Abstract

We present a simple model for performing high-density all-optical magnetic recording using a solid immersion lens. The magnetization distribution in the magneto-optic film placed in the vicinity of the solid immersion lens is studied using the vector diffraction theory and the inverse Faraday effect. Simulation results show that although the transverse components of magnetization are nonzero, the axial component dominates. The magnetization direction of the axial component can be reversed by changing the helicity of the incident circularly polarized laser pulses. For a lower-numerical-aperture (NA) system, a larger and circular magnetization zone is obtained and the deviation angle of magnetization direction departing from the optical axis is smaller in the effective magnetization zone, which is useful to vertical magnetic recording. For a higher-NA system, a smaller magnetization zone is generated, but the three-dimensional magnetization distribution has to be considered.

© 2008 Optical Society of America

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  1. S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615-2616 (1990).
    [CrossRef]
  2. B. D. Terris, H. J. Mamin, and D. Ruger, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388-390 (1994).
    [CrossRef]
  3. L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501-503 (1999).
    [CrossRef]
  4. M. Yoshita, K. Koyama, M. Baba, and H. Akiyama, “Fourier imaging study of efficient near-field optical coupling in solid immersion fluorescence microscopy,” J. Appl. Phys. 92, 862-865 (2002).
    [CrossRef]
  5. S. B. Ippolito, S. A. Thorne, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, “High spatial resolution subsurface thermal emission microscopy,” Appl. Phys. Lett. 84, 4529-4531 (2004).
    [CrossRef]
  6. D. Ganic, X. Gan, and M. Gu, “Trapping force and optical lifting under focused evanescent wave illumination,” Opt. Express 12, 5533-5538 (2004).
    [CrossRef] [PubMed]
  7. M. Gu, S. Kuriakose, and X. Gan, “A single beam near-field laser trap for optical stretching, folding and rotation of erythrocytes,” Opt. Express 15, 1369-1375 (2007).
    [CrossRef] [PubMed]
  8. I. Ichimura, S. Hayashi, and G. S. Kino, “High-density optical recording using a solid immersion lens,” Appl. Opt. 36, 4339-4348 (1997).
    [CrossRef] [PubMed]
  9. F. Guo, T. E. Schlesinger, and D. D. Stancil, “Optical field study of near-field optical recording with a solid immersion lens,” Appl. Opt. 39, 324-332 (2000).
    [CrossRef]
  10. Y. Zhang, H. Xiao, and C. Zhang, “Diffractive super-resolution elements applied to near-field optical data storage with solid immersion lens,” New J. Phys. 6, 75 (2004).
    [CrossRef]
  11. Y. Zhang and X. Ye, “Three-zone phase-only filter increasing the focal depth of optical storage systems with a solid immersion lens,” Appl. Phys. B 86, 97-103 (2007).
    [CrossRef]
  12. Y. Zhang, “Optical data storage system with a plano-ellipsoidal solid immersion mirror illuminated directly by a point light source,” Appl. Opt. 45, 8653-8658 (2006).
    [CrossRef] [PubMed]
  13. Y. Zhang, “Theoretical study of near-field optical storage with a solid immersion lens,” J. Opt. Soc. Am. A 23, 2132-2136 (2006).
    [CrossRef]
  14. C. H. Back, R. Allenspach, W. Weber, S. S. P. Parkin, D. Weller, E. L. Garwin, and H. C. Siegmann, “Minimum field strength in precessional magnetization reversal,” Science 285, 864-867 (1999).
    [CrossRef] [PubMed]
  15. R. Gómez-Abal, O. Ney, K. Satitkovitchai, and W. Hübner, “All-optical subpicosecond magnetic switching in NiO(001),” Phys. Rev. Lett. 92, 227402 (2004).
    [CrossRef] [PubMed]
  16. A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, “Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses,” Nature 435, 655-657 (2005).
    [CrossRef] [PubMed]
  17. C. D. Stanciu, A. V. Kimel, F. Hansteen, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast spin dynamics across compensation points in ferrimagnetic GdFeCo: the role of angular momentum compensation,” Phys. Rev. B 73, 220402(R) (2006).
    [CrossRef]
  18. C. A. Perroni and A. Liebsch, “Coherent control of magnetization via inverse Faraday effect,” J. Phys.: Condens. Matter 18, 7063-7078 (2006).
    [CrossRef]
  19. C. A. Perroni and A. Liebsch, “Magnetization dynamics in dysprosium orthoferrites via the inverse Faraday effect,” Phys. Rev. B 74, 134430 (2006).
    [CrossRef]
  20. C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
    [CrossRef] [PubMed]
  21. Y. Zhang and J. Bai, “High-density all-optical magnetic recording using a high-NA lens illuminated by circularly polarized pulse lights,” Phys. Lett. A 372, 6294-6297 (2008).
    [CrossRef]
  22. V. V. Kruglyak, M. E. Portnoi, and R. J. Hickenc, “Use of the Faraday optical transformer for ultrafast magnetization reversal of nanomagnets,” J. Nanophotonics 1, 013502 (2007).
    [CrossRef]
  23. A. Rebei and J. Hohlfeld, “The magneto-optical Barnett effect: circularly polarized light induced femtosecond magnetization reversal,” Phys. Lett. A 372, 1915-1918 (2008).
    [CrossRef]
  24. C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast interaction of the angular momentum of photons with spins in the metallic amorphous alloy GdFeCo,” Phys. Rev. Lett. 98, 207401 (2007).
    [CrossRef] [PubMed]
  25. J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190-193 (1965).
    [CrossRef]
  26. Y. Zhang, X. Ye, and J. Chen, “Converging spherical wave propagation in a hemispherical solid lens,” J. Opt. A, Pure Appl. Opt. 8, 578-583 (2006).
    [CrossRef]
  27. A. S. van de Nes, L. Billy, S. F. Pereira, and J. J. M. Braat, “Calculation of the vectorial field distribution in a stratified focal region of a high numerical aperture imaging system,” Opt. Express 12, 1281-1295 (2004).
    [CrossRef] [PubMed]
  28. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
    [CrossRef]
  29. L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun. 191, 161-172 (2001).
    [CrossRef]
  30. B. Bomzon, M. Gu, and J. Shamir, “Angular momentum and geometrical phases in tight-focused circularly polarized plane waves,” Appl. Phys. Lett. 89, 241104 (2006).
    [CrossRef]
  31. R. Hertel, “Theory of the inverse Faraday effect in metals,” J. Magn. Magn. Mater. 303, L1-L4 (2006).
    [CrossRef]

