Abstract

We present a powerful design and optimization method for devices in a photonic crystal. The method is based on a Wannier basis field expansion and efficient matrix analysis techniques for searching through a vast number of designs. The method permits the design of many compact optical devices with complex and novel functions. We present a design example of a very compact mode separator that is 8.2 µm×13.3 µm in size that demultiplexes the three modes of an input photonic crystal multimode waveguide into three single-mode output waveguides. We verify the method with finite-difference time-domain calculations.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2000).
  2. S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  3. R. Wilson, T. J. Karle, I. Moerman, and T. F. Krauss, J. Opt. A Pure Appl. Opt. 5, S76 (2003).
    [CrossRef]
  4. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, IEEE J. Quantum Electron. 38, 850 (2002).
    [CrossRef]
  5. Z. Y. Li and K. M. Ho, Phys. Rev. B 68, 155101 (2003).
    [CrossRef]
  6. E. Moreno, D. Erni, and C. Hafner, Phys. Rev. E 66, 036618 (2002).
    [CrossRef]
  7. J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, Phys. Rev. B 61, 4381 (2000).
    [CrossRef]
  8. K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
    [CrossRef]
  9. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge U. Press, Cambridge, England, 1990), p. 561.
  10. B. T. Lee and S. Y. Shin, Opt. Lett. 28, 1660 (2003).
    [CrossRef] [PubMed]
  11. J. Leuthold, J. Eckner, E. Gamper, P. A. Besse, and H. Melchior, J. Lightwave Technol. 16, 1228 (1998).
    [CrossRef]
  12. Y. Jiao, S. Fan, and D. A. B. Miller, “Photonic crystal device sensitivity analysis with Wannier basis gradients,” Opt. Lett. (to be published).

2003 (4)

R. Wilson, T. J. Karle, I. Moerman, and T. F. Krauss, J. Opt. A Pure Appl. Opt. 5, S76 (2003).
[CrossRef]

Z. Y. Li and K. M. Ho, Phys. Rev. B 68, 155101 (2003).
[CrossRef]

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
[CrossRef]

B. T. Lee and S. Y. Shin, Opt. Lett. 28, 1660 (2003).
[CrossRef] [PubMed]

2002 (2)

E. Moreno, D. Erni, and C. Hafner, Phys. Rev. E 66, 036618 (2002).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, IEEE J. Quantum Electron. 38, 850 (2002).
[CrossRef]

2001 (1)

2000 (1)

J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, Phys. Rev. B 61, 4381 (2000).
[CrossRef]

1998 (1)

Albert, J. P.

J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, Phys. Rev. B 61, 4381 (2000).
[CrossRef]

Bertho, D.

J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, Phys. Rev. B 61, 4381 (2000).
[CrossRef]

Besse, P. A.

Busch, K.

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
[CrossRef]

Cassagne, D.

J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, Phys. Rev. B 61, 4381 (2000).
[CrossRef]

Eckner, J.

Erni, D.

E. Moreno, D. Erni, and C. Hafner, Phys. Rev. E 66, 036618 (2002).
[CrossRef]

Fan, S.

Y. Jiao, S. Fan, and D. A. B. Miller, “Photonic crystal device sensitivity analysis with Wannier basis gradients,” Opt. Lett. (to be published).

Gamper, E.

Garcia-Martin, A.

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
[CrossRef]

Hafner, C.

E. Moreno, D. Erni, and C. Hafner, Phys. Rev. E 66, 036618 (2002).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2000).

Hermann, D.

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
[CrossRef]

Ho, K. M.

Z. Y. Li and K. M. Ho, Phys. Rev. B 68, 155101 (2003).
[CrossRef]

Horn, R. A.

R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge U. Press, Cambridge, England, 1990), p. 561.

Jiao, Y.

Y. Jiao, S. Fan, and D. A. B. Miller, “Photonic crystal device sensitivity analysis with Wannier basis gradients,” Opt. Lett. (to be published).

Joannopoulos, J. D.

Johnson, C. R.

