Abstract

Rigorous two-dimensional vector-diffraction patterns of a focused beam incident on an optical disk, specifically, a digital versatile disk (DVD), are examined both in the near field and in the far field. An efficient finite-difference frequency-domain method is developed for calculating the electromagnetic fields in the neighborhood of subwavelength dielectric and metallic structures. The results of vector-diffraction theory are compared with those of scalar-diffraction theory for pressed DVD features that consist of pits or of bumps. The sum (data) and difference (tracking) signals from a split photodetector are also calculated for different disk features and for different polarizations. The subwavelength features of a DVD result in considerable vector-diffraction effects both in the near-field profiles and in the detector signals, depending not only on the polarization of illumination but also on whether the features are pits or bumps. This paper provides important insight into the vector-diffraction effects encountered in high-density optical data storage systems.

© 1999 Optical Society of America

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  34. B. L. Buzbee, G. H. Golub, C. W. Nielson, “On direct methods for solving Poisson’s equations,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 7, 627–656 (1970).
    [CrossRef]
  35. P. N. Swarztrauber, “The methods of cyclic reduction, Fourier analysis and the FACR algorithm for the discrete solution of Poisson’s equation on a rectangle,” SIAM (Soc. Ind. Appl. Math.) Rev. 19, 490–501 (1977).
  36. R. A. Sweet, “A cyclic reduction algorithm for solving block tridiagonal systems of arbitrary dimension,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 14, 706–720 (1977).
    [CrossRef]
  37. P. N. Swarztrauber, R. A. Sweet, “Vector and parallel methods for the direct solution of Poisson’s equation,” J. Comput. Appl. Math. 27, 241–263 (1989).
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  38. E. Gallopoulos, Y. Saad, “A parallel block cyclic reduction algorithm for the fast solution of elliptic equations,” Parallel Comput. 10, 143–159 (1989).
    [CrossRef]
  39. Y. Saad, M. H. Schultz, “GMRES: a general minimal residual algorithm for solving nonsymmetric linear systems,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856–869 (1986).
    [CrossRef]
  40. C. D. Dimitropoulos, A. N. Beris, “An efficient and robust spectral solver for nonseparable elliptic equations,” J. Comput. Phys. 133, 186–191 (1997).
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  41. B. Engquist, A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629–651 (1977).
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  42. B. Engquist, A. Majda, “Radiation boundary conditions for acoustic and elastic wave calculations,” Commun. Pure Appl. Math. 32, 313–357 (1979).
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  43. G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
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  44. R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation,” Math. Comput. 47, 437–459 (1986).
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    [CrossRef]
  46. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).
  47. J. J. Grefet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
    [CrossRef]
  48. A. Madrazo, M. Nieto-Vesperinas, “Surface structure and polariton interactions in the scattering of electromagnetic wave from a cylinder in front of a conducting grating: theory for the reflection photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 785–795 (1996).
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1998 (2)

O. W. Shih, “Near-field diffraction by a slit in a thick perfectly conducting screen flying above a magneto-optical disk,” J. Appl. Phys. 84, 6485–6498 (1998).
[CrossRef]

W.-C. Liu, M. W. Kowarz, “Vector diffraction from subwavelength optical disk structures: two-dimensional near-field profiles,” Opt. Express 2, 191–197 (1998).
[CrossRef] [PubMed]

1997 (9)

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

D. S. Marx, D. Psaltis, “Polarization quadrature measurement of subwavelength diffracting structures,” Appl. Opt. 36, 6434–6440 (1997).
[CrossRef]

O. Mata-Mendez, J. Sumaya-Martinez, “Scattering of TE-polarized waves by a finite grating: giant resonant enhancement of the electric field within the grooves,” J. Opt. Soc. Am. A 14, 2203–2211 (1997).
[CrossRef]

K. Hirayama, E. Glytsis, T. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).
[CrossRef]

C. D. Dimitropoulos, A. N. Beris, “An efficient and robust spectral solver for nonseparable elliptic equations,” J. Comput. Phys. 133, 186–191 (1997).
[CrossRef]

J. Bae, T. Okamoto, T. Fujii, K. Mizuno, T. Nozokido, “Experimental demonstration for scanning near-field optical microscopy using a metal micro-slit probe at millimeter wavelengths,” Appl. Phys. Lett. 71, 3581–3583 (1997).
[CrossRef]

