Abstract

A theoretical approach to the calculation of a diffracted electromagnetic field and to the modeling of magneto-optical images is discussed. This approach is based on the application of dyadic electrodynamic Green functions. It is shown that dyadic Green functions are convenient and powerful theoretical tools. One of their possible applications, the calculation of second-harmonic magneto-optical Kerr effects, is described. Some typical features of intense second-harmonic magneto-optical Kerr effects are studied.

© 2005 Optical Society of America

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  1. A. A. Maradudin and D. L. Mills, "Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness," Phys. Rev. B 11, 1392-1415 (1975).
    [CrossRef]
  2. O. J. F. Martin and N. B. Piller, "Electromagnetic scattering in polarizable backgrounds," Phys. Rev. E 58, 3909-3915 (1998).
    [CrossRef]
  3. V. A. Kosobukin, "Peculiarities of surface plasmon propagation in dielectric films," Phys. Solid State 35, 884-891 (1993).
  4. V. I. Belotelov, A. P. Pyatakov, S. A. Eremin, G. G. Musaev, and A. K. Zvezdin, "New nonlinear intensity Kerr effect in the polar geometry," Phys. Solid State 42, 1873-1880 (2000).
    [CrossRef]
  5. V. I. Belotelov, A. P. Pyatakov, G. G. Musaev, S. A. Eremin, and A. K. Zvezdin, "Nonlinear intensity-related magneto-optical Kerr effects in the planar geometry," Opt. Spectrosc. 91, 626-634 (2001).
    [CrossRef]
  6. V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, V. A. Kotov, and A. S. Logginov, "Numerical simulation of nanoparticleimages in scanning near-field optical microscopy," Tech. Phys. 48, 1-6 (2003).
    [CrossRef]
  7. M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Green's tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
    [CrossRef]
  8. V. A. Kosobukin, "To the theory of magneto-optical near field microscopy," J. Tech. Phys. 43, 824-832 (1998).
    [CrossRef]
  9. O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74, 526-529 (1995).
    [CrossRef] [PubMed]
  10. A. P. Vinogradov, A. A. Kalachev, A. N. Lagarkov, V. E. Romanenko, and G. V. Kazantseva, "Effects of spatial dispersion in composite materials in microwave range," Dokl. Akad. Nauk 349, 182-184 (1996).
  11. V. I. Belotelov, A. S. Logginov, and A. V. Nikolaev, "Detection and study of magnetic micro- and nanostructures using dark-field optical microscopy," Phys. Solid State 45, 519-528 (2003).
    [CrossRef]
  12. P. Guyot-Sionnest and Y. R. Shen, "Local and nonlocal surface nonlinearities for surface optical second-harmonic generation," Phys. Rev. B 35, 4420-4426 (1987).
    [CrossRef]
  13. U. Pustogowa, W. Hübner, and K. H. Benneman, "Theory for the nonlinear magneto-optical Kerr effect at ferromagnetic transition-metal surfaces," Phys. Rev. B 48, 8607-8616 (1993).
    [CrossRef]
  14. R.-P. Pan, P. D. Wel, and Y. R. Shen, "Optical second-harmonic generation from magnetized surfaces," Phys. Rev. B 39, 1229-1234 (1989).
    [CrossRef]
  15. A. K. Zvezdin and N. F. Kubrakov, "Nonlinear magneto-optical Kerr effects," JETP 116, 141-156 (1999).
  16. U. Pustogowa, W. Hübner, and K. H. Benneman, "Enhancement of the magneto-optical Kerr angle in nonlinear optical response," Phys. Rev. B 49, 10031-10034 (1994).
    [CrossRef]
  17. O. A. Aktsipetrov, E. A. Gan'shina, and V. S. Guschin, "Magneto-induced second harmonic generation and magneto-optical Kerr effect in Co-Cu granular films," J. Micromech. Microeng. 196, 80-82 (1999).
  18. B. Koopmans, M. J. K. Koerkamp, and Th. Rasing, "Observation of large Kerr angles in the nonlinear optical response from magnetic multilayers," Phys. Rev. Lett. 74, 3692-3695 (1995).
    [CrossRef] [PubMed]
  19. T. M. Crawford, C. T. Rogers, and T. J. Silva, "Nonlinear optical investigations of magnetic heterostructures," J. Appl. Phys. 81, 4354-4358 (1997).
    [CrossRef]
  20. V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, and V. A. Kotov, "Numerical simulation of images in nonlinear magneto-optical observation," Funct. Mater. 9, 119-124 (2002).
  21. A. K. Zvezdin, V. I. Belotelov, and P. Perlo, "Magnetooptics of granular materials and new optical methods of magnetic nanoparticles and nanostructure imaging," in Metal-Polymer Nanocomposites , L. Nicolais and G. Carotenuto, eds. (Wiley, New York, 2004).
  22. V. I. Belotelov, "Interaction of electromagnetic radiation with magnetic micro- and nanostructures," doctoral dissertation (M. V. Lomosonov Moscow State University, Moscow, Russia, 2004); in Russian.

2003

V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, V. A. Kotov, and A. S. Logginov, "Numerical simulation of nanoparticleimages in scanning near-field optical microscopy," Tech. Phys. 48, 1-6 (2003).
[CrossRef]

V. I. Belotelov, A. S. Logginov, and A. V. Nikolaev, "Detection and study of magnetic micro- and nanostructures using dark-field optical microscopy," Phys. Solid State 45, 519-528 (2003).
[CrossRef]

2002

V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, and V. A. Kotov, "Numerical simulation of images in nonlinear magneto-optical observation," Funct. Mater. 9, 119-124 (2002).

