Abstract

The finite-element method is applied to model phase-change recording in a grooved recording stack. A rigorous model for the scattering of a three-dimensional focused spot by a one-dimensional periodic grating is used to determine the absorbed light in a three-dimensional region inside the phase-change layer. The optical model is combined with a three-dimensional thermal model to compute the temperature distribution. Land and groove recording and polarization dependence are studied, and the model is applied to the Blu-ray Disc.

© 2005 Optical Society of America

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References

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  1. 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]
  2. 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]
  3. D. S. Marx, D. Psaltis, “Optical diffraction of focused spots and subwavelength structures,” J. Opt. Soc. Am. A 14, 1268–1278 (1997).
    [CrossRef]
  4. W.-H. Yeh, L. Li, M. Mansuripur, “Vector diffraction and polarization effects in optical disk systems,” Appl. Opt. 37, 6983–6988 (1998).
    [CrossRef]
  5. C. Peng, M. Mansuripur, “Thermal cross-track cross talk in phase-change optical disk data storage,” J. Appl. Phys. 88, 1214–1220 (2000).
    [CrossRef]
  6. Y. Nishi, T. Shimano, H. Kando, M. Terao, T. Maeda, “Simulations of marks formed on phase-change, land/groove disks,” Jpn. J. Appl. Phys. 41, 2931–2938 (2002).
    [CrossRef]
  7. J. M. Brok, H. P. Urbach, “Rigorous model of the scattering of a focused spot by a grating and its application in optical recording,” J. Opt. Soc. Am. A 20, 256–272 (2003).
    [CrossRef]
  8. SEPRAN is a finite-element package of SEPRA (Ingenieursbureau), Den Haag, The Netherlands ( www.sepra.nl ).
  9. H. P. Urbach, R. T. M. Merkx, “Finite element simulation of electromagnetic plane wave diffraction at gratings for arbitrary angles of incidence,” G. Cohen, L. Halpern, P. Joly, eds., in Mathematical and Numerical Aspects of Wave Propagation Phenomena, Proceedings of SIAM First Conference on Mathematical and Numerical Aspects of Wave Propagation (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1992), pp. 89–99.
  10. DIFFRACT is a product of MM Research, Inc., Tucson, Ariz. Its theoretical basis has, e.g., been described by M. Mansuripurin, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6, 786–805 (1989).
    [CrossRef]
  11. V. S. Ignatowsky, “Diffraction by an objective lens with arbitrary aperture,” Trans. Opt. Inst. Petrograd 1, 1–36 (1921).
  12. B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
    [CrossRef]

2003 (1)

2002 (1)

Y. Nishi, T. Shimano, H. Kando, M. Terao, T. Maeda, “Simulations of marks formed on phase-change, land/groove disks,” Jpn. J. Appl. Phys. 41, 2931–2938 (2002).
[CrossRef]

2000 (1)

C. Peng, M. Mansuripur, “Thermal cross-track cross talk in phase-change optical disk data storage,” J. Appl. Phys. 88, 1214–1220 (2000).
[CrossRef]

1999 (1)

1998 (1)

1997 (1)

1995 (1)

1989 (1)

1959 (1)

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

1921 (1)

V. S. Ignatowsky, “Diffraction by an objective lens with arbitrary aperture,” Trans. Opt. Inst. Petrograd 1, 1–36 (1921).

Brok, J. M.

Ignatowsky, V. S.

V. S. Ignatowsky, “Diffraction by an objective lens with arbitrary aperture,” Trans. Opt. Inst. Petrograd 1, 1–36 (1921).

Judkins, J. B.

Kando, H.

Y. Nishi, T. Shimano, H. Kando, M. Terao, T. Maeda, “Simulations of marks formed on phase-change, land/groove disks,” Jpn. J. Appl. Phys. 41, 2931–2938 (2002).
[CrossRef]

Kowarz, M. W.

Li, L.

Liu, W.-C.

Maeda, T.

Y. Nishi, T. Shimano, H. Kando, M. Terao, T. Maeda, “Simulations of marks formed on phase-change, land/groove disks,” Jpn. J. Appl. Phys. 41, 2931–2938 (2002).
[CrossRef]

Mansuripur, M.

C. Peng, M. Mansuripur, “Thermal cross-track cross talk in phase-change optical disk data storage,” J. Appl. Phys. 88, 1214–1220 (2000).
[CrossRef]

W.-H. Yeh, L. Li, M. Mansuripur, “Vector diffraction and polarization effects in optical disk systems,” Appl. Opt. 37, 6983–6988 (1998).
[CrossRef]

Mansuripurin, M.

