Rigorous 3D Calculation of Effects of Pit Structure in TwoDOS Systems
Optics Express, Vol. 15, Issue 5, pp. 2075-2097 (2007)
http://dx.doi.org/10.1364/OE.15.002075
Acrobat PDF (747 KB)
Abstract
A computer program based on the finite element method is used to study variations in pit visibility for a pit structure that is similar to those used in TwoDOS systems. It is concluded that pit visibility is best enhanced by making the pit width larger, and that destructive interference by making pit depth d =λ_{ Poly }/4 (where λ_{ Poly } is the wavelength in Polycarbonate) does not play a major role. Also, pit visibility depends strongly on the thickness of the Al layer. The simulations are compared with experiments and with a scalar model.
© 2007 Optical Society of America
1. Introduction
2. J.M. Brok and H.P. Urbach, “Rigorous model of the scattering of a focussed spot by a grating, and its application in optical recording,” J. Opt. Soc. Am. A 20256–272 (2003). [CrossRef]
7. L. Fagoonee, W.M.J. Coene, A. Moinian, and B. Honary, “Nonlinear Signal-Processing Model for Signal Generation in Multilevel Two-Dimensional Optical Storage,” Opt. Lett. , 29, 385–387 (2004) [CrossRef] [PubMed]
2. TwoDOS characteristics
- • The wavelength λ of the light of the incoming spot is chosen small. Typically, we haveThis is also the wavelength that is used in a blue ray disc (BD) system.
- • The lens that is used to focus the incoming light has a high numerical aperture. Typically,
- • In practice, circularly polarized light is used, which is a combination of two directions of linear polarization. In our simulations, to be able to discern the effects of these two directions of polarization, we used linearly polarized light. We define a coordinate system in such a way, that the z-axis is the optical axis of the system, and that the x- and y-axes are perpendicular to it. When an x-polarized plane wave is focussed by the lens, a spot occurs in the focal plane, that is predominantly polarized parallel to the x-direction, and has the shape of an Airy function. This type of spot will henceforth be called called “x-polarized Airy spot” for short. The spot has a full width half maximumLikewise we can create a “y-polarized Airy spot”. The effects of a circularly polarized spot can be derived from those of the linearly polarized spots. Because in the case of one circular spot, the effects of x- and y-polarized spots should be similar, we can in this case compare the resulting far field intensities that are computed, directly with the measurements.
- • The pits and “land” structures are organized into a hexagonal 2D lattice, which is a close packed structure in 2 dimensions for circular structures (hence the name Two Dimensional Optical Storage). This is different from the previously used method of optical storage, in which single (one-dimensional) tracks of pits were used. In current practice, the 2D lattice of the TwoDOS system is organized into a “supertrack” of 7–11 single tracks wide. These tracks will be read simultaneously by a number of laser beams, which increases the read-out rate. Typically, the hexagon separation has a value [6], [7
6. W.M.J. Coene, “Nonlinear Signal-Processing Model for Scalar Diffraction in Optical Recording,” Appl. Opt. 42, 6525–6535 (2003) [CrossRef] [PubMed]
]7. L. Fagoonee, W.M.J. Coene, A. Moinian, and B. Honary, “Nonlinear Signal-Processing Model for Signal Generation in Multilevel Two-Dimensional Optical Storage,” Opt. Lett. , 29, 385–387 (2004) [CrossRef] [PubMed]
which corresponds to a factor of 2 relative to a BD system. Ideally, the pits are circular with a width that should fit into the hexagonal lattice. The width should be chosen in such a way, that the contrast between a pit and a land structure is as high as possible. This means that the pit width cannot be too large, because otherwise the signal emanating from a number of adjacent pits will become the same as that of a land structure [6]. On the other hand, the pit width should be large enough for the pit to still be visible. In practice the pits are often elliptical with a width varying between b = 80 nm and b = 120 nm. Thus, there is roughly 50% “pit area” and 50% “land area” in a “pit bit structure” (and of course 100% “land area” in a “land bit structure”.6. W.M.J. Coene, “Nonlinear Signal-Processing Model for Scalar Diffraction in Optical Recording,” Appl. Opt. 42, 6525–6535 (2003) [CrossRef] [PubMed]
- • By lack of rigorous analysis so far, it was assumed (see [6], [7
6. W.M.J. Coene, “Nonlinear Signal-Processing Model for Scalar Diffraction in Optical Recording,” Appl. Opt. 42, 6525–6535 (2003) [CrossRef] [PubMed]
]) that, to obtain maximum modulation, the pit depth should ideally be7. L. Fagoonee, W.M.J. Coene, A. Moinian, and B. Honary, “Nonlinear Signal-Processing Model for Signal Generation in Multilevel Two-Dimensional Optical Storage,” Opt. Lett. , 29, 385–387 (2004) [CrossRef] [PubMed]
so as to make the destructive interference between the light that is reflected from the bottom of the pit, and that which is reflected from the land, as large as possible. (n_{Poly} = 1.619 is the index of refraction of the Poly). However, because the pit diameter is smaller than the cut-off value for the guiding of waves in cylindrical waveguides with a perfectly conducting wall [8],this assumption could be incorrect. In fact, this seems to be confirmed by our simulations (see below). - • The thickness of the Al layer should be chosen in such a way, that the difference in contrast between a land and a pit structure is high, but is still not too sensitive to variations in the thickness of the Al. Typically, the layer thickness of a disc can be chosen to lie between t = 5 nm and t = 25 nm, with a variation of 1 nm around the chosen thickness. Thus, the optimal thickness will be a compromise between visibility and precision of deposition.
