Skip to main content
Log in

Bloch analysis of finite periodic microring chains

  • Published:
Applied Physics B Aims and scope Submit manuscript

Abstract

We apply Bloch analysis to the study of finite periodic cascading of microring resonators. Diagonalization of the standard transfer matrix approach not only allows one to find an exact analytic expression for transmission and reflection, but also to derive a closed form solution for the field in every point of the structure. To gain more physical insight we have analyzed the main features of the transmission resonances in a finite chain and we have given some hints for their experimental verification .

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J.D. Jannopoulos, R.D. Meade, J.N. Winn: Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton 1995)

  2. J.E. Heebner, R.W. Boyd, Q-H. Park: Phys. Rev. E 65, 0366191 (2002)

    Article  Google Scholar 

  3. Y. Chen, S. Blair: J. Opt. Soc. Am. B 20, 2125 (2003)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  5. A. Melloni, F. Morichetti: Opt. Quantum Electron. 35, 365 (2003)

    Article  Google Scholar 

  6. S. Blair: Opt. Lett. 27, 613 (2002)

    Article  ADS  Google Scholar 

  7. A. Yariv S. Mookherjea: Phys. Rev. E 65, 0266071 (2002)

    Google Scholar 

  8. P. Yeh: Optical Waves in Layered Media (Wiley, New York 1988)

  9. J.J.K.S. Poon, J. Scheuer, S. Mookherjea, G.T. Paloczi, Y. Huang, A. Yariv: Opt. Exp. 12, 90 (2004)

    Article  ADS  Google Scholar 

  10. B.E. Little, S.T. Chu, H.A. Haus, J. Foresi, J.-P. Laine: IEEE J. Lightwave Technol. 15, 998 (1997)

    Article  ADS  Google Scholar 

  11. M. de Sterke, J.E. Sipe: Phys. Rev. A 38, 5149 (1988)

    Article  ADS  Google Scholar 

  12. S. Mookherjea, A. Yariv: Phys. Rev. E 65, 0566011 (2002)

    Google Scholar 

  13. P.T. Leung, S.Y. Liu, K. Young: Phys. Rev. A 49, 3057 (1994)

    Article  ADS  Google Scholar 

  14. A. Settimi, S. Severini, N. Mattiucci, C. Sibilia, M. Centini, G. D’Aguanno; M. Bertolotti, M. Scalora, M. Bloemer, C.M. Bowden: Phys. Rev. E 68, 0266141 (2003)

    Article  Google Scholar 

  15. M. Cherchi: Phys. Rev. E 69, 0666021 (2004)

    Article  Google Scholar 

  16. H.A. Haus: Waves and fields in optoelectronics (Prentice Hall, Englewood Cliffs 1984)

  17. S. Blair: J. Opt. Soc. Am. B 18, 1943 (2001)

    Article  ADS  Google Scholar 

  18. R. Orta, P. Savi, R. Mascone, D. Trinchero: IEEE Photon. Technol. Lett. 7, 1447 (1995)

    Article  ADS  Google Scholar 

  19. A. Melloni, M. Martinelli: J. Lightwave Technol. 20, 296 (2002)

    Article  ADS  Google Scholar 

  20. S.H. Huang, H. Cao, S.T. Ho: IEEE J. Quantum Electron. QE-39, 364 (2003)

  21. M. Bertolotti, A. Driessen, F. Michelotti (Eds.): Microresonators as building blocks for VLSI photonics, AIP Conference Proceedings, Melville, New York, Vol. 709 (2004); Proceedings of the International School of Quantum Electronics, 39th course, Erice, Sicily (October 2003)

  22. A. Rosseau, B. Boutevin: ibid., p. 214

  23. R. Grover, P.P. Absil, T.A. Ibrahim, P.-T. Ho: ibid., p. 110; R. Baets et al.: ibid., p. 308

  24. J. Müller, M. Mahnke, G. Schoer, S. Wiechman: ibid., p. 268

  25. A. Melloni, R. Costa, G. Cusmai, F. Morichetti, P. Rosotti, M. Martinelli: ibid., p. 130

  26. T. Barwicz, M.A. Popović, P.T. Rakich, M.R. Watts, H.A. Haus, E.P. Ippen, H.I. Smith: Opt. Express 12, 1437 (2004)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Cherchi.

Additional information

PACS

42.70.Qs; 42.82.Gw; 42.60.Da

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cherchi, M. Bloch analysis of finite periodic microring chains. Appl. Phys. B 80, 109–113 (2005). https://doi.org/10.1007/s00340-004-1671-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00340-004-1671-7

Keywords

Navigation