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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 19 — Sep. 19, 2005
  • pp: 7304–7318

Efficient design and optimization of photonic crystal waveguides and couplers: The Interface Diffraction Method

Alexander A. Green, Emanuel Istrate, and Edward H. Sargent  »View Author Affiliations


Optics Express, Vol. 13, Issue 19, pp. 7304-7318 (2005)
http://dx.doi.org/10.1364/OPEX.13.007304


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Abstract

We present the interface diffraction method (IDM), an efficient technique to determine the response of planar photonic crystal waveguides and couplers containing arbitrary defects. Field profiles in separate regions of a structure are represented through two contrasting approaches: the plane wave expansion method in the cladding and a scattering matrix method in the core. These results are combined through boundary conditions at the interface between regions to model fully a device. In the IDM, the relevant interface properties of individual device elements can be obtained from unit cell computations, stored, and later combined with other elements as needed, resulting in calculations that are over an order of magnitude faster than supercell simulation techniques. Dispersion relations for photonic crystal waveguides obtained through the IDM agree with the conventional plane wave expansion method to within 2.2% of the stopband width.

© 2005 Optical Society of America

OCIS Codes
(230.3990) Optical devices : Micro-optical devices
(230.7370) Optical devices : Waveguides

ToC Category:
Research Papers

History
Original Manuscript: July 21, 2005
Revised Manuscript: August 29, 2005
Published: September 19, 2005

Citation
Alexander Green, Emanuel Istrate, and Edward Sargent, "Efficient design and optimization of photonic crystal waveguides and couplers: The Interface Diffraction Method," Opt. Express 13, 7304-7318 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-19-7304


