Abstract

A three-dimensional combined vectorial method, which is based on the finite-difference time-domain algorithm and vectorial diffraction formulation, is introduced to analyze the interaction of a realistic focused beam with a metallic grating in an optical storage system. The diffracted field patterns and the detected signals are calculated for gratings with different geometries, and the polarization-dependent characteristics are studied. The combined method can give accurately the detected signals and the field pattern at any desired position of the optical storage system.

© 2004 Optical Society of America

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References

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  1. H. H. Hopkins, “Diffraction theory of laser read-out systems for optical video disks,” J. Opt. Soc. Am. 69, 4–24 (1979).
    [CrossRef]
  2. H. Ito, T. Kojima, “Analysis of higher information density pregroove model by boundary element method,” Electron. Lett. 27, 1511–1512 (1991).
    [CrossRef]
  3. T. Kojima, K. Wakabayashi, “Three-dimensional analysis of light-beam scattering from pit and emboss marks of optical disk models,” in Proceedings of the IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 2, pp. 882–885.
  4. D. S. Marx, D. Psaltis, “Optical diffraction of focused spots and subwavelength structures,” J. Opt. Soc. Am. A 14, 1268–1278 (1997).
    [CrossRef]
  5. P. Sheng, “Theoretical consideration of optical diffraction from RCA video disk signal,” RCA Rev. 39, 512–555 (1978).
  6. X. F. Cheng, “Vector diffraction analysis of optical disk readout,” Appl. Opt. 39, 6436–6440 (2000).
    [CrossRef]
  7. W. C. Liu, M. W. Kowarz, “Vector diffraction from subwavelength optical disk structures: two-dimensional modeling of near-field profiles, far-field intensities, and detector signals from a DVD,” Appl. Opt. 38, 3787–3797 (1999).
    [CrossRef]
  8. A. Taflove, Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1998).
  9. J. B. Judkins, R. W. Ziolkowski, “Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings,” J. Opt. Soc. Am. A 12, 1974–1983 (1995).
    [CrossRef]
  10. Y. He, T. Kojima, “Three-dimensional analysis of light-beam scattering from magneto-optical disk structure by FDTD method,” in Proceedings of the 1997 Antennas and Propagation Society Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 4, pp. 2148–2151.
  11. M. Mansuripur, “Effects of high-numerical-aperture focusing on the state of polarization in optical and magneto-optics data storage systems,” Appl. Opt. 30, 3154–3162 (1991).
    [CrossRef] [PubMed]
  12. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 66–73.
  13. M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6, 786–805 (1989).
    [CrossRef]
  14. M. Mansuripur, “Certain computational aspects of vector diffraction problems: erratum,” J. Opt. Soc. Am. A 10, 382–383 (1993).
    [CrossRef]
  15. S. A. Cummer, “An analysis of new and existing FDTD methods for isotropic cold plasma and a method for improving their accuracy,” IEEE Trans. Antennas Propag. 45, 392–400 (1997).
    [CrossRef]
  16. J. L. Young, R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag., February2001, pp. 61–126.
  17. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]
  18. D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microw. Guid. Wave Lett. 4, 268–270 (1994).
    [CrossRef]
  19. Ref. 12, pp. 415–416.

2001 (1)

J. L. Young, R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag., February2001, pp. 61–126.

2000 (1)

1999 (1)

1997 (2)

S. A. Cummer, “An analysis of new and existing FDTD methods for isotropic cold plasma and a method for improving their accuracy,” IEEE Trans. Antennas Propag. 45, 392–400 (1997).
[CrossRef]

D. S. Marx, D. Psaltis, “Optical diffraction of focused spots and subwavelength structures,” J. Opt. Soc. Am. A 14, 1268–1278 (1997).
[CrossRef]

1995 (1)

1994 (2)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microw. Guid. Wave Lett. 4, 268–270 (1994).
[CrossRef]

1993 (1)

1991 (2)

H. Ito, T. Kojima, “Analysis of higher information density pregroove model by boundary element method,” Electron. Lett. 27, 1511–1512 (1991).
[CrossRef]

M. Mansuripur, “Effects of high-numerical-aperture focusing on the state of polarization in optical and magneto-optics data storage systems,” Appl. Opt. 30, 3154–3162 (1991).
[CrossRef] [PubMed]

1989 (1)

1979 (1)

1978 (1)

P. Sheng, “Theoretical consideration of optical diffraction from RCA video disk signal,” RCA Rev. 39, 512–555 (1978).

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Cheng, X. F.

