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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 8 — Apr. 19, 2004
  • pp: 1592–1604

Photonic crystal devices modelled as grating stacks: matrix generalizations of thin film optics

L. C. Botten, T. P. White, C. Martijn de Sterke, R. C. McPhedran, A. A. Asatryan, and T. N. Langtry  »View Author Affiliations


Optics Express, Vol. 12, Issue 8, pp. 1592-1604 (2004)
http://dx.doi.org/10.1364/OPEX.12.001592


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Abstract

A rigorous semi-analytic approach to the modelling of coupling, guiding and propagation in complex microstructures embedded in two-dimensional photonic crystals is presented. The method, which is based on Bloch mode expansions and generalized Fresnel coefficients, is shown to be able to treat photonic crystal devices in ways which are analogous to those used in thin film optics with uniform media. Asymptotic methods are developed and exemplified through the study of a serpentine waveguide, a potential slow wave device.

© 2004 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(290.4210) Scattering : Multiple scattering

ToC Category:
Focus Issue: Photonic crystals and holey fibers

History
Original Manuscript: March 1, 2004
Revised Manuscript: April 5, 2004
Published: April 19, 2004

Citation
L. Botten, T. White, C. de Sterke, R. McPhedran, A. Asatryan, and T. Langtry, "Photonic crystal devices modelled as grating stacks: matrix generalizations of thin film optics," Opt. Express 12, 1592-1604 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-8-1592


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References

  1. C. M. Soukoulis, Photonic Crystals and Light Localization in the 21st Century, (Kluwer, Dordrecht 2001).
  2. A. Chutinan, and S. Noda, �??Waveguides and waveguide bends in two-dimensional photonic crystal slabs,�?? Phys. Rev. B 62, 4488-4492 (2000). [CrossRef]
  3. A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, �??Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs,�?? Appl. Phys. Lett. 79, 2690-2692 (2001). [CrossRef]
  4. Z. Wang, S. Fan, �??Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines,�?? Phys. Rev. E 68, 066616 (2003). [CrossRef]
  5. T. D. Happ, I.I. Tartakovskii, V.D. Kulakovskii, J.-P. Reithmaier, M.Kamp, and A. Forchel, �??Enhanced light emission of InxGa1-xAs quantum dots in a two-dimensional photonic-crystal defect microcavity,�?? Phys. Rev. B 66, 041303(R) (2002). [CrossRef]
  6. A. Mekis, J.C. Chen, I. Kurland, S. Fan, P.R. Villeneuve, and J.D. Joannopoulos, �??High transmission through sharp bends in photonic crystal waveguides,�?? Phys. Rev. Lett. 77, 3787-3790 (1996). [CrossRef] [PubMed]
  7. J. Yonekura, M. Ikeda, and T. Baba, �??Analysis of Finite 2-D photonic crystals of columns and lightwave devices using the scattering matrix method,�?? J. Lightwave Technol. 17, 1500-1508 (1999). [CrossRef]
  8. S.Fan, P.R. Villeneuve, and J.D. Joannopoulos, �??Channel Drop Tunnelling through Localized States,�?? Phys. Rev. Lett. 80, 960-963 (1998). [CrossRef]
  9. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, �??Photonic crystals for micro lightwave circuits using wavelength dependent angular beam steering,�?? Appl. Phys. Lett. 74, 1370-1372 (1999). [CrossRef]
  10. A. Martinez, A. Griol, P. Sanchis, and J. Marti, �??Mach-Zehnder interferometer employing coupled-resonator optical waveguides,�?? Opt. Lett. 28, 405-407 (2003). [CrossRef] [PubMed]
  11. T.P.White, L.C. Botten, R.C. McPhedran and C.M.de Sterke, �??Ultracompact resonant filters in photonic crystals,�?? Opt. Lett. 28, 2452-2454 (2003). [CrossRef] [PubMed]
  12. L.C. Botten, N.A. Nicorovici, R.C. McPhedran, C.M. de Sterke, and A.A. Asatryan, �??Photonic band structure calculations using scattering matrices,�?? Phys. Rev. E 64, 046603 (2001). [CrossRef]
  13. L.C. Botten, A.A. Asatryan, T.N. Langtry, T.P. White, C.M.de Sterke, and R.C. McPhedran, �??Semi-analytic treatment for propagation in finite photonic crystal waveguides,�?? Opt. Lett. 28, 854-856 (2003). [CrossRef] [PubMed]
  14. S.F. Mingaleev, and K. Busch, �??Scattering matrix approach to large-scale photonic crystal circuits,�?? Opt. Lett. 28, 619-621 (2003). [CrossRef] [PubMed]
  15. Z.-Y. Li, and K.-M. Ho, �??Light propagation in semi-infinite photonic crystals and related waveguide structures,�?? Phys. Rev. E 68, 155101 (2003).
  16. S. Chen, R. C. McPhedran, C. M. De Sterke, and L. C. Botten, �??Optimal tapers in photonic crystal waveguides,�?? submitted to Appl. Phys. Lett.
  17. L.C. Botten, N.A. Nicorovici, A.A. Asatryan, R.C. McPhedran, C.M. de Sterke, and P.A. Robinson, �??Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part 1, Method,�?? J. Opt. Soc. Am. A. 17, 2165-2176 (2000). [CrossRef]
  18. G.H. Smith, L.C. Botten, R.C. McPhedran, and N.A. Nicorovici, �??Cylinder gratings in conical incidence with applications to woodpile structures,�?? Phys. Rev. E 67, 056620 (2003). [CrossRef]
  19. B. Gralak, S. Enoch, and G. Tayeb, �??From scattering or impedance matrices to Bloch modes of photonic crystals,�?? J. Opt. Soc. Am. A 19, 1547-1554 (2002). [CrossRef]
  20. L.C. Botten, N.A. Nicorovici, A.A. Asatryan, R.C. McPhedran, C.M. de Sterke, and P.A. Robinson, �??Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part 2, Method,�?? J. Opt. Soc. Am. A. 17, 2177-2190 (2000). [CrossRef]
  21. M. Hamermesh, Group theory and its application to physical problems, (Addison-Wesley, Reading, 1962).
  22. L. C. Botten, T. P. White, C. M. de Sterke, R. C. McPhedran, A. A. Asatryan and T. N. Langtry, �??Bloch mode scattering matrix methods for modelling extended photonic crystal structures,�?? in preparation.
  23. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1970).
  24. 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, 1233�??1254 (2003). [CrossRef]
  25. W. H. Press, B. P. Flannery, S. A. Teulolsky and W. T. Vetterling, Numerical Recipes in Fortran (Cambridge University Press, Cambridge, 1988).
  26. M. Bayindir and E. Ozbay, �??Band-dropping via coupled photonic crystal waveguides,�?? Opt. Express 10, 1279�??1284 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1279">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1279</a> [CrossRef] [PubMed]
  27. S. Pereira, P. Chak, and J.E. Sipe, �??Gap-soliton switching in short microresonator structures,�?? J. Opt. Soc. Am. B 19, 2191�??2202 (2002) [CrossRef]
  28. P. Yeh, Optical waves in layered media, (Wiley, New York, 1988), Ch. 6.
  29. S. Wolfram, The Mathematica Book, 3rd Ed., (Wolfram Media / Cambridge University Press, 1996).

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