Abstract

The transmission-line analogy of the planar electromagnetic reflection problem is exploited to obtain a transmission-line model that can be used to design effective, robust, and wideband interference-based matching stages. The proposed model based on a new definition for a scalar impedance is obtained by using the reflection coefficient of the zeroth-order diffracted plane wave outside the photonic crystal. It is shown to be accurate for in-band applications, where the normalized frequency is low enough to ensure that the zeroth-order diffracted plane wave is the most important factor in determining the overall reflection. The frequency limitation of employing the proposed approach is explored, highly dispersive photonic crystals are considered, and wideband matching stages based on binomial impedance transformers are designed to work at the first two photonic bands.

© 2010 Optical Society of America

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References

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  1. T. Baba and D. Ohsaki, Jpn. J. Appl. Phys. Part 1 40, 5920 (2001).
    [CrossRef]
  2. P. Rabiei and A. F. J. Levi, in Proceedings of Conference on Lasers and Electro-Optics (Optical Society of America, 2001), p. 590.
  3. B. Momeni and A. Adibi, Appl. Phys. Lett. 87, 171104 (2005).
    [CrossRef]
  4. F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, Appl. Phys. Lett. 93, 121114 (2008).
    [CrossRef]
  5. F. J. Lawrence, L. C. Botten, K. B. Dossou, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. A 80, 023826 (2009).
    [CrossRef]
  6. R. Biswas, Z. Y. Li, and K. M. Ho, Appl. Phys. Lett. 84, 1254 (2004).
    [CrossRef]
  7. B. Momeni, A. A. Eftekhar, and A. Adibi, Opt. Lett. 32, 778 (2007).
    [CrossRef] [PubMed]
  8. R. E. Collin, Foundations for Microwave Engineering, 2nd ed., IEEE Series on Electromagnetic Wave Theory (IEEE, 2001).
    [CrossRef]
  9. A. Khavasi, A. K. Jahromi, and K. Mehrany, J. Opt. Soc. Am. A 25, 1564 (2008).
    [CrossRef]

2009

F. J. Lawrence, L. C. Botten, K. B. Dossou, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. A 80, 023826 (2009).
[CrossRef]

2008

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

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

2007

2005

B. Momeni and A. Adibi, Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

2004

R. Biswas, Z. Y. Li, and K. M. Ho, Appl. Phys. Lett. 84, 1254 (2004).
[CrossRef]

2001

T. Baba and D. Ohsaki, Jpn. J. Appl. Phys. Part 1 40, 5920 (2001).
[CrossRef]

Adibi, A.

Baba, T.

T. Baba and D. Ohsaki, Jpn. J. Appl. Phys. Part 1 40, 5920 (2001).
[CrossRef]

Biswas, R.

R. Biswas, Z. Y. Li, and K. M. Ho, Appl. Phys. Lett. 84, 1254 (2004).
[CrossRef]

Botten, L. C.

F. J. Lawrence, L. C. Botten, K. B. Dossou, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. A 80, 023826 (2009).
[CrossRef]

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

Collin, R. E.

R. E. Collin, Foundations for Microwave Engineering, 2nd ed., IEEE Series on Electromagnetic Wave Theory (IEEE, 2001).
[CrossRef]

de Sterke, C. M.

F. J. Lawrence, L. C. Botten, K. B. Dossou, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. A 80, 023826 (2009).
[CrossRef]

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

Dossou, K. B.

F. J. Lawrence, L. C. Botten, K. B. Dossou, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. A 80, 023826 (2009).
[CrossRef]

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

Eftekhar, A. A.

Ho, K. M.

R. Biswas, Z. Y. Li, and K. M. Ho, Appl. Phys. Lett. 84, 1254 (2004).
[CrossRef]

Jahromi, A. K.

Khavasi, A.

Lawrence, F. J.

F. J. Lawrence, L. C. Botten, K. B. Dossou, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. A 80, 023826 (2009).
[CrossRef]

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

Levi, A. F. J.

P. Rabiei and A. F. J. Levi, in Proceedings of Conference on Lasers and Electro-Optics (Optical Society of America, 2001), p. 590.

Li, Z. Y.

R. Biswas, Z. Y. Li, and K. M. Ho, Appl. Phys. Lett. 84, 1254 (2004).
[CrossRef]

McPhedran, R. C.

F. J. Lawrence, L. C. Botten, K. B. Dossou, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. A 80, 023826 (2009).
[CrossRef]

Mehrany, K.

Momeni, B.

Ohsaki, D.

T. Baba and D. Ohsaki, Jpn. J. Appl. Phys. Part 1 40, 5920 (2001).
[CrossRef]

Rabiei, P.

P. Rabiei and A. F. J. Levi, in Proceedings of Conference on Lasers and Electro-Optics (Optical Society of America, 2001), p. 590.

Appl. Phys. Lett.

B. Momeni and A. Adibi, Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

F. J. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, Appl. Phys. Lett. 93, 121114 (2008).
[CrossRef]

R. Biswas, Z. Y. Li, and K. M. Ho, Appl. Phys. Lett. 84, 1254 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys. Part 1

T. Baba and D. Ohsaki, Jpn. J. Appl. Phys. Part 1 40, 5920 (2001).
[CrossRef]

Opt. Lett.

Phys. Rev. A

F. J. Lawrence, L. C. Botten, K. B. Dossou, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. A 80, 023826 (2009).
[CrossRef]

Other

P. Rabiei and A. F. J. Levi, in Proceedings of Conference on Lasers and Electro-Optics (Optical Society of America, 2001), p. 590.

R. E. Collin, Foundations for Microwave Engineering, 2nd ed., IEEE Series on Electromagnetic Wave Theory (IEEE, 2001).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Constant characteristic-impedance contours and constant electric-length contours corresponding to a square-lattice photonic crystal of length l = a y with circular air holes of radius r a and an aspect ratio of a y a .

Fig. 2
Fig. 2

E-polarized reflection of a photonic crystal structure for four different cases: a two-section binomial transformer designed by using the proposed characteristic-impedance (solid curve), a two-section binomial trans former designed by using the impedance definitions of [6, 7] (dotted and dashed curves, respectively), and no matching stages (dashed–dotted curve).

Fig. 3
Fig. 3

E-polarized reflection of the semi-infinite photonic crystal analyzed in Fig. 2 of [4]; the original two-stage matching layer presented in [4] (solid curve), the redesign of the original matching stage in [4] by using the here proposed scalar impedance (dotted curve), and a two-stage binomial transformer (dashed–dotted curve).

Equations (1)

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Z in = Z c Z L + j Z c tan ( β l ) Z c + j Z L tan ( β l ) .

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