Abstract

We present an extremely compact wavelength division multiplexer design, as well as a general framework for designing and optimizing frequency selective devices embedded in photonic crystals satisfying arbitrary design constraints. Our method is based on the Dirichlet-to-Neumman simulation method and uses low rank updates to the system to efficiently scan through many device designs.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
    [CrossRef]
  2. S. Kim, I. Park, H. Lim, and C.-S. Kee, Opt. Express 12, 5518(2004).
    [CrossRef] [PubMed]
  3. A. Sharkawy, S. Shi, and D. W. Prather, Appl. Opt. 40, 2247(2001).
    [CrossRef]
  4. B.-S. Song, T. Asano, Y. Akahane, Y. Tanaka, and S. Noda, J. Lightwave Technol. 23, 1449 (2005).
    [CrossRef]
  5. C.-W. Kuo, C.-F. Chang, M.-H. Chen, S.-Y. Chen, and Y.-D. Wu, Opt. Express 15, 198 (2007).
    [CrossRef] [PubMed]
  6. E. Centeno, B. Guizal, and D. Felbacq, J. Opt. A 1, L10 (1999).
    [CrossRef]
  7. M. Koshiba, J. Lightwave Technol. 19, 1970 (2001).
    [CrossRef]
  8. T. Niemi, L. H. Frandsen, K. K. Hede, A. Harpoth, P. I. Borel, and M. Kristensen, IEEE Photon. Technol. Lett. 18, 226 (2006).
    [CrossRef]
  9. K. B. Chung and S. W. Hong, Appl. Phys. Lett. 81, 1549(2002).
    [CrossRef]
  10. M. Gerken and D. A. B. Miller, IEEE Photon. Technol. Lett. 15, 1097 (2003).
    [CrossRef]
  11. A. Jugessur, L. Wu, A. Bakhtazad, A. Kirk, T. Krauss, and R. De La Rue, Opt. Express 14, 1632 (2006).
    [CrossRef] [PubMed]
  12. C. Jin, S. Fan, S. Han, and D. Zhang, IEEE J. Quantum Electron. 39, 160 (2003).
    [CrossRef]
  13. Y. Huang and Y. Y. Lu, J. Lightwave Technol. 24, 3448(2006).
    [CrossRef]
  14. Z. Hu and Y. Y. Lu, Opt. Express 16, 17383 (2008).
    [CrossRef] [PubMed]
  15. Y. Huang, Y. Y. Lu, and S. Li, J. Opt. Soc. Am. B 24, 2860(2007).
    [CrossRef]
  16. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University, 1990).
  17. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
    [CrossRef] [PubMed]
  18. K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233(2003).
    [CrossRef]
  19. Y. Jiao, S. Fan, and D. A. B. Miller, Opt. Lett. 30, 141 (2005).
    [CrossRef] [PubMed]

2008 (1)

2007 (2)

2006 (3)

2005 (2)

2004 (1)

2003 (3)

M. Gerken and D. A. B. Miller, IEEE Photon. Technol. Lett. 15, 1097 (2003).
[CrossRef]

C. Jin, S. Fan, S. Han, and D. Zhang, IEEE J. Quantum Electron. 39, 160 (2003).
[CrossRef]

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

2002 (1)

K. B. Chung and S. W. Hong, Appl. Phys. Lett. 81, 1549(2002).
[CrossRef]

2001 (2)

1999 (1)

E. Centeno, B. Guizal, and D. Felbacq, J. Opt. A 1, L10 (1999).
[CrossRef]

1998 (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Akahane, Y.

Asano, T.

Bakhtazad, A.

Borel, P. I.

T. Niemi, L. H. Frandsen, K. K. Hede, A. Harpoth, P. I. Borel, and M. Kristensen, IEEE Photon. Technol. Lett. 18, 226 (2006).
[CrossRef]

Busch, K.

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

Centeno, E.

E. Centeno, B. Guizal, and D. Felbacq, J. Opt. A 1, L10 (1999).
[CrossRef]

Chang, C.-F.

Chen, M.-H.

Chen, S.-Y.

Chung, K. B.

K. B. Chung and S. W. Hong, Appl. Phys. Lett. 81, 1549(2002).
[CrossRef]

De La Rue, R.

Fan, S.

Y. Jiao, S. Fan, and D. A. B. Miller, Opt. Lett. 30, 141 (2005).
[CrossRef] [PubMed]

C. Jin, S. Fan, S. Han, and D. Zhang, IEEE J. Quantum Electron. 39, 160 (2003).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Felbacq, D.

E. Centeno, B. Guizal, and D. Felbacq, J. Opt. A 1, L10 (1999).
[CrossRef]

Frandsen, L. H.