G. S. Kino, “Near-field optical storage,” Opt. Photon. News 8(11), 38–39 (1997).
[CrossRef]

M. Mansuripur, G. Sincerbox, “Principles and techniques of optical data storage,” Proc. IEEE 85, 1780–1796 (1997).
[CrossRef]

A. Madrazo, M. Nieto-Vesperinas, “Model near field calculations for optical data storage readout,” Appl. Phys. Lett. 70, 31–33 (1997).
[CrossRef]

1996 (6)

C. Girard, A. Dereux, “Near-field optics theories,” Rep. Prog. Phys. 59, 657–699 (1996).
[CrossRef]

J. B. Judkins, C. W. Haggans, R. W. Ziolkowski, “Two-dimensional finite-difference time-domain simulation for rewritable optical disk surface structure design,” Appl. Opt. 35, 2477–2487 (1996).
[CrossRef] [PubMed]

B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
[CrossRef]

B.-N. Jiang, J. Wu, L. A. Povinelli, “The origin of spurious solutions in computational electromagnetics,” J. Comput. Phys. 125, 104–123 (1996).
[CrossRef]

M. Ogawa, M. Nakada, R. Katayama, M. Okada, M. Itoh, “Analysis of scattering light from magnetic material with land/groove by three-dimensional boundary element method,” Jpn. J. Appl. Phys. 35, 336–341 (1996).
[CrossRef]

A. Madrazo, M. Nieto-Vesperinas, “Surface structure and polariton interactions in the scattering of electromagnetic wave from a cylinder in front of a conducting grating: theory for the reflection photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 785–795 (1996).
[CrossRef]

1995 (3)

1994 (4)

D. Courjon, C. Bainier, “Near field microscopy and near field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[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]

K. D. Paulsen, “Finite-element solution of Maxwell’s equations with Helmholtz forms,” J. Opt. Soc. Am. A 11, 1434–1444 (1994).
[CrossRef]

R. Depine, D. Skigin, “Scattering from metallic surfaces having a finite number of rectangular grooves,” J. Opt. Soc. Am. A 11, 2844–2850 (1994).
[CrossRef]

1993 (2)

K. Kobayashi, “Vector diffraction modeling: polarization dependence of optical read-out/servo signals,” Jpn. J. Appl. Phys. 32, 3175–3184 (1993).
[CrossRef]

T. Park, H. Eom, K. Yoshitomi, “Analysis of TM scattering from finite rectangular grooves in a conducting plane,” J. Opt. Soc. Am. A 10, 905–911 (1993).
[CrossRef]

1992 (2)

Y.-L. Kok, “Boundary-value solution to electromagnetic scattering by a rectangular groove in a ground plane,” J. Opt. Soc. Am. A 9, 302–311 (1992).
[CrossRef]

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

1991 (3)

H. Ooki, “Vector diffraction theory for magnetooptical disc systems,” Optik 89, 15–22 (1991).

T. Kojima, J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn. Part 2 Electron. 74, 11–19 (1991).
[CrossRef]

Y. Miyazaki, K. Manabe, “Scattered near-field and induced current of a beam wave by pits on optical disks using boundary element analysis,” Radio Sci. 26, 281–289 (1991).
[CrossRef]

1989 (2)

P. N. Swarztrauber, R. A. Sweet, “Vector and parallel methods for the direct solution of Poisson’s equation,” J. Comput. Appl. Math. 27, 241–263 (1989).
[CrossRef]

E. Gallopoulos, Y. Saad, “A parallel block cyclic reduction algorithm for the fast solution of elliptic equations,” Parallel Comput. 10, 143–159 (1989).
[CrossRef]

1987 (1)

R. L. Higdon, “Numerical absorbing boundary conditions for the wave equation,” Math. Comput. 49, 65–90 (1987).
[CrossRef]

1986 (2)

R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation,” Math. Comput. 47, 437–459 (1986).

Y. Saad, M. H. Schultz, “GMRES: a general minimal residual algorithm for solving nonsymmetric linear systems,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856–869 (1986).
[CrossRef]

1981 (1)

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

1979 (2)

B. Engquist, A. Majda, “Radiation boundary conditions for acoustic and elastic wave calculations,” Commun. Pure Appl. Math. 32, 313–357 (1979).
[CrossRef]

J. G. Dil, B. A. J. Jacobs, “Apparent size of reflecting polygonal obstacles of the order one wavelength,” J. Opt. Soc. Am. 69, 950–960 (1979).
[CrossRef]

1977 (3)

B. Engquist, A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629–651 (1977).
[CrossRef]

P. N. Swarztrauber, “The methods of cyclic reduction, Fourier analysis and the FACR algorithm for the discrete solution of Poisson’s equation on a rectangle,” SIAM (Soc. Ind. Appl. Math.) Rev. 19, 490–501 (1977).