2008 (2)

Y. Zhang and J. Bai, “High-density all-optical magnetic recording using a high-NA lens illuminated by circularly polarized pulse lights,” Phys. Lett. A 372, 6294-6297 (2008).
[CrossRef]

A. Rebei and J. Hohlfeld, “The magneto-optical Barnett effect: circularly polarized light induced femtosecond magnetization reversal,” Phys. Lett. A 372, 1915-1918 (2008).
[CrossRef]

2007 (5)

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast interaction of the angular momentum of photons with spins in the metallic amorphous alloy GdFeCo,” Phys. Rev. Lett. 98, 207401 (2007).
[CrossRef] [PubMed]

V. V. Kruglyak, M. E. Portnoi, and R. J. Hickenc, “Use of the Faraday optical transformer for ultrafast magnetization reversal of nanomagnets,” J. Nanophotonics 1, 013502 (2007).
[CrossRef]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

M. Gu, S. Kuriakose, and X. Gan, “A single beam near-field laser trap for optical stretching, folding and rotation of erythrocytes,” Opt. Express 15, 1369-1375 (2007).
[CrossRef] [PubMed]

Y. Zhang and X. Ye, “Three-zone phase-only filter increasing the focal depth of optical storage systems with a solid immersion lens,” Appl. Phys. B 86, 97-103 (2007).
[CrossRef]

2006 (8)

Y. Zhang, “Optical data storage system with a plano-ellipsoidal solid immersion mirror illuminated directly by a point light source,” Appl. Opt. 45, 8653-8658 (2006).
[CrossRef] [PubMed]

Y. Zhang, “Theoretical study of near-field optical storage with a solid immersion lens,” J. Opt. Soc. Am. A 23, 2132-2136 (2006).
[CrossRef]

B. Bomzon, M. Gu, and J. Shamir, “Angular momentum and geometrical phases in tight-focused circularly polarized plane waves,” Appl. Phys. Lett. 89, 241104 (2006).
[CrossRef]

R. Hertel, “Theory of the inverse Faraday effect in metals,” J. Magn. Magn. Mater. 303, L1-L4 (2006).
[CrossRef]

C. D. Stanciu, A. V. Kimel, F. Hansteen, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast spin dynamics across compensation points in ferrimagnetic GdFeCo: the role of angular momentum compensation,” Phys. Rev. B 73, 220402(R) (2006).
[CrossRef]

C. A. Perroni and A. Liebsch, “Coherent control of magnetization via inverse Faraday effect,” J. Phys.: Condens. Matter 18, 7063-7078 (2006).
[CrossRef]

