Abstract

An efficient finite-difference frequency-domain method is developed for calculating electromagnetic fields in the neighborhood of subwavelength dielectric and metallic structures. The method is used to investigate two-dimensional near-field and far-field patterns of a focused beam diffracted from an optical disk, specifically from a DVD (Digital Versatile Disk). It is shown that the polarization of illumination has a significant impact on diffraction patterns as expected and that scalar theory does not provide an accurate analysis of diffraction from a DVD.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. B. Judkins, C. W. Haggans, and 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]
  2. M. Ogawa, M. Nakada, R. Katayama, M. Okada, and 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]
  3. D. S. Marx and D. Psaltis, “Optical diffraction of focused spots and subwavelength structures,” J. Opt. Soc. Am. A 14, 1268–1278 (1997).
    [CrossRef]
  4. B.-N. Jiang, J. Wu, and L. A. Povinelli, “The origin of spurious solutions in computational electromagnetics,” J. Comput. Phys. 125, 104–123 (1996).
    [CrossRef]
  5. P. Concus and G. H. Golub, “Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations,” SIAM J. Numer. Anal. 10, 1103–1120 (1973).
    [CrossRef]
  6. B. L. Buzbee, G. H. Golub, and C. W. Nielson, “On direct methods for solving Poisson’s equations,” SIAM J. Numer. Anal. 7, 627–656 (1970).
    [CrossRef]
  7. R. A. Sweet, “A cyclic reduction algorithm for solving block tridiagonal systems of arbitrary dimension,” SIAM J. Numer. Anal. 14, 706–720 (1977).
    [CrossRef]
  8. Y. Saad and M. H. Schultz, “GMRES: a general minimal residual algorithm for solving nonsym-metric linear systems,” SIAM J. Sci. Stat. Comput. 7, 856–869 (1986).
    [CrossRef]
  9. C. D. Dimitropoulos and A. N. Beris, “An efficient and robust spectral solver for nonseparable elliptic equations,” J. Comput. Phys. 133, 186–191 (1997).
    [CrossRef]
  10. B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629–651 (1977).
    [CrossRef]
  11. 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]
  12. R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multidimensional wave equation,” Math. Comput. 47, 437–459 (1986).
  13. 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).
  14. R. E. Gerber and M. Mansuripur, “Dependence of the tracking performance of an optical disk on the direction of the incident-light polarization,” Appl. Opt. 34, 8192–8200 (1995).
    [CrossRef] [PubMed]

1997 (2)

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

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

1996 (3)

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

J. B. Judkins, C. W. Haggans, and 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]

M. Ogawa, M. Nakada, R. Katayama, M. Okada, and 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]

1995 (1)

1986 (2)

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

Y. Saad and M. H. Schultz, “GMRES: a general minimal residual algorithm for solving nonsym-metric linear systems,” SIAM J. Sci. Stat. Comput. 7, 856–869 (1986).
[CrossRef]

1981 (1)

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]

1977 (2)

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

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

1973 (1)

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

1970 (1)

B. L. Buzbee, G. H. Golub, and C. W. Nielson, “On direct methods for solving Poisson’s equations,” SIAM 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).

Beris, A. N.

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

Buzbee, B. L.

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

Concus, P.

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

Dimitropoulos, C. D.

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

Gerber, R. E.

Golub, G. H.

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

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

Haggans, C. W.

Higdon, R. L.

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

Itoh, M.

M. Ogawa, M. Nakada, R. Katayama, M. Okada, and 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]

Jiang, B.-N.

B.-N. Jiang, J. Wu, and 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, and 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]

Majda, A.

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

Mansuripur, M.

Marx, D. S.

Mur,

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]

Nakada, M.

M. Ogawa, M. Nakada, R. Katayama, M. Okada, and 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, and C. W. Nielson, “On direct methods for solving Poisson’s equations,” SIAM J. Numer. Anal. 7, 627–656 (1970).
[CrossRef]

Ogawa, M.

M. Ogawa, M. Nakada, R. Katayama, M. Okada, and 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]

Okada, M.

M. Ogawa, M. Nakada, R. Katayama, M. Okada, and 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]

Povinelli, L. A.

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

Psaltis, D.

Saad, Y.

Y. Saad and M. H. Schultz, “GMRES: a general minimal residual algorithm for solving nonsym-metric linear systems,” SIAM J. Sci. Stat. Comput. 7, 856–869 (1986).
[CrossRef]

Schultz, M. H.

Y. Saad and M. H. Schultz, “GMRES: a general minimal residual algorithm for solving nonsym-metric linear systems,” SIAM J. Sci. Stat. Comput. 7, 856–869 (1986).
[CrossRef]

Sweet, R. A.

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

Wu, J.

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

Yee, K. S.

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).

Ziolkowski, R. W.

Appl. Opt. (2)

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)

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. Comput. Phys. (2)

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

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

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

Jpn. J. Appl. Phys. (1)

M. Ogawa, M. Nakada, R. Katayama, M. Okada, and 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. (2)

B. Engquist and 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 multidimensional wave equation,” Math. Comput. 47, 437–459 (1986).

SIAM J. Numer. Anal. (3)

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

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

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

SIAM J. Sci. Stat. Comput. (1)

Y. Saad and M. H. Schultz, “GMRES: a general minimal residual algorithm for solving nonsym-metric linear systems,” SIAM J. Sci. Stat. Comput. 7, 856–869 (1986).
[CrossRef]

Supplementary Material (2)

» Media 1: MOV (254 KB)     
» Media 2: MOV (268 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Figure 1.
Figure 1.

Cross section of the 2D model of the DVD surface.

Figure 2.
Figure 2.

Movies of near-field profiles of the x̂ component of the electric field for TE illumination and the ŷ component of the electric field for TM illumination. The color shows the phase and the amplitude of near-field profiles. White denotes amplitudes larger than 2.0. The white dotted line shows the interface between the substrate and the aluminum. The pit heights are between 0.1–0.8 λs. The unit of length is the wavelength in the substrate, λs = 406 nm. [Media 1] [Media 2]

Figure 3.
Figure 3.

Far-field intensities I = |E|2 in the normal direction as a function of pit height for the DVD. The intensities are normalized so that unity corresponds to no pit present. The solid line is for TE illumination, the dashed line for TM illumination, and the dotted line for scalar theory. The unit of length is the wavelength in the substrate, λs = 406 nm.

Equations (8)

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

× E = i ω H , · ( E ) = 0 ,
× H = i ω H , · H = 0 ,
2 E + ω 2 E = ( · E ) ,
· ( E ) = 0 .
( 2 + ω 2 ( y , z ) ) E i = i ( · E ) ,
( 2 + ω 2 0 ) E i k = ω 2 ( ( y , z ) 0 ) E i k 1 + i ( · E k 1 ) .
[ ( cos α 1 i k z ) ( cos α 2 i k z ) ] E = 0 ,
E x ( θ ) = A ( R ) dye iky sin θ × ( E x k cos θ i E x z ) .

Metrics