R. A. Sweet, “A cyclic reduction algorithm for solving block tridiagonal systems of arbitrary dimension,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 14, 706–720 (1977).
[CrossRef]

1973 (1)

P. Concus, G. H. Golub, “Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 10, 1103–1120 (1973).
[CrossRef]

1970 (1)

B. L. Buzbee, G. H. Golub, C. W. Nielson, “On direct methods for solving Poisson’s equations,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 7, 627–656 (1970).
[CrossRef]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

Bae, J.

J. Bae, T. Okamoto, T. Fujii, K. Mizuno, T. Nozokido, “Experimental demonstration for scanning near-field optical microscopy using a metal micro-slit probe at millimeter wavelengths,” Appl. Phys. Lett. 71, 3581–3583 (1997).
[CrossRef]

Bainier, C.

D. Courjon, C. Bainier, “Near field microscopy and near field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

Beris, A. N.

C. D. Dimitropoulos, A. N. Beris, “An efficient and robust spectral solver for nonseparable elliptic equations,” J. Comput. Phys. 133, 186–191 (1997).
[CrossRef]

Betzig, E.

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

Bouwhuis, G.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. S. Immink, Principles of Optical Disc Systems (Hilger, Bristol, UK, 1985).

Braat, J.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. S. Immink, Principles of Optical Disc Systems (Hilger, Bristol, UK, 1985).

Buzbee, B. L.

B. L. Buzbee, G. H. Golub, C. W. Nielson, “On direct methods for solving Poisson’s equations,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 7, 627–656 (1970).
[CrossRef]

Carminati, R.

J. J. Grefet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

Chang, C.-H.

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

Concus, P.

P. Concus, G. H. Golub, “Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 10, 1103–1120 (1973).
[CrossRef]

Courjon, D.

D. Courjon, C. Bainier, “Near field microscopy and near field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

Depine, R.

Dereux, A.

C. Girard, A. Dereux, “Near-field optics theories,” Rep. Prog. Phys. 59, 657–699 (1996).
[CrossRef]

Dil, J. G.

Dimitropoulos, C. D.

C. D. Dimitropoulos, A. N. Beris, “An efficient and robust spectral solver for nonseparable elliptic equations,” J. Comput. Phys. 133, 186–191 (1997).
[CrossRef]

Engquist, B.

B. Engquist, A. Majda, “Radiation boundary conditions for acoustic and elastic wave calculations,” Commun. Pure Appl. Math. 32, 313–357 (1979).
[CrossRef]

B. Engquist, A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629–651 (1977).
[CrossRef]

Eom, H.

Fillard, J. P.

J. P. Fillard, Near Field Optics and Nanoscopy (World Scientific, Singapore, 1996).
[CrossRef]

Finn, P. L.

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

Fujii, T.

J. Bae, T. Okamoto, T. Fujii, K. Mizuno, T. Nozokido, “Experimental demonstration for scanning near-field optical microscopy using a metal micro-slit probe at millimeter wavelengths,” Appl. Phys. Lett. 71, 3581–3583 (1997).
[CrossRef]

Gallopoulos, E.

E. Gallopoulos, Y. Saad, “A parallel block cyclic reduction algorithm for the fast solution of elliptic equations,” Parallel Comput. 10, 143–159 (1989).
[CrossRef]

Gaylord, T.

Gerber, R. E.

Girard, C.

C. Girard, A. Dereux, “Near-field optics theories,” Rep. Prog. Phys. 59, 657–699 (1996).
[CrossRef]

Glytsis, E.

Golub, G. H.

P. Concus, G. H. Golub, “Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 10, 1103–1120 (1973).
[CrossRef]

B. L. Buzbee, G. H. Golub, C. W. Nielson, “On direct methods for solving Poisson’s equations,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 7, 627–656 (1970).
[CrossRef]

Grefet, J. J.

J. J. Grefet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

Gyorgy, E. M.

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

Haggans, C. W.

Higdon, R. L.

R. L. Higdon, “Numerical absorbing boundary conditions for the wave equation,” Math. Comput. 49, 65–90 (1987).
[CrossRef]

R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation,” Math. Comput. 47, 437–459 (1986).

Hirayama, K.