Marx, D. S.

Merkx, R. T. M.

H. P. Urbach, R. T. M. Merkx, “Finite element simulation of electromagnetic plane wave diffraction at gratings for arbitrary angles of incidence,” G. Cohen, L. Halpern, P. Joly, eds., in Mathematical and Numerical Aspects of Wave Propagation Phenomena, Proceedings of SIAM First Conference on Mathematical and Numerical Aspects of Wave Propagation (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1992), pp. 89–99.

Nishi, Y.

Y. Nishi, T. Shimano, H. Kando, M. Terao, T. Maeda, “Simulations of marks formed on phase-change, land/groove disks,” Jpn. J. Appl. Phys. 41, 2931–2938 (2002).
[CrossRef]

Peng, C.

C. Peng, M. Mansuripur, “Thermal cross-track cross talk in phase-change optical disk data storage,” J. Appl. Phys. 88, 1214–1220 (2000).
[CrossRef]

Psaltis, D.

Richards, B.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Shimano, T.

Y. Nishi, T. Shimano, H. Kando, M. Terao, T. Maeda, “Simulations of marks formed on phase-change, land/groove disks,” Jpn. J. Appl. Phys. 41, 2931–2938 (2002).
[CrossRef]

Terao, M.

Y. Nishi, T. Shimano, H. Kando, M. Terao, T. Maeda, “Simulations of marks formed on phase-change, land/groove disks,” Jpn. J. Appl. Phys. 41, 2931–2938 (2002).
[CrossRef]

Urbach, H. P.

J. M. Brok, H. P. Urbach, “Rigorous model of the scattering of a focused spot by a grating and its application in optical recording,” J. Opt. Soc. Am. A 20, 256–272 (2003).
[CrossRef]

H. P. Urbach, R. T. M. Merkx, “Finite element simulation of electromagnetic plane wave diffraction at gratings for arbitrary angles of incidence,” G. Cohen, L. Halpern, P. Joly, eds., in Mathematical and Numerical Aspects of Wave Propagation Phenomena, Proceedings of SIAM First Conference on Mathematical and Numerical Aspects of Wave Propagation (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1992), pp. 89–99.

Wolf, E.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Yeh, W.-H.

Ziolkowski, R. W.

Appl. Opt. (2)

J. Appl. Phys. (1)

C. Peng, M. Mansuripur, “Thermal cross-track cross talk in phase-change optical disk data storage,” J. Appl. Phys. 88, 1214–1220 (2000).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

Y. Nishi, T. Shimano, H. Kando, M. Terao, T. Maeda, “Simulations of marks formed on phase-change, land/groove disks,” Jpn. J. Appl. Phys. 41, 2931–2938 (2002).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Trans. Opt. Inst. Petrograd (1)

V. S. Ignatowsky, “Diffraction by an objective lens with arbitrary aperture,” Trans. Opt. Inst. Petrograd 1, 1–36 (1921).

Other (2)

SEPRAN is a finite-element package of SEPRA (Ingenieursbureau), Den Haag, The Netherlands ( www.sepra.nl ).

H. P. Urbach, R. T. M. Merkx, “Finite element simulation of electromagnetic plane wave diffraction at gratings for arbitrary angles of incidence,” G. Cohen, L. Halpern, P. Joly, eds., in Mathematical and Numerical Aspects of Wave Propagation Phenomena, Proceedings of SIAM First Conference on Mathematical and Numerical Aspects of Wave Propagation (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1992), pp. 89–99.

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Figures (20)

Fig. 1
Fig. 1

Schematic visualization of the unit cell Ω in a cross section of an optical disk.

Fig. 2
Fig. 2

Section of ( k x ,   k y ) space showing a fragment of the Brillouin zone B × R (hatched). The grid distance Δ k x is taken such that 2 π / p is a multiple of Δ k x (in the figure 2 π / p = 2 Δ k x ) . For clarity, the spacing in the k y direction, Δ k y , is chosen equal to Δ k x . The encircled points, on the one hand, and the crossed grid points, on the other hand, are sets of grid points that are each other’s order.

Fig. 3
Fig. 3

Extended geometry. The cell on which the BVPs are formulated is called the computational cell. The extended region is taken large enough to contain at least the region in which the intensity of the laser spot is essentially nonzero.

Fig. 4
Fig. 4

Tetrahedral mesh used in the thermal calculations. In the region in which the absorbed energy is mapped, the grid size is taken of the same order in size as that of the triangular mesh of the optical model.

