Abstract

A simple and efficient transmission line model is proposed here to study how the transmission characteristics of photonic crystal waveguides are tailored by introduction of stubs patterned in the photonic crystal lattice. It is shown that band-pass and band-stop optical filters can be easily designed and optimized when stubs of appropriate length are brought in. Since the lengths of the designed stubs are not necessarily integer multiples of the photonic crystal lattice constant, a geometric shift in a portion of the photonic crystal structure is shown to be essential. The proposed model is verified by using a rigorous numerical method. An excellent agreement is observed between the numerical results and the transmission characteristics as extracted by the proposed model.

© 2012 Optical Society of America

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References

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  1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals Molding the Flow of Light (Princeton University, 2008).
  2. S. J. McNab, N. Moll, and Y. A. Vlasov, Opt. Express 11, 2927 (2003).
    [CrossRef]
  3. R. Costa, A. Melloni, and M. Martinelli, IEEE Photon. Technol. Lett. 15, 401 (2003).
    [CrossRef]
  4. M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and T. Tanaka, J. Lightwave Technol. 20, 873 (2002).
    [CrossRef]
  5. M. Koshiba, Y. Tsuji, and M. Hikari, J. Lightwave Technol. 18, 102 (2000).
    [CrossRef]
  6. R. Stoffer, H. J. W. M. Hoekstra, R. M. Deridder, E. Van Groesen, and F. P. H. Van Beckum, Opt. Quantum Electron. 32, 947 (2000).
    [CrossRef]
  7. K. Ogusu and K. Takayama, Opt. Lett. 32, 2185 (2007).
    [CrossRef]
  8. N. Habibi, A. Khavasi, M. Miri, and K. Mehrany, J. Opt. Soc. Am. B 29, 170 (2012).
    [CrossRef]
  9. P. Sarrafi, A. Naqavi, K. Mehrany, S. Khorasani, and B. Rashidian, Opt. Commun. 281, 2826 (2008).
    [CrossRef]
  10. M. A. Miri, A. Khavasi, M. Miri, and K. Mehrany, IEEE Photon. J. 2, 677 (2010).
    [CrossRef]
  11. A. Khavasi, A. K. Jahromi, and K. Mehrany, J. Opt. Soc. Am. A 25, 1564 (2008).
    [CrossRef]
  12. M. Qiu, “F2P: Finite-difference time-domain 2D simulator for photonic devices,” http://www.imit.kth.se/info/FOFU/PC/F2P/ .

2012 (1)

2010 (1)

M. A. Miri, A. Khavasi, M. Miri, and K. Mehrany, IEEE Photon. J. 2, 677 (2010).
[CrossRef]

2008 (2)

P. Sarrafi, A. Naqavi, K. Mehrany, S. Khorasani, and B. Rashidian, Opt. Commun. 281, 2826 (2008).
[CrossRef]

A. Khavasi, A. K. Jahromi, and K. Mehrany, J. Opt. Soc. Am. A 25, 1564 (2008).
[CrossRef]

2007 (1)

2003 (2)

S. J. McNab, N. Moll, and Y. A. Vlasov, Opt. Express 11, 2927 (2003).
[CrossRef]

R. Costa, A. Melloni, and M. Martinelli, IEEE Photon. Technol. Lett. 15, 401 (2003).
[CrossRef]

2002 (1)

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and T. Tanaka, J. Lightwave Technol. 20, 873 (2002).
[CrossRef]

2000 (2)

R. Stoffer, H. J. W. M. Hoekstra, R. M. Deridder, E. Van Groesen, and F. P. H. Van Beckum, Opt. Quantum Electron. 32, 947 (2000).
[CrossRef]

M. Koshiba, Y. Tsuji, and M. Hikari, J. Lightwave Technol. 18, 102 (2000).
[CrossRef]

Chutinan, A.

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and T. Tanaka, J. Lightwave Technol. 20, 873 (2002).
[CrossRef]

Costa, R.

R. Costa, A. Melloni, and M. Martinelli, IEEE Photon. Technol. Lett. 15, 401 (2003).
[CrossRef]

Deridder, R. M.

R. Stoffer, H. J. W. M. Hoekstra, R. M. Deridder, E. Van Groesen, and F. P. H. Van Beckum, Opt. Quantum Electron. 32, 947 (2000).
[CrossRef]

Habibi, N.

Hikari, M.

Hoekstra, H. J. W. M.

R. Stoffer, H. J. W. M. Hoekstra, R. M. Deridder, E. Van Groesen, and F. P. H. Van Beckum, Opt. Quantum Electron. 32, 947 (2000).
[CrossRef]

Imada, M.

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and T. Tanaka, J. Lightwave Technol. 20, 873 (2002).
[CrossRef]

Jahromi, A. K.

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals Molding the Flow of Light (Princeton University, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals Molding the Flow of Light (Princeton University, 2008).

Khavasi, A.

Khorasani, S.

P. Sarrafi, A. Naqavi, K. Mehrany, S. Khorasani, and B. Rashidian, Opt. Commun. 281, 2826 (2008).
[CrossRef]

Koshiba, M.

Martinelli, M.

R. Costa, A. Melloni, and M. Martinelli, IEEE Photon. Technol. Lett. 15, 401 (2003).
[CrossRef]

McNab, S. J.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals Molding the Flow of Light (Princeton University, 2008).

Mehrany, K.

