Abstract

The use of a solid immersion lens (SIL) is an important technique for increasing areal density in optical recording. Here an approximate method is presented for analyzing the optical fields in a SIL above a half-space and a SIL above a multilayer recording medium. Both propagating and evanescent components are included in the distribution of fields below the SIL. An approximate closed-form expression is given for the decay of the intensity away from the SIL surface above a half-space. In the case of a SIL above a recording medium the model describes the strong oscillations that are observed in the reflected Kerr rotation and ellipticity as the medium spacing is varied. These oscillations are attributed to standing waves in the propagating field component.

© 2000 Optical Society of America

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References

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  1. E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
    [CrossRef]
  2. P. Torok, C. J. R. Sheppard, P. Varga, “Study of evanescent waves for transmission near-field optical microscopy,” J. Mod. Opt. 43, 1167–1183 (1996).
    [CrossRef]
  3. R. D. Grober, T. Rutherford, T. D. Harris, “Modal approximation for the electromagnetic field of a near-field optical probe,” Appl. Opt. 35, 3488–3495 (1996).
    [CrossRef] [PubMed]
  4. S. M. Mansfield, G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
    [CrossRef]
  5. S. M. Mansfield, “Solid immersion microscopy,” G. L. Report 4949, Ph.D. dissertation (Edward L. Ginzton Laboratory, Stanford University, Stanford, Calif., 1992).
  6. B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
    [CrossRef]
  7. I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, G. S. Kino, “High density optical disk system using a solid immersion lens,” in Optical Data Storage, G. R. Knight, H. Ooki, Y. Tyan, eds., Proc. SPIE2514, 176–181 (1995).
  8. T. Suzuki, Y. Itoh, M. Birukawa, W. Van Drent, “Solid immersion lens near field optical approach for high density optical recording,” IEEE Trans. Magn. 34, 399–403 (1998).
    [CrossRef]
  9. I. Ichimura, S. Hayashi, G. S. Kino, “High-density optical recording using a solid immersion lens,” Appl. Opt. 36, 4339–4348 (1997).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  14. D. G. Flagello, T. Milster, A. E. Rosenbluth, “Theory of high-NA imaging in homogeneous thin films,” J. Opt. Soc. Am. A 13, 53–64 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. P. H. Lissberger, “Thin film magneto-optics,” in Applied Magnetism, R. Gerber, C. D. Wright, G. Asti, eds. NATO ASI Ser. E253,
  21. T. D. Milster, J. S. Jo, K. Hirota, K. Shimura, Y. Zhang, “The nature of the coupling field in optical data storage using solid immersion lenses,” Jpn. J. Appl. Phys. Part 1 38, 1793–1794 (1999).
    [CrossRef]
  22. T. D. Milster, J. S. Jo, K. Hirota, “Roles of propagating and evanescent waves in solid immersion lens systems,” Appl. Opt. 38, 5046–5056 (1999).
    [CrossRef]

1999

T. D. Milster, J. S. Jo, K. Hirota, K. Shimura, Y. Zhang, “The nature of the coupling field in optical data storage using solid immersion lenses,” Jpn. J. Appl. Phys. Part 1 38, 1793–1794 (1999).
[CrossRef]

T. D. Milster, J. S. Jo, K. Hirota, “Roles of propagating and evanescent waves in solid immersion lens systems,” Appl. Opt. 38, 5046–5056 (1999).
[CrossRef]

1998

T. Suzuki, Y. Itoh, M. Birukawa, W. Van Drent, “Solid immersion lens near field optical approach for high density optical recording,” IEEE Trans. Magn. 34, 399–403 (1998).
[CrossRef]

1997

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

D. G. Flagello, T. D. Milster, “High-numerical-aperture effects in photoresist,” Appl. Optics 36, 8944–8951 (1997).
[CrossRef]

1996

1994

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

1992

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

1991

1990

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

M. Mansuripur, “Analysis of multilayer thin film structures containing magneto-optic and anisotropic media at oblique incidence using 2 × 2 matrices,” J. Appl. Phys. 67, 6466–6475 (1990).
[CrossRef]

1986

1984

1965

D. O. Smith, “Magneto-optical scattering from multi-layer magnetic and dielectric films. Part I. General theory,” Opt. Acta 12, 13–45 (1965).
[CrossRef]

1959

B. Richards, 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]

Betzig, E.

