## Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method

JOSA A, Vol. 19, Issue 10, pp. 2018-2029 (2002)

http://dx.doi.org/10.1364/JOSAA.19.002018

Acrobat PDF (603 KB)

### Abstract

The effects of finite number of periods (FNP) and finite incident beams on the diffraction efficiencies of holographic gratings are investigated by the finite-difference frequency-domain (FDFD) method. Gratings comprising 20, 15, 10, 5, and 3 periods illuminated by TE and TM incident light with various beam sizes are analyzed with the FDFD method and compared with the rigorous coupled-wave analysis (RCWA). Both unslanted and slanted gratings are treated in transmission as well as in reflection configurations. In general, the effect of the FNP is a decrease in the diffraction efficiency with a decrease in the number of periods of the grating. Similarly, a decrease in incident-beam width causes a decrease in the diffraction efficiency. Exceptions appear in off-Bragg incidence in which a smaller beam width could result in higher diffraction efficiency. For beam widths greater than 10 grating periods and for gratings with more than 20 periods in width, the diffraction efficiencies slowly converge to the values predicted by the RCWA (infinite incident beam and infinite-number-of-periods grating) for both TE and TM polarizations. Furthermore, the effects of FNP holographic gratings on their diffraction performance are found to be comparable to their counterparts of FNP surface-relief gratings.

© 2002 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

**Citation**

Shun-Der Wu and Elias 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)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-10-2018

Sort: Year | Journal | Reset

### References

- D. A. B. Miller, “Physical reasons for optical interconnection,” Special Issue on Smart Pixels, Int. J. Optoelectron. 11, 155–168 (1997).
- D. A. B. Miller, “Rationale and challenges for optical interconnects to electric chips,” Proc. IEEE 88, 728–749 (2000).
- D. A. B. Miller, “Optical interconnects to silicon,” IEEE J. Sel. Top. Quantum Electron. 6, 1312–1317 (2000).
- M. C. Wu, “Micromachining for optical and optoelectronic systems,” Proc. IEEE 85, 1833–1856 (1997).
- 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).
- G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, and H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
- D. T. Neilson and E. Schenfeld, “Free-space optical relay for the interconnection of multimode fibers,” Appl. Opt. 38, 2291–2296 (1999).
- 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).
- 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).
- 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).
- D. Mehuys, A. Hardy, D. F. Welch, R. G. Waarts, and R. Parke, “Analysis of detuned second-order grating output couplers with an integrated superlattice reflector,” IEEE Photon. Technol. Lett. 3, 342–344 (1991).
- N. Eriksson, M. Hagberg, and A. Larsson, “Highly efficient grating-coupled surface-emitters with single outcoupling elements,” IEEE Photon. Technol. Lett. 7, 1394–1396 (1995).
- J. C. Brazas, L. Li, and A. L. Mckeon, “High-efficiency input coupling into optical waveguides using gratings with double-surface corrugation,” Appl. Opt. 34, 604–609 (1995).
- M. Hagberg, T. Kjellberg, N. Eriksson, and A. G. Larsson, “Demonstration of blazing effect in second order gratings under resonant condition,” Electron. Lett. 30, 410–412 (1994).
- M. Hagberg, N. Eriksson, T. Kjellberg, and A. G. Larsson, “Demonstration of blazing effect in detuned second order gratings,” Electron. Lett. 30, 570–571 (1994).
- T. Liao, S. Sheard, M. Li, J. Zhu, and P. Prewett, “High-efficiency focusing waveguide grating couplers with parallelogramic groove profiles,” J. Lightwave Technol. 15, 1142–1148 (1997).
- Z. Hegedus and R. Netterfield, “Low sideband guided-mode resonant filter,” Appl. Opt. 39, 1469–1473 (2000).
- T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
- 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 F. Chavez-Rivas, “Diffraction of Gaussian and Hermite–Gaussian beams by finite gratings,” J. Opt. Soc. Am. A 18, 537–545 (2001).
- W.-C. Liu and M. W. Kowarz, “Vector diffraction from subwavelength optical disk structures: two-dimensional modeling of near-field profiles, far-field intensities, and detector signals from DVD,” Appl. Opt. 38, 3787–3797 (1999).
- Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
- S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
- A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 2000), Chaps. 6 and 7.
- P. P. Silvester and R. L. Ferrari, Finite Elements for Electrical Engineers (Cambridge U. Press, New York, 1996).
- J. P. Bérenger, “Perfectly matched layer for the FDTD solution of wave-structure interaction problems,” IEEE Trans. Antennas Propag. 44, 110–117 (1996).
- J. P. Bérenger, “Improved PML for the FDTD solution of wave-structure interaction problems,” IEEE Trans. Antennas Propag. 45, 466–473 (1997).
- J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, “Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses,” J. Opt. Soc. Am. A 15, 1822–1837 (1998).

## 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.

« Previous Article | Next Article »

OSA is a member of CrossRef.