Fig. 5
Fig. 5

To compute the absorbed energy in a nodal point (circles) of the tetrahedral mesh for the thermal model, we first calculate the values in the intersections X with the two enclosing expanded cells of the optical model. These values are linearly interpolated by using the piecewise linear basis functions on the triangles. The absorbed energy in the nodal point is then the linearly interpolated value of the values in the intersection points.

Fig. 6
Fig. 6

Cross section of the stack as used in configuration C1 according to Peng and Mansuripur.5 The structure is translation invariant in the y direction.

Fig. 7
Fig. 7

Dominant field components (arbitrary units) and absorbed energy ( W / p 3 ) in the unit cell for a TM-polarized spot that is incident on a flat version of the multilayered stack of Fig. 6. (a) | H y | and (b) absorbed energy. The spot is focused in air in the middle of the PC layer.  

Fig. 8
Fig. 8

Top view of the absorbed energy ( 10 4   W / μ m 3 ) and the temperature distribution [degrees Celsius (°C)] halfway in the PC layer for a TM-polarized spot incident on a flat version of the stack shown in Fig. 6. (a) Absorbed energy, (b) temperature distribution.

Fig. 9
Fig. 9

Temperature distribution (°C) for a TM-polarized spot (a) in a cross section perpendicular to the groove direction and (b) a cross section of (a) perpendicular to the interfaces along the optical axis. The stack is that of Fig. 6 except that the interfaces are flat. The temperature values are much too large because the effect of latent heat is neglected, but the shape of the cross sections should be correct.

Fig. 10
Fig. 10

Absorbed energy distributions ( 10 4   W / μ m 3 ) halfway in the PC layer for a TE-polarized spot that is incident on the grooved multilayer of Fig. 6. (a) Center of the spot is in the groove, (b) center of the spot is on the land.

Fig. 11
Fig. 11

Absorbed energy distributions ( 10 4   W / μ m 3 ) halfway in the PC layer for a TM-polarized spot that is incident on the grooved multilayer of Fig. 6. (a) Center of the spot is in the groove, (b) center of the spot is on the land.

Fig. 12
Fig. 12

Temperature distributions (°C) halfway in the PC layer for a TE-polarized spot that is incident on the grooved multilayer of Fig. 6. (a) Center of the spot is in the groove, (b) center of the spot is on the land. (Temperatures should be corrected for latent heat.)

Fig. 13
Fig. 13

Temperature distributions (°C) halfway in the PC layer for a TM-polarized spot that is incident on the grooved multilayer of Fig. 6. (a) Center of the spot is in the groove, (b) center of the spot is on the land. (Temperatures should be corrected for latent heat.)

Fig. 14
Fig. 14

Cross sections of the temperature distributions (°C) halfway in the PC layer as shown in Figs. 12 and 13. (a) Center of the spot is (a) in the groove, (b) on the land. (Temperatures should be corrected for latent heat.)

Fig. 15
Fig. 15

Temperature distribution (°C) for a TE-polarized spot in a cross section perpendicular to the groove direction for the stack of Fig. 6. (a) For groove recording, (b) for land recording. (The temperature values are much too large because the effect of latent heat is neglected).

Fig. 16
Fig. 16

Temperature distribution (°C) for a TM-polarized spot in a cross section perpendicular to the groove direction for the stack of Fig. 6. (a) For groove recording, (b) for land recording. (The temperature values are much too large because the effect of latent heat is neglected).

Fig. 17
Fig. 17

Cross section of the stack as used for the Blu-ray Disc simulation.

Fig. 18
Fig. 18

Absorbed energy distributions ( 10 4   W / μ m 3 ) halfway in the PC layer for a TM-polarized spot that is incident on the grooved multilayer for the Blu-ray Disc (stack is shown in Fig. 15). The NA of the lens is 0.85, the wavelength of the light is 405 nm. (a) Center of the spot is in the groove, (b) center of the spot is on the land.

Fig. 19
Fig. 19

Temperature distributions (°C) halfway in the PC layer for a TM-polarized spot that is incident on the grooved multilayer for the Blu-ray Disc of Fig. 15. (a) Center of the spot is in the groove, (b) center of the spot is on the land. (Temperatures should be corrected for latent heat.)

Fig. 20
Fig. 20

Temperature distribution (°C) for a TM-polarized spot in a cross section perpendicular to the groove direction for the Blu-ray stack of Fig. 15. (a) Center of the spot is in the groove, (b) center of the spot is on the land. (Temperatures should be corrected for latent heat.

