OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 25, Iss. 2 — Feb. 1, 2008
  • pp: 202–209

Wannier-function based scattering-matrix formalism for photonic crystal circuitry

Daniel Hermann, Matthias Schillinger, Sergei F. Mingaleev, and Kurt Busch  »View Author Affiliations


JOSA B, Vol. 25, Issue 2, pp. 202-209 (2008)
http://dx.doi.org/10.1364/JOSAB.25.000202


View Full Text Article

Enhanced HTML    Acrobat PDF (1041 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A guided-mode scattering matrix approach to photonic crystal integrated devices, based on the expansion of the electromagnetic field in Wannier functions is presented and its applicability to large-scale photonic circuits is demonstrated. In particular, we design two components typically used in wavelength division multi/demultiplexing applications, namely, a directional coupler and a Mach–Zehnder interferometer, and we analyze the transmission spectra as a function of the coupler length and/or delay line length, respectively. These examples demonstrate that by cascading basic functional elements, large-scale circuits can be accurately described and efficiently designed with minimal numerical effort.

© 2008 Optical Society of America

OCIS Codes
(230.3120) Optical devices : Integrated optics devices
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: September 10, 2007
Manuscript Accepted: November 19, 2007
Published: January 29, 2008

Citation
Daniel Hermann, Matthias Schillinger, Sergei F. Mingaleev, and Kurt Busch, "Wannier-function based scattering-matrix formalism for photonic crystal circuitry," J. Opt. Soc. Am. B 25, 202-209 (2008)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-25-2-202


Sort:  Year  |  Journal  |  Reset  

References

  1. K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007). [CrossRef]
  2. A. Mekis, J. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996). [CrossRef] [PubMed]
  3. A. A. Green, E. Istrate, and E. H. Sargent, "Efficient design and optimization of photonic crystal waveguides and couplers: the interface diffraction method," Opt. Express 13, 7304-7318 (2005). [CrossRef] [PubMed]
  4. A. Chutinan, M. Okano, and S. Noda, "Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 80, 1698-1700 (2002). [CrossRef]
  5. S. F. Mingaleev, M. Schillinger, D. Hermann, and K. Busch, "Tunable photonic crystal circuits: concepts and designs based on single-pore infiltration," Opt. Lett. 29, 2858-2860 (2004). [CrossRef]
  6. M. Koshiba, "Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers," J. Lightwave Technol. 19, 1970-1975 (2001). [CrossRef]
  7. S.-H. Jeong, N. Yamamoto, J.-I. Sugisaka, M. Okano, and K. Komori, "GaAs-based two-dimensional photonic crystal slab ring resonator consisting of a directional coupler and bent waveguides," J. Opt. Soc. Am. B 24, 1951-1959 (2007). [CrossRef]
  8. M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, "Photonic-crystal slow-light enhancement of nonlinear phase sensitivity," J. Opt. Soc. Am. B 19, 2052-2059 (2002). [CrossRef]
  9. K. Guven and E. Ozbay, "Coupling and phase analysis of cavity structures in two-dimensional photonic crystals," Phys. Rev. B 71, 085108 (2005). [CrossRef]
  10. K. Busch and S. John, "Liquid crystal photonic band gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999). [CrossRef]
  11. K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999). [CrossRef]
  12. H. Takeda and K. Yoshino, "Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals utilizing liquid crystals as linear defects," Phys. Rev. B 67, 073106 (2003). [CrossRef]
  13. T. Yasuda, Y. Tsuji, and M. Koshiba, "Tunable light propagation in photonic crystal coupler filled with liquid crystal," IEEE Photon. Technol. Lett. 17, 55-57 (2005). [CrossRef]
  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. 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, R1233-1256 (2003). [CrossRef]
  16. A. Birner, R. Wehrspohn, U. Gösele, and K. Busch, "Silicon-based photonic crystals," Adv. Mater. (Weinheim, Ger.) 13, 377-388 (2001). [CrossRef]
  17. F. Intonti, S. Vignolini, V. Türck, M. Colocci, P. Bettotti, L. Pavesi, S. L. Schweizer, R. Wehrspohn, and D. Wiersma, "Rewritable photonic circuits," Appl. Phys. Lett. 89, 211117 (2006). [CrossRef]
  18. K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E 58, 3896-3908 (1998). [CrossRef]
  19. H. Brand, Schaltungslehre Linearer Mikrowellennetze (Hirzel Verlag, 1970).
  20. M. Schillinger, "Maximally localized photonic Wannier functions for the highly efficient description of integrated photonic crystal circuits," Ph.D. dissertation (University of Karlsruhe, 2006).
  21. Y. Jiao, S. Fan, and D. Miller, "Demonstration of systematic photonic crystal device design and optimization by low-rank adjustments: an extremely compact mode separator," Opt. Lett. 30, 141-143 (2005). [CrossRef] [PubMed]
  22. Y. Jiao, S. F. Mingaleev, M. Schillinger, D. Miller, S. Fan, and K. Busch, "Wannier basis design and optimization of a photonic crystal waveguide crossing," IEEE Photon. Technol. Lett. 17, 1875-1877 (2005). [CrossRef]
  23. K. Jinguji, N. Takato, Y. Hida, T. Kitoh, and M. Kawachi, "Two-port optical wavelength circuits composed of cascaded Mach-Zehnder interferometers with point-symmetrical configurations," J. Lightwave Technol. 14, 2301-2310 (1996). [CrossRef]
  24. M. Cherchi, "Design scheme for Mach-Zehnder interferometric coarse wavelength division multiplexing splitters and combiners," J. Opt. Soc. Am. B 23, 1752-1756 (2006). [CrossRef]

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.

CrossCheck Deposited