C. A. Perroni and A. Liebsch, “Magnetization dynamics in dysprosium orthoferrites via the inverse Faraday effect,” Phys. Rev. B 74, 134430 (2006).
[CrossRef]

Y. Zhang, X. Ye, and J. Chen, “Converging spherical wave propagation in a hemispherical solid lens,” J. Opt. A, Pure Appl. Opt. 8, 578-583 (2006).
[CrossRef]

2005 (1)

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, “Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses,” Nature 435, 655-657 (2005).
[CrossRef] [PubMed]

2004 (5)

R. Gómez-Abal, O. Ney, K. Satitkovitchai, and W. Hübner, “All-optical subpicosecond magnetic switching in NiO(001),” Phys. Rev. Lett. 92, 227402 (2004).
[CrossRef] [PubMed]

Y. Zhang, H. Xiao, and C. Zhang, “Diffractive super-resolution elements applied to near-field optical data storage with solid immersion lens,” New J. Phys. 6, 75 (2004).
[CrossRef]

S. B. Ippolito, S. A. Thorne, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, “High spatial resolution subsurface thermal emission microscopy,” Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

D. Ganic, X. Gan, and M. Gu, “Trapping force and optical lifting under focused evanescent wave illumination,” Opt. Express 12, 5533-5538 (2004).
[CrossRef] [PubMed]

A. S. van de Nes, L. Billy, S. F. Pereira, and J. J. M. Braat, “Calculation of the vectorial field distribution in a stratified focal region of a high numerical aperture imaging system,” Opt. Express 12, 1281-1295 (2004).
[CrossRef] [PubMed]

2002 (1)

M. Yoshita, K. Koyama, M. Baba, and H. Akiyama, “Fourier imaging study of efficient near-field optical coupling in solid immersion fluorescence microscopy,” J. Appl. Phys. 92, 862-865 (2002).
[CrossRef]

2001 (1)

L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun. 191, 161-172 (2001).
[CrossRef]

2000 (1)

1999 (2)

C. H. Back, R. Allenspach, W. Weber, S. S. P. Parkin, D. Weller, E. L. Garwin, and H. C. Siegmann, “Minimum field strength in precessional magnetization reversal,” Science 285, 864-867 (1999).
[CrossRef] [PubMed]

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

1997 (1)

1994 (1)

B. D. Terris, H. J. Mamin, and D. Ruger, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388-390 (1994).
[CrossRef]

1990 (1)

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615-2616 (1990).
[CrossRef]

1965 (1)

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190-193 (1965).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
[CrossRef]

Akiyama, H.

M. Yoshita, K. Koyama, M. Baba, and H. Akiyama, “Fourier imaging study of efficient near-field optical coupling in solid immersion fluorescence microscopy,” J. Appl. Phys. 92, 862-865 (2002).
[CrossRef]

Allenspach, R.

C. H. Back, R. Allenspach, W. Weber, S. S. P. Parkin, D. Weller, E. L. Garwin, and H. C. Siegmann, “Minimum field strength in precessional magnetization reversal,” Science 285, 864-867 (1999).
[CrossRef] [PubMed]

Baba, M.

M. Yoshita, K. Koyama, M. Baba, and H. Akiyama, “Fourier imaging study of efficient near-field optical coupling in solid immersion fluorescence microscopy,” J. Appl. Phys. 92, 862-865 (2002).
[CrossRef]

Back, C. H.

C. H. Back, R. Allenspach, W. Weber, S. S. P. Parkin, D. Weller, E. L. Garwin, and H. C. Siegmann, “Minimum field strength in precessional magnetization reversal,” Science 285, 864-867 (1999).
[CrossRef] [PubMed]

Bai, J.

Y. Zhang and J. Bai, “High-density all-optical magnetic recording using a high-NA lens illuminated by circularly polarized pulse lights,” Phys. Lett. A 372, 6294-6297 (2008).
[CrossRef]

Balbashov, A. M.

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, “Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses,” Nature 435, 655-657 (2005).
[CrossRef] [PubMed]

Billy, L.

Bomzon, B.

B. Bomzon, M. Gu, and J. Shamir, “Angular momentum and geometrical phases in tight-focused circularly polarized plane waves,” Appl. Phys. Lett. 89, 241104 (2006).
[CrossRef]

Braat, J. J. M.

Chen, J.

Y. Zhang, X. Ye, and J. Chen, “Converging spherical wave propagation in a hemispherical solid lens,” J. Opt. A, Pure Appl. Opt. 8, 578-583 (2006).
[CrossRef]

Crozier, K. B.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Elings, V. B.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Eraslan, M. G.

