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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 3 — Mar. 1, 2009
  • pp: 715–722

Diffraction pattern of triangular grating in the resonance domain

Tetsuya Hoshino, Saswatee Banerjee, Masahide Itoh, and Toyohiko Yatagai  »View Author Affiliations

JOSA A, Vol. 26, Issue 3, pp. 715-722 (2009)

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We propose a combination of ray optics and Fraunhofer multiple-slit diffraction theory for calculating the two-dimensional triangular periodic grating in the resonance domain. The peak of the envelope pattern of angular distribution of diffraction efficiency is calculated by ray optics while the peak width is calculated using Fraunhofer theory. It was clarified, using rigorous coupled-wave analysis and a nonstandard-finite-difference time-domain method, that the envelope pattern of the diffraction of the grating could be calculated easily and understood intuitively for the design of displays and lighting.

© 2009 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1970) Diffraction and gratings : Diffractive optics
(230.1950) Optical devices : Diffraction gratings
(230.3990) Optical devices : Micro-optical devices
(050.5745) Diffraction and gratings : Resonance domain
(240.3990) Optics at surfaces : Micro-optical devices

ToC Category:
Diffraction and Gratings

Original Manuscript: October 30, 2008
Revised Manuscript: December 24, 2008
Manuscript Accepted: December 28, 2008
Published: February 27, 2009

Tetsuya Hoshino, Saswatee Banerjee, Masahide Itoh, and Toyohiko Yatagai, "Diffraction pattern of triangular grating in the resonance domain," J. Opt. Soc. Am. A 26, 715-722 (2009)

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  1. M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Ouderkirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451-2456 (2000). [CrossRef] [PubMed]
  2. A. M. Nuijs and J. J. L. Horikx, “Diffraction and scattering at antiglare structures for display devices,” Appl. Opt. 33, 4058-4068 (1994). [CrossRef] [PubMed]
  3. S. X. Jin, J. Li, J. Y. Lin, and H. X. Jiang, “InGaNOGaN quantum well interconnected microdisk light emitting diodes,” Appl. Phys. Lett. 77, 3236-3238 (2000). [CrossRef]
  4. G. S. White and J. F. Marchiando, “Scattering from a V-shaped groove in the resonance domain,” Appl. Opt. 22, 2308-2312 (1983). [CrossRef] [PubMed]
  5. T. Hoshino, M. Itoh, and T. Yatagai, “An antireflective grating in the resonance domain for displays,” Appl. Opt. 46, 648-656 (2007). [CrossRef] [PubMed]
  6. T. Hoshino, S. Banerjee, M. Itoh, and T. Yatagai, “Design of a wavelength independent grating in the resonance domain,” Appl. Opt. 46, 7948-7962 (2007). [CrossRef]
  7. T.-X. Lee, C.-Y. Lin, S.-H. Ma, and C.-C. Sun, “Analysis of position-dependent light extraction of GaN-based LEDs,” Opt. Express 13, 4175-4179 (2005). [CrossRef] [PubMed]
  8. M. G. Moharam and T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385-1392 (1982). [CrossRef]
  9. M. G. Moharam and T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105-1112 (1983). [CrossRef]
  10. M. D. Feit and J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990-3998 (1978). [CrossRef] [PubMed]
  11. J. V. Roey, J. van der Donk, and P. E. Lagasse, “Beam-propagation method: analysis and assessment,” J. Opt. Soc. Am. 71, 803-810 (1981). [CrossRef]
  12. S. R. Park, O. J. Kwon, D. Shin, S.-H. Song, H.-S. Lee, and H. Y. Choi, “Grating micro-dot patterned light guide plates for LED backlights,” Opt. Express 15, 2888-2899 (2007). [CrossRef] [PubMed]
  13. K. Kalil, M. Shingo, K. Tatsuya, and M. Toshiyuki, “Backlight unit with double surface light emission using a single micro-structured light-guide plate,” IEICE Trans. Electron. E87-C, 1954-1961 (2004).
  14. T.-X. Lee, K.-F. Gao, W.-T. Chien, and C.-C. Sun, “Light extraction analysis of GaN-based light-emitting diodes with surface texture and/or patterned substrate,” Opt. Express 15, 6670-6676 (2007). [CrossRef] [PubMed]
  15. S. Ahmed and E. N. Glytsis, “Comparison of beam propagation method and rigorous coupled-wave analysis for single and multiplexed volume gratings,” Appl. Opt. 35, 4426-4435 (1996). [CrossRef] [PubMed]
  16. S. Mellin and G. Nordin, “Limits of scalar diffraction theory and an iterative angular spectrum algorithm for finite aperture diffractive optical element design,” Opt. Express 8, 705-722 (2001). [CrossRef] [PubMed]
  17. J. E. Harvey, A. Krywonos, and D. Bogunovic, “Nonparaxial scalar treatment of sinusoidal phase gratings,” J. Opt. Soc. Am. A 23, 858-865 (2006). [CrossRef]
  18. G. H. Spencer and M. V. R. K. Murty, “General ray-tracing procedure,” J. Opt. Soc. Am. 52, 672-678 (1962). [CrossRef]
  19. W. C. Sweatt, “Describing holographic optical elements as lenses,” J. Opt. Soc. Am. 67, 803-808 (1977). [CrossRef]
  20. M. Testorf, “Perturbation theory as a unified approach to describe diffractive optical elements,” J. Opt. Soc. Am. A 16, 1115-1123 (1999). [CrossRef]
  21. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge U. Press, 1999). [PubMed]
  22. G. S. White and A. Feldman, “Diffraction from a shallow rectangular groove,” Appl. Opt. 20, 2585-2589 (1981). [CrossRef] [PubMed]
  23. J. B. Cole, S. Banerjee, and M. Haftel, “High accuracy nonstandard finite-difference time-domain algorithms for computational electromagnetics: applications to optics and photonics,” in Advances in the Applications of Nonstandard Finite Difference Schemes, R.E.Mickens, ed. (World Scientific, 2006), pp. 89-189.
  24. J. B. Cole and S. Banerjee, “Applications of nonstandard finite difference models to computational electromagnetics,” J. Differ. Equations 9, 1099-1112 (2003). [CrossRef]
  25. J. B. Cole and S. Banerjee, “Improved version of the second-order Mur absorbing boundary condition based on a nonstandard finite difference model,” in Proceedings of The 23rd Annual Review of Progress in Applied Computational Electromagnetics (Applied Computational Electromagnetics, 2007), pp. 1531-1535.
  26. M. Ouyang, Y. Cao, H. Gao, J. Shi, J. Zhou, and D. Liu, “Analysis on polarization dependence of Fraunhofer diffraction by metallic grating with short period,” Opt. Laser Technol. 40, 201-207 (2008). [CrossRef]

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