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.

© Optical Society of America

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References

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  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).<br>
    [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).<br>
    [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).<br>
    [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).<br>
    [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).<br>
    [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).<br>
    [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).<br>
    [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).<br>
    [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).<br>
    [CrossRef]
  10. B. Engquist and A. Majda, "Absorbing boundary conditions for the numerical simulation of waves," Math. Comput. 31, 629-651 (1977).<br>
    [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 multi- dimensional wave equation," Math. Comput. 47, 437-459 (1986).<br>
  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).<br>
  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]

Other (14)

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).<br>
[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).<br>
[CrossRef]

D. S. Marx and D. Psaltis, "Optical diffraction of focused spots and subwavelength structures," J. Opt. Soc. Am. A 14, 1268-1278 (1997).<br>
[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).<br>
[CrossRef]

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).<br>
[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).<br>
[CrossRef]

R. A. Sweet, "A cyclic reduction algorithm for solving block tridiagonal systems of arbitrary dimension," SIAM J. Numer. Anal. 14, 706-720 (1977).<br>
[CrossRef]

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).<br>
[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).<br>
[CrossRef]

B. Engquist and A. Majda, "Absorbing boundary conditions for the numerical simulation of waves," Math. Comput. 31, 629-651 (1977).<br>
[CrossRef]

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]

R. L. Higdon, "Absorbing boundary conditions for difference approximations to the multi- dimensional wave equation," Math. Comput. 47, 437-459 (1986).<br>

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).<br>

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]

Supplementary Material (2)

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

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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)

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× 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 ) .

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