2001

V. I. Belotelov, A. P. Pyatakov, G. G. Musaev, S. A. Eremin, and A. K. Zvezdin, "Nonlinear intensity-related magneto-optical Kerr effects in the planar geometry," Opt. Spectrosc. 91, 626-634 (2001).
[CrossRef]

2000

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Green's tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
[CrossRef]

V. I. Belotelov, A. P. Pyatakov, S. A. Eremin, G. G. Musaev, and A. K. Zvezdin, "New nonlinear intensity Kerr effect in the polar geometry," Phys. Solid State 42, 1873-1880 (2000).
[CrossRef]

1999

A. K. Zvezdin and N. F. Kubrakov, "Nonlinear magneto-optical Kerr effects," JETP 116, 141-156 (1999).

O. A. Aktsipetrov, E. A. Gan'shina, and V. S. Guschin, "Magneto-induced second harmonic generation and magneto-optical Kerr effect in Co-Cu granular films," J. Micromech. Microeng. 196, 80-82 (1999).

1998

O. J. F. Martin and N. B. Piller, "Electromagnetic scattering in polarizable backgrounds," Phys. Rev. E 58, 3909-3915 (1998).
[CrossRef]

V. A. Kosobukin, "To the theory of magneto-optical near field microscopy," J. Tech. Phys. 43, 824-832 (1998).
[CrossRef]

1997

T. M. Crawford, C. T. Rogers, and T. J. Silva, "Nonlinear optical investigations of magnetic heterostructures," J. Appl. Phys. 81, 4354-4358 (1997).
[CrossRef]

1996

A. P. Vinogradov, A. A. Kalachev, A. N. Lagarkov, V. E. Romanenko, and G. V. Kazantseva, "Effects of spatial dispersion in composite materials in microwave range," Dokl. Akad. Nauk 349, 182-184 (1996).

1995

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74, 526-529 (1995).
[CrossRef] [PubMed]

B. Koopmans, M. J. K. Koerkamp, and Th. Rasing, "Observation of large Kerr angles in the nonlinear optical response from magnetic multilayers," Phys. Rev. Lett. 74, 3692-3695 (1995).
[CrossRef] [PubMed]

1994

U. Pustogowa, W. Hübner, and K. H. Benneman, "Enhancement of the magneto-optical Kerr angle in nonlinear optical response," Phys. Rev. B 49, 10031-10034 (1994).
[CrossRef]

1993

U. Pustogowa, W. Hübner, and K. H. Benneman, "Theory for the nonlinear magneto-optical Kerr effect at ferromagnetic transition-metal surfaces," Phys. Rev. B 48, 8607-8616 (1993).
[CrossRef]

V. A. Kosobukin, "Peculiarities of surface plasmon propagation in dielectric films," Phys. Solid State 35, 884-891 (1993).

1989

R.-P. Pan, P. D. Wel, and Y. R. Shen, "Optical second-harmonic generation from magnetized surfaces," Phys. Rev. B 39, 1229-1234 (1989).
[CrossRef]

1987

P. Guyot-Sionnest and Y. R. Shen, "Local and nonlocal surface nonlinearities for surface optical second-harmonic generation," Phys. Rev. B 35, 4420-4426 (1987).
[CrossRef]

1975

A. A. Maradudin and D. L. Mills, "Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness," Phys. Rev. B 11, 1392-1415 (1975).
[CrossRef]

Aktsipetrov, O. A.

O. A. Aktsipetrov, E. A. Gan'shina, and V. S. Guschin, "Magneto-induced second harmonic generation and magneto-optical Kerr effect in Co-Cu granular films," J. Micromech. Microeng. 196, 80-82 (1999).

Belotelov, V. I.

V. I. Belotelov, A. S. Logginov, and A. V. Nikolaev, "Detection and study of magnetic micro- and nanostructures using dark-field optical microscopy," Phys. Solid State 45, 519-528 (2003).
[CrossRef]

V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, V. A. Kotov, and A. S. Logginov, "Numerical simulation of nanoparticleimages in scanning near-field optical microscopy," Tech. Phys. 48, 1-6 (2003).
[CrossRef]

V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, and V. A. Kotov, "Numerical simulation of images in nonlinear magneto-optical observation," Funct. Mater. 9, 119-124 (2002).

V. I. Belotelov, A. P. Pyatakov, G. G. Musaev, S. A. Eremin, and A. K. Zvezdin, "Nonlinear intensity-related magneto-optical Kerr effects in the planar geometry," Opt. Spectrosc. 91, 626-634 (2001).
[CrossRef]

V. I. Belotelov, A. P. Pyatakov, S. A. Eremin, G. G. Musaev, and A. K. Zvezdin, "New nonlinear intensity Kerr effect in the polar geometry," Phys. Solid State 42, 1873-1880 (2000).
[CrossRef]

Benneman, K. H.

U. Pustogowa, W. Hübner, and K. H. Benneman, "Enhancement of the magneto-optical Kerr angle in nonlinear optical response," Phys. Rev. B 49, 10031-10034 (1994).
[CrossRef]

U. Pustogowa, W. Hübner, and K. H. Benneman, "Theory for the nonlinear magneto-optical Kerr effect at ferromagnetic transition-metal surfaces," Phys. Rev. B 48, 8607-8616 (1993).
[CrossRef]

Crawford, T. M.

