Abstract

We perform a simple sensitivity analysis of a W1 waveguide bend in a photonic crystal (PhC) where we use the information obtained to optimize the PhC bend’s frequency response. Within a single optimization step we already achieve very low power reflection coefficients over almost the entire frequency range of the photonic bandgap (PBG), i.e., an achromatic bend. A further analysis shows that there is a single critical rod in the optimized bend structure that exhibits an extraordinary high sensitivity at a given frequency. Hence power reflection becomes tunable from 0% up to 100% involving only small changes in the critical rod’s properties. This opens the door to novel topologies for compact switches and sensor applications.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals ??? Molding the Flow of Light (Princeton University Press, New Jersey, 1995).
  2. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, 2001).
  3. K. M. Ho, C. T. Chan, C. M. Soukolis, ???Existence of a photonic gap in periodic dielectric structures,??? Phys. Rev. Lett. 65, 3152-3155 (1990).
    [CrossRef] [PubMed]
  4. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villenueve, H. A. Haus, J. D. Joannopoulos, ???High-density integrated optics,??? J. Lightwave Technol. 17, 1682-1692 (1999).
    [CrossRef]
  5. R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, K. Kash, ???Novel applications of photonic band gap materials: Low-loss bends and high Q cavities,??? J. Appl. Phys. 75, 4753-4755 (1994).
    [CrossRef]
  6. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, ???High transmission through sharp bends in photonic crystal waveguides,??? Phys. Rev. Lett. 77, 3787-3790 (1996).
    [CrossRef] [PubMed]
  7. A. Chutinan, M. Okano, S. Noda, ???Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,??? Appl. Phys. Lett. 80, 1698-1700 (2002).
    [CrossRef]
  8. R. L. Espinola, R. U. Ahmad, F. Pizzuto, M. J. Steel, and R. M. Osgood, "A study of high-index-contrast 90 degree waveguide bend structures," Opt. Express 8, 517-528 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-9-517">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-9-517</a>
    [CrossRef] [PubMed]
  9. P. Buchman, and H. Kaufman, ???GaAs Single-Mode Rib Waveguides with Ion-Etched Totally Reflecting Corner Mirrors,??? J. Lightwave Technol. 3, 785-788 (1985).
    [CrossRef]
  10. Christian Hafner, Post-modern Electromagnetics Using Intelligent MaXwell Solvers (John Wiley & Sons, Chichester, 1999).
  11. Ch. Hafner, MaX-1: A Visual Electromagnetics Platform (John Wiley & Sons, Chichester, 1998).
  12. Ch. Hafner, J. Smajic, The Computational Optics Group Web Page (IFH, ETH Zurich), <a href="http://alphard.ethz.ch/">http://alphard.ethz.ch/</a>
  13. E. Moreno, D. Erni, Ch. Hafner, ???Modeling of discontinuities in photonic crystal waveguides with the multiple multipole method,??? Phys. Rev. E 66, 036618 (2002).
    [CrossRef]
  14. J. Smajic, Ch. Hafner, D. Erni, ???Automatic calculation of band diagrams of photonic crystals using the multiple multipole method???, ACES Journal, (to be published).
  15. J. Smajic, C. Hafner, and D. Erni, "On the design of photonic crystal multiplexers," Opt. Express 11, 566-571 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-566">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-566</a>
    [CrossRef] [PubMed]
  16. A. S. Sharkawy, S. Shi, D. W. Prather, and R. A. Soref, "Electro-optical switching using coupled photonic crystal waveguides," Opt. Express 10, 1048-1059 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-20-1048">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-20-1048</a>
    [CrossRef] [PubMed]
  17. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop filters in photonic crystals," Opt. Express 3, 4-11 (1998), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-1-4">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-1-4</a>
    [CrossRef] [PubMed]

ACES Journal (1)

J. Smajic, Ch. Hafner, D. Erni, ???Automatic calculation of band diagrams of photonic crystals using the multiple multipole method???, ACES Journal, (to be published).

