Finite-difference-time-domain analysis of finite-number-of-periods holographic and surface-relief gratings
Applied Optics, Vol. 47, Issue 12, pp. 1981-1994 (2008)
http://dx.doi.org/10.1364/AO.47.001981
Enhanced HTML Acrobat PDF (3152 KB)
Abstract
The total-field–scattered-field formulation of the finite-difference time-domain method (FDTD) is used to analyze the diffraction of finite incident beams by finite-number-of-periods holographic and surface-relief gratings. Both second-order and fourth-order FDTD formulations are used with various averaging schemes to treat permittivity discontinuities and a comparative study is made with alternative numerical methods. The diffraction efficiencies for gratings of several periods and various beam sizes, for both TE and TM polarization cases, are calculated and the FDTD results are compared with the finite- difference frequency-domain (FDFD) method results in the case of holographic gratings, and with the boundary element method results in the case of surface-relief gratings. Furthermore, the convergence of the FDTD results to the rigorous coupled-wave analysis results is investigated as the number of grating periods and the incident beam size increase.
© 2008 Optical Society of America
OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(050.7330) Diffraction and gratings : Volume gratings
(260.2110) Physical optics : Electromagnetic optics
ToC Category:
Diffraction and Gratings
History
Original Manuscript: January 22, 2008
Revised Manuscript: March 3, 2008
Manuscript Accepted: March 4, 2008
Published: April 11, 2008
Citation
Aristeides D. Papadopoulos and Elias N. Glytsis, "Finite-difference-time-domain analysis of finite-number-of-periods holographic and surface-relief gratings," Appl. Opt. 47, 1981-1994 (2008)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-12-1981
Sort: Year | Journal | Reset
References
- Feature issue on “Diffractive optics applications,” Appl. Opt. 34, 2399-2559 (1995).
- S. Sinzinger and J. Janns, “Integrated micro-optical imaging system with a high interconnection capacity fabricated in planar optics,” Appl. Opt. 36, 4729-4735 (1997).
- A. C. Walker, T.-Y. Yang, J. Gourlay, J. A. B. Danes, M. G. Forbes, S. M. Prince, D. A. Baillie, D. T. Neilson, R. Williams, L. C. Wilkinson, G. R. Smith, M. P. Y. Desmulliez, G. S. Buller, M. R. Taghizadeh, A. Waddie, I. Underwood, C. R. Stanley, F. Pottier, B. Vögele, and W. Sibbett, “Optoelectronic systems based on InGaAs-complementary-metal-oxide-semiconductor smart-pixel arrays and free-space optical interconnects,” Appl. Opt. 37, 2822-2830 (1998).
- R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B.Picor, M. K. Hibbs-Brenner, J. Bristow, and Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780-793 (2000). [CrossRef]
- J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, “Focusing diffractive cylindrical mirrors: rigorous evaluation of various design methods,” J. Opt. Soc. Am. A 18, 1487-1494 (2001). [CrossRef]
- S. M. Schultz, E. N. Glytsis, and T. K. Gaylord, “Design of a high-efficiency volume grating couplers for line focusing,” Appl. Opt. 37, 2278-2287 (1998).
- S. M. Schultz, E. N. Glytsis, and T. K. Gaylord, “Volume grating preferential-order focusing waveguide coupler,” Opt. Lett. 24, 1708-1710 (1999).
- S. M. Schultz, E. N. Glytsis, and T. K. Gaylord, “Design, fabrication, and performance of preferential-order volume grating waveguide couplers,” Appl. Opt. 39, 1223-1232 (2000).
- T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894-937(1985).
- M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068-1076 (1995).
- M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced trasmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077-1086 (1995).
- E. E. Kriezis, P. K. Pandelakis, and A. G. Papagiannakis, “Diffraction of a Gaussian beam from a periodic planar screen,” J. Opt. Soc. Am. A 11, 630-636 (1994).
- J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, “Guided-mode resonant subwavelength gratings: effects of finite beams and finite gratings ,” J. Opt. Soc. Am. A 18, 1912-1928 (2001).
- Y.-L. Kok, “General solution to the multiple-metallic-grooves scattering problem: the fast-polarization case,” Appl. Opt. 32, 2573-2581 (1993).
- O. Mata-Mendez and J. Sumaya-Martinez, “Scattering of TE-polarized waves by a finite-grating: giant resonant enhancement of the electric field within the grooves,” J. Opt. Soc. Am. A 14, 2203-2211 (1997).