3. Measurements performed so far; scalar theory
7. L. Fagoonee, W.M.J. Coene, A. Moinian, and B. Honary, “Nonlinear Signal-Processing Model for Signal Generation in Multilevel Two-Dimensional Optical Storage,” Opt. Lett. , 29, 385–387 (2004) [CrossRef] [PubMed]
6. W.M.J. Coene, “Nonlinear Signal-Processing Model for Scalar Diffraction in Optical Recording,” Appl. Opt. 42, 6525–6535 (2003) [CrossRef] [PubMed]
7. L. Fagoonee, W.M.J. Coene, A. Moinian, and B. Honary, “Nonlinear Signal-Processing Model for Signal Generation in Multilevel Two-Dimensional Optical Storage,” Opt. Lett. , 29, 385–387 (2004) [CrossRef] [PubMed]
7. L. Fagoonee, W.M.J. Coene, A. Moinian, and B. Honary, “Nonlinear Signal-Processing Model for Signal Generation in Multilevel Two-Dimensional Optical Storage,” Opt. Lett. , 29, 385–387 (2004) [CrossRef] [PubMed]
4. Computer simulations of TwoDOS pit structure
4.1. Finite element program
9. J.P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J.Comput. Phys 114, 185–200 (1994). [CrossRef]
11. J. Nédélec, “Mixed finite elements in ℝ^{3},” Numer. Math. 35, 315–341 (1980). [CrossRef]
4.2. Macroscopic set-up
14. DIFFRACT is a product of MM Research Inc. Tucson Ariz. Its theoretical basis has been described in, e.g. M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am.6, 786–805 (1989). [CrossRef]
4.3. Simulations
4.3.1. Parameters used
4.3.2. Layered structure
4.3.3. Single “realistic” pit; comparison with “straight” pit
4.3.4. Single straight pit: varying the pit ptructure
6. W.M.J. Coene, “Nonlinear Signal-Processing Model for Scalar Diffraction in Optical Recording,” Appl. Opt. 42, 6525–6535 (2003) [CrossRef] [PubMed]
7. L. Fagoonee, W.M.J. Coene, A. Moinian, and B. Honary, “Nonlinear Signal-Processing Model for Signal Generation in Multilevel Two-Dimensional Optical Storage,” Opt. Lett. , 29, 385–387 (2004) [CrossRef] [PubMed]
4.3.5. Two pits
Convergence of “large-box” calculations
Results of calculations
5. Comparison of the simulations with the scalar model
6. W.M.J. Coene, “Nonlinear Signal-Processing Model for Scalar Diffraction in Optical Recording,” Appl. Opt. 42, 6525–6535 (2003) [CrossRef] [PubMed]
7. L. Fagoonee, W.M.J. Coene, A. Moinian, and B. Honary, “Nonlinear Signal-Processing Model for Signal Generation in Multilevel Two-Dimensional Optical Storage,” Opt. Lett. , 29, 385–387 (2004) [CrossRef] [PubMed]
6. Summary and conclusions
A. Scattered far field
Acknowledgments
References and links
1. | X. Wei, A.J.H. Wachters, and H.P. Urbach: “Finite Element Model for Three-Dimensional Optical Storage Problem,” to be published. |
2. | J.M. Brok and H.P. Urbach, “Rigorous model of the scattering of a focussed spot by a grating, and its application in optical recording,” J. Opt. Soc. Am. A 20256–272 (2003). [CrossRef] |
3. | see e.g. P.G. Ciarlet, “The Finite Element Method for Elliptic Problems,” SIAM 2002. |
4. | X. Wei, H.P. Urbach, A. Wachters, and Y. Aksenov: “3D Rigorous Simulation of Mask Induced Polarization,” to be published. |
5. | W.M.J. Coene, D.M. Bruls, A.H.J. Immink, A.M. van der Lee, A.P. Hekstra, J. Riani, S. van Beneden, M. Ciacci, J.W.M. Bergmans, and M. Furuki, “Two-Dimensional Optical Storage,” IEEE Proceedings of the International Conference on Acoustics, Speed and Signal Processing 5749–752 (2005). |
6. | W.M.J. Coene, “Nonlinear Signal-Processing Model for Scalar Diffraction in Optical Recording,” Appl. Opt. 42, 6525–6535 (2003) [CrossRef] [PubMed] |