Cummer, S. A.

S. A. Cummer, “An analysis of new and existing FDTD methods for isotropic cold plasma and a method for improving their accuracy,” IEEE Trans. Antennas Propag. 45, 392–400 (1997).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 66–73.

He, Y.

Y. He, T. Kojima, “Three-dimensional analysis of light-beam scattering from magneto-optical disk structure by FDTD method,” in Proceedings of the 1997 Antennas and Propagation Society Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 4, pp. 2148–2151.

Hopkins, H. H.

Ito, H.

H. Ito, T. Kojima, “Analysis of higher information density pregroove model by boundary element method,” Electron. Lett. 27, 1511–1512 (1991).
[CrossRef]

Judkins, J. B.

Katz, D. S.

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microw. Guid. Wave Lett. 4, 268–270 (1994).
[CrossRef]

Kojima, T.

H. Ito, T. Kojima, “Analysis of higher information density pregroove model by boundary element method,” Electron. Lett. 27, 1511–1512 (1991).
[CrossRef]

T. Kojima, K. Wakabayashi, “Three-dimensional analysis of light-beam scattering from pit and emboss marks of optical disk models,” in Proceedings of the IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 2, pp. 882–885.

Y. He, T. Kojima, “Three-dimensional analysis of light-beam scattering from magneto-optical disk structure by FDTD method,” in Proceedings of the 1997 Antennas and Propagation Society Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 4, pp. 2148–2151.

Kowarz, M. W.

Liu, W. C.

Mansuripur, M.

Marx, D. S.

Nelson, R. O.

J. L. Young, R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag., February2001, pp. 61–126.

Psaltis, D.

Sheng, P.

P. Sheng, “Theoretical consideration of optical diffraction from RCA video disk signal,” RCA Rev. 39, 512–555 (1978).

Taflove, A.

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microw. Guid. Wave Lett. 4, 268–270 (1994).
[CrossRef]

A. Taflove, Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1998).

Thiele, E. T.

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microw. Guid. Wave Lett. 4, 268–270 (1994).
[CrossRef]

Wakabayashi, K.

T. Kojima, K. Wakabayashi, “Three-dimensional analysis of light-beam scattering from pit and emboss marks of optical disk models,” in Proceedings of the IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 2, pp. 882–885.

Young, J. L.

J. L. Young, R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag., February2001, pp. 61–126.

Ziolkowski, R. W.

Appl. Opt. (3)

Electron. Lett. (1)

H. Ito, T. Kojima, “Analysis of higher information density pregroove model by boundary element method,” Electron. Lett. 27, 1511–1512 (1991).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

J. L. Young, R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag., February2001, pp. 61–126.

IEEE Microw. Guid. Wave Lett. (1)

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microw. Guid. Wave Lett. 4, 268–270 (1994).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

S. A. Cummer, “An analysis of new and existing FDTD methods for isotropic cold plasma and a method for improving their accuracy,” IEEE Trans. Antennas Propag. 45, 392–400 (1997).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

RCA Rev. (1)

P. Sheng, “Theoretical consideration of optical diffraction from RCA video disk signal,” RCA Rev. 39, 512–555 (1978).

Other (5)

A. Taflove, Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1998).

Y. He, T. Kojima, “Three-dimensional analysis of light-beam scattering from magneto-optical disk structure by FDTD method,” in Proceedings of the 1997 Antennas and Propagation Society Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 4, pp. 2148–2151.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 66–73.

T. Kojima, K. Wakabayashi, “Three-dimensional analysis of light-beam scattering from pit and emboss marks of optical disk models,” in Proceedings of the IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 2, pp. 882–885.

Ref. 12, pp. 415–416.

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram of the optical storage system.

Fig. 2
Fig. 2

Geometry of the metallic grating. (a) Unit cell of the grating, (b) periodic structures of the grating. O1, center of a mesa; O2, center between two mesas along the x axis.

Fig. 3
Fig. 3

Diagram of the polarization-rotation effect.

Fig. 4
Fig. 4

Total-field and scattered-field regions in the FDTD algorithm. PML, perfectly matched layer.

Fig. 5
Fig. 5

Positions of the field components in a cubic unit cell of the Yee lattice.

