Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Localization in silicon nanophotonic slow-light waveguides

Abstract

Slowing down light on a chip can lead to the development of optical buffers1, filters2,3 and memory elements4 useful for optical interconnects and for resonantly enhanced chip-based nonlinear optics5,6. Several approaches to slow light rely on the phenomenon of light interference in a sequence of coupled resonators1,2,3,4,7,8,9,10,11; however, light interference is also responsible, in disordered structures, for the localization of light, an effect particularly prominent in one-dimensional devices12,13. Until now, the length of the waveguides investigated has been less than the localization length. Here we report the first observation of light localization in compact silicon nanophotonic slow-light waveguides consisting of long sequences of coupled resonators. Our results show that disorder limits how much light can be slowed, and that localization leads to spatially concentrated and locally trapped light in a quasi-one-dimensional waveguide at wavelengths near the band edge.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Dispersion and density of states for a weakly disordered slow-wave structure.
Figure 2: Spectral distribution of localization.
Figure 3: Slow-wave coupled-resonator waveguides.
Figure 4: Experimental measurements of localization.

Similar content being viewed by others

References

  1. Xia, F., Sekaric, L. & Vlasov, Y. Ultracompact optical buffers on a silicon chip. Nature Photonics 1, 65–71 (2007).

    Article  ADS  Google Scholar 

  2. Melloni, A., Morichetti, F. & Martinelli, M. Optical slow wave structures. Optics and Photonics News 14, 44–48 (2003).

    Article  ADS  Google Scholar 

  3. Poon, J. K. S., Zhu, L., DeRose, G. & Yariv, A. Transmission and group delay of microring coupled-resonator optical waveguides. Opt. Lett. 31, 456–458 (2006).

    Article  ADS  Google Scholar 

  4. Khurgin, J. B. Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis. J. Opt. Soc. Am. B 22, 1062–1074 (2005).

    Article  ADS  Google Scholar 

  5. Hill, M. T. et al. A fast low-power optical memory based on coupled micro-ring lasers. Nature 432, 206–209 (2004).

    Article  ADS  Google Scholar 

  6. Heebner, J. E., Chak, P., Pereira, S., Sipe, J. E. & Boyd, R. W. Distributed and localized feedback in microresonator sequences for linear and nonlinear optics. J. Opt. Soc. Am. B 21, 1818–1832 (2004).

    Article  ADS  Google Scholar 

  7. Stefanou, N. & Modinos, A. Impurity bands in photonic insulators. Phys. Rev. B 57, 12127–12133 (1998).

    Article  ADS  Google Scholar 

  8. Yariv, A., Xu, Y., Lee, R. K. & Scherer, A. Coupled-resonator optical waveguide: a proposal and analysis. Opt. Lett. 24, 711–713 (1999).

    Article  ADS  Google Scholar 

  9. Bayer, M. et al. Optical demonstration of a crystal band structure formation. Phys. Rev. Lett. 83, 5374–5377 (1999).

    Article  ADS  Google Scholar 

  10. Olivier, S. et al. Miniband transmission in a photonic crystal coupled-resonator optical waveguide. Opt. Lett. 26, 1019–1021 (2001).

    Article  ADS  Google Scholar 

  11. Mookherjea, S. & Yariv, A. Coupled resonator optical waveguides. IEEE J. Sel. Top. Quant. Electron. 8, 448–456 (2002).

    Article  ADS  Google Scholar 

  12. Mott, N. F. & Twose, W. D. The theory of impurity conduction. Adv. Phys. 10, 107–163 (1961).

    Article  ADS  Google Scholar 

  13. John, S., Sompolinksy, H. & Stephen, M. J. Localization in a disordered elastic medium near two dimensions. Phys. Rev. B 27, 5592–5603 (1983).

    Article  ADS  Google Scholar 

  14. Slater, J. C. Microwave Electronics (Dover, New York, 1969).

    MATH  Google Scholar 

  15. Happ, T. D., Kamp, M., Forchel, A., Gentner, J.-L. & Goldstein, L. Two-dimensional photonic crystal coupled-defect laser diode. Appl. Phys. Lett. 82, 4–6 (2003).