Huijser, A.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. S. Immink, Principles of Optical Disc Systems (Hilger, Bristol, UK, 1985).

Ido, J.

T. Kojima, J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn. Part 2 Electron. 74, 11–19 (1991).
[CrossRef]

Immink, K. S.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. S. Immink, Principles of Optical Disc Systems (Hilger, Bristol, UK, 1985).

Itoh, M.

M. Ogawa, M. Nakada, R. Katayama, M. Okada, M. Itoh, “Analysis of scattering light from magnetic material with land/groove by three-dimensional boundary element method,” Jpn. J. Appl. Phys. 35, 336–341 (1996).
[CrossRef]

Jacobs, B. A. J.

Jiang, B.-N.

B.-N. Jiang, J. Wu, L. A. Povinelli, “The origin of spurious solutions in computational electromagnetics,” J. Comput. Phys. 125, 104–123 (1996).
[CrossRef]

Judkins, J. B.

Katayama, R.

M. Ogawa, M. Nakada, R. Katayama, M. Okada, M. Itoh, “Analysis of scattering light from magnetic material with land/groove by three-dimensional boundary element method,” Jpn. J. Appl. Phys. 35, 336–341 (1996).
[CrossRef]

Kino, G. S.

G. S. Kino, “Near-field optical storage,” Opt. Photon. News 8(11), 38–39 (1997).
[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]

Kobayashi, K.

K. Kobayashi, “Vector diffraction modeling: polarization dependence of optical read-out/servo signals,” Jpn. J. Appl. Phys. 32, 3175–3184 (1993).
[CrossRef]

Kojima, T.

T. Kojima, J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn. Part 2 Electron. 74, 11–19 (1991).
[CrossRef]

Kok, Y.-L.

Kowarz, M. W.

W.-C. Liu, M. W. Kowarz, “Vector diffraction from subwavelength optical disk structures: two-dimensional near-field profiles,” Opt. Express 2, 191–197 (1998).
[CrossRef] [PubMed]

M. W. Kowarz, “Diffraction effects in the near field,” Ph.D. dissertation (University of Rochester, Rochester, N.Y., 1995).

Kryder, M. H.

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

Liu, W.-C.

Madrazo, A.

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B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
[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]

Manabe, K.

Y. Miyazaki, K. Manabe, “Scattered near-field and induced current of a beam wave by pits on optical disks using boundary element analysis,” Radio Sci. 26, 281–289 (1991).
[CrossRef]

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[CrossRef]

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M. Ogawa, M. Nakada, R. Katayama, M. Okada, M. Itoh, “Analysis of scattering light from magnetic material with land/groove by three-dimensional boundary element method,” Jpn. J. Appl. Phys. 35, 336–341 (1996).
[CrossRef]

Nielson, C. W.

B. L. Buzbee, G. H. Golub, C. W. Nielson, “On direct methods for solving Poisson’s equations,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 7, 627–656 (1970).
[CrossRef]

Nieto-Vesperinas, M.

Nozokido, T.

J. Bae, T. Okamoto, T. Fujii, K. Mizuno, T. Nozokido, “Experimental demonstration for scanning near-field optical microscopy using a metal micro-slit probe at millimeter wavelengths,” Appl. Phys. Lett. 71, 3581–3583 (1997).
[CrossRef]

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M. Ogawa, M. Nakada, R. Katayama, M. Okada, M. Itoh, “Analysis of scattering light from magnetic material with land/groove by three-dimensional boundary element method,” Jpn. J. Appl. Phys. 35, 336–341 (1996).
[CrossRef]

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M. Ogawa, M. Nakada, R. Katayama, M. Okada, M. Itoh, “Analysis of scattering light from magnetic material with land/groove by three-dimensional boundary element method,” Jpn. J. Appl. Phys. 35, 336–341 (1996).
[CrossRef]

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J. Bae, T. Okamoto, T. Fujii, K. Mizuno, T. Nozokido, “Experimental demonstration for scanning near-field optical microscopy using a metal micro-slit probe at millimeter wavelengths,” Appl. Phys. Lett. 71, 3581–3583 (1997).
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B.-N. Jiang, J. Wu, L. A. Povinelli, “The origin of spurious solutions in computational electromagnetics,” J. Comput. Phys. 125, 104–123 (1996).
[CrossRef]

Psaltis, D.

Rugar, D.