T. M. Crawford, C. T. Rogers, and T. J. Silva, "Nonlinear optical investigations of magnetic heterostructures," J. Appl. Phys. 81, 4354-4358 (1997).
[CrossRef]

Dereux, A.

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74, 526-529 (1995).
[CrossRef] [PubMed]

Eremin, S. A.

V. I. Belotelov, A. P. Pyatakov, G. G. Musaev, S. A. Eremin, and A. K. Zvezdin, "Nonlinear intensity-related magneto-optical Kerr effects in the planar geometry," Opt. Spectrosc. 91, 626-634 (2001).
[CrossRef]

V. I. Belotelov, A. P. Pyatakov, S. A. Eremin, G. G. Musaev, and A. K. Zvezdin, "New nonlinear intensity Kerr effect in the polar geometry," Phys. Solid State 42, 1873-1880 (2000).
[CrossRef]

Gan'shina, E. A.

O. A. Aktsipetrov, E. A. Gan'shina, and V. S. Guschin, "Magneto-induced second harmonic generation and magneto-optical Kerr effect in Co-Cu granular films," J. Micromech. Microeng. 196, 80-82 (1999).

Gay-Balmaz, P.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Green's tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
[CrossRef]

Girard, C.

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74, 526-529 (1995).
[CrossRef] [PubMed]

Guschin, V. S.

O. A. Aktsipetrov, E. A. Gan'shina, and V. S. Guschin, "Magneto-induced second harmonic generation and magneto-optical Kerr effect in Co-Cu granular films," J. Micromech. Microeng. 196, 80-82 (1999).

Guyot-Sionnest , P.

P. Guyot-Sionnest and Y. R. Shen, "Local and nonlocal surface nonlinearities for surface optical second-harmonic generation," Phys. Rev. B 35, 4420-4426 (1987).
[CrossRef]

Hübner, W.

U. Pustogowa, W. Hübner, and K. H. Benneman, "Enhancement of the magneto-optical Kerr angle in nonlinear optical response," Phys. Rev. B 49, 10031-10034 (1994).
[CrossRef]

U. Pustogowa, W. Hübner, and K. H. Benneman, "Theory for the nonlinear magneto-optical Kerr effect at ferromagnetic transition-metal surfaces," Phys. Rev. B 48, 8607-8616 (1993).
[CrossRef]

Kalachev, A. A.

A. P. Vinogradov, A. A. Kalachev, A. N. Lagarkov, V. E. Romanenko, and G. V. Kazantseva, "Effects of spatial dispersion in composite materials in microwave range," Dokl. Akad. Nauk 349, 182-184 (1996).

Kazantseva, G. V.

A. P. Vinogradov, A. A. Kalachev, A. N. Lagarkov, V. E. Romanenko, and G. V. Kazantseva, "Effects of spatial dispersion in composite materials in microwave range," Dokl. Akad. Nauk 349, 182-184 (1996).

Koerkamp, M. J. K.

B. Koopmans, M. J. K. Koerkamp, and Th. Rasing, "Observation of large Kerr angles in the nonlinear optical response from magnetic multilayers," Phys. Rev. Lett. 74, 3692-3695 (1995).
[CrossRef] [PubMed]

Koopmans, B.

B. Koopmans, M. J. K. Koerkamp, and Th. Rasing, "Observation of large Kerr angles in the nonlinear optical response from magnetic multilayers," Phys. Rev. Lett. 74, 3692-3695 (1995).
[CrossRef] [PubMed]

Kosobukin, V. A.

V. A. Kosobukin, "To the theory of magneto-optical near field microscopy," J. Tech. Phys. 43, 824-832 (1998).
[CrossRef]

V. A. Kosobukin, "Peculiarities of surface plasmon propagation in dielectric films," Phys. Solid State 35, 884-891 (1993).

Kotov, V. A.

V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, V. A. Kotov, and A. S. Logginov, "Numerical simulation of nanoparticleimages in scanning near-field optical microscopy," Tech. Phys. 48, 1-6 (2003).
[CrossRef]

V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, and V. A. Kotov, "Numerical simulation of images in nonlinear magneto-optical observation," Funct. Mater. 9, 119-124 (2002).

Kubrakov, N. F.

A. K. Zvezdin and N. F. Kubrakov, "Nonlinear magneto-optical Kerr effects," JETP 116, 141-156 (1999).

Lagarkov, A. N.

A. P. Vinogradov, A. A. Kalachev, A. N. Lagarkov, V. E. Romanenko, and G. V. Kazantseva, "Effects of spatial dispersion in composite materials in microwave range," Dokl. Akad. Nauk 349, 182-184 (1996).

Logginov, A. S.

V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, V. A. Kotov, and A. S. Logginov, "Numerical simulation of nanoparticleimages in scanning near-field optical microscopy," Tech. Phys. 48, 1-6 (2003).
[CrossRef]

V. I. Belotelov, A. S. Logginov, and A. V. Nikolaev, "Detection and study of magnetic micro- and nanostructures using dark-field optical microscopy," Phys. Solid State 45, 519-528 (2003).
[CrossRef]

Maradudin , A. A.