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References

  1. K. M. Ho, C. T. Chan, and C. M. Soukoulis, �??Existence of a photonic gap in periodic dielectric structures,�?? Phys. Rev. Lett. 65, 3152�??3155 (1990). [CrossRef] [PubMed]
  2. K. Busch and S. John, �??Photonic band gap formation in certain self-organizing systems,�?? Phys. Rev. E 58, 3896�??3908 (1998). [CrossRef]
  3. S. G. Johnson and J. D. Joannopoulos, �??Block-iterative frequency-domain methods for Maxwell�??s equations in a planewave basis,�?? Opt. Express 8, 173�??190 (2001). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173</a>. [CrossRef] [PubMed]
  4. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, �??Guided modes in photonic crystal slabs,�?? Phys. Rev. B 60, 5751�??5758 (1999). [CrossRef]
  5. K. S. Yee, �??Numerical solution of initial boundary value problems involving maxwells equations in isotropic media,�?? IEEE Trans. Antennas Propag. 14, 302�??307 (1966). [CrossRef]
  6. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, MA, 2000).
  7. G. Bastard, �??Superlattice band structure in the envelope-function approximation,�?? Phys. Rev. B 24, 5693�??5697 (1981). [CrossRef]
  8. C. M. de Sterke and J. E. Sipe, �??Envelope-function approach for the electrodynamics of nonlinear periodic structures,�?? Phys. Rev. A 38, 5149�??5165 (1988). [CrossRef] [PubMed]
  9. E. Istrate, M. Charbonneau-Lefort, and E. H. Sargent, �??Theory of photonic crystal heterostructures,�?? Phys. Rev. B 66(075121), 075,121 (2002). [CrossRef]
  10. N. A. R. Bhat and J. E. Sipe, �??Optical pulse propagation in nonlinear photonic crystals,�?? Phys. Rev. E 64(056604), 056,604�??1�??16 (2001). [CrossRef]
  11. J. Poon, E. Istrate, M. Allard, and E. H. Sargent, �??Multiple-scales analysis of photonic crystal waveguides,�?? IEEE J. Quantum Electron. 39(6), 778�??786 (2003). [CrossRef]
  12. J. P. Albert, D. Cassagne, and D. Bertho, �??Generalized Wannier function for photonic crystals,�?? Phys. Rev. B 61, 4381�??4384 (2000). [CrossRef]
  13. O. Painter, K. Srinivasan, and P. E. Barclay, �??Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals,�?? Phys. Rev. B 68(035214), 035,214 (2003). [CrossRef]
  14. K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, �??The Wannier function approach to photonic crystal circuits,�?? J. Phys.: Condens. Matter 15, R1233�??R1256 (2003). [CrossRef]
  15. K. Sakoda, Optical Properties of Photonic Crystals, chap. 4 (Springer, 2001).
  16. E. Istrate, A. A. Green, and E. H. Sargent, �??Behavior of light at photonic crystal interfaces,�?? Phys. Rev. B 71(195122), 195,122�??1�??7 (2005). [CrossRef]
  17. E. Istrate and E. H. Sargent, �??Photonic CrystalWaveguide Analysis Using Interface Boundary Conditions,�?? IEEE J. Quantum Electron. 41, 461�??467 (2005). [CrossRef]
  18. T. Baba, N. Fukaya, and J. Yonekura, �??Observation of light propagation in photonic crystal waveguides with bends,�?? Electron. Lett. 35, 654�??655 (1999). [CrossRef]
  19. S. McNab, N. Moll, and Y. Vlasov, �??Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,�?? Opt. Express 11, 2927�??2938 (2003). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2927">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2927</a>. [CrossRef] [PubMed]
  20. A. Adibi, R. K. Lee, Y. Xu, A. Yariv, and A. Scherer, �??Design of photonic crystal optical waveguides with singlemode propagation in the photonic band gap,�?? Electron. Lett. 36, 1376�??1378 (2000). [CrossRef]
  21. A. Chutinan and S. Noda, �??Waveguides and waveguide bends in two-dimensional photonic crystal slabs,�?? Phys. Rev. B 62, 4488�??4492 (2000). [CrossRef]
  22. K. Yamada, H. Morita, A. Shinya, and M. Notomi, �??Improved line-defect structures for photonic-crystal waveguides with high group velocities,�?? Opt. Commun. 198, 395�??402 (2001). [CrossRef]
  23. Z.-Y. Li and K.-M. Ho, �??Light propagation in semi-infinite photonic crystals and related waveguide structures,�?? Phys. Rev. B 68, 155,101�??1 (2003). [CrossRef]
  24. Z.-Y. Li and L.-L. Lin, �??Photonic band structures solved by a plane-wave-based transfer-matrix method,�?? Phys. Rev. E 67, 046,607 (2003). [CrossRef]
  25. J. B. Pendry, �??Photonic band structures,�?? J. Mod. Opt. 41, 209�??229 (1994). [CrossRef]
  26. L. Lifeng, �??Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,�?? J. Opt. Soc. Am. A 13, 1024�??1035 (1996). [CrossRef]
  27. S. Noda, A. Chutinan, and M. Imada, �??Trapping and emission of photons by a single defect in a photonic bandgap structure,�?? Nature (London) 407(6804), 608�??610 (2000). [CrossRef]
  28. Y. Akahane, T. Asano, B. S. Song, and S. Noda, �??High-Q photonic nanocavity in a two-dimensional photonic crystal,�?? Nature (London) 425(6961), 944�??947 (2003). [CrossRef]
  29. B. S. Song, S. Noda, T. Asano, and Y. Akahane, �??Ultra-high-Q photonic double-heterostructure nanocavity,�?? Nat. Mater. 4, 207�??210 (2005). [CrossRef]
  30. R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users�?? Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM, Philadelphia, 1998). <a href="http://www.caam.rice.edu/software/ARPACK/">http://www.caam.rice.edu/software/ARPACK/</a>.
  31. E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users�?? Guide, 3rd ed. (SIAM, Philadelphia, 1999). <a href="http://www.netlib.org/lapack/lug/index.html">http://www.netlib.org/lapack/lug/index.html</a>.
  32. S. Boscolo, M. Midrio, and C. G. Someda, �??Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides,�?? IEEE J. Quantum Electron. 38, 47�??53 (2002). [CrossRef]
  33. D. M. Whittaker and I. S. Culshaw, �??Scattering-matrix treatment of patterned multilayer photonic structures,�?? Phys. Rev. B 60, 2610�??2618 (1999). [CrossRef]
  34. A. R. Cowan, P. Paddon, V. Pacradouni, and J. F. Young, �??Resonant scattering and mode coupling in twodimensional textured planar waveguides,�?? J. Opt. Soc. Am. A 18, 1160�??1170 (2001). [CrossRef]
  35. L. C. Andreani and M. Agio, �??Photonic bands and gap maps in a photonic crystal slab,�?? IEEE J. Quantum Electron. 38, 891�??898 (2002). [CrossRef]
  36. S. F. Mingaleev and K. Busch, �??Scattering matrix approach to large-scale photonic crystal circuits,�?? Opt. Lett. 28, 619�??621 (2003). [CrossRef] [PubMed]

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