N. Habibi, A. Khavasi, M. Miri, and K. Mehrany, J. Opt. Soc. Am. B 29, 170 (2012).
[CrossRef]

M. A. Miri, A. Khavasi, M. Miri, and K. Mehrany, IEEE Photon. J. 2, 677 (2010).
[CrossRef]

P. Sarrafi, A. Naqavi, K. Mehrany, S. Khorasani, and B. Rashidian, Opt. Commun. 281, 2826 (2008).
[CrossRef]

A. Khavasi, A. K. Jahromi, and K. Mehrany, J. Opt. Soc. Am. A 25, 1564 (2008).
[CrossRef]

Melloni, A.

R. Costa, A. Melloni, and M. Martinelli, IEEE Photon. Technol. Lett. 15, 401 (2003).
[CrossRef]

Miri, M.

N. Habibi, A. Khavasi, M. Miri, and K. Mehrany, J. Opt. Soc. Am. B 29, 170 (2012).
[CrossRef]

M. A. Miri, A. Khavasi, M. Miri, and K. Mehrany, IEEE Photon. J. 2, 677 (2010).
[CrossRef]

Miri, M. A.

M. A. Miri, A. Khavasi, M. Miri, and K. Mehrany, IEEE Photon. J. 2, 677 (2010).
[CrossRef]

Mochizuki, M.

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and T. Tanaka, J. Lightwave Technol. 20, 873 (2002).
[CrossRef]

Moll, N.

Naqavi, A.

P. Sarrafi, A. Naqavi, K. Mehrany, S. Khorasani, and B. Rashidian, Opt. Commun. 281, 2826 (2008).
[CrossRef]

Noda, S.

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and T. Tanaka, J. Lightwave Technol. 20, 873 (2002).
[CrossRef]

Ogusu, K.

Rashidian, B.

P. Sarrafi, A. Naqavi, K. Mehrany, S. Khorasani, and B. Rashidian, Opt. Commun. 281, 2826 (2008).
[CrossRef]

Sarrafi, P.

P. Sarrafi, A. Naqavi, K. Mehrany, S. Khorasani, and B. Rashidian, Opt. Commun. 281, 2826 (2008).
[CrossRef]

Stoffer, R.

R. Stoffer, H. J. W. M. Hoekstra, R. M. Deridder, E. Van Groesen, and F. P. H. Van Beckum, Opt. Quantum Electron. 32, 947 (2000).
[CrossRef]

Takayama, K.

Tanaka, T.

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and T. Tanaka, J. Lightwave Technol. 20, 873 (2002).
[CrossRef]

Tsuji, Y.

Van Beckum, F. P. H.

R. Stoffer, H. J. W. M. Hoekstra, R. M. Deridder, E. Van Groesen, and F. P. H. Van Beckum, Opt. Quantum Electron. 32, 947 (2000).
[CrossRef]

Van Groesen, E.

R. Stoffer, H. J. W. M. Hoekstra, R. M. Deridder, E. Van Groesen, and F. P. H. Van Beckum, Opt. Quantum Electron. 32, 947 (2000).
[CrossRef]

Vlasov, Y. A.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals Molding the Flow of Light (Princeton University, 2008).

IEEE Photon. J. (1)

M. A. Miri, A. Khavasi, M. Miri, and K. Mehrany, IEEE Photon. J. 2, 677 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

R. Costa, A. Melloni, and M. Martinelli, IEEE Photon. Technol. Lett. 15, 401 (2003).
[CrossRef]

J. Lightwave Technol. (2)

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and T. Tanaka, J. Lightwave Technol. 20, 873 (2002).
[CrossRef]

M. Koshiba, Y. Tsuji, and M. Hikari, J. Lightwave Technol. 18, 102 (2000).
[CrossRef]

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

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

Opt. Commun. (1)

P. Sarrafi, A. Naqavi, K. Mehrany, S. Khorasani, and B. Rashidian, Opt. Commun. 281, 2826 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

R. Stoffer, H. J. W. M. Hoekstra, R. M. Deridder, E. Van Groesen, and F. P. H. Van Beckum, Opt. Quantum Electron. 32, 947 (2000).
[CrossRef]

Other (2)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals Molding the Flow of Light (Princeton University, 2008).

M. Qiu, “F2P: Finite-difference time-domain 2D simulator for photonic devices,” http://www.imit.kth.se/info/FOFU/PC/F2P/ .

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Figures (5)

Fig. 1.
Fig. 1.

A typical PCW with four stubs and its corresponding transmission line model.

Fig. 2.
Fig. 2.

(a) A typical stub whose length is Lstub=2a+δ. The admittance of the stub is Ystub=Y1Y2. (b) The loaded transmission line whose input admittance is Yin=Y1, and (c) the loaded transmission line whose input admittance is Yin=Y2.

Fig. 3.
Fig. 3.

A semi-infinite photonic crystal whose reflection coefficient; R, yields the load impedance ZL.

Fig. 4.
Fig. 4.

Transmission of the designed bandpass filter versus normalized frequency: the proposed transmission line model (solid line) and the FDTD (circles).

Fig. 5.
Fig. 5.

Transmission of the designed bandstop filter versus normalized frequency: the proposed transmission line model (solid line) and the FDTD (circles).

Equations (1)

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ZL=1+R(ωn,βW(ωn))1R(ωn,βW(ωn))ZW.

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