A. A. Maradudin and D. L. Mills, "Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness," Phys. Rev. B 11, 1392-1415 (1975).
[CrossRef]

Martin, O. J. F.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Green's tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
[CrossRef]

Martin , O. J. F.

O. J. F. Martin and N. B. Piller, "Electromagnetic scattering in polarizable backgrounds," Phys. Rev. E 58, 3909-3915 (1998).
[CrossRef]

Martin, O. J. F.

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74, 526-529 (1995).
[CrossRef] [PubMed]

Mills, D. L.

A. A. Maradudin and D. L. Mills, "Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness," Phys. Rev. B 11, 1392-1415 (1975).
[CrossRef]

Musaev, G. G.

V. I. Belotelov, A. P. Pyatakov, G. G. Musaev, S. A. Eremin, and A. K. Zvezdin, "Nonlinear intensity-related magneto-optical Kerr effects in the planar geometry," Opt. Spectrosc. 91, 626-634 (2001).
[CrossRef]

V. I. Belotelov, A. P. Pyatakov, S. A. Eremin, G. G. Musaev, and A. K. Zvezdin, "New nonlinear intensity Kerr effect in the polar geometry," Phys. Solid State 42, 1873-1880 (2000).
[CrossRef]

Nikolaev, A. V.

V. I. Belotelov, A. S. Logginov, and A. V. Nikolaev, "Detection and study of magnetic micro- and nanostructures using dark-field optical microscopy," Phys. Solid State 45, 519-528 (2003).
[CrossRef]

Pan, R.-P.

R.-P. Pan, P. D. Wel, and Y. R. Shen, "Optical second-harmonic generation from magnetized surfaces," Phys. Rev. B 39, 1229-1234 (1989).
[CrossRef]

Paulus, M.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Green's tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
[CrossRef]

Piller, N. B.

O. J. F. Martin and N. B. Piller, "Electromagnetic scattering in polarizable backgrounds," Phys. Rev. E 58, 3909-3915 (1998).
[CrossRef]

Pustogowa, U.

U. Pustogowa, W. Hübner, and K. H. Benneman, "Enhancement of the magneto-optical Kerr angle in nonlinear optical response," Phys. Rev. B 49, 10031-10034 (1994).
[CrossRef]

U. Pustogowa, W. Hübner, and K. H. Benneman, "Theory for the nonlinear magneto-optical Kerr effect at ferromagnetic transition-metal surfaces," Phys. Rev. B 48, 8607-8616 (1993).
[CrossRef]

Pyatakov, A. P.

V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, V. A. Kotov, and A. S. Logginov, "Numerical simulation of nanoparticleimages in scanning near-field optical microscopy," Tech. Phys. 48, 1-6 (2003).
[CrossRef]

V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, and V. A. Kotov, "Numerical simulation of images in nonlinear magneto-optical observation," Funct. Mater. 9, 119-124 (2002).

V. I. Belotelov, A. P. Pyatakov, G. G. Musaev, S. A. Eremin, and A. K. Zvezdin, "Nonlinear intensity-related magneto-optical Kerr effects in the planar geometry," Opt. Spectrosc. 91, 626-634 (2001).
[CrossRef]

V. I. Belotelov, A. P. Pyatakov, S. A. Eremin, G. G. Musaev, and A. K. Zvezdin, "New nonlinear intensity Kerr effect in the polar geometry," Phys. Solid State 42, 1873-1880 (2000).
[CrossRef]

Rasing, Th.

B. Koopmans, M. J. K. Koerkamp, and Th. Rasing, "Observation of large Kerr angles in the nonlinear optical response from magnetic multilayers," Phys. Rev. Lett. 74, 3692-3695 (1995).
[CrossRef] [PubMed]

Rogers, C. T.

T. M. Crawford, C. T. Rogers, and T. J. Silva, "Nonlinear optical investigations of magnetic heterostructures," J. Appl. Phys. 81, 4354-4358 (1997).
[CrossRef]

Romanenko, V. E.

A. P. Vinogradov, A. A. Kalachev, A. N. Lagarkov, V. E. Romanenko, and G. V. Kazantseva, "Effects of spatial dispersion in composite materials in microwave range," Dokl. Akad. Nauk 349, 182-184 (1996).

Shen, Y. R.

R.-P. Pan, P. D. Wel, and Y. R. Shen, "Optical second-harmonic generation from magnetized surfaces," Phys. Rev. B 39, 1229-1234 (1989).
[CrossRef]

P. Guyot-Sionnest and Y. R. Shen, "Local and nonlocal surface nonlinearities for surface optical second-harmonic generation," Phys. Rev. B 35, 4420-4426 (1987).
[CrossRef]

Silva, T. J.

T. M. Crawford, C. T. Rogers, and T. J. Silva, "Nonlinear optical investigations of magnetic heterostructures," J. Appl. Phys. 81, 4354-4358 (1997).
[CrossRef]

Vinogradov, A. P.

A. P. Vinogradov, A. A. Kalachev, A. N. Lagarkov, V. E. Romanenko, and G. V. Kazantseva, "Effects of spatial dispersion in composite materials in microwave range," Dokl. Akad. Nauk 349, 182-184 (1996).

Wel, P. D.

R.-P. Pan, P. D. Wel, and Y. R. Shen, "Optical second-harmonic generation from magnetized surfaces," Phys. Rev. B 39, 1229-1234 (1989).
[CrossRef]

Zvezdin, A. K.

