer systems based on electric point-dipole radiation - application to magnetic multilayers," Phys. Rev. B 68, 144401-1-144401-28 (2003).
[CrossRef]

Frölich, D.

R. V. Pisarev, B. B. Krichevtsov, V. N. Gridnev, V. P. Klin, D. Frölich, and Ch. Pahlke-Lerch, "Optical second-harmonic generation in magnetic garnet thin film," J. Phys.: Condens. Matter 5, 8621-8628 (1993).

Gridnev, V. N.

V. N. Gridnev, V. V. Pavlov, R. V. Pisarev, A. Kirilyuk, and Th. Rasing, "Second harmonic generation in anisotropic magnetic films," Phys. Rev. B 63, 184407 (2001).
[CrossRef]

R. V. Pisarev, B. B. Krichevtsov, V. N. Gridnev, V. P. Klin, D. Frölich, and Ch. Pahlke-Lerch, "Optical second-harmonic generation in magnetic garnet thin film," J. Phys.: Condens. Matter 5, 8621-8628 (1993).

Guslienko, K. Y.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, K. Y. Guslienko, and Th. Rasing, "Nonlinear magneto-optical diffraction by two-dimensional magnetic structures," Appl. Phys. B 74, 711-714 (2002).
[CrossRef]

Hamrle, J.

J. Hamrle, L. Polerecky, and J. Ferré, "Theory of SHG from multilayer systems based on electric point-dipole radiation - application to magnetic multilayers," Phys. Rev. B 68, 144401-1-144401-28 (2003).
[CrossRef]

Kirilyuk, A.

S. V. Lazarenko, A. Kirilyuk, Th. Rasing, and J. C. Lodder, "Linear and nonlinear magneto-optical diffraction from one-dimensional periodic structures," J. Appl. Phys. 93, 7903-7905 (2003).
[CrossRef]

V. N. Gridnev, V. V. Pavlov, R. V. Pisarev, A. Kirilyuk, and Th. Rasing, "Second harmonic generation in anisotropic magnetic films," Phys. Rev. B 63, 184407 (2001).
[CrossRef]

V. Kirilyuk, A. Kirilyuk, and Th. Rasing, "A combined nonlinear and linear magneto-optical microscopy," Appl. Phys. Lett. 70, 2306-2308 (1997).
[CrossRef]

Kirilyuk, V.

V. Kirilyuk, A. Kirilyuk, and Th. Rasing, "A combined nonlinear and linear magneto-optical microscopy," Appl. Phys. Lett. 70, 2306-2308 (1997).
[CrossRef]

Klin, V. P.

R. V. Pisarev, B. B. Krichevtsov, V. N. Gridnev, V. P. Klin, D. Frölich, and Ch. Pahlke-Lerch, "Optical second-harmonic generation in magnetic garnet thin film," J. Phys.: Condens. Matter 5, 8621-8628 (1993).

Krichevtsov, B. B.

R. V. Pisarev, B. B. Krichevtsov, V. N. Gridnev, V. P. Klin, D. Frölich, and Ch. Pahlke-Lerch, "Optical second-harmonic generation in magnetic garnet thin film," J. Phys.: Condens. Matter 5, 8621-8628 (1993).

Lazarenko, S. V.

S. V. Lazarenko, A. Kirilyuk, Th. Rasing, and J. C. Lodder, "Linear and nonlinear magneto-optical diffraction from one-dimensional periodic structures," J. Appl. Phys. 93, 7903-7905 (2003).
[CrossRef]

Lodder, J. C.

S. V. Lazarenko, A. Kirilyuk, Th. Rasing, and J. C. Lodder, "Linear and nonlinear magneto-optical diffraction from one-dimensional periodic structures," J. Appl. Phys. 93, 7903-7905 (2003).
[CrossRef]

Lyubchanskii, I. L.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, K. Y. Guslienko, and Th. Rasing, "Nonlinear magneto-optical diffraction by two-dimensional magnetic structures," Appl. Phys. B 74, 711-714 (2002).
[CrossRef]

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, and Th. Rasing, "Nonlinear diffraction by two-dimensional magnetic photonic crystal (magnetic bubble lattice)," Trans. Magn. Soc. Jpn. 2, 160-162 (2002).
[CrossRef]

N. N. Dadoenkova, I. L. Lyubchanskii, M. I. Lyubchanskii, and Th. Rasing, "Nonlinear magneto-optical diffraction from periodic domain structures in magnetic films," Appl. Phys. Lett. 74, 1880-1882 (1999).
[CrossRef]

A. V. Petukhov, I. L. Lyubchanskii, and Th. Rasing, "Theory of nonlinear magneto-optical imaging of magnetic domains and domain walls," Phys. Rev. B 56, 2680-2687 (1997).
[CrossRef]

V. G. Bar'yakhtar, I. L. Lyubchanskii, Yu. V. Melikhov, and L. N. Ovander, "Raman and Brillouin scattering of light by magnetic-bubble lattice fluctuations," Sov. Phys. Solid State 24, 1021-1024 (1982).