- G. Pelosi, G. Manara, and G. Toso, “Heuristic diffraction coefficient for plane-wave scattering from edges in periodic planar surfaces,” J. Opt. Soc. Am. A 13, 1689-1697 (1996).
- K. Hirayama, E. N. Glytsis, T. K. Gaylord, and D. W. Wilson, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219-2231 (1996).
- K. Hirayama, E. N. Glytsis, and T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907-917 (1997).
- O. Mata-Mendez and J. Sumaya-Martinez, “Diffraction of Gaussian and Hermite-Gaussian beams by finite gratings,” J. Opt. Soc. Am. A 18, 537-545 (2001). [CrossRef]
- S. D. Wu and E. N. Glytsis, “Finite-number-of-periods holographic gratings with finite-width incident beams: Analysis using the finite-difference frequency domain method,” J. Opt. Soc. Am. A 19, 2018-2029 (2002). [CrossRef]
- B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313-3326 (2004). [CrossRef]
- B. Wang, J. Jiang, and G. P. Nordin, “Systematic design process for slanted grating couplers,” Appl. Opt. 45, 6223-6226(2006).
- S. Banerjee, J. B. Cole, and T. Yatagai, “Calculation of diffraction characteristics of subwavelength conducting gratings using a high accuracy nonstandard finite-difference time-domain method,” Opt. Rev. 12, 274-280 (2005). [CrossRef]
- A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005), Ch. 3-5 and 7.
- A. Taflove, Editor, Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1998), Ch. 2.
- S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630-1639 (1996). [CrossRef]
- N. V. Kantartzis and T. D. Tsiboukis, Higher Order FDTD Schemes for Waveguides and Antenna Structures, Ch. 2 (Morgan and Claypool, 2006).
- T. T. Zygiridis and T. D. Tsiboukis, “Low-dispersion algorithms based on the higher order (2.4) FDTD method,” IEEE Trans. Microwave Theory Tech. 52, 1321-1327 (2004). [CrossRef]
- A. Yefet and P. G. Petropoulos, “A staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations,” J. Comput. Phys. 168, 286-315 (2001).
- D. T. Prescott and N. V. Shuley, “Reducing solution time in monochromatic FDTD waveguide simulations,” IEEE Trans. Microwave Theory Tech. 42, 1582-1584 (1994). [CrossRef]
- L. Gurel and U. Oguz, “Signal-processing techniques to reduce the sinusoidal steady-state error in the FDTD method,” IEEE Trans. Antennas Propagat. 48, 585-593 (2000).
- T. Hirono, Y. Shibata, W. W.Lui, S. Seki, and Y. Yoshikuni, “The second-order condition for the dielectric interface orthogonal to the Yee-lattice axis in the FDTD scheme,” IEEE Microwave Guided Lett. 10, 359-361 (2000).
- U. Anderson, “Time domain methods for the Maxwell equations,” Ph.D. dissertation, Royal Institute of Technology, Sweden (2001).
- K. P. Hwang and A. C. Cangellaris, “Effective permittivities for second-order accurate FDTD equations at dielectric interfaces,” IEEE Microwave Wireless Comp. Lett. 11, 158-160(2001).
- E. Kashdan and E. Turkel, “High-order accurate modeling of electromagnetic wave propagation across media--grid conforming bodies,” J. Comput. Phys. 218, 816-835 (2006). [CrossRef]
- P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779-784 (1996).
- L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870-1876 (1996).
- P. G. Petropoulos, “Phase error control for the FD-TD methods of second and fourth order accuracy,” IEEE Trans. Antennas Propagat. 42, 859-862 (1994).
- S. D. Wu and E. N. Glytsis, “Volume holographic grating couplers: rigorous analysis by use of the finite-difference frequency-domain method,” Appl. Opt. 43, 1009-1023 (2004). [CrossRef]
Cited By |
Alert me when this paper is cited |
OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.
Figures
Fig. 1 | Fig. 2 | Fig. 3 |
Fig. 4 | Fig. 5 | Fig. 6 |
Fig. 7 | Fig. 8 | Fig. 9 |
Fig. 10 | Fig. 11 | Fig. 12 |
Fig. 13 | Fig. 14 | Fig. 15 |
« Previous Article | Next Article »
OSA is a member of CrossRef.