V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, V. A. Kotov, and A. S. Logginov, "Numerical simulation of nanoparticleimages in scanning near-field optical microscopy," Tech. Phys. 48, 1-6 (2003).
[CrossRef]

V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, and V. A. Kotov, "Numerical simulation of images in nonlinear magneto-optical observation," Funct. Mater. 9, 119-124 (2002).

V. I. Belotelov, A. P. Pyatakov, G. G. Musaev, S. A. Eremin, and A. K. Zvezdin, "Nonlinear intensity-related magneto-optical Kerr effects in the planar geometry," Opt. Spectrosc. 91, 626-634 (2001).
[CrossRef]

V. I. Belotelov, A. P. Pyatakov, S. A. Eremin, G. G. Musaev, and A. K. Zvezdin, "New nonlinear intensity Kerr effect in the polar geometry," Phys. Solid State 42, 1873-1880 (2000).
[CrossRef]

Zvezdin , A. K.

A. K. Zvezdin and N. F. Kubrakov, "Nonlinear magneto-optical Kerr effects," JETP 116, 141-156 (1999).

Dokl. Akad. Nauk

A. P. Vinogradov, A. A. Kalachev, A. N. Lagarkov, V. E. Romanenko, and G. V. Kazantseva, "Effects of spatial dispersion in composite materials in microwave range," Dokl. Akad. Nauk 349, 182-184 (1996).

Funct. Mater.

V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, and V. A. Kotov, "Numerical simulation of images in nonlinear magneto-optical observation," Funct. Mater. 9, 119-124 (2002).

J. Appl. Phys.

T. M. Crawford, C. T. Rogers, and T. J. Silva, "Nonlinear optical investigations of magnetic heterostructures," J. Appl. Phys. 81, 4354-4358 (1997).
[CrossRef]

J. Micromech. Microeng.

O. A. Aktsipetrov, E. A. Gan'shina, and V. S. Guschin, "Magneto-induced second harmonic generation and magneto-optical Kerr effect in Co-Cu granular films," J. Micromech. Microeng. 196, 80-82 (1999).

J. Tech. Phys.

V. A. Kosobukin, "To the theory of magneto-optical near field microscopy," J. Tech. Phys. 43, 824-832 (1998).
[CrossRef]

JETP

A. K. Zvezdin and N. F. Kubrakov, "Nonlinear magneto-optical Kerr effects," JETP 116, 141-156 (1999).

Opt. Spectrosc.

V. I. Belotelov, A. P. Pyatakov, G. G. Musaev, S. A. Eremin, and A. K. Zvezdin, "Nonlinear intensity-related magneto-optical Kerr effects in the planar geometry," Opt. Spectrosc. 91, 626-634 (2001).
[CrossRef]

Phys. Rev. B

A. A. Maradudin and D. L. Mills, "Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness," Phys. Rev. B 11, 1392-1415 (1975).
[CrossRef]

U. Pustogowa, W. Hübner, and K. H. Benneman, "Enhancement of the magneto-optical Kerr angle in nonlinear optical response," Phys. Rev. B 49, 10031-10034 (1994).
[CrossRef]

P. Guyot-Sionnest and Y. R. Shen, "Local and nonlocal surface nonlinearities for surface optical second-harmonic generation," Phys. Rev. B 35, 4420-4426 (1987).
[CrossRef]

U. Pustogowa, W. Hübner, and K. H. Benneman, "Theory for the nonlinear magneto-optical Kerr effect at ferromagnetic transition-metal surfaces," Phys. Rev. B 48, 8607-8616 (1993).
[CrossRef]

R.-P. Pan, P. D. Wel, and Y. R. Shen, "Optical second-harmonic generation from magnetized surfaces," Phys. Rev. B 39, 1229-1234 (1989).
[CrossRef]

Phys. Rev. E

O. J. F. Martin and N. B. Piller, "Electromagnetic scattering in polarizable backgrounds," Phys. Rev. E 58, 3909-3915 (1998).
[CrossRef]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Green's tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
[CrossRef]

Phys. Rev. Lett.

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74, 526-529 (1995).
[CrossRef] [PubMed]

B. Koopmans, M. J. K. Koerkamp, and Th. Rasing, "Observation of large Kerr angles in the nonlinear optical response from magnetic multilayers," Phys. Rev. Lett. 74, 3692-3695 (1995).
[CrossRef] [PubMed]

Phys. Solid State

V. I. Belotelov, A. S. Logginov, and A. V. Nikolaev, "Detection and study of magnetic micro- and nanostructures using dark-field optical microscopy," Phys. Solid State 45, 519-528 (2003).
[CrossRef]

V. A. Kosobukin, "Peculiarities of surface plasmon propagation in dielectric films," Phys. Solid State 35, 884-891 (1993).

V. I. Belotelov, A. P. Pyatakov, S. A. Eremin, G. G. Musaev, and A. K. Zvezdin, "New nonlinear intensity Kerr effect in the polar geometry," Phys. Solid State 42, 1873-1880 (2000).
[CrossRef]

Tech. Phys.

V. I. Belotelov, A. P. Pyatakov, A. K. Zvezdin, V. A. Kotov, and A. S. Logginov, "Numerical simulation of nanoparticleimages in scanning near-field optical microscopy," Tech. Phys. 48, 1-6 (2003).
[CrossRef]

Other

A. K. Zvezdin, V. I. Belotelov, and P. Perlo, "Magnetooptics of granular materials and new optical methods of magnetic nanoparticles and nanostructure imaging," in Metal-Polymer Nanocomposites , L. Nicolais and G. Carotenuto, eds. (Wiley, New York, 2004).