B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
[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]

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E. Gallopoulos, Y. Saad, “A parallel block cyclic reduction algorithm for the fast solution of elliptic equations,” Parallel Comput. 10, 143–159 (1989).
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Y. Saad, M. H. Schultz, “GMRES: a general minimal residual algorithm for solving nonsymmetric linear systems,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856–869 (1986).
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J. J. Grefet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
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O. W. Shih, “Near-field diffraction by a slit in a thick perfectly conducting screen flying above a magneto-optical disk,” J. Appl. Phys. 84, 6485–6498 (1998).
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M. Mansuripur, G. Sincerbox, “Principles and techniques of optical data storage,” Proc. IEEE 85, 1780–1796 (1997).
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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).
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P. N. Swarztrauber, R. A. Sweet, “Vector and parallel methods for the direct solution of Poisson’s equation,” J. Comput. Appl. Math. 27, 241–263 (1989).
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B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
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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).
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E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, M. H. Kryder, C.-H. Chang, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
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B.-N. Jiang, J. Wu, L. A. Povinelli, “The origin of spurious solutions in computational electromagnetics,” J. Comput. Phys. 125, 104–123 (1996).
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Appl. Opt. (3)

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

J. Bae, T. Okamoto, T. Fujii, K. Mizuno, T. Nozokido, “Experimental demonstration for scanning near-field optical microscopy using a metal micro-slit probe at millimeter wavelengths,” Appl. Phys. Lett. 71, 3581–3583 (1997).
[CrossRef]

A. Madrazo, M. Nieto-Vesperinas, “Model near field calculations for optical data storage readout,” Appl. Phys. Lett. 70, 31–33 (1997).
[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]

B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
[CrossRef]

Commun. Pure Appl. Math. (1)

B. Engquist, A. Majda, “Radiation boundary conditions for acoustic and elastic wave calculations,” Commun. Pure Appl. Math. 32, 313–357 (1979).
[CrossRef]

Electron. Commun. Jpn. Part 2 Electron. (1)

T. Kojima, J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn. Part 2 Electron. 74, 11–19 (1991).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

IEEE Trans. Electromagn. Compat. (1)

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

J. Appl. Phys. (1)

O. W. Shih, “Near-field diffraction by a slit in a thick perfectly conducting screen flying above a magneto-optical disk,” J. Appl. Phys. 84, 6485–6498 (1998).
[CrossRef]

J. Comput. Appl. Math. (1)

P. N. Swarztrauber, R. A. Sweet, “Vector and parallel methods for the direct solution of Poisson’s equation,” J. Comput. Appl. Math. 27, 241–263 (1989).
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J. Comput. Phys. (2)

C. D. Dimitropoulos, A. N. Beris, “An efficient and robust spectral solver for nonseparable elliptic equations,” J. Comput. Phys. 133, 186–191 (1997).
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B.-N. Jiang, J. Wu, L. A. Povinelli, “The origin of spurious solutions in computational electromagnetics,” J. Comput. Phys. 125, 104–123 (1996).
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M. Ogawa, M. Nakada, R. Katayama, M. Okada, M. Itoh, “Analysis of scattering light from magnetic material with land/groove by three-dimensional boundary element method,” Jpn. J. Appl. Phys. 35, 336–341 (1996).
[CrossRef]

Math. Comput. (3)

B. Engquist, A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629–651 (1977).
[CrossRef]

R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation,” Math. Comput. 47, 437–459 (1986).

R. L. Higdon, “Numerical absorbing boundary conditions for the wave equation,” Math. Comput. 49, 65–90 (1987).
[CrossRef]

Opt. Commun. (1)

J. J. Grefet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

Opt. Express (1)

Opt. Photon. News (1)

G. S. Kino, “Near-field optical storage,” Opt. Photon. News 8(11), 38–39 (1997).
[CrossRef]

Optik (1)

H. Ooki, “Vector diffraction theory for magnetooptical disc systems,” Optik 89, 15–22 (1991).

Parallel Comput. (1)

E. Gallopoulos, Y. Saad, “A parallel block cyclic reduction algorithm for the fast solution of elliptic equations,” Parallel Comput. 10, 143–159 (1989).
[CrossRef]

Proc. IEEE (1)

M. Mansuripur, G. Sincerbox, “Principles and techniques of optical data storage,” Proc. IEEE 85, 1780–1796 (1997).
[CrossRef]

Radio Sci. (1)

Y. Miyazaki, K. Manabe, “Scattered near-field and induced current of a beam wave by pits on optical disks using boundary element analysis,” Radio Sci. 26, 281–289 (1991).
[CrossRef]

