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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 6 — Jun. 1, 2006
  • pp: 1488–1502

Integral equation analysis of coupling in symmetric grating-assisted optical waveguides

Nikolaos L. Tsitsas, Dimitra I. Kaklamani, and Nikolaos K. Uzunoglu  »View Author Affiliations


JOSA A, Vol. 23, Issue 6, pp. 1488-1502 (2006)
http://dx.doi.org/10.1364/JOSAA.23.001488


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Abstract

The propagation and coupling phenomena in grating-assisted optical couplers are analyzed by using an integral equation formulation and applying an entire-domain Galerkin technique. The proposed method constitutes a special type of the method of moments and provides high numerical stability and controllable accuracy. The electric field in the grating region is the unknown quantity and the resulting integral equation is subsequently solved by using Galerkin’s method. The propagation constants of the guided waves are computed accurately by determining the singular points of the corresponding system’s matrix. Numerical results regarding the propagation constants are presented for various coupler parameters, and the effect of the grating’s physical and geometric characteristics on the coupling process is investigated.

© 2006 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(230.3120) Optical devices : Integrated optics devices
(230.7370) Optical devices : Waveguides
(230.7400) Optical devices : Waveguides, slab

ToC Category:
Optical Devices

History
Original Manuscript: October 14, 2005
Revised Manuscript: November 28, 2005
Manuscript Accepted: December 1, 2005

Citation
Nikolaos L. Tsitsas, Dimitra I. Kaklamani, and Nikolaos K. Uzunoglu, "Integral equation analysis of coupling in symmetric grating-assisted optical waveguides," J. Opt. Soc. Am. A 23, 1488-1502 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-6-1488


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References

  1. D. Marcuse, Integrated Optics (IEEE Press, 1973).
  2. T. Tamir, Integrated Optics (Springer-Verlag, 1975).
  3. F. Liu, H. Hier, and T. Worchesky, "Dual-side processed demultiplexer using grating-assisted codirectional coupler," IEEE Photon. Technol. Lett. 17, 600-602 (2005). [CrossRef]
  4. R. C. Alferness, T. L. Kock, L. L. Buhl, F. Storz, F. Heismann, and M. J. R. Martyak, "Grating assisted InGaAsP/InP vertical co-directional coupler filter," Appl. Phys. Lett. 55, 2011-2013 (1989). [CrossRef]
  5. K. Ogawa, W. Chang, B. Sopori, and F. Rosenbaum, "A theoretical analysis of edged grating couplers for integrated optics," IEEE J. Quantum Electron. QE-9, 29-42 (1973). [CrossRef]
  6. S. Zhang and T. Tamir, "Analysis and design of broadband grating couplers," IEEE J. Quantum Electron. 29, 2813-2824 (1993). [CrossRef]
  7. D. Marcuse, "Directional couplers made of nonidentical asymmetric slabs. Part I: Synchronous couplers," J. Lightwave Technol. LT-5, 113-118 (1987). [CrossRef]
  8. D. Marcuse, "Directional couplers made of nonidentical assymetrical slabs. Part II: Grating-assisted couplers," J. Lightwave Technol. LT-5, 268-273 (1987). [CrossRef]
  9. G. Griffel, M. Itzkovich, and A. A. Hardy, "Coupled mode formulation for directional couplers with longitudinal perturbation," IEEE J. Quantum Electron. 27, 985-994 (1991). [CrossRef]
  10. W. Huang, B. E. Little, and S. K. Chaudhuri, "A new approach to grating-assisted couplers," J. Lightwave Technol. 9, 721-727 (1991). [CrossRef]
  11. W. P. Huang, "Coupled-mode theory for optical waveguides: an overview," J. Opt. Soc. Am. A 11, 963-983 (1994). [CrossRef]
  12. S. Zhang and T. Tamir, "Rigorous theory of grating-assisted couplers," J. Opt. Soc. Am. A 13, 2403-2413 (1996). [CrossRef]
  13. N. Sun, J. Butler, G. Evans, L. Pang, and P. Congdon, "Analysis of grating-assisted directional couplers using the Floquet-Bloch theory," J. Lightwave Technol. 15, 2301-2315 (1997). [CrossRef]
  14. J. Butler, N. Sun, G. Evans, L. Pang, and P. Congdon, "Grating-assisted coupling of light between semiconductor and glass waveguides," J. Lightwave Technol. 16, 1038-1048 (1998). [CrossRef]
  15. V. Passaro, "Optimal design of grating-assisted directional couplers," J. Lightwave Technol. 18, 973-984 (2000). [CrossRef]
  16. P. G. Dinesen, J. S. Hesthaven, J. P. Lynov, and L. Lading, "Pseudospectral method for the analysis of diffractive optical elements," J. Opt. Soc. Am. A 16, 1124-1130 (1999). [CrossRef]
  17. U. Levy, M. Nezhad, H.-C. Kim, C.-H. Tsai, L. Pang, and Y. Fainman, "Implementation of a graded-index medium by use of subwavelength structures with graded fill factor," J. Opt. Soc. Am. A 22, 724-733 (2005). [CrossRef]
  18. H. Ichikawa and H. Kikuta, "Dynamic guided-mode resonant grating filter with quadratic electro-optic effect," J. Opt. Soc. Am. A 22, 1311-1318 (2005). [CrossRef]
  19. D. S. Jones, Theory of Electromagnetism (Pergamon, 1964).
  20. G. Hadjicostas, J. Butler, G. Evans, N. Carlson, and R. Amantea, "A numerical investigation of wave interactions in dielectric waveguides with periodic surface corrugations," IEEE J. Quantum Electron. 26, 893-902 (1990). [CrossRef]
  21. J. Butler, W. Ferguson, G. Evans, P. Stabile, and A. Rosen, "A boundary element technique applied to the analysis of waveguides with periodic surface corrugations," IEEE J. Quantum Electron. 28, 1701-1709 (1992). [CrossRef]
  22. J. S. Bagby, D. P. Nyquist, and B. C. Drachman, "Integral formulation for analysis of integrated dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-33, 906-915 (1985). [CrossRef]
  23. A. Sommerfeld, Partial Differential Equations in Physics (Academic, 1949).
  24. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).
  25. I. D. Chremmos and N. K. Uzunoglu, "Analysis of coupling between two slab waveguides in the presence of ring resonators," J. Opt. Soc. Am. A 21, 267-279 (2004). [CrossRef]
  26. N. K. Uzunoglu and J. G. Fikioris, "Scattering from an inhomogeneity inside a dielectric slab waveguide," J. Opt. Soc. Am. 72, 628-637 (1982). [CrossRef]
  27. S. T. Peng, "Rigorous formulation of scattering and guidance by dielectric grating waveguides: general case of oblique incidence," J. Opt. Soc. Am. A 6, 1869-1883 (1989). [CrossRef]
  28. T. E. Rozzi and G. H. In't Veld, "Field and network analysis of interacting step discontinuities in planar dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-27, 303-309 (1979). [CrossRef]
  29. M. Nishimoto and H. Ikuno, "Analysis of electromagnetic wave diffraction by a semi-infinite strip grating and evaluation of end effects," in Proceedings of Progress in Electromagnetic Research (PIERS) (1999), Vol. 23, pp. 39-58; http://emacademy.org/piers. [CrossRef]
  30. J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, and D. L. Brundrett, "Guided-mode resonant subwavelength gratings: effects of finite beams and finite gratings," J. Opt. Soc. Am. A 18, 1912-1928 (2001). [CrossRef]

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