V. I. Belotelov, "Interaction of electromagnetic radiation with magnetic micro- and nanostructures," doctoral dissertation (M. V. Lomosonov Moscow State University, Moscow, Russia, 2004); in Russian.

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Figures (7)

Fig. 1
Fig. 1

Configuration under consideration: E, electric field of the incident wave; E˜, electric field of the reflected field at the second harmonic.

Fig. 2
Fig. 2

Variation δ in the intensity of reflected light versus polarization angle ψ at several incident angles θ in the polar geometry: 1, 0°; 2, 60°; 3, 80°, and 4, 90°.

Fig. 3
Fig. 3

Variation δ in the intensity of reflected light versus polarization angle ψ at various incident angles θ in the longitudinal geometry: 1, 10°; 2, 40°; 3, 60°; and 4, 90°; 5 is the same for the corresponding linear intensity effect (θ90°).

Fig. 4
Fig. 4

Variation δ in the intensity of reflected light versus polarization angle ψ at various incident angles θ in the transverse geometry: 1, 3°; 2, 10°; 3, 20°; and 4, 70°.

Fig. 5
Fig. 5

Images for the domain with magnetization perpendicular to the surface and a domain wall of the Bloch type. Angle of polarization ψ=90°. Corresponding magnetization configurations are shown below the images.

Fig. 6
Fig. 6

Images for the domain the with magnetization perpendicular to the surface and a domain wall of the Bloch type between them. Angle of polarization, ψ=70°. Corresponding magnetization configurations are shown below the images.

Fig. 7
Fig. 7

Green functions for the three-media case. Light propagates from the first semi-infinite medium.

Equations (120)