    Article  ADS  Google Scholar 

  16. Möller, B. M., Artemyev, M. V. & Woggon, U. Coupled-resonator optical waveguides doped with nanocrystals. Opt. Lett. 30, 2116–2118 (2005).

    Article  ADS  Google Scholar 

  17. Astratov, V. N., Franchak, J. P. & Ashili, S. P. Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder. Appl. Phys. Lett. 85, 5508–5510 (2004).

    Article  ADS  Google Scholar 

  18. Bayindir, M., Temelkuran, B. & Ozbay, E. Tight-binding description of the coupled defect modes in three-dimensional photonic crystals. Phys. Rev. Lett. 84, 2140–2143 (2000).

    Article  ADS  Google Scholar 

  19. Poon, J. K. S. et al. Matrix analysis of microring coupled-resonator optical waveguides. Opt. Express 12, 90–103 (2004).

    Article  ADS  Google Scholar 

  20. Mookherjea, S. Spectral characteristics of coupled resonators. J. Opt. Soc. Am. B 23, 1137–1145 (2006).

    Article  ADS  Google Scholar 

  21. Mookherjea, S. & Oh, A. Effect of disorder on slow light velocity in optical slow-wave structures. Opt. Lett. 32, 289–291 (2007).

    Article  ADS  Google Scholar 

  22. Economou, E. N. Green's Functions in Quantum Physics 3rd edn (Springer, Berlin, 2006).

    Book  Google Scholar 

  23. Sheng, P. Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (Academic Press, San Diego, 1995).

    Google Scholar 

  24. Malyshev, V. & Moreno, P. Hidden structure of the low-energy spectrum of a one-dimensional localized Frenkel exciton. Phys. Rev. B 51, 14587–14593 (1995).

    Article  ADS  Google Scholar 

  25. Bertolotti, J., Gottardo, S., Wiersma, D., Ghulinyan, M. & Pavesi, L. Optical necklace states in Anderson localized 1D systems. Phys. Rev. Lett. 94, 113903 (2005).

    Article  ADS  Google Scholar 

  26. Volkov, V. S., Bozhevolnyi, S. I., Frandsen, L. H. & Kristensen, M. Direct observation of surface mode excitation and slow light coupling in photonic crystal waveguides. Nano Lett. 7, 2341–2345 (2007).

    Article  ADS  Google Scholar 

  27. Theodorou, G. & Cohen, M. C. Extended states in a one-dimensional system with off-diagonal disorder. Phys. Rev. B 13, 4597–4601 (1976).

    Article  ADS  Google Scholar 

  28. Yanik, M. F. & Fan, S. Stopping light all optically. Phys. Rev. Lett. 92, 083901 (2004).

    Article  ADS  Google Scholar 

  29. Soljacˇic´, M. et al. Photonic crystal slow light enhancement of nonlinear phase sensitivity. J. Opt. Soc. Am. B 19, 2052–2059 (2002).

    Article  ADS  Google Scholar 

  30. Firester, A. H., Heller, M. E. & Sheng, P. Knife-edge scanning measurements of sub-wavelength focused light beams. Appl. Opt. 16, 1971 (1977).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the US National Science Foundation under grants ECCS-0642603 and ECCS-0403589. J.P. acknowledges sponsorship support provided by the National Science Graduate Student Fellowship. The authors are grateful to the San Diego Supercomputer Center for computational resources, and to Y. Fainman for making his lapping machine available to us. A. Oh provided assistance with numerical simulations.

Author information

Authors and Affiliations

Authors

Contributions

S.M. contributed to all aspects of the project. J.S.P. contributed to experimental work and data analysis. S.H.Y. and P.B. contributed materials. All authors contributed to discussing the results and writing the paper.

Corresponding author

Correspondence to Shayan Mookherjea.

Supplementary information

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mookherjea, S., Park, J., Yang, SH. et al. Localization in silicon nanophotonic slow-light waveguides. Nature Photon 2, 90–93 (2008). https://doi.org/10.1038/nphoton.2007.278

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2007.278

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing