Skip to main content
SpringerLink
Log in

Roughness losses and volume-current methods in photonic-crystal waveguides

  • Published:
Applied Physics B Aims and scope Submit manuscript

Abstract

We present predicted relative scattering losses from sidewall roughness in a strip waveguide compared to an identical waveguide surrounded by a photonic crystal with a complete or incomplete gap in both 2d and 3d. To do so, we develop a new semi-analytical extension of the classic “volume-current method” (Green’s functions with a Born approximation), correcting a longstanding limitation of such methods to low-index contrast systems (the classic method may be off by an order of magnitude in high-contrast systems). The resulting loss predictions show that even incomplete gap structures such as photonic-crystal slabs should, with proper design, be able to reduce losses by a factor of two compared to an identical strip waveguide; however, incautious design can lead to increased losses in the photonic-crystal system, a phenomena that we explain in terms of the band structure of the unperturbed crystal.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A.W. Snyder, J.D. Love, Optical Waveguide Theory (London, Chapman and Hall, 1983)

    Google Scholar 

  2. W.C. Chew, Waves and Fields in Inhomogeneous Media (New York, NY, IEEE Press, 1995)

    Google Scholar 

  3. M. Kuznetsov, H.A. Haus, IEEE J. Quantum Electron. 19, 1505 (1983)

    Article  Google Scholar 

  4. F.P. Payne, J.P.R. Lacey, Opt. Quantum Elec. 26, 977 (1994)

    Article  Google Scholar 

  5. R.H. Jordan, D.G. Hall, Appl. Phys. Lett. 64, 3077 (1994)

    Article  Google Scholar 

  6. B.E. Little, S.T. Chu, Opt. Lett. 21, 1390 (1996)

    Google Scholar 

  7. K.K. Lee, D.R. Lim, H.-C. Luan, A. Agarwal, J. Foresi, L.C. Kimerling, Appl. Phys. Lett. 77(11), 1617 (2000)

    Article  Google Scholar 

  8. Y. Li, M. Froggatt, T. Erdogan, J. Lightwave Tech. 19(10), 1580 (2001)

    Article  Google Scholar 

  9. B.Z. Steinberg, A. Boag, R. Lisitsin, J. Opt. Soc. Am. A 20(1), 138 (2003)

    Google Scholar 

  10. W. Bogaerts, P. Bienstman, R. Baets, Opt. Lett. 28 (May), 689 (2003)

    PubMed  Google Scholar 

  11. D. Gerace, L.C. Andreani, Opt. Lett. 29(16), 1897 (2004)

    Article  PubMed  Google Scholar 

  12. S. Hughes, L. Ramunno, J.F. Young, J.E. Sipe, Phys. Rev. Lett. 94, 033903, (2005)

    Article  PubMed  Google Scholar 

  13. M.A. Kaliteevski, J.M. Martinez, D. Cassagne, J.P. Albert, Phys. Rev. B 66, 113101 (2002)

    Article  Google Scholar 

  14. M.L. Povinelli, S.G. Johnson, E. Lidorikis, J.D. Joannopoulos, M. Soljačić, Appl. Phys. Lett. 84, 3639 (2004)

    Article  Google Scholar 

  15. W.R. Frei, H.T. Johnson, Phys. Rev. B 70, 165116 (2004)

    Article  Google Scholar 

  16. K.-C. Kwan, X. Zhang, Z.-Q. Zhang, C.T. Chan, Appl. Phys. Lett. 82(25), 4414 (2003)

    Article  Google Scholar 

  17. T.N. Langtry, A.A. Asatryan, L.C. Botten, C.M. de Sterke, R.C. McPhedran, P.A. Robinson, Phys. Rev. E 68(2), 026611, (2003)

    Article  Google Scholar 

  18. B.C. Gupta, Z. Ye, J. Appl. Phys. 94(4), 2173 (2003)

    Article  Google Scholar 

  19. J.D. Joannopoulos, R.D. Meade, J.N. Winn, Photonic Crystals: Molding the Flow of Light. Princeton Univ. Press, (1995)

  20. S.G. Johnson, S. Fan, P.R. Villeneuve, J.D. Joannopoulos, L.A. Kolodziejski, Phys. Rev. B 60, 5751 (1999)

    Article  Google Scholar 

  21. S.G. Johnson, S. Fan, P.R. Villeneuve, J.D. Joannopoulos, Phys. Rev. B 62, 8212 (2000)

    Article  Google Scholar 

  22. S.G. Johnson, M. Ibanescu, M.A. Skorobogatiy, O. Weisberg, J.D. Joannopoulos, Y. Fink, Phys. Rev. E 65, 066611 (2002)

    Article  Google Scholar 

  23. S.G. Johnson, P. Bienstman, M. Skorobogatiy, M. Ibanescu, E. Lidorikis, J.D. Joannopoulos, Phys. Rev. E 66, 066608 (2002)

    Article  Google Scholar 

  24. M. Skorobogatiy, S.A. Jacobs, S.G. Johnson, Y. Fink, Opt. Express 10(21), 1227 (2002)

    Google Scholar 

  25. M. Skorobogatiy, Phys. Rev. E 70, 046609 (2004)

    Article  Google Scholar 

  26. D. Marcuse, Theory of Dielectric Optical Waveguides. San Diego: Academic Press, 2nd edn., (1991)

    Google Scholar 

  27. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001)

    Article  PubMed  Google Scholar 

  28. S.G. Johnson, M.L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Soljačić, M. Ibanescu, E. Lidorikis, J.D. Joannopoulos, in Proc. 2003 5th Intl. Conf. on Transparent Optical Networks and 2nd European Symp. on Photonic Crystals, 1, 103 (2003)

    Article  Google Scholar 

  29. J.H. Jang, W. Zhao, J.W. Bae, D. Selvanathan, S.L. Rommel, I. Adesida, A. Lepore, M. Kwakernaak, J.H. Abeles, Appl. Phys. Lett. 83(20), 4116 (2003)

    Article  Google Scholar 

  30. N.R. Hill, Phys. Rev. B 24(12), 7112 (1981)

    Article  Google Scholar 

  31. J.D. Jackson, Classical Electrodynamics. New York: Wiley, 3rd edn., (1998)

    Google Scholar 

  32. J. Avelin, R. Sharma, I. Hänninen, A.H. Sihvola, IEEE Trans. Anten. Prop. 49(3), 451 (2001)

    Article  Google Scholar 

  33. S.G. Johnson, J.D. Joannopoulos, Opt. Express 8(3), 173 (2001)

    Google Scholar 

  34. M. Lončar, D. Nedeljković, T. Doll, J. Vučković, A. Scherer, T.P. Pearsall, Appl. Phys. Lett. 77(13), 1937 (2000)

    Article  Google Scholar 

  35. Y. Akahane, T. Asano, B.-S. Song, S. Noda, Appl. Phys. Lett. 83(8), 1512 (2003)

    Article  Google Scholar 

  36. Y. Sugimoto, Y. Tanaka, N. Ikeda, Y. Nakamura, K. Asakawa, Opt. Express 12(6), 1090 (2004)

    Article  Google Scholar 

  37. Y. Tanaka, Y. Sugimoto, N. Ikeda, H. Nakamura, K. Asakawa, K. Inoue, S.G. Johnson, Electron. Lett. 40(3), 174 (2004)

    Article  Google Scholar 

  38. W.T. Lau, S. Fan, Appl. Phys. Lett. 81, 3915 (2002)

    Article  Google Scholar 

  39. A. Taflove, S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method. Norwood, MA: Artech, (2000)

  40. R.D. Meade, A.M. Rappe, K.D. Brommer, J.D. Joannopoulos, O.L. Alerhand, Phys. Rev. B 48, 8434 (1993). Erratum: S.G. Johnson, ibid. 55, 15942 (1997)

    Google Scholar 

  41. D.P. Fussell, R.C. McPhedran, C.M. de Sterke, Phys. Rev. E 70, 066608 (2004)

    Article  Google Scholar 

  42. C.A. Balanis, Antenna Theory: Analysis and Design. New York: Wiley, 2nd ed., (1996)

    Google Scholar 

  43. Y. Tanaka, T. Asano, Y. Akahane, B.-S. Song, S. Noda, Appl. Phys. Lett. 82(11), 1661 (2003)

    Article  Google Scholar 

  44. Y.A. Vlasov, N. Moll, S.J. McNab, J. Appl. Phys. 95(9), 4538 (2004)

    Article  Google Scholar 

  45. C. Cohen-Tannoudji, B. Din, F. Laloë, Quantum Mechanics. Paris: Hermann, (1977)

    Google Scholar 

  46. N.W. Ashcroft, N.D. Mermin, Solid State Physics. Philadelphia: Holt Saunders, (1976)

    Google Scholar 

  47. A. Yariv, Y. Xu, R.K. Lee, A. Scherer, Opt. Lett. 24, 711 (1999)

    Google Scholar 

  48. M. Soljačić, S.G. Johnson, S. Fan, M. Ibanescu, E. Ippen, J.D. Joannopoulos, J. Opt. Soc. Am. B 19, 2052 (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    S. G. Johnson, M. Soljačić, A. Karalis & J. D. Joannopoulos

  2. Ginzton Laboratory, Stanford University, Stanford, CA, 94305, USA

    M. L. Povinelli

  3. OmniGuide Communications, One Kendall Square, Building 100 #3, Cambridge, MA, 02139, USA

    S. Jacobs

Authors
  1. S. G. Johnson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. L. Povinelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Soljačić
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Karalis
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. S. Jacobs
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. J. D. Joannopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. G. Johnson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Johnson, S.G., Povinelli, M.L., Soljačić, M. et al. Roughness losses and volume-current methods in photonic-crystal waveguides. Appl. Phys. B 81, 283–293 (2005). https://doi.org/10.1007/s00340-005-1823-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00340-005-1823-4

PACS

Search

Navigation