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Applied Optics

Applied Optics


  • Vol. 44, Iss. 21 — Jul. 20, 2005
  • pp: 4447–4453

Angular sensitivities of volume gratings for substrate-mode optical interconnects

Shun-Der Wu, Thomas K. Gaylord, Elias N. Glytsis, and Yu-Ming Wu  »View Author Affiliations

Applied Optics, Vol. 44, Issue 21, pp. 4447-4453 (2005)

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The angular sensitivities of slanted volume gratings (VGs) illuminated by three-dimensional (3-D) converging–diverging spherical Gaussian beams for substrate-mode optical interconnects in microelectronics are analyzed by application of 3-D finite-beam rigorous coupled-wave analysis. Angular misalignments about the z, y, and x axes that correspond to yaw, pitch, and roll misalignments resulting from manufacturing tolerances of chips are investigated. Two cases of linear polarization of the central beam of the Gaussian are considered: EK and HK, where K is the grating vector. From worst-case manufacturing tolerances, the ranges of yaw, pitch, and roll misalignment angles are α = ±1.17°, β = ±3.04°, and γ = ±3.04°, respectively. Based on these ranges of misalignment angles, the decreases of diffraction efficiencies for slanted VGs that are due to both the yaw and the roll misalignments are relatively small. However, the efficiency of substrate-mode optical interconnects achieved by slanted VGs could be reduced by 61.04% for EK polarization and by 58.63% for HK polarization because of the pitch misalignment. Thus the performance of a VG optical interconnect is most sensitive to pitch misalignment.

© 2005 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

Original Manuscript: November 19, 2004
Revised Manuscript: February 16, 2005
Manuscript Accepted: February 23, 2005
Published: July 20, 2005

Shun-Der Wu, Thomas K. Gaylord, Elias N. Glytsis, and Yu-Ming Wu, "Angular sensitivities of volume gratings for substrate-mode optical interconnects," Appl. Opt. 44, 4447-4453 (2005)

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  1. J.-H. Yeh, R. K. Kostuk, “Substrate-mode holograms used in optical interconnects: design issues,” Appl. Opt. 34, 3152–3164 (1995). [CrossRef] [PubMed]
  2. J.-H. Yeh, R. K. Kostuk, “Free-space holographic optical interconnects for board-to-board and chip-to-chip interconnects,” Opt. Lett. 21, 1274–1276 (1996). [CrossRef] [PubMed]
  3. Q. Huang, P. R. Ashley, “Holographic Bragg grating input–output couplers for polymer waveguides at an 850-nm wavelength,” Appl. Opt. 36, 1198–1203 (1997). [CrossRef] [PubMed]
  4. S. M. Schultz, E. N. Glytsis, T. K. Gaylord, “Design, fabrication, and performance of preferential-order volume grating waveguide couplers,” Appl. Opt. 39, 1223–1232 (2000). [CrossRef]
  5. R. A. Villalaz, E. N. Glytsis, T. K. Gaylord, “Volume grating couplers: polarization and loss effect,” Appl. Opt. 41, 5223–5229 (2002). [CrossRef] [PubMed]
  6. S.-D. Wu, E. N. Glytsis, “Volume holographic grating couplers: rigorous analysis using the finite-difference frequency-domain method,” Appl. Opt. 43, 1009–1023 (2004). [CrossRef] [PubMed]
  7. S.-D. Wu, E. N. Glytsis, T. K. Gaylord, “Optimization of finite-length input volume holographic grating couplers illuminated by finite-width incident beams,” Appl. Opt. 44, 4435–4446 (2005). [CrossRef] [PubMed]
  8. E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, N. Massey, “Holographic data storage in three-dimensional media,” Appl. Opt. 5, 1303–1311 (1966). [CrossRef] [PubMed]
  9. H. Kogelnik, “Coupled-wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969). [CrossRef]
  10. A. A. Friesem, J. L. Walker, “Thick absorption recording media in holography,” Appl. Opt. 9, 201–214 (1970). [CrossRef] [PubMed]
  11. T. Kubota, “Characteristics of thick hologram grating recorded in absorptive medium,” Opt. Acta 25, 1035–1053 (1987). [CrossRef]
  12. M. J. Damzen, Y. Matsumoto, G. J. Grofts, R. P. M. Green, “Bragg-selectivity of a volume gain grating,” Opt. Commun. 123, 182–188 (1996). [CrossRef]
  13. R.-S. Chu, J.-A. Kong, “Modal theory of spatially periodic media,” IEEE Trans. Microwave Theory Tech. 25, 18–24 (1977). [CrossRef]
  14. M. R. Chatterjee, D. D. Reagan, “Examination of beam propagation in misaligned holographic gratings and comparison with the acousto-optic transfer function model for profiled beams,” Opt. Eng. 38, 1113–1121 (1999). [CrossRef]
  15. M. R. Wang, “Analysis and observation of finite beam Bragg diffraction by a thick planar phase grating,” Appl. Opt. 35, 582–592 (1996). [CrossRef] [PubMed]
  16. J. A. Frantz, R. K. Kostuk, D. A. Waldman, “Model of noise-grating selectivity in volume holographic recording materials by use of Monte Carlo simulations,” J. Opt. Soc. Am. A 21, 378–387 (2004). [CrossRef]
  17. M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983). [CrossRef]
  18. S.-D. Wu, T. K. Gaylord, E. N. Glytsis, Y.-M. Wu, “Three-dimensional converging/diverging Gaussian beam diffraction by a volume grating,” J. Opt. Soc. Am. A (to be published).
  19. ITRS, “International technology roadmap for semiconductors 2003: assembly and packaging,” http://public.itrs.net/ (2003), pp. 14–20.

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