Lyubchanskii, M. I.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, and Th. Rasing, "Nonlinear diffraction by two-dimensional magnetic photonic crystal (magnetic bubble lattice)," Trans. Magn. Soc. Jpn. 2, 160-162 (2002).
[CrossRef]

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, K. Y. Guslienko, and Th. Rasing, "Nonlinear magneto-optical diffraction by two-dimensional magnetic structures," Appl. Phys. B 74, 711-714 (2002).
[CrossRef]

N. N. Dadoenkova, I. L. Lyubchanskii, M. I. Lyubchanskii, and Th. Rasing, "Nonlinear magneto-optical diffraction from periodic domain structures in magnetic films," Appl. Phys. Lett. 74, 1880-1882 (1999).
[CrossRef]

Melikhov, Yu. V.

V. G. Bar'yakhtar, I. L. Lyubchanskii, Yu. V. Melikhov, and L. N. Ovander, "Raman and Brillouin scattering of light by magnetic-bubble lattice fluctuations," Sov. Phys. Solid State 24, 1021-1024 (1982).

Ovander, L. N.

V. G. Bar'yakhtar, I. L. Lyubchanskii, Yu. V. Melikhov, and L. N. Ovander, "Raman and Brillouin scattering of light by magnetic-bubble lattice fluctuations," Sov. Phys. Solid State 24, 1021-1024 (1982).

Pahlke-Lerch, Ch.

R. V. Pisarev, B. B. Krichevtsov, V. N. Gridnev, V. P. Klin, D. Frölich, and Ch. Pahlke-Lerch, "Optical second-harmonic generation in magnetic garnet thin film," J. Phys.: Condens. Matter 5, 8621-8628 (1993).

Pavlov, V. V.

V. N. Gridnev, V. V. Pavlov, R. V. Pisarev, A. Kirilyuk, and Th. Rasing, "Second harmonic generation in anisotropic magnetic films," Phys. Rev. B 63, 184407 (2001).
[CrossRef]

Petukhov, A. V.

A. V. Petukhov, I. L. Lyubchanskii, and Th. Rasing, "Theory of nonlinear magneto-optical imaging of magnetic domains and domain walls," Phys. Rev. B 56, 2680-2687 (1997).
[CrossRef]

Pisarev, R. V.

V. N. Gridnev, V. V. Pavlov, R. V. Pisarev, A. Kirilyuk, and Th. Rasing, "Second harmonic generation in anisotropic magnetic films," Phys. Rev. B 63, 184407 (2001).
[CrossRef]

R. V. Pisarev, B. B. Krichevtsov, V. N. Gridnev, V. P. Klin, D. Frölich, and Ch. Pahlke-Lerch, "Optical second-harmonic generation in magnetic garnet thin film," J. Phys.: Condens. Matter 5, 8621-8628 (1993).

Polerecky, L.

J. Hamrle, L. Polerecky, and J. Ferré, "Theory of SHG from multilayer systems based on electric point-dipole radiation - application to magnetic multilayers," Phys. Rev. B 68, 144401-1-144401-28 (2003).
[CrossRef]

Rasing, Th.

S. V. Lazarenko, A. Kirilyuk, Th. Rasing, and J. C. Lodder, "Linear and nonlinear magneto-optical diffraction from one-dimensional periodic structures," J. Appl. Phys. 93, 7903-7905 (2003).
[CrossRef]

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, and Th. Rasing, "Nonlinear diffraction by two-dimensional magnetic photonic crystal (magnetic bubble lattice)," Trans. Magn. Soc. Jpn. 2, 160-162 (2002).
[CrossRef]

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, K. Y. Guslienko, and Th. Rasing, "Nonlinear magneto-optical diffraction by two-dimensional magnetic structures," Appl. Phys. B 74, 711-714 (2002).
[CrossRef]

V. N. Gridnev, V. V. Pavlov, R. V. Pisarev, A. Kirilyuk, and Th. Rasing, "Second harmonic generation in anisotropic magnetic films," Phys. Rev. B 63, 184407 (2001).
[CrossRef]

N. N. Dadoenkova, I. L. Lyubchanskii, M. I. Lyubchanskii, and Th. Rasing, "Nonlinear magneto-optical diffraction from periodic domain structures in magnetic films," Appl. Phys. Lett. 74, 1880-1882 (1999).
[CrossRef]

A. V. Petukhov, I. L. Lyubchanskii, and Th. Rasing, "Theory of nonlinear magneto-optical imaging of magnetic domains and domain walls," Phys. Rev. B 56, 2680-2687 (1997).
[CrossRef]

V. Kirilyuk, A. Kirilyuk, and Th. Rasing, "A combined nonlinear and linear magneto-optical microscopy," Appl. Phys. Lett. 70, 2306-2308 (1997).
[CrossRef]

Shapovalov, E. A.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, and Th. Rasing, "Nonlinear diffraction by two-dimensional magnetic photonic crystal (magnetic bubble lattice)," Trans. Magn. Soc. Jpn. 2, 160-162 (2002).
[CrossRef]

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, K. Y. Guslienko, and Th. Rasing, "Nonlinear magneto-optical diffraction by two-dimensional magnetic structures," Appl. Phys. B 74, 711-714 (2002).
[CrossRef]

Zabolotin, A. E.

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, K. Y. Guslienko, and Th. Rasing, "Nonlinear magneto-optical diffraction by two-dimensional magnetic structures," Appl. Phys. B 74, 711-714 (2002).
[CrossRef]

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, and Th. Rasing, "Nonlinear diffraction by two-dimensional magnetic photonic crystal (magnetic bubble lattice)," Trans. Magn. Soc. Jpn. 2, 160-162 (2002).
[CrossRef]

Appl. Phys. B (1)

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, K. Y. Guslienko, and Th. Rasing, "Nonlinear magneto-optical diffraction by two-dimensional magnetic structures," Appl. Phys. B 74, 711-714 (2002).
[CrossRef]

Appl. Phys. Lett. (2)

N. N. Dadoenkova, I. L. Lyubchanskii, M. I. Lyubchanskii, and Th. Rasing, "Nonlinear magneto-optical diffraction from periodic domain structures in magnetic films," Appl. Phys. Lett. 74, 1880-1882 (1999).
[CrossRef]

V. Kirilyuk, A. Kirilyuk, and Th. Rasing, "A combined nonlinear and linear magneto-optical microscopy," Appl. Phys. Lett. 70, 2306-2308 (1997).
[CrossRef]

J. Appl. Phys. (1)

S. V. Lazarenko, A. Kirilyuk, Th. Rasing, and J. C. Lodder, "Linear and nonlinear magneto-optical diffraction from one-dimensional periodic structures," J. Appl. Phys. 93, 7903-7905 (2003).
[CrossRef]

J. Phys.: Condens. Matter (1)

R. V. Pisarev, B. B. Krichevtsov, V. N. Gridnev, V. P. Klin, D. Frölich, and Ch. Pahlke-Lerch, "Optical second-harmonic generation in magnetic garnet thin film," J. Phys.: Condens. Matter 5, 8621-8628 (1993).

Philips Res. Rep. (1)

W. F. Druyvesteyn and J. W. F. Dorleijn, "Calculations on periodic magnetic domain structures," Philips Res. Rep. 26, 11-28 (1971).

Phys. Rev. B (3)

A. V. Petukhov, I. L. Lyubchanskii, and Th. Rasing, "Theory of nonlinear magneto-optical imaging of magnetic domains and domain walls," Phys. Rev. B 56, 2680-2687 (1997).
[CrossRef]

V. N. Gridnev, V. V. Pavlov, R. V. Pisarev, A. Kirilyuk, and Th. Rasing, "Second harmonic generation in anisotropic magnetic films," Phys. Rev. B 63, 184407 (2001).
[CrossRef]

J. Hamrle, L. Polerecky, and J. Ferré, "Theory of SHG from multilayer systems based on electric point-dipole radiation - application to magnetic multilayers," Phys. Rev. B 68, 144401-1-144401-28 (2003).
[CrossRef]

Sov. J. Quantum Electron. (1)

O. A. Aktsipetrov, O. V. Braginskii, and D. A. Esikov, "Nonlinear optics of gyrotropic media: second harmonic generation in rare-earth iron garnets," Sov. J. Quantum Electron. 20, 259-263 (1990).
[CrossRef]

Sov. Phys. Solid State (1)

V. G. Bar'yakhtar, I. L. Lyubchanskii, Yu. V. Melikhov, and L. N. Ovander, "Raman and Brillouin scattering of light by magnetic-bubble lattice fluctuations," Sov. Phys. Solid State 24, 1021-1024 (1982).

Trans. Magn. Soc. Jpn. (1)

I. L. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, A. E. Zabolotin, and Th. Rasing, "Nonlinear diffraction by two-dimensional magnetic photonic crystal (magnetic bubble lattice)," Trans. Magn. Soc. Jpn. 2, 160-162 (2002).
[CrossRef]

Other (4)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, New York, 1984).

A. Hubert and R. Schäfer, Magnetic Domains (Springer, Berlin, 1998).

K.-H. Hellewege and A. M. Hellewege, eds., Landolt-Bornstein, Numerical Data and Functional Relationships in Science and Technology, New Series. Group III: Crystal and Solid State Physics, Vol. 12: Magnetic and Another Properties of Oxides and Related Compounds (Springer, Berlin, 1978).

A. K. Zvezdin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (Institute of Physics, Bristol, UK, 1997).

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 (5)

Fig. 1
Fig. 1

Schematic image of nonlinear diffraction on magnetic bubble lattice.

Fig. 2
Fig. 2

Dependencies of (a) the normalized magnetic bubble radius and (b) the MBL period on the normalized external magnetic field.

Fig. 3
Fig. 3

Dependence of |mZ|2 on the normalized wave vector qh for the different values of the external magnetic field H/4πMs. In the legends magnetic bubble radii R and MBL periods are given in the units of the film thickness h. The solid curve corresponds to the magnetic bubbles’ collapse and transition to the uniform magnetization state. The calculations carried out for the incidence angles are (a) θω=30°, (b) θω=60°.

Fig. 4
Fig. 4

Azimuthal dependencies of the first-order diffracted SHG light for different values of the external magnetic field and MBL parameters: (a) H0/4πMs=0, D/h=5.08, 2R/h=3.72; (b) H0/4πMs=0.18, D/h=4.98, 2R/h=2.46; (c) H0/4πMs=0.25, D/h=6.92, 2R/h=2.17; (d) H0/4πMs=0.28, D/h=16.90, 2R/h=2.11. The laser spot radius is RL=20h.

Fig. 5
Fig. 5

Angle of NMOD as a function of the period of MBL for the first order of the nonlinear diffraction (l1=l2=1).

Equations (24)

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

mZ(r)=MZ(r)Ms=1-2kθ(Rk-|r-rk|),
2E(r, t)+nω2c22E(r, t)t2=-4πc2PNL(r, t),
PiNL(2ω)=χijk(-2ω:ω, ω)Ej(ω)Ek(ω),
χijk=χijk(0)+χijk(m),
χijk(m)=χijkL(m,1)mL.
χxzx(0)=χyzy(0)=χxxz(0)=χyyz(0),
χzxx(0)=χzyy(0),χzzz(0),
χxyzZ(m,1)=-χyxzZ(m,1).
PxNL(2ω, r)=2χxzx(0)Ex(ω)Ez(ω)+2χxyzZ(m,1)mZ(r)Ey(ω)Ez(ω),
PyNL(2ω, r)=2χyxzZ(m,1)mZ(r)Ex(ω)Ez(ω)+2χyyz(0)Ey(ω)Ez(ω),
PzNL(2ω, r)=χzxx(0)Ex2(ω)+χzyy(0)Ey2(ω)+χzzz(0)Ez2(ω).
2ik2ω,ilEl(2ω, r)=-ω2c2PiNL(2ω, r)exp(iqr),
Ei(2ω, q)=-AVVdrPiNL(2ω, r)exp(iqr),
Es(2ω)Ep(2ω)=χs;ssχs;ppχp;ssχp;ppEs2(ω)Ep2(ω),
χs;ss=0,
χs;pp=χyxz(m,1)mZ(q)sin θω cos θω,
χp;ss=χzyy(0)(sin θ2ω)-1,
χp;pp=(χzxx(0) cos2 θω+χzzz(0) sin2 θω)sin θ2ω+χxxz(0) sin 2θω cos θ2ω.
mZ(q)=1V0hdzSm(r)exp(iqr)dr,
|mZ(q)|2(Is2ω)2(Ipω)2|χs;pp|2.
χijkL(m,1)=lχijkL(m,1)(l)exp(iQlr),
Ql=l1-12l2ex+32l2ey,
k2ω=2kω+Ql.
sin θ2ω(l1,l2)=nωn2ω sin θω+λ2ωDl1-12l2cos φ+32l2 sin φ,

Metrics