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

Birukawa, M.

T. Suzuki, Y. Itoh, M. Birukawa, W. Van Drent, “Solid immersion lens near field optical approach for high density optical recording,” IEEE Trans. Magn. 34, 399–403 (1998).
[CrossRef]

Finn, P. L.

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

Flagello, D. G.

D. G. Flagello, T. D. Milster, “High-numerical-aperture effects in photoresist,” Appl. Optics 36, 8944–8951 (1997).
[CrossRef]

D. G. Flagello, T. Milster, A. E. Rosenbluth, “Theory of high-NA imaging in homogeneous thin films,” J. Opt. Soc. Am. A 13, 53–64 (1996).
[CrossRef]

Grober, R. D.

Gyorgy, E. M.

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

Harris, T. D.

Hayashi, S.

Hirota, K.

T. D. Milster, J. S. Jo, K. Hirota, K. Shimura, Y. Zhang, “The nature of the coupling field in optical data storage using solid immersion lenses,” Jpn. J. Appl. Phys. Part 1 38, 1793–1794 (1999).
[CrossRef]

T. D. Milster, J. S. Jo, K. Hirota, “Roles of propagating and evanescent waves in solid immersion lens systems,” Appl. Opt. 38, 5046–5056 (1999).
[CrossRef]

Ichimura, I.

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

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, G. S. Kino, “High density optical disk system using a solid immersion lens,” in Optical Data Storage, G. R. Knight, H. Ooki, Y. Tyan, eds., Proc. SPIE2514, 176–181 (1995).

Itoh, Y.

T. Suzuki, Y. Itoh, M. Birukawa, W. Van Drent, “Solid immersion lens near field optical approach for high density optical recording,” IEEE Trans. Magn. 34, 399–403 (1998).
[CrossRef]

Jo, J. S.

T. D. Milster, J. S. Jo, K. Hirota, “Roles of propagating and evanescent waves in solid immersion lens systems,” Appl. Opt. 38, 5046–5056 (1999).
[CrossRef]

T. D. Milster, J. S. Jo, K. Hirota, K. Shimura, Y. Zhang, “The nature of the coupling field in optical data storage using solid immersion lenses,” Jpn. J. Appl. Phys. Part 1 38, 1793–1794 (1999).
[CrossRef]

Kino, G. S.

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

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

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

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, G. S. Kino, “High density optical disk system using a solid immersion lens,” in Optical Data Storage, G. R. Knight, H. Ooki, Y. Tyan, eds., Proc. SPIE2514, 176–181 (1995).

G. S. Kino, “Fields associated with the solid immersion lens,” in Far- and Near-Field Optics: Physics and Information Processing, S. Jutamulia, T. Asakura, eds., Proc. SPIE3467, 128–137 (1998).

Lee, S.-W.

Ling, H.

Maeda, F.

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, G. S. Kino, “High density optical disk system using a solid immersion lens,” in Optical Data Storage, G. R. Knight, H. Ooki, Y. Tyan, eds., Proc. SPIE2514, 176–181 (1995).

Mamin, H. J.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

Mansfield, S. M.

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

S. M. Mansfield, “Solid immersion microscopy,” G. L. Report 4949, Ph.D. dissertation (Edward L. Ginzton Laboratory, Stanford University, Stanford, Calif., 1992).

Mansuripur, M.

Mathews, J.

J. Mathews, R. L. Walker, Mathematical Methods of Physics, 2nd ed. (Benjamin, New York, 1970), p. 109.

Milster, T.

Milster, T. D.

T. D. Milster, J. S. Jo, K. Hirota, K. Shimura, Y. Zhang, “The nature of the coupling field in optical data storage using solid immersion lenses,” Jpn. J. Appl. Phys. Part 1 38, 1793–1794 (1999).
[CrossRef]

T. D. Milster, J. S. Jo, K. Hirota, “Roles of propagating and evanescent waves in solid immersion lens systems,” Appl. Opt. 38, 5046–5056 (1999).
[CrossRef]

D. G. Flagello, T. D. Milster, “High-numerical-aperture effects in photoresist,” Appl. Optics 36, 8944–8951 (1997).
[CrossRef]

Ooki, H.