Tables (2)

Tables Icon

Table 1 Numerical Values for the Complex Refractive Index n, Heat Capacity ρ C , and Thermal Conductivity κ as Used in Simulations for the Configuration of Fig. 6

Tables Icon

Table 2 Numerical Values for the Complex Refractive Index n, Heat Capacity ρ C , and Thermal Conductivity κ as Used in the Simulations of the Blu-Ray Disc

Equations (27)

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Ω = ( x ,   z ) | - p 2 < x < p 2 ,   a < z < b .
F ( E i ) ( k x ,   k y ,   z i ) = - - E i ( x ,   y ,   z i ) × exp [ - i ( k x x + k y y ) ] d x d y .
E i ( x ,   y ,   z i ) = 1 4 π 2 - - F ( E i ) ( k x ,   k y ,   z i ) × exp [ i ( k x x + k y y ) ] d k x d k y ,
E i ( x ,   y ,   z ) = 1 4 π 2 - - F ( E i ) ( k x ,   k y ,   z i ) × exp { i [ k x x + k y y + k z ( z - z i ) ] } d k x d k y .
E i ( x ,   y ,   z )
= 1 4 π 2 - - F ( E i ) ( k x ,   k y ,   z i ) × exp { i [ k x x + k y y + k z ( z - z i ) ] } d k x d k y = 1 4 π 2 m = - - - π / p + 2 π m / p π / p + 2 π m / p F ( E i ) ( k x ,   k y ,   z i ) × exp { i [ k x x + k y y + k z ( z - z i ) ] } d k x d k y = 1 4 π 2 m = - - - π / p π / p F ( E i ) k x + 2 π m p ,   k y ,   z i × exp i k x + 2 π m p x + ik y y + k z m ( z - z i ) d k x d k y = - - π / p π / p E k x , k y i ( x ,   z ) exp [ i ( k x x + k y y ) ] d k x d k y ,
k z m = - [ ω 2 0 u μ 0 - ( k x + 2 π m / p ) 2 - k y 2 ] 1 / 2 ,
E k x , k y i ( x ,   z ) exp [ i ( k x x + k y y ) ] = 1 4 π 2 m = - F ( E i ) k x + 2 π m p ,   k y ,   z i × exp i k x + 2 π m p x + ik y y + ik z m ( z - z i ) .
× E i = i ω μ 0 H i ,
× H i = - i ω 0 u E i ,
F ( H i ) ( k x ,   k y ,   z ) = k ω μ 0 × F ( E i ) ( k x ,   k y ,   z ) .
H i ( x ,   y ,   z ) = - - π / p π / p H k x , k y i ( x ,   z ) × exp [ i ( k x x + k y y ) ] d k x d k y ,
H k x , k y i ( x ,   z ) exp [ i ( k x x + k y y ) ] = 1 4 π 2 m = - k m ω μ 0 × F ( E i ) k x + 2 π m p ,   k y ,   z i × exp i k x + 2 π m p x + ik y y + ik z m ( z - z i ) .
E k x , k y i ( x ,   z ) exp [ i ( k x x + k y y ) ] ,
H k x , k y i ( x ,   z ) exp [ i ( k x x + k y y ) ] ,
B = k x | - π p < k x < π p .
E tot ( x ,   y ,   z ) = - - π / p π / p E k x , k y tot ( x ,   z ) × exp [ i ( k x x + k y y ) ] d k x d k y ,
H tot ( x ,   y ,   z ) = - - π / p π / p H k x , k y tot ( x ,   z ) × exp [ i ( k x x + k y y ) ] d k x d k y ,
F ( E z i ) = - 1 k z   [ k x F ( E x i ) + k y F ( E y i ) ] .
2 π / p = ν Δ k x ,
k x i + 2 π m p ,   k y j = ( k x ν m ,   k y j ) ,
k x i + 2 π m p ,   k y j ,   m integer ,
E tot ( x ¯ + μ p ,   y ,   z ) = - - π / p π / p E k x , k y tot ( x ¯ ,   z ) exp [ ik x ( x ¯ + μ p ) + ik y ν Δ y ] d k x d k y ,
H tot ( x ¯ + μ p ,   y ,   z ) = - - π / p π / p H k x , k y tot ( x ¯ ,   z ) exp [ ik x ( x ¯ + μ p ) + ik y ν Δ y ] d k x d k y ,
Q ( r ) = 1 2 ω 0 Im [ ( r ) ] | E tot ( r ) | 2 ,
ρ C   T t - [ κ T ] = Q ( x ,   y + vt ,   z ) ,
T / n = 0 ,

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