Abstract

We introduce a novel method to calculate the local dispersion relation in photonic crystal waveguides, based on the finite-difference time-domain simulation and filter diagonalization method (FDM). In comparison with the spatial Fourier transform method (SFT), the highly local dispersion calculations based on FDM are considerably superior and pronounced. For the first time to our knowledge, the presented numerical technique allows comparing the dispersion in straight and bent waveguides.

© 2007 Optical Society of America

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2007 (2)

J. Zarbakhsh, A. Mohtashami, and K. Hingerl, Opt. Quantum Electron. 39, 395 (2007).
[CrossRef]

A. Mohtashami, J. Zarbakhsh, and K. Hingerl, Opt. Quantum Electron. 39, 387 (2007).
[CrossRef]

2006 (1)

M. Bergmair, M. Huber, and K. Hingerl, Appl. Phys. Lett. 89, 081907 (2006).
[CrossRef]

2005 (3)

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

A. Yu-Petrov and M. Eich, IEEE J. Quantum Electron. 41, 1502 (2005).
[CrossRef]

J. Chaloupka, J. Zarbakhsh, and K. Hingerl, Phys. Rev. B 72, 085122 (2005).
[CrossRef]

2004 (2)

J. Zarbakhsh, F. Hagmann, S. F. Mingaleev, K. Busch, and K. Hingerl, Appl. Phys. Lett. 84, 4687 (2004).
[CrossRef]

A. Jafarpour, C. M. Reinke, A. Adibi, Y. Xu, and R. K. Lee, IEEE J. Quantum Electron. 40, 1060 (2004).
[CrossRef]

2002 (2)

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 66608 (2002).
[CrossRef]

B. Gralak, S. Enoch, and G. Tayeb, J. Opt. Soc. Am. A 19, 1547 (2002).
[CrossRef]

2000 (2)

1997 (1)

V. A. Mandelshtam and H. S. Taylor, J. Chem. Phys. 107, 6756 (1997).
[CrossRef]

1995 (2)

M. R. Wall and D. Neuhauser, J. Chem. Phys. 102, 8011 (1995).
[CrossRef]

C. T. Chan, Q. L. Yu, and K. M. Ho, Phys. Rev. B 51, 16635 (1995).
[CrossRef]

Appl. Phys. Lett. (2)

M. Bergmair, M. Huber, and K. Hingerl, Appl. Phys. Lett. 89, 081907 (2006).
[CrossRef]

J. Zarbakhsh, F. Hagmann, S. F. Mingaleev, K. Busch, and K. Hingerl, Appl. Phys. Lett. 84, 4687 (2004).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. Jafarpour, C. M. Reinke, A. Adibi, Y. Xu, and R. K. Lee, IEEE J. Quantum Electron. 40, 1060 (2004).
[CrossRef]

A. Yu-Petrov and M. Eich, IEEE J. Quantum Electron. 41, 1502 (2005).
[CrossRef]

J. Chem. Phys. (3)

V. A. Mandelshtam and H. S. Taylor, J. Chem. Phys. 107, 6756 (1997).
[CrossRef]

M. R. Wall and D. Neuhauser, J. Chem. Phys. 102, 8011 (1995).
[CrossRef]

J. Chen and V. A. Mandelshtam, J. Chem. Phys. 112, 4429 (2000).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Quantum Electron. (2)

J. Zarbakhsh, A. Mohtashami, and K. Hingerl, Opt. Quantum Electron. 39, 395 (2007).
[CrossRef]

A. Mohtashami, J. Zarbakhsh, and K. Hingerl, Opt. Quantum Electron. 39, 387 (2007).
[CrossRef]

Phys. Rev. B (2)

C. T. Chan, Q. L. Yu, and K. M. Ho, Phys. Rev. B 51, 16635 (1995).
[CrossRef]

J. Chaloupka, J. Zarbakhsh, and K. Hingerl, Phys. Rev. B 72, 085122 (2005).
[CrossRef]

Phys. Rev. E (1)

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 66608 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Other (1)

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

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Figures (3)

Fig. 1
Fig. 1

(a) E-polarization field profile in W2 waveguide at normalized frequency a λ = 0.4 . The horizontal lines show the maximum size and positions of windows. (b)–(e) Local dispersion relation for W2-PCW, comparison between PWE (solid curves) and SFT (crosses) method, for different window sizes, w = 3.2 a , w = 6.4 a , w = 9.6 a , and w = 12.8 a , respectively.

Fig. 2
Fig. 2

(a)–(d) Local dispersion relation for W2-PCW, comparison between PWE (solid curves) and FDM (crosses), for different window sizes, w = 0.4 a , w = a , w = 2 a , and w = 3.5 a , respectively.

Fig. 3
Fig. 3

(a) CPCW with different hole sizes of air in silicon background, and H-polarized field calculated by FDTD. (b) Calculated local dispersion relation along the center of curved waveguide compared to PWE results (solid curves) for equivalent hexagonal structure.

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