T. Niemi, L. H. Frandsen, K. K. Hede, A. Harpoth, P. I. Borel, and M. Kristensen, IEEE Photon. Technol. Lett. 18, 226 (2006).
[CrossRef]

Garcia-Martin, A.

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

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Gerken, M.

M. Gerken and D. A. B. Miller, IEEE Photon. Technol. Lett. 15, 1097 (2003).
[CrossRef]

Guizal, B.

E. Centeno, B. Guizal, and D. Felbacq, J. Opt. A 1, L10 (1999).
[CrossRef]

Han, S.

C. Jin, S. Fan, S. Han, and D. Zhang, IEEE J. Quantum Electron. 39, 160 (2003).
[CrossRef]

Harpoth, A.

T. Niemi, L. H. Frandsen, K. K. Hede, A. Harpoth, P. I. Borel, and M. Kristensen, IEEE Photon. Technol. Lett. 18, 226 (2006).
[CrossRef]

Haus, H. A.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Hede, K. K.

T. Niemi, L. H. Frandsen, K. K. Hede, A. Harpoth, P. I. Borel, and M. Kristensen, IEEE Photon. Technol. Lett. 18, 226 (2006).
[CrossRef]

Hermann, D.

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

Hong, S. W.

K. B. Chung and S. W. Hong, Appl. Phys. Lett. 81, 1549(2002).
[CrossRef]

Horn, R. A.

R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University, 1990).

Hu, Z.

Huang, Y.

Jiao, Y.

Jin, C.

C. Jin, S. Fan, S. Han, and D. Zhang, IEEE J. Quantum Electron. 39, 160 (2003).
[CrossRef]

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Johnson, C. R.

R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University, 1990).

Jugessur, A.

Kee, C.-S.

Kim, S.

Kirk, A.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Koshiba, M.

Krauss, T.

Kristensen, M.

T. Niemi, L. H. Frandsen, K. K. Hede, A. Harpoth, P. I. Borel, and M. Kristensen, IEEE Photon. Technol. Lett. 18, 226 (2006).
[CrossRef]

Kuo, C.-W.

Li, S.

Lim, H.

Lu, Y. Y.

Miller, D. A. B.

Y. Jiao, S. Fan, and D. A. B. Miller, Opt. Lett. 30, 141 (2005).
[CrossRef] [PubMed]

M. Gerken and D. A. B. Miller, IEEE Photon. Technol. Lett. 15, 1097 (2003).
[CrossRef]

Mingaleev, S. F.

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

Niemi, T.

T. Niemi, L. H. Frandsen, K. K. Hede, A. Harpoth, P. I. Borel, and M. Kristensen, IEEE Photon. Technol. Lett. 18, 226 (2006).
[CrossRef]

Noda, S.

Park, I.

Prather, D. W.

Schillinger, M.

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

Sharkawy, A.

Shi, S.

Song, B.-S.

Tanaka, Y.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Wu, L.

Wu, Y.-D.

Zhang, D.

C. Jin, S. Fan, S. Han, and D. Zhang, IEEE J. Quantum Electron. 39, 160 (2003).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

K. B. Chung and S. W. Hong, Appl. Phys. Lett. 81, 1549(2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. Jin, S. Fan, S. Han, and D. Zhang, IEEE J. Quantum Electron. 39, 160 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

M. Gerken and D. A. B. Miller, IEEE Photon. Technol. Lett. 15, 1097 (2003).
[CrossRef]

T. Niemi, L. H. Frandsen, K. K. Hede, A. Harpoth, P. I. Borel, and M. Kristensen, IEEE Photon. Technol. Lett. 18, 226 (2006).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. A (1)

E. Centeno, B. Guizal, and D. Felbacq, J. Opt. A 1, L10 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

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 (4)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Other (1)

R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University, 1990).

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 (2)

Fig. 1
Fig. 1

(a) Optimized WDM structure. Filled circles indicate dielectric rods. The coupler region is highlighted in yellow. The cavities are highlighted in different colors with hollow circles. The solid horizontal lines indicate the positions where the waveguide power flux is measured, while the dashed lines indicate PEC boundary conditions. (b) Initial unoptimized structure. The response spectra for each structure are shown below the respective structure. The solid black curves are the reflection spectra in the input waveguide. The colored dashed curves are the transmission spectra for each output waveguide, with the colors matching the color code of the cavity. The target frequencies are indicated by arrows.

Fig. 2
Fig. 2

E z field patterns at each of the three target frequencies.

Equations (5)

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

A ( ω ) x ( ω ) = b ( ω ) ,
p i = x H B i x ,
p i = x H B i x + x H B i x = 2 Re ( x H B i x ) = 2 Re ( x H B i A 1 A x ) ,
( A + δ A ) x = b ,
( A + U Δ V T ) 1 = A 1 A 1 U ( Δ 1 + V T A 1 U ) 1 V T A 1 ,

Metrics