Fig. 6
Fig. 6

Differential signal Sd as the displacement Δyc increases for various polarizations of incidence in case 1.

Fig. 7
Fig. 7

Differential signal Sd as the displacement Δyc increases for various polarizations of incidence in case 2.

Fig. 8
Fig. 8

Near-field distribution (amplitude and phase) of the dominant component on the yz plane passing the focusing center (0, Py/4) for case 1 with θ=20° (axis unit: 10-7 m). (a) Ex for x-polarized incidence, (b) Ey for y-polarized incidence.

Fig. 9
Fig. 9

Near-field distribution (amplitude and phase) of the dominant component on the yz plane passing the focusing center (0, Py/4) for case 2 with θ=20° (axis unit: 10-7 m). (a) Ex for x-polarized incidence, (b) Ey for y-polarized incidence.

Fig. 10
Fig. 10

Distribution of the far-field intensity at the detector plane in cases 1 and 2 with θ=20° for (a) and (d) x-polarized incidence, (b) and (e) y-polarized incidence, and (c) and (f) circular-polarized incidence, when the focusing center is located at (0, Py/4) (axis unit: 10-4 m). The white dashed circles denote the aperture of the objective lens. The energy outside the aperture is shown only for reference and is actually truncated when the detected signal is calculated.

Fig. 11
Fig. 11

Distribution of the far-field intensity along the intersectional line at the detector plane for case 2 with θ=20°, when the focusing center is located at (0, Py/4). The intensity distributions are calculated with the present combined method, a less rigorous method (with the standard scalar Fresnel diffraction formulations used to calculate the field propagation between the focusing lens and the grating), and a conventional scalar method.1

Fig. 12
Fig. 12

Central aperture (CA) signal Sc as the slope angle θ increases for various polarizations of incidence in cases 1 and 2.

Fig. 13
Fig. 13

Total backward-diffracted energy as the slope angle θ increases for various polarizations of incidence in cases 1 and 2.

Tables (2)

Tables Icon

Table 1 Parameters of the Optical Storage System Used in the Numerical Simulation

Tables Icon

Table 2 Geometrical Parameters for the Two Gratings Used in the Numerical Simulation

Equations (23)

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E2x(x2, y2)E2y(x2, y2)=exp(jkf)jλf×-Tp(x1, y1)Ψ(σx, σy)×expjk(Δz-f)1-x12+y12f21/2×E1x(x1, y1)E1y(x1, y1)exp-j 2πλf (x1x2+y1y2)dx1dy1,
Tp(x1, y1)=1,x12+y12rp0,x12+y12>rp,
Ψ(σx, σy)=1σz1-σx21+σz-σxσy1+σz-σxσy1+σz1-σy21+σz,
E1x(x1, y1)E1y(x1, y1)=exp(jkf)jλf Tp(x1, y1)Ψ(σx, σy)×expjk(Δz-f)×1-x12+y12f21/2-E2x(x2, y2)E2y(x2, y2)×exp-j 2πλf (x1x2+y1y2)dx2dy2,
Ψ(σx, σy)=1σz1-σy21+σzσxσy1+σzσxσy1+σz1-σx21+σz.
0Et=×H-Jp,
μ0Ht=-×E,
dJpdt=0ωp2E-νJp,
(ω)0=r+ji=(nr+jni)2=1+ωp2-ω2-jνω.
ν=2nrniω1-nr2-ni2,
ωp=ω1-nr2-ni2+4nr2ni21-nr2-ni21/2.
Em+1=Em+Δt0 (×Hm+1/2-Jpm+1/2),
Hm+1/2=Hm-1/2-Δtμ0 ×Em,
Jpm+1/2=1-0.5νΔt1+0.5νΔt Jpm-1/2+0ωp2Δt1+0.5νΔt Em,
Δtminδsnsc, 4δs24c2+δs2ωp21/2,
E2α(x2, y2)=A(x2, y2)exp[jϕ(x2, y2)]=2jTt0t0+TEscat α(x2, y2, zs, t)exp(jωt)dt,
I=D(|Edx|2+|Edy|2)dx1dy1,
Edx(x1, y1)Edy(x1, y1)=J  E2x(x1, y1)E2y(x1, y1).
Sd=(I1-I2)/(I1+I2),
Sc=(I1+I2)/Iinc,
1000
0001
12001-j

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