Appl. Phys. Lett. (1)

A. Chutinan, M. Okano, S. Noda, ???Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,??? Appl. Phys. Lett. 80, 1698-1700 (2002).
[CrossRef]

J. Appl. Phys. (1)

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, K. Kash, ???Novel applications of photonic band gap materials: Low-loss bends and high Q cavities,??? J. Appl. Phys. 75, 4753-4755 (1994).
[CrossRef]

J. Lightwave Technol. (2)

C. Manolatou, S. G. Johnson, S. Fan, P. R. Villenueve, H. A. Haus, J. D. Joannopoulos, ???High-density integrated optics,??? J. Lightwave Technol. 17, 1682-1692 (1999).
[CrossRef]

P. Buchman, and H. Kaufman, ???GaAs Single-Mode Rib Waveguides with Ion-Etched Totally Reflecting Corner Mirrors,??? J. Lightwave Technol. 3, 785-788 (1985).
[CrossRef]

Opt. Express (4)

Phys. Rev. E (1)

E. Moreno, D. Erni, Ch. Hafner, ???Modeling of discontinuities in photonic crystal waveguides with the multiple multipole method,??? Phys. Rev. E 66, 036618 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, ???High transmission through sharp bends in photonic crystal waveguides,??? Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, C. M. Soukolis, ???Existence of a photonic gap in periodic dielectric structures,??? Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Other (5)

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals ??? Molding the Flow of Light (Princeton University Press, New Jersey, 1995).

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, 2001).

Christian Hafner, Post-modern Electromagnetics Using Intelligent MaXwell Solvers (John Wiley & Sons, Chichester, 1999).

Ch. Hafner, MaX-1: A Visual Electromagnetics Platform (John Wiley & Sons, Chichester, 1998).

Ch. Hafner, J. Smajic, The Computational Optics Group Web Page (IFH, ETH Zurich), <a href="http://alphard.ethz.ch/">http://alphard.ethz.ch/</a>

Supplementary Material (7)

» Media 1: MOV (402 KB)     
» Media 2: MOV (410 KB)     
» Media 3: MOV (391 KB)     
» Media 4: MOV (393 KB)     
» Media 5: MOV (387 KB)     
» Media 6: MOV (239 KB)     
» Media 7: MOV (397 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

(Movie file for the light propagation 401 KB) Scheme of the PhC 90° W1 waveguide bend (left). As will be discussed in section 3 two sets of rods are selected, characterized a potential increase (+) or decrease (-) of the rod’s radius. The performance of this initial bend is given by the spectral response of the reflectance R and transmittance T (right). The light propagation is depicted as the magnitude of the Poynting field (movie, right inset).

Fig. 2.
Fig. 2.

Sensitivity analysis of the power reflectivity R concerning only a restricted area of the PhC bend structure: The variations ΔR are assigned to each rod while decreasing the corresponding rod’s radius Δr=- 10% (left) and for an increase of the rod’s radius Δr=+10% (right), both at a frequency of ω·a/(2·π·c)=0.42. The background color indicates zero variation ΔR=0.

Fig. 3.
Fig. 3.

The frequency response of the modified bend after a ±10% radius variation of the seleced rods (left). The corresponding Poynting field is given in the inset (movie for the light propagation, 410 KB). The frequency response after a ±13.27% radius variation shows two small maxima for R (right). The corresponding Poynting fields for both maxima are given in the insets (movie for the first maximum 391 KB, on left; movie for the second maximum 394 KB, on right).

Fig. 4.
Fig. 4.

Sensitivity analysis regarding the first maximum of R (at ω·a/(2·π·c)=0.367) for a negative radius variation Δr=- 2% (left), and for a positive radius variation Δr=+2% (right).

Fig. 5.
Fig. 5.

Sensitivity analysis regarding the second maximum of R (at ω·a/(2·π·c)=0.417) for a negative radius variation Δr=- 2% (left), and for a positive radius variation Δr=+2% (right).

Fig. 6.
Fig. 6.

The frequency response for the predicted - 30% radius variation of the critical rod. The Poynting field for three different operating points is depicted in the insets (light propagation movies for the first 387 KB, second 240 KB, and third 397 KB operating point).

Metrics