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Lˆψ(r)=f(r),
LˆG(r, r)=δ(r-r).
ψ(r)=ψ0(r)+G(r, r)f(r)dr,
ΔE(r)+k02E(r)=F(r),
G(r, r)=-14πexp(ik0|r-r|)|r-r|,
××E(r, ω)-k02(z, ω)E(r, ω)=(k02/0)P1(r, ω),
××E˜(r, 2ω)-4k02˜̑(z, 2ω)E˜(r, 2ω)=(4k02/0)P˜surf(r, 2ω)δ(z),
2xλxμ-δλμ2xμ2-α2k02(z, αω)δλμGμν(r, r, αω)=-δλνδ(r-r),
Gμν(r, r, ω)=δμν+ikR-1k2R2δμν+3-3ikR-k2R2k2R4RμRν exp(ikR)4πR,
Eu=GxuGyuGzu,u=x, y, z
Eμ(r, ω)=Eμ(0)(r, ω)-(k02/0)×d3rGμν(r, r, ω)P1v(r, ω),
E˜μ(r, 2ω)=E˜μ(0)(r, 2ω)-(4k02/0)×d3rGμν(r, r, 2ω)P˜vsurf(r, 2ω),
Eμ(r, ω)=Eμ(0)(r, ω)+Eμ(1)(r, ω),
E˜μ(r, 2ω)=E˜μ(0)(r, 2ω)+E˜μ(1)(r, 2ω),
Gμν(r, r, αω)=(1/4π2)d2k exp[ik(r-r)]×gμν(z, z, αω, k),
Pv(0)(r, αω)=(1/4π2)d2k exp(ikr)Pˆv(0)×(z, αω, k),
Eˆμ(1)(z, ω, k)=-(k02/16π4)dzgμν×(z, z, ω, k)Pˆ1v(z, ω, k).
E˜ˆμ(1)(z, 2ω, k)=-(k02/4π4)dzgμν×(z, z, 2ω, k)P˜ˆvsurf(0)(z, 2ω, k).
Ps2ω=χijk(2)EjEk,
Ps2ω=Ps02ω+Psm2ω,
Ps02ω=χ1E(EN)+χ2E2N,
Psm2ω=χ3E[E(mN)]+χ4E2[mN]+χ5[Eμ](EN)+χ6[EN](Em)
0000e150000e1500e31e31e33000.
Ptot=0χ̑E(r)exp(iωt)+0χ˜̑E˜(r)exp(i2ωt)+P˜surf exp(i2ωt)δ(z),
D=0̑(r)E(r)exp(iωt)+0˜̑(r)E˜(r)exp(i2ωt)+P˜surf exp(i2ωt)δ(z),
̑=n21-Im3 QIm2 QIm3 Q1-Im1 Q-Im2 QIm1 Q1,z<0;
̑=100010001,z>0,
˜̑=n˜21-Im3 Q˜Im2 Q˜Im3 Q˜1-Im1 Q˜-Im2 Q˜Im1 Q˜1,z<0,
˜̑=100010001,z>0,
rotrot E(r)-ω2c2̑E(r)=0,
rotrot E˜(r)-4ω2c2˜̑E˜(r)=104ω2c2P˜surfδ(z).
2xμxv-δμν2xv2-˜μν(r)4ω2c2E˜v(r)=104ω2c2P˜μsurfδ(z).
L̑μν0=2xμxv-δμν2xv2-n˜24ω2c2δμν,
L̑μν1=4ω2c2Δ˜μν.
(L̑μν0-L̑μν1)E˜ν(r)=104ω2c2P˜μsurf(r)δ(z).
E˜(r)=E˜00(r)+E˜0m(r)+E˜1(r),
L̑μν0E˜ν00(r)=104ω2c2P˜μ00(r)δ(z),
L̑μν0E˜ν0m(r)=104ω2c2P˜μ0m(r)δ(z),
L̑μν0E˜ν1(r)=104ω2c2P˜μm(r)δ(z)+L̑μν1E˜ν00(r).
E˜μ00(r)=-104ω2c2 drGμν(r, r, 2ω)P˜v00(r)δ(z),
E˜μ0m(r)=-104ω2c2 drGμν(r, r, 2ω)P˜v0m(r)δ(z),
E˜μ1(r)=-104ω2c2drGμν(r, r, 2ω)P˜vm(r)δ(z)+0z<0drGμν(r, r, 2ω)Δ˜νκE˜k00(r).
Eν0(r)=exp(ikr)Eν0(z),
Eνm(r)=exp(ikr)Eνm(z).
E˜μ00(r)=-104ω2c2exp(2ikr)gμν×(2k, 2ω, z, 0-)P˜v00(0-)
E˜μ0m(r)=-104ω2c2exp(2ikr)gμν×(2k, 2ω, z, 0-)P˜v0m(0-),
E˜μ1(r)=-104ω2c2exp(2ikr)×gμν(2k, 2ω, z, 0-)P˜vm(0-)+0-0dzgμν(2k, 2ω, z, z)×Δ˜vkE˜k00(z),
gμν(2k, 2ω, z, 0-)=limz0-gμν(2k, 2ω, z, z),
P˜vm(0-)=limz0-P˜vm(z),P˜vm(z)exp(2ikr)=P˜vm(r).
Ep(i)Es(i)=E(i)cos ψsin ψ,
EpNM=αNMp[Ep(i)]2+βNMp[Es(i)]2,
EsNM=γNMsEp(i)Es(i),
EpM±=γMpEp(i)Es(i),
EsM±={αMs[Ep(i)]2+βMs[Es(i)]2},
EpM±={αMp[Ep(i)]2+βMp[Es(i)]2},
EsM±=γMsEp(i)Es(i),
I±=(E˜s±+E˜p±)(E˜s±+E˜p±)*=(EsNM+EsM±)(EsNM+EsM±)*+(EpNM+EpM±)(EpNM+EpM±)*.
δ=I+-I-I++I-=EsNM(EsM+)*+(EsNM)*EsM++EpNM(EpM+)*+(EpNM)*EpM+|EsNM|2+|EsM+|2+|EpNM|2+|EpM+|2,
Eμ(1)=14π2 {k}dkȆμ(1) exp(ikr).
g11(z, z, ω, k)=-ik02kz1kz2(kz2+kz1)×exp[i(kz1z-kz2z)],
g13(z, z, ω, k)=-ik02kz1k(kz2+kz1)×exp[i(kz1z-kz2z)],
g22(z, z, ω, k)=-i1(kz2+kz1)×exp[i(kz1z-kz2z)],
g31(z, z, ω, k)=ik02kz2k(kz2+kz1)×exp[i(kz1z-kz2z)],
g33(z, z, ω, k)=ik02k2(kz2+n2kz1)×exp[i(kz1z-kz2z)],
g12=g21=g23=g32=0.
g11(z, z, ω, k)=ik12k02kz2-kz1(kz2+kz1)×exp[-ikz2(z+z)]-exp[ikz2|z-z|],
g13(z, z, ω, k)=-ik2k02kz2-kz1(kz2+kz1)×exp[-ikz2(z+z)]-exp(ikz2|z-z|)sgn(z-z),
g22(z, z, ω, k)=-i2kz2kz2-kz1kz2+kz1exp[-ikz2(z+z)]+exp(ikz2|z-z|),