S. B. Ippolito, S. A. Thorne, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, “High spatial resolution subsurface thermal emission microscopy,” Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

Gan, X.

Ganic, D.

Garwin, E. L.

C. H. Back, R. Allenspach, W. Weber, S. S. P. Parkin, D. Weller, E. L. Garwin, and H. C. Siegmann, “Minimum field strength in precessional magnetization reversal,” Science 285, 864-867 (1999).
[CrossRef] [PubMed]

Ghislain, L. P.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Goldberg, B. B.

S. B. Ippolito, S. A. Thorne, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, “High spatial resolution subsurface thermal emission microscopy,” Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

Gómez-Abal, R.

R. Gómez-Abal, O. Ney, K. Satitkovitchai, and W. Hübner, “All-optical subpicosecond magnetic switching in NiO(001),” Phys. Rev. Lett. 92, 227402 (2004).
[CrossRef] [PubMed]

Gu, M.

Guo, F.

Hansteen, F.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast interaction of the angular momentum of photons with spins in the metallic amorphous alloy GdFeCo,” Phys. Rev. Lett. 98, 207401 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, A. V. Kimel, F. Hansteen, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast spin dynamics across compensation points in ferrimagnetic GdFeCo: the role of angular momentum compensation,” Phys. Rev. B 73, 220402(R) (2006).
[CrossRef]

Hayashi, S.

Helseth, L. E.

L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun. 191, 161-172 (2001).
[CrossRef]

Hertel, R.

R. Hertel, “Theory of the inverse Faraday effect in metals,” J. Magn. Magn. Mater. 303, L1-L4 (2006).
[CrossRef]

Hickenc, R. J.

V. V. Kruglyak, M. E. Portnoi, and R. J. Hickenc, “Use of the Faraday optical transformer for ultrafast magnetization reversal of nanomagnets,” J. Nanophotonics 1, 013502 (2007).
[CrossRef]

Hohlfeld, J.

A. Rebei and J. Hohlfeld, “The magneto-optical Barnett effect: circularly polarized light induced femtosecond magnetization reversal,” Phys. Lett. A 372, 1915-1918 (2008).
[CrossRef]

Hübner, W.

R. Gómez-Abal, O. Ney, K. Satitkovitchai, and W. Hübner, “All-optical subpicosecond magnetic switching in NiO(001),” Phys. Rev. Lett. 92, 227402 (2004).
[CrossRef] [PubMed]

Ichimura, I.

Ippolito, S. B.

S. B. Ippolito, S. A. Thorne, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, “High spatial resolution subsurface thermal emission microscopy,” Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

Itoh, A.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast interaction of the angular momentum of photons with spins in the metallic amorphous alloy GdFeCo,” Phys. Rev. Lett. 98, 207401 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, A. V. Kimel, F. Hansteen, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast spin dynamics across compensation points in ferrimagnetic GdFeCo: the role of angular momentum compensation,” Phys. Rev. B 73, 220402(R) (2006).
[CrossRef]

Kimel, A. V.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast interaction of the angular momentum of photons with spins in the metallic amorphous alloy GdFeCo,” Phys. Rev. Lett. 98, 207401 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, A. V. Kimel, F. Hansteen, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast spin dynamics across compensation points in ferrimagnetic GdFeCo: the role of angular momentum compensation,” Phys. Rev. B 73, 220402(R) (2006).
[CrossRef]

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, “Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses,” Nature 435, 655-657 (2005).
[CrossRef] [PubMed]

Kino, G. S.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

I. Ichimura, S. Hayashi, and G. S. Kino, “High-density optical recording using a solid immersion lens,” Appl. Opt. 36, 4339-4348 (1997).
[CrossRef] [PubMed]

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615-2616 (1990).
[CrossRef]

Kirilyuk, A.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast interaction of the angular momentum of photons with spins in the metallic amorphous alloy GdFeCo,” Phys. Rev. Lett. 98, 207401 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, A. V. Kimel, F. Hansteen, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast spin dynamics across compensation points in ferrimagnetic GdFeCo: the role of angular momentum compensation,” Phys. Rev. B 73, 220402(R) (2006).
[CrossRef]

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, “Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses,” Nature 435, 655-657 (2005).
[CrossRef] [PubMed]

Koyama, K.

M. Yoshita, K. Koyama, M. Baba, and H. Akiyama, “Fourier imaging study of efficient near-field optical coupling in solid immersion fluorescence microscopy,” J. Appl. Phys. 92, 862-865 (2002).
[CrossRef]

Kruglyak, V. V.

V. V. Kruglyak, M. E. Portnoi, and R. J. Hickenc, “Use of the Faraday optical transformer for ultrafast magnetization reversal of nanomagnets,” J. Nanophotonics 1, 013502 (2007).
[CrossRef]

Kuriakose, S.

Leblebici, Y.

S. B. Ippolito, S. A. Thorne, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, “High spatial resolution subsurface thermal emission microscopy,” Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

Liebsch, A.

C. A. Perroni and A. Liebsch, “Coherent control of magnetization via inverse Faraday effect,” J. Phys.: Condens. Matter 18, 7063-7078 (2006).
[CrossRef]

C. A. Perroni and A. Liebsch, “Magnetization dynamics in dysprosium orthoferrites via the inverse Faraday effect,” Phys. Rev. B 74, 134430 (2006).
[CrossRef]

Malmstrom, L. D.

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190-193 (1965).
[CrossRef]

Mamin, H. J.

B. D. Terris, H. J. Mamin, and D. Ruger, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388-390 (1994).
[CrossRef]

Manalis, S. R.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Mansfield, S. M.

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615-2616 (1990).
[CrossRef]

Minne, S. C.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Ney, O.

R. Gómez-Abal, O. Ney, K. Satitkovitchai, and W. Hübner, “All-optical subpicosecond magnetic switching in NiO(001),” Phys. Rev. Lett. 92, 227402 (2004).
[CrossRef] [PubMed]

Parkin, S. S. P.

C. H. Back, R. Allenspach, W. Weber, S. S. P. Parkin, D. Weller, E. L. Garwin, and H. C. Siegmann, “Minimum field strength in precessional magnetization reversal,” Science 285, 864-867 (1999).
[CrossRef] [PubMed]

Pereira, S. F.

Perroni, C. A.

C. A. Perroni and A. Liebsch, “Magnetization dynamics in dysprosium orthoferrites via the inverse Faraday effect,” Phys. Rev. B 74, 134430 (2006).
[CrossRef]

C. A. Perroni and A. Liebsch, “Coherent control of magnetization via inverse Faraday effect,” J. Phys.: Condens. Matter 18, 7063-7078 (2006).
[CrossRef]

Pershan, P. S.

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190-193 (1965).
[CrossRef]

Pisarev, R. V.

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, “Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses,” Nature 435, 655-657 (2005).
[CrossRef] [PubMed]

Portnoi, M. E.

V. V. Kruglyak, M. E. Portnoi, and R. J. Hickenc, “Use of the Faraday optical transformer for ultrafast magnetization reversal of nanomagnets,” J. Nanophotonics 1, 013502 (2007).
[CrossRef]

Quate, C. F.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Rasing, T.

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, “Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses,” Nature 435, 655-657 (2005).
[CrossRef] [PubMed]

Rasing, Th.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast interaction of the angular momentum of photons with spins in the metallic amorphous alloy GdFeCo,” Phys. Rev. Lett. 98, 207401 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, A. V. Kimel, F. Hansteen, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast spin dynamics across compensation points in ferrimagnetic GdFeCo: the role of angular momentum compensation,” Phys. Rev. B 73, 220402(R) (2006).
[CrossRef]

Rebei, A.

A. Rebei and J. Hohlfeld, “The magneto-optical Barnett effect: circularly polarized light induced femtosecond magnetization reversal,” Phys. Lett. A 372, 1915-1918 (2008).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
[CrossRef]

Ruger, D.

B. D. Terris, H. J. Mamin, and D. Ruger, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388-390 (1994).
[CrossRef]

Satitkovitchai, K.

R. Gómez-Abal, O. Ney, K. Satitkovitchai, and W. Hübner, “All-optical subpicosecond magnetic switching in NiO(001),” Phys. Rev. Lett. 92, 227402 (2004).
[CrossRef] [PubMed]

Schlesinger, T. E.

Shamir, J.

B. Bomzon, M. Gu, and J. Shamir, “Angular momentum and geometrical phases in tight-focused circularly polarized plane waves,” Appl. Phys. Lett. 89, 241104 (2006).
[CrossRef]

Siegmann, H. C.

C. H. Back, R. Allenspach, W. Weber, S. S. P. Parkin, D. Weller, E. L. Garwin, and H. C. Siegmann, “Minimum field strength in precessional magnetization reversal,” Science 285, 864-867 (1999).
[CrossRef] [PubMed]

Stancil, D. D.

Stanciu, C. D.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast interaction of the angular momentum of photons with spins in the metallic amorphous alloy GdFeCo,” Phys. Rev. Lett. 98, 207401 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, A. V. Kimel, F. Hansteen, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast spin dynamics across compensation points in ferrimagnetic GdFeCo: the role of angular momentum compensation,” Phys. Rev. B 73, 220402(R) (2006).
[CrossRef]

Terris, B. D.