Rep. Prog. Phys. (2)

D. Courjon, C. Bainier, “Near field microscopy and near field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
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SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. (3)

P. Concus, G. H. Golub, “Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 10, 1103–1120 (1973).
[CrossRef]

B. L. Buzbee, G. H. Golub, C. W. Nielson, “On direct methods for solving Poisson’s equations,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 7, 627–656 (1970).
[CrossRef]

R. A. Sweet, “A cyclic reduction algorithm for solving block tridiagonal systems of arbitrary dimension,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 14, 706–720 (1977).
[CrossRef]

SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. (1)

Y. Saad, M. H. Schultz, “GMRES: a general minimal residual algorithm for solving nonsymmetric linear systems,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856–869 (1986).
[CrossRef]

SIAM (Soc. Ind. Appl. Math.) Rev. (1)

P. N. Swarztrauber, “The methods of cyclic reduction, Fourier analysis and the FACR algorithm for the discrete solution of Poisson’s equation on a rectangle,” SIAM (Soc. Ind. Appl. Math.) Rev. 19, 490–501 (1977).

Other (6)

M. A. Paesler, P. J. Moyer, Near-Field Optics: Theory, Instrumentation, and Applications (Wiley, New York, 1996).

J. P. Fillard, Near Field Optics and Nanoscopy (World Scientific, Singapore, 1996).
[CrossRef]

M. W. Kowarz, “Diffraction effects in the near field,” Ph.D. dissertation (University of Rochester, Rochester, N.Y., 1995).

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. S. Immink, Principles of Optical Disc Systems (Hilger, Bristol, UK, 1985).

A. B. Marchant, Optical Recording: A Technical Overview (Addison-Wesley, Reading, Mass., 1990).

M. Mansuripur, The Physical Principles of Magneto-Optical Recording (Cambridge U. Press, New York, 1995).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Cross section of the two-dimensional model of the DVD surface. The axes are in units of wavelengths. (a) Disk with pits, (b) disk with bumps.

Fig. 2
Fig. 2

Near-field profile of (a) the E x component for TE illumination, (b) the E y component for TM illumination, (c) the E z component for TM illumination. The pit height is 0.3 λ s . The unit of length here and in subsequent figures is the wavelength in the substrate λ s = 406 nm.

Fig. 3
Fig. 3

Near-field profile of (a) the E x component for TE illumination, (b) the E y component for TM illumination, (c) the E z component for TM illumination. The pit height is 0.6 λ s .

Fig. 4
Fig. 4

Near-field profile of the amplitude of the E x component for TE illumination. The pit heights are varied between 0.1 and 0.8 λ s .

Fig. 5
Fig. 5

Near-field profile of the amplitude of the E y component for TM illumination. The pit heights are varied between 0.1 and 0.8 λ s .

Fig. 6
Fig. 6

Near-field profile of the amplitude of the E x component for TE illumination. The bump heights are varied between 0.1 and 0.8 λ s .

Fig. 7
Fig. 7

Near-field profile of the amplitude of the E y component for TM illumination. The bump heights are varied between 0.1 and 0.8 λ s .

Fig. 8
Fig. 8

Far-field intensities in the normal direction as functions of (a) pit and (b) bump heights. Solid curve, TE illumination; dashed curve, TM illumination; dotted curve, scalar theory.

Fig. 9
Fig. 9

Angular distributions of far-field intensities for pit and bump heights varied from 0.1 to 0.8 λ s . (a) Pit configuration, (b) bump configuration. Solid curve, TE illumination; dashed curve, TM illumination. Horizontal axis, diffracting angle in polycarbonate.

Fig. 10
Fig. 10

I SUM as a function of pit and bump heights.

Fig. 11
Fig. 11

Contour plot of I DIF as a function of pit height and displacement of the focus point of the incident Gaussian beam relative to the center pit for the TE and the TM cases.

Fig. 12
Fig. 12

Contour plot of I DIF as a function of bump height and displacement of the focus point of the incident Gaussian beam relative to the center bump for the TE and the TM cases.

Equations (8)

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

×E=iωH,·E=0,×H=-iωE,·H=0,
2E+ω2E=·E,
·E=0.
2Ey, z+ω20zEy, z=fy, z,
2+ω2y, zEi=i·E,
2+ω20Eik=-ω2y, z-0Eik-1+i·Ek-1.
cos α1-ikzcos α2-ikzE=0,
Exθ=AR  dy expiky sin θEx cos θ+Exz,

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