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, G. S. Kino, “High density optical disk system using a solid immersion lens,” in Optical Data Storage, G. R. Knight, H. Ooki, Y. Tyan, eds., Proc. SPIE2514, 176–181 (1995).

Osato, K.

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, G. S. Kino, “High density optical disk system using a solid immersion lens,” in Optical Data Storage, G. R. Knight, H. Ooki, Y. Tyan, eds., Proc. SPIE2514, 176–181 (1995).

Owa, H.

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, G. S. Kino, “High density optical disk system using a solid immersion lens,” in Optical Data Storage, G. R. Knight, H. Ooki, Y. Tyan, eds., Proc. SPIE2514, 176–181 (1995).

Richards, B.

B. Richards, 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]

Rosenbluth, A. E.

Rugar, D.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

Rutherford, T.

Sheppard, C. J. R.

P. Torok, C. J. R. Sheppard, P. Varga, “Study of evanescent waves for transmission near-field optical microscopy,” J. Mod. Opt. 43, 1167–1183 (1996).
[CrossRef]

Shimura, K.

T. D. Milster, J. S. Jo, K. Hirota, K. Shimura, Y. Zhang, “The nature of the coupling field in optical data storage using solid immersion lenses,” Jpn. J. Appl. Phys. Part 1 38, 1793–1794 (1999).
[CrossRef]

Smith, D. O.

D. O. Smith, “Magneto-optical scattering from multi-layer magnetic and dielectric films. Part I. General theory,” Opt. Acta 12, 13–45 (1965).
[CrossRef]

Studenmund, W. R.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

Suzuki, T.

T. Suzuki, Y. Itoh, M. Birukawa, W. Van Drent, “Solid immersion lens near field optical approach for high density optical recording,” IEEE Trans. Magn. 34, 399–403 (1998).
[CrossRef]

Terris, B. D.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

Torok, P.

P. Torok, C. J. R. Sheppard, P. Varga, “Study of evanescent waves for transmission near-field optical microscopy,” J. Mod. Opt. 43, 1167–1183 (1996).
[CrossRef]

Trautman, J. K.

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

Van Drent, W.

T. Suzuki, Y. Itoh, M. Birukawa, W. Van Drent, “Solid immersion lens near field optical approach for high density optical recording,” IEEE Trans. Magn. 34, 399–403 (1998).
[CrossRef]

Varga, P.

P. Torok, C. J. R. Sheppard, P. Varga, “Study of evanescent waves for transmission near-field optical microscopy,” J. Mod. Opt. 43, 1167–1183 (1996).
[CrossRef]

Walker, R. L.

J. Mathews, R. L. Walker, Mathematical Methods of Physics, 2nd ed. (Benjamin, New York, 1970), p. 109.

Wolf, E.

B. Richards, 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]

Wolfe, R.

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

Zhang, Y.

T. D. Milster, J. S. Jo, K. Hirota, K. Shimura, Y. Zhang, “The nature of the coupling field in optical data storage using solid immersion lenses,” Jpn. J. Appl. Phys. Part 1 38, 1793–1794 (1999).
[CrossRef]

Appl. Opt.

Appl. Optics

D. G. Flagello, T. D. Milster, “High-numerical-aperture effects in photoresist,” Appl. Optics 36, 8944–8951 (1997).
[CrossRef]

Appl. Phys. Lett.

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

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

IEEE Trans. Magn.

T. Suzuki, Y. Itoh, M. Birukawa, W. Van Drent, “Solid immersion lens near field optical approach for high density optical recording,” IEEE Trans. Magn. 34, 399–403 (1998).
[CrossRef]

J. Appl. Phys.

M. Mansuripur, “Analysis of multilayer thin film structures containing magneto-optic and anisotropic media at oblique incidence using 2 × 2 matrices,” J. Appl. Phys. 67, 6466–6475 (1990).
[CrossRef]

J. Mod. Opt.

P. Torok, C. J. R. Sheppard, P. Varga, “Study of evanescent waves for transmission near-field optical microscopy,” J. Mod. Opt. 43, 1167–1183 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys. Part 1