B. D. Terris, H. J. Mamin, and D. Ruger, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388-390 (1994).
[CrossRef]

Thorne, S. A.

S. B. Ippolito, S. A. Thorne, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, “High spatial resolution subsurface thermal emission microscopy,” Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

Tsukamoto, A.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast interaction of the angular momentum of photons with spins in the metallic amorphous alloy GdFeCo,” Phys. Rev. Lett. 98, 207401 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, A. V. Kimel, F. Hansteen, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast spin dynamics across compensation points in ferrimagnetic GdFeCo: the role of angular momentum compensation,” Phys. Rev. B 73, 220402(R) (2006).
[CrossRef]

Ünlü, M. S.

S. B. Ippolito, S. A. Thorne, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, “High spatial resolution subsurface thermal emission microscopy,” Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

Usachev, P. A.

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, “Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses,” Nature 435, 655-657 (2005).
[CrossRef] [PubMed]

van de Nes, A. S.

van der Ziel, J. P.

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190-193 (1965).
[CrossRef]

Weber, W.

C. H. Back, R. Allenspach, W. Weber, S. S. P. Parkin, D. Weller, E. L. Garwin, and H. C. Siegmann, “Minimum field strength in precessional magnetization reversal,” Science 285, 864-867 (1999).
[CrossRef] [PubMed]

Weller, D.

C. H. Back, R. Allenspach, W. Weber, S. S. P. Parkin, D. Weller, E. L. Garwin, and H. C. Siegmann, “Minimum field strength in precessional magnetization reversal,” Science 285, 864-867 (1999).
[CrossRef] [PubMed]

Wilder, K.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
[CrossRef]

Xiao, H.

Y. Zhang, H. Xiao, and C. Zhang, “Diffractive super-resolution elements applied to near-field optical data storage with solid immersion lens,” New J. Phys. 6, 75 (2004).
[CrossRef]

Ye, X.

Y. Zhang and X. Ye, “Three-zone phase-only filter increasing the focal depth of optical storage systems with a solid immersion lens,” Appl. Phys. B 86, 97-103 (2007).
[CrossRef]

Y. Zhang, X. Ye, and J. Chen, “Converging spherical wave propagation in a hemispherical solid lens,” J. Opt. A, Pure Appl. Opt. 8, 578-583 (2006).
[CrossRef]

Yoshita, M.

M. Yoshita, K. Koyama, M. Baba, and H. Akiyama, “Fourier imaging study of efficient near-field optical coupling in solid immersion fluorescence microscopy,” J. Appl. Phys. 92, 862-865 (2002).
[CrossRef]

Zhang, C.

Y. Zhang, H. Xiao, and C. Zhang, “Diffractive super-resolution elements applied to near-field optical data storage with solid immersion lens,” New J. Phys. 6, 75 (2004).
[CrossRef]

Zhang, Y.

Y. Zhang and J. Bai, “High-density all-optical magnetic recording using a high-NA lens illuminated by circularly polarized pulse lights,” Phys. Lett. A 372, 6294-6297 (2008).
[CrossRef]

Y. Zhang and X. Ye, “Three-zone phase-only filter increasing the focal depth of optical storage systems with a solid immersion lens,” Appl. Phys. B 86, 97-103 (2007).
[CrossRef]

Y. Zhang, “Theoretical study of near-field optical storage with a solid immersion lens,” J. Opt. Soc. Am. A 23, 2132-2136 (2006).
[CrossRef]

Y. Zhang, “Optical data storage system with a plano-ellipsoidal solid immersion mirror illuminated directly by a point light source,” Appl. Opt. 45, 8653-8658 (2006).
[CrossRef] [PubMed]

Y. Zhang, X. Ye, and J. Chen, “Converging spherical wave propagation in a hemispherical solid lens,” J. Opt. A, Pure Appl. Opt. 8, 578-583 (2006).
[CrossRef]

Y. Zhang, H. Xiao, and C. Zhang, “Diffractive super-resolution elements applied to near-field optical data storage with solid immersion lens,” New J. Phys. 6, 75 (2004).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. B (1)

Y. Zhang and X. Ye, “Three-zone phase-only filter increasing the focal depth of optical storage systems with a solid immersion lens,” Appl. Phys. B 86, 97-103 (2007).
[CrossRef]

Appl. Phys. Lett. (5)

S. B. Ippolito, S. A. Thorne, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, “High spatial resolution subsurface thermal emission microscopy,” Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615-2616 (1990).
[CrossRef]

B. D. Terris, H. J. Mamin, and D. Ruger, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388-390 (1994).
[CrossRef]

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

B. Bomzon, M. Gu, and J. Shamir, “Angular momentum and geometrical phases in tight-focused circularly polarized plane waves,” Appl. Phys. Lett. 89, 241104 (2006).
[CrossRef]

J. Appl. Phys. (1)

M. Yoshita, K. Koyama, M. Baba, and H. Akiyama, “Fourier imaging study of efficient near-field optical coupling in solid immersion fluorescence microscopy,” J. Appl. Phys. 92, 862-865 (2002).
[CrossRef]

J. Magn. Magn. Mater. (1)

R. Hertel, “Theory of the inverse Faraday effect in metals,” J. Magn. Magn. Mater. 303, L1-L4 (2006).
[CrossRef]

J. Nanophotonics (1)

V. V. Kruglyak, M. E. Portnoi, and R. J. Hickenc, “Use of the Faraday optical transformer for ultrafast magnetization reversal of nanomagnets,” J. Nanophotonics 1, 013502 (2007).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

Y. Zhang, X. Ye, and J. Chen, “Converging spherical wave propagation in a hemispherical solid lens,” J. Opt. A, Pure Appl. Opt. 8, 578-583 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys.: Condens. Matter (1)

C. A. Perroni and A. Liebsch, “Coherent control of magnetization via inverse Faraday effect,” J. Phys.: Condens. Matter 18, 7063-7078 (2006).
[CrossRef]

Nature (1)

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, “Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses,” Nature 435, 655-657 (2005).
[CrossRef] [PubMed]

New J. Phys. (1)

Y. Zhang, H. Xiao, and C. Zhang, “Diffractive super-resolution elements applied to near-field optical data storage with solid immersion lens,” New J. Phys. 6, 75 (2004).
[CrossRef]

Opt. Commun. (1)

L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun. 191, 161-172 (2001).
[CrossRef]

Opt. Express (3)

Phys. Lett. A (2)

Y. Zhang and J. Bai, “High-density all-optical magnetic recording using a high-NA lens illuminated by circularly polarized pulse lights,” Phys. Lett. A 372, 6294-6297 (2008).
[CrossRef]

A. Rebei and J. Hohlfeld, “The magneto-optical Barnett effect: circularly polarized light induced femtosecond magnetization reversal,” Phys. Lett. A 372, 1915-1918 (2008).
[CrossRef]

Phys. Rev. B (2)

C. D. Stanciu, A. V. Kimel, F. Hansteen, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast spin dynamics across compensation points in ferrimagnetic GdFeCo: the role of angular momentum compensation,” Phys. Rev. B 73, 220402(R) (2006).
[CrossRef]

C. A. Perroni and A. Liebsch, “Magnetization dynamics in dysprosium orthoferrites via the inverse Faraday effect,” Phys. Rev. B 74, 134430 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

R. Gómez-Abal, O. Ney, K. Satitkovitchai, and W. Hübner, “All-optical subpicosecond magnetic switching in NiO(001),” Phys. Rev. Lett. 92, 227402 (2004).
[CrossRef] [PubMed]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Tsukamoto, A. Itoh, A. Kirilyuk, and Th. Rasing, “Ultrafast interaction of the angular momentum of photons with spins in the metallic amorphous alloy GdFeCo,” Phys. Rev. Lett. 98, 207401 (2007).
[CrossRef] [PubMed]

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190-193 (1965).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
[CrossRef]

Science (1)

C. H. Back, R. Allenspach, W. Weber, S. S. P. Parkin, D. Weller, E. L. Garwin, and H. C. Siegmann, “Minimum field strength in precessional magnetization reversal,” Science 285, 864-867 (1999).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Schematic setup of the all-optical magnetic recording with a hemisphere SIL. The MO film is placed near the planar surface of the SIL and the gap between the SIL and MO is air.

Fig. 2
Fig. 2

Three-dimensional surfaces (left column) and contours (right column) of magnetization distribution for a low-NA SIL system illuminated by an incident right-handed circularly polarized light. (a) and (d) are the magnitude of the transverse component and total magnetization M ρ σ and M σ , respectively. (b) and (c) are the axial components M z R and M z L for the right- and left-hand circular polarizations of incidence, respectively. The air gap between the SIL and MO film is h = 50 nm , the refractive index n = 1.518 , and the numerical aperture of the system NA = 0.759 ( α = 30 ° ) in calculations.

Fig. 3
Fig. 3

Normalized magnetization distributions along the transverse direction for the system of h = 50 nm , n = 1.518 , and NA = 0.759 ( α = 30 ° ) . M ρ σ , M z σ , and M σ are the magnitude of the transverse, axial, and total magnetizations, respectively.

Fig. 4
Fig. 4

Angle between the magnetization vector and the z axis in the effective magnetization zone. (a) and (b) are the cases for the incident right-handed polarization and for the incident left-handed polarization, respectively. The unit of inserted numbers in contour plots is in degrees. The calculation parameters are h = 50 nm , n = 1.518 , and NA = 0.759 ( α = 30 ° ) .

Fig. 5
Fig. 5

Three-dimensional surfaces (left column) and contours (right column) of magnetization distribution for a high-NA SIL system illuminated by an incident right-handed circularly polarized light. (a) and (d) are the magnitude of the transverse component and total magnetization M ρ σ and M σ , respectively. (b) and (c) are the axial components M z R and M z L for the right- and left-hand circular polarizations of incidence, respectively. The calculation parameters are h = 50 nm , n = 1.518 , and NA = 1.4437 ( α = 72 ° ) .

Fig. 6
Fig. 6

Normalized magnetization distributions along the transverse direction for the system of h = 50 nm , n = 1.518 , and NA = 1.4437 ( α = 72 ° ) .

Fig. 7
Fig. 7

Contour plots for the angle between the magnetization vector and the z axis in the effective magnetization zone. (a) and (b) are the cases for the incident right-handed polarization and for the incident left-handed polarization, respectively. The unit of inserted numbers in contour plots is in degrees. The calculation parameters are h = 50 nm , n = 1.518 , and NA = 1.4437 ( α = 72 ° )

Equations (13)

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

E ( ρ c , ϕ c , h ) = [ e x e y e z ] = [ i A ( I 0 + I 2 cos 2 ϕ c ) i A I 2 sin 2 ϕ c 2 A I 1 cos ϕ c ] ,
I 0 = 0 α ( t s + t p 1 ( n sin θ ) 2 ) cos θ sin θ J 0 ( n k ρ c sin θ ) exp [ i k h 1 ( n sin θ ) 2 ] d θ ,
I 1 = 0 α n t p cos θ sin 2 θ J 1 ( n k ρ c sin θ ) exp [ i k h 1 ( n sin θ ) 2 ] d θ ,
I 2 = 0 α ( t s t p 1 ( n sin θ ) 2 ) cos θ sin θ J 2 ( n k ρ c sin θ ) exp [ i k h 1 ( n sin θ ) 2 ] d θ ,
E ( ρ c , ϕ c , h ) = [ e x e y e z ] = [ i A I 2 sin 2 ϕ c i A ( I 0 + I 2 cos 2 ϕ c ) 2 A I 1 cos ϕ c ] = [ i A I 2 sin 2 ϕ c i A ( I 0 I 2 cos 2 ϕ c ) 2 A I 1 sin ϕ c ] ,
E circ L ( ρ c , ϕ c , h ) = [ i e x + e x i e y + e y i e z + e z ] = [ A ( I 0 + I 2 e i 2 ϕ c ) i A ( I 0 I 2 e i 2 ϕ c ) 2 i A I 1 e i ϕ c ] ,
E circ R ( ρ c , ϕ c , h ) = [ i e x + e x i e y + e y i e z + e z ] = [ A ( I 0 + I 2 e i 2 ϕ c ) i A ( I 0 I 2 e i 2 ϕ c ) 2 i A I 1 e i ϕ c ] .
e ̂ ϕ = e ̂ y cos ϕ c e ̂ x sin ϕ c ,
e ̂ ρ = e ̂ x cos ϕ c + e ̂ y sin ϕ c ,
E circ L ( ρ c , ϕ c , h ) = [ E ρ L E ϕ L E z L ] = A e i ϕ c [ ( I 0 + I 2 ) i ( I 0 I 2 ) 2 i I 1 ] ,
E circ R ( ρ c , ϕ c , h ) = [ E ρ R E ϕ R E z R ] = A e i ϕ c [ ( I 0 + I 2 ) i ( I 0 I 2 ) 2 i I 1 ] .
M ( ρ c , ϕ c , h ) = i γ E × E * ,
M σ ( ρ c , ϕ c , h ) = [ M x σ M y σ M z σ ] = i A 2 [ E circ , y σ E circ , z σ * E circ , z σ E circ , y σ * E circ , z σ E circ , x σ * E circ , x σ E circ , z σ * E circ , x σ E circ , y σ * E circ , y σ E circ , x σ * ] .

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