R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge U. Press, Cambridge, England, 1990), p. 561.

Johnson, S. G.

Jouanin, C.

J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, Phys. Rev. B 61, 4381 (2000).
[CrossRef]

Karle, T. J.

R. Wilson, T. J. Karle, I. Moerman, and T. F. Krauss, J. Opt. A Pure Appl. Opt. 5, S76 (2003).
[CrossRef]

Krauss, T. F.

R. Wilson, T. J. Karle, I. Moerman, and T. F. Krauss, J. Opt. A Pure Appl. Opt. 5, S76 (2003).
[CrossRef]

Lee, B. T.

Leuthold, J.

Li, Z. Y.

Z. Y. Li and K. M. Ho, Phys. Rev. B 68, 155101 (2003).
[CrossRef]

Loncar, M.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, IEEE J. Quantum Electron. 38, 850 (2002).
[CrossRef]

Mabuchi, H.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, IEEE J. Quantum Electron. 38, 850 (2002).
[CrossRef]

Melchior, H.

Miller, D. A. B.

Y. Jiao, S. Fan, and D. A. B. Miller, “Photonic crystal device sensitivity analysis with Wannier basis gradients,” Opt. Lett. (to be published).

Mingaleev, S. F.

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
[CrossRef]

Moerman, I.

R. Wilson, T. J. Karle, I. Moerman, and T. F. Krauss, J. Opt. A Pure Appl. Opt. 5, S76 (2003).
[CrossRef]

Moreno, E.

E. Moreno, D. Erni, and C. Hafner, Phys. Rev. E 66, 036618 (2002).
[CrossRef]

Scherer, A.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, IEEE J. Quantum Electron. 38, 850 (2002).
[CrossRef]

Schillinger, M.

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
[CrossRef]

Shin, S. Y.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2000).

Vuckovic, J.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, IEEE J. Quantum Electron. 38, 850 (2002).
[CrossRef]

Wilson, R.

R. Wilson, T. J. Karle, I. Moerman, and T. F. Krauss, J. Opt. A Pure Appl. Opt. 5, S76 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, IEEE J. Quantum Electron. 38, 850 (2002).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A Pure Appl. Opt. (1)

R. Wilson, T. J. Karle, I. Moerman, and T. F. Krauss, J. Opt. A Pure Appl. Opt. 5, S76 (2003).
[CrossRef]

J. Phys. Condens. Matter (1)

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (2)

J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, Phys. Rev. B 61, 4381 (2000).
[CrossRef]

Z. Y. Li and K. M. Ho, Phys. Rev. B 68, 155101 (2003).
[CrossRef]

Phys. Rev. E (1)

E. Moreno, D. Erni, and C. Hafner, Phys. Rev. E 66, 036618 (2002).
[CrossRef]

Other (3)

R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge U. Press, Cambridge, England, 1990), p. 561.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2000).

Y. Jiao, S. Fan, and D. A. B. Miller, “Photonic crystal device sensitivity analysis with Wannier basis gradients,” Opt. Lett. (to be published).

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 (3)

Fig. 1
Fig. 1

(a) Initial guess as to the mode separator structure. The PC parameters are given in the text. The arrows show the input and output ports. The dotted rectangle shows the design region of the structure that is altered in the search process. (b) Final design of the mode separator.

Fig. 2
Fig. 2

Mode separator in action. The three field patterns are for each of the three input waveguide modes. Lighter shading indicates a larger field. The structure is superimposed onto the field patterns. The irregularities in the input fields are due to the small reflections -10 dB from the device.

Fig. 3
Fig. 3

From top to bottom, the FDTD simulation transmission and reflection spectra for fundamental, first-order, and second-order input waveguide modes. Ports 1–3 refer to the three output waveguides.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Bq=p,
B+δDq=p,
δDnR,mS=R2Wn,R*rδrWm,Srd2r.
δDα,i=XiEαYi,
Eα=VαFαWα,
B+δDα,i-1=B-1-B-1XV×F-1WYB-1XV-1WYB-1,

Metrics