T. D. Milster, J. S. Jo, K. Hirota, K. Shimura, Y. Zhang, “The nature of the coupling field in optical data storage using solid immersion lenses,” Jpn. J. Appl. Phys. Part 1 38, 1793–1794 (1999).
[CrossRef]

Opt. Acta

D. O. Smith, “Magneto-optical scattering from multi-layer magnetic and dielectric films. Part I. General theory,” Opt. Acta 12, 13–45 (1965).
[CrossRef]

Proc. R. Soc. London Ser. A

B. Richards, 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]

Other

J. Mathews, R. L. Walker, Mathematical Methods of Physics, 2nd ed. (Benjamin, New York, 1970), p. 109.

P. H. Lissberger, “Thin film magneto-optics,” in Applied Magnetism, R. Gerber, C. D. Wright, G. Asti, eds. NATO ASI Ser. E253,

G. S. Kino, “Fields associated with the solid immersion lens,” in Far- and Near-Field Optics: Physics and Information Processing, S. Jutamulia, T. Asakura, eds., Proc. SPIE3467, 128–137 (1998).

I. Ichimura, K. Osato, F. Maeda, H. Owa, H. Ooki, G. S. Kino, “High density optical disk system using a solid immersion lens,” in Optical Data Storage, G. R. Knight, H. Ooki, Y. Tyan, eds., Proc. SPIE2514, 176–181 (1995).

S. M. Mansfield, “Solid immersion microscopy,” G. L. Report 4949, Ph.D. dissertation (Edward L. Ginzton Laboratory, Stanford University, Stanford, Calif., 1992).

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Figures (10)

Fig. 1
Fig. 1

Intensity of (a) the x component of the electric field, (b) the y component, and (c) the z component in the focal plane of an optical system with N.A. = 1.7 with the theory of Richards and Wolf.11

Fig. 2
Fig. 2

Comparison between the intensity profile for the x component of the electric field from the Richards and Wolf theory (solid curve) and the intensity from the Gaussian approximation given by Eq. (11) (dashed curve).

Fig. 3
Fig. 3

Geometry of the SIL above a half-space.

Fig. 4
Fig. 4

Distribution of magnitude of the optical field with radius r at ζ = 0, 0.125λ0, 0.25λ0, and 0.5λ0.

Fig. 5
Fig. 5

Increase of the diameter of the transmitted beam with distance away from the SIL surface.

Fig. 6
Fig. 6

Plot of the optical field along the z axis (r = 0): (a) total optical field, (b) the propagating part of the field, (c) the evanescent part of the field, (d) low-N.A. approximation [Eq. (24)].

Fig. 7
Fig. 7

Geometry of the SIL above a multilayer medium.

Fig. 8
Fig. 8

Spreading of the reflected beam intensity at z = 10λ0, 25λ0, and 40λ0 with air-gap thickness of g = 0.50λ0.

Fig. 9
Fig. 9

Rotation and ellipticity of the reflected field along the z axis.

Fig. 10
Fig. 10

Plots of (a) rotation, (b) ellipticity of the reflected field as the air gap changes for Si3Ni4 overcoat layer thicknesses of t = 0.05λ0, 0.10λ0, 0.15λ0, and 0.20λ0. The MO layer thickness is d = 0.03λ0, and the calculations are for z = 50λ0 to ensure far-field conditions.

Tables (2)

Tables Icon

Table 1 Optical MO Constants of the Layers in SIL at Wavelength of 825 nma,b

Tables Icon

Table 2 Reflectivity, Rotation Angle, and Ellipticity of Reflected Beam in the Case of SIL above a Multilayer Recording Mediuma

Equations (60)