7. | L. Fagoonee, W.M.J. Coene, A. Moinian, and B. Honary, “Nonlinear Signal-Processing Model for Signal Generation in Multilevel Two-Dimensional Optical Storage,” Opt. Lett. , 29, 385–387 (2004) [CrossRef] [PubMed] |
8. | J.D. Jackson, “Classical Electrodynamics,” Wiley, 1975 |
9. | J.P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J.Comput. Phys 114, 185–200 (1994). [CrossRef] |
10. | |
11. | J. Nédélec, “Mixed finite elements in ℝ^{3},” Numer. Math. 35, 315–341 (1980). [CrossRef] |
12. | Y. Saad, “Iterative methods for sparse linear systems,” SIAM, 2^{nd} edition, 2003. |
13. | J.W. Goodman, “Introduction to Fourier Optics,” mcGraw-Hill, 1996. |
14. | DIFFRACT is a product of MM Research Inc. Tucson Ariz. Its theoretical basis has been described in, e.g. M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am.6, 786–805 (1989). [CrossRef] |
15. | J. van Bladel, “Singular Electromagnetic Fields and Sources,” Oxford1991. |
OCIS Codes
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(210.4590) Optical data storage : Optical disks
(210.4770) Optical data storage : Optical recording
(260.1960) Physical optics : Diffraction theory
ToC Category:
Diffraction and Gratings
History
Original Manuscript: June 14, 2006
Revised Manuscript: August 25, 2006
Manuscript Accepted: August 28, 2006
Published: March 5, 2007
Citation
J. A. Veerman, A. J. Wachters, A. M. van der Lee, and H. P. Urbach, "Rigorous 3D calculation of effects of pit structure in TwoDOS systems," Opt. Express 15, 2075-2097 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-2075
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References
- X. Wei, A. J. H. Wachters and H. P. Urbach: "Finite element model for three-dimensional optical storage problem," to be published.
- J. M. Brok and H. P. Urbach, "Rigorous model of the scattering of a focussed spot by a grating, and its application in optical recording," J. Opt. Soc. Am. A 20256-272 (2003). [CrossRef]
- see e.g. P. G. Ciarlet, "The Finite Element Method for Elliptic Problems," SIAM 2002.
- X. Wei, H. P. Urbach, A. Wachters and Y. Aksenov: "3D Rigorous simulation of mask induced polarization," to be published.
- W. M. J. Coene, D. M. Bruls, A. H. J. Immink, A. M. van der Lee, A. P. Hekstra, J. Riani, S. van Beneden, M. Ciacci, J. W. M. Bergmans, M. Furuki, "Two-dimensional Optical Storage," IEEE Proceedings of the International Conference on Acoustics, Speed and Signal Processing 5, 749-752 (2005).
- W. M. J. Coene, "Nonlinear Signal-Processing Model for Scalar Diffraction in Optical Recording," Appl. Opt. 42, 6525-6535 (2003) [CrossRef] [PubMed]
- L. Fagoonee, W. M. J. Coene, A. Moinian, and B. Honary, "Nonlinear signal-processing model for signal generation in multilevel two-dimensional optical storage," Opt. Lett., 29, 385-387 (2004) [CrossRef] [PubMed]
- J. D. Jackson, Classical Electrodynamics (Wiley, 1975)mj
- J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys 114, 185-200 (1994). [CrossRef]
- http://www.sara.nl/userinfo/reservoir/sepran/index.html
- J. Nedelec, "Mixed finite elements in R3," Numer. Math. 35, 315-341 (1980). [CrossRef]
- Y. Saad, " Iterative methods for sparse linear systems," SIAM, 2nd edition, 2003.
- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
- DIFFRACT is a product of MM Research Inc. Tucson Ariz. Its theoretical basis has been described in, e.g. M.Mansuripur, "Certain computational aspects of vector diffraction problems," J. Opt. Soc. Am. 6, 786-805 (1989). [CrossRef]
- J. van Bladel, Singular Electromagnetic Fields and Sources (Oxford 1991).
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