g31(z, z, ω, k)=ik2k02kz2-kz1(kz2+kz1)×exp[-ikz2(z+z)]+exp(ikz2|z-z|)×sgn(z-z),
g33(z, z, ω, k)=-ik22kz2k02kz2-kz1(kz2+kz1)×exp[-ikz2(z+z)]+exp(ikz2|z-z|)+1k02δ(z-z),
g12=g21=g23=g32=0.
g11(12)=-i2k02β2t21(p)(0)Δpexp(ikz1z)[exp(-ikz2z)+r23(p)(l)exp(ikz2z)]=kz1kg31(12),
g13(12)=-i2k02β2kkz2t21(p)(0)Δpexp(ikz1z)×[exp(-ikz2z)-r23(p)(l)exp(ikz2z)]=kz1kg33(12),
g11(22)=-i2k02β2exp(ikz2|z-z|)+1Δp[r21(p)×(0)exp(-ikz2{z+z})+r23(p)×(l)exp(ikz2{z+z})+2r21(p)(0)r23(p)×(l)cos(kz2{z-z})],
g31(22)=i2k02β2kkz2sgn(z-z)exp(ikz2|z-z|)+1Δp[r21(p)(0)exp(-ikz2{z+z})-r23(p)×(l)exp(ikz2{z+z})-2ir21(p)(0)r23(p)×(l)sin(kz2{z-z})],
g13(22)=i2k02β2kkz2 sgn(z-z)exp(ikz2|z-z|)-1Δp[r21(p)(0)exp(-ikz2{z+z})-r23(p)×(l)exp(ikz2{z+z})+2ir21(p)(0)r23(p)×(l)sin(kz2{z-z})],
g33(22)=-i2k02β2kkz22exp(ikz2|z-z|)-1Δp[r21(p)(0)exp(-ikz2{z+z})+r23(p)×(l)exp(ikz2{z+z})-2r21(p)(0)r23(p)×(l)cos(kz2{z-z})]+12k02δ(z-z),
g11(32)=-i2k02β2t23(p)(l)Δpexp(-ikz3z)×[exp(ikz2z)+r21(p)(0)exp(-ikz2z)]=-kz3kg31(32),
g13(32)=i2k02β2t23(p)(l)Δpexp(-ikz3z)×[exp(ikz2z)-r21(p)(0)exp(-ikz2z)]=-kz3kg33(32),
rmn(p)(l)=βm-βnβm+βnexp[2ikzml sgn(m-n)],
tmn(p)(l)=2βmβm+βnexp[i(kzm-kzn)l×sgn(m-n)],
βn=n/kzn,kzn=(nk02-k2)1/2,
Δp=1-r21(p)(0)r23(p)(l).
d11=kx2g11+ky2g22k2,
d12=kxky(g11-g22)k2,d13=kxg13k,
d22=ky2g11+kx2g22k2,d21=d12,d23=kyg13k,
d31=kxg31k,d32=kyg31k,d33=g33,
E1=E10+E1m,E10=2q cos θYEp(i),
E1m=±iQn2 cos2 θXYEs(i),
E2=E20+E2m,E20=2 cos θXEs(i),
E2m=iQn2 cos θXYEp(i),
E3=E30+E3m,E30=sin 2θYEp(i),
E3m=iQ sin 2θ2XYEs(i).
E1=E10+E1m,E10=2q cos θYEp(i),
E1m=±in2Q sin θ cos2 θXYqEs(i),
E2=E20+E2m,E20=2 cos θXEs(i),
E2m=±in2Q sin 2θ2XYqEp(i),
E3=E30+E3m,E30=sin 2θYEp(i),
E3m=2iQ cos θXYY+sin2 θ2qEs(i).
E1=E10+E1m,E10=2q cos θYEp(i),
E1m=2in2Q sin θ cos2 θY2Ep(i),
E2=E20+E2m,E20=2 cos θXEs(i),
E2m=0,
E3=E30+E3m,E30=sin 2θYEp(i),
E3m=±2in2Q cos θY2(1+q cos θ)Ep(i),
αNMp=-2ki sin θ(2 cos θ)20Y˜×χ1Y2{qq˜-α2}-χ2n2Y2,
βNMp=2ki sin θ(2 cos θ)20Y˜χ2X2,
γNMs=-2ki sin θχ1(2 cos θ)20X˜XY,
γMp=2k sin θ(2 cos θ)20Y˜χ1Q2Y2X(qq˜-n2q˜ cos θ-2 sin2 θ)-χ1Q˜n˜22XX˜Y+χ2Qn2q cos θY2X-sin2 θY2X-n2X2Y+i(χ5+χ6)q˜XY,
αMs=2k sin θ(2 cos θ)20X˜χ1Q2n2Y2X+χ1Q˜2Y˜n˜2qY2 cos θ+sin2 θY2+χ2n2Y2-i(χ5+χ6)qY2,
βMs=2k sin θ(2 cos θ)20X˜χ1Q2X2Y+χ2X2.
αNMp=8ki sin θ cos2 θ0Y˜Y2[χ1(sin2 θ-qq˜)+χ2n2],
βNMp=8ki sin φ cos2 θ0Y˜X2χ2,
γNMs=-8ki sin θ cos2 θ0XX˜Yχ1,
γMp=8ki cos2 θ0XYY˜iχ1Qq˜n2 sin2 θ cos θ2Yq-q-sin2 θ2Y+2 sin2 θ1+sin2 θ2qY+Q˜ n˜2 sin2 θ2q˜X˜-iχ2 sin2 θQn2 cos θY-2-sin2 θqY+n2Xq+χ3(sin2 θ-qq˜)+χ5 sin2 θ+χ6qq˜,
αMs=8ki cos2 θ0X˜Y2iχ1 sin2 θQ2Xqn2+Q˜1+n˜2q cos θ+sin2 θ2q˜Y˜+iχ2Q˜n21+sin2 θ2Y˜q˜-χ4n2+χ5 sin2 θ-χ6q2,
βMs=-8ki cos2 θ0X˜X2iχ1Q2Yq(sin2 θ+2qY)-iχ2Q˜1+sin2 θ2Y˜q˜+χ3+χ4.
αMp=8ki cos2 θ0Y˜Y2iχ1Qn2q˜1-2 sin2 θ cos θY-2 sin2 θY(1+q cos θ)-Q˜n˜2 sin2 θY˜×[1+(q+q˜)cos θ]-iχ22Qn2 sin2 θY+Q˜n˜2n2Y˜(1+q˜ cos θ)-χ3(sin2 θ-qq˜)q+χ4q˜n2-χ5 sin2 θ(q+q˜),
βMp=8ki cos2 θ0Y˜X2-iχ2Q˜n˜2Y˜(1+q˜ cos θ)+χ4q˜+χ6q˜,
γMs=8ki cos2 θ0XYX˜iχ1YQn2(1+q cos θ)+χ3q-χ6q,

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