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

exr, ϕ, z=-iAI0r, z+I2r, zcos 2ϕ,
eyr, ϕ, z=-iAI2r, zsin 2ϕ,
ezr, ϕ, z=-2AI1r, zcos ϕ,
I0r, z=0αcos1/2 θ sin θ1+cos θ×J0k0nr sin θexpik0nz cos θdθ,
I1r, z=0αcos1/2 θ sin2 θ×J1k0nr sin θexpik0nz cos θdθ,
I2r, z=0αcos1/2 θ sin θ1-cos θ×J2k0nr sin θexpik0nz cos θdθ;
2+k2E=0,
E=φr, zxˆ=φr, zcos θrˆ-sin θθˆ=Errˆ+Eθθˆ.
2+k2φr, z=0.
φeigenkr, r, z=J0krrexpikzz,
kr2+kz2=k02,
φr, z=0 ckrφeigenkr, r, zkrdkr,
Er, z=0 ckrEeigenkr, r, zkrdkr,
Eeigenkr, r, z=J0krrexpikzzxˆ.
Er, z=0=exp-r2/ω02xˆ,
ω0=λ02NA2 ln 21/2.
ckr=0 φr, z=0J0krrrdr=0exp-r2/ω02J0krrrdr=ω022exp-ω02kr2/4.
φin+φre=φtr,
zφin+φre=z φtr,
φin=0 cinkrJ0krrexpikz1ζkrdkr,
φre=0 crekrJ0krrexp-ikz1ζkrdkr,
φtr=0 ctrkrJ0krrexpikz2ζkrdkr,
cinkr+crekr=ctrkr,
kz1cinkr-crekr=kz2ctrkr.
ctrkr=21+kz2/kz1 cinkrfkrcinkr.
Einr, z=0=exp-r2/ω02xˆ.
cinkr=ω02/2exp-ω02kr2/4.
Etrr,ζ=φtrr, ζxˆ,φtrr, ζ=ω0220 fkrexp-ω02kr2/4×J0krrexpikz2ζkrdkr.
fkr21+k2/k1,
kz2k2-kr2/2k2.
φtrr, ζ=21+k2/k1ω022expik2ζ0exp-ω0kr/22×J0krrexp-ikr2ζ/2k2krdkr=21+k2/k111+i2ζ/ω02k2×exp-r2ω02+i2ζ/k2expik2ζ=21+k2/k1ω0ωζexp-r2/ω2ζ×expik2ζ+r2/2Rζ-iϕζ,
|Etrζ/λ, r=0|=21+k2/k1ω0ωζ/λ.
2+KEr, θ, z=0,
K=ω2μ=k2iκ20-iκ2k2000k2.
El,rr, θ, z=cos θi sin θrˆi cos θ±sin θθˆφl,rr, z,
2+k2±κ2φl,rr, z=0,
φl,rr, z=J0krrexpikzl,rz,
kr2+kzl,r2=k2±κ2.
E1|z=0=E2|z=0,
zE1z=0=zE2z=0.
E±p=J0krrexp±ikzpz,
E˜=E+x, E-x, E+y, E-yT in dielectric media,
E˜=E+l, E-l, E+r, E-rT in MO media.
E˜2=M2,1E˜1.
E1+xE1-xE1+yE1-y=121+kz2kz11-kz2kz101-kz2kz11+kz2kz101+kz2kz11-kz2kz11-kz2kz11+kz2kz1E2+xE2-xE2+yE2-y.
E1+xE1-xE1+yE1-y=121+klzkz1-klzkz1+krzkz1-krzkz1-klzkz1+klzkz1-krzkz1+krzkzi1+klzkzi1-klzkz-i1+krzkz-i1-krzkzi1-klzkzi1+klzkz-i1-krzkz-i1+krzkzE2+lE2-lE2+rE2-r.
E˜z+z0=Mz0E˜zE+aE-aE+bE-bz+z0=expikzaz0exp-ikzaz0expikzbz0exp-ikzbz0E+aE-aE+bE-bz,
E˜MO,0kr=pkr, -pkr, qkr, -qkrT,
E˜SILkr=MSIL,ag·Magg·Mag,oc·Moct·Moc,MO·MMOd·E˜MO,0kr,
E˜SILkr=Einxkr, Erexkr, Einykr, EreykrT.
Einxkr=ω022exp-ω02kr24,
Einykr=0.
Erex=0 ErexkrJ0krrexpikzzkrdkr,
Erey=0 EreykrJ0krrexpikzzkrdkr.
θ˜=Ey/Ex=θ+i.
zˆ×H1-H2z=0=0.
zˆ××E1-E2z=0=0.
zˆ××E=zˆ·E-zˆ·E=-zˆ·E=-Ez,
E1zz=0=E2zz=0,
E1=φin+φrexˆ,E2=φtrxˆ,

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