Abstract

The direction of propagation followed by a monochromatic beam in a periodic structure is generally deduced from the isofrequency diagram, which is related to the group velocity. However, the group velocity is the derivative of ω with respect to the wavenumber, while the behavior of the beam should depend on ω only. In the subwavelength regime, a method for choosing the relevant branch of the isofrequency diagram and relying on the behavior of the system at ω only is described.

© 2008 Optical Society of America

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References

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  1. A. Bers, Am. J. Phys. 68, 482 (2000).
    [CrossRef]
  2. F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq, Foundations of Photonic Crystal Fibers (Imperial College Press, 2005).
    [CrossRef]
  3. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2005).
  4. D. Felbacq, B. Guizal, and F. Zolla, J. Opt. A Pure Appl. Opt. 2, L30 (2000).
    [CrossRef]
  5. T. Matsumoto, K. S. Eom, and T. Baba, Opt. Lett. 31, 2786 (2006).
    [CrossRef] [PubMed]
  6. M. Notomi, Phys. Rev. B 62, 10696 (2000).
    [CrossRef]
  7. P. Yeh, Optical Waves in Layered Media (Wiley, 2005).
  8. D. Felbacq, B. Guizal, and F. Zolla, Opt. Commun. 152, 119 (1998).
    [CrossRef]
  9. D. Felbacq and R. Smaâli, Phys. Rev. Lett. 92, 193902 (2004).
    [CrossRef] [PubMed]
  10. D. Felbacq and F. Zolla, Wave Motion 42, 75 (2005).
    [CrossRef]
  11. B. Guizal, D. Felbacq, and R. Smaâli, arXiv.org e-print archive, arXiv:0801.3161, January 21, 2008, http://arXiv.org/abs/0801.3161 (submited to Phys. Rev. E).
  12. B. Guizal, D. Barchiesi, and D. Felbacq, J. Opt. Soc. Am. A 20, 2274 (2003).
    [CrossRef]
  13. R. Smaâli, D. Felbacq, and G. Granet, Physica E (Amsterdam) 18, 443 (2003).
    [CrossRef]

2006 (1)

2005 (1)

D. Felbacq and F. Zolla, Wave Motion 42, 75 (2005).
[CrossRef]

2004 (1)

D. Felbacq and R. Smaâli, Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef] [PubMed]

2003 (2)

B. Guizal, D. Barchiesi, and D. Felbacq, J. Opt. Soc. Am. A 20, 2274 (2003).
[CrossRef]

R. Smaâli, D. Felbacq, and G. Granet, Physica E (Amsterdam) 18, 443 (2003).
[CrossRef]

2000 (3)

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

A. Bers, Am. J. Phys. 68, 482 (2000).
[CrossRef]

D. Felbacq, B. Guizal, and F. Zolla, J. Opt. A Pure Appl. Opt. 2, L30 (2000).
[CrossRef]

1998 (1)

D. Felbacq, B. Guizal, and F. Zolla, Opt. Commun. 152, 119 (1998).
[CrossRef]

Baba, T.

Barchiesi, D.

Bers, A.

A. Bers, Am. J. Phys. 68, 482 (2000).
[CrossRef]

Eom, K. S.

Felbacq, D.

D. Felbacq and F. Zolla, Wave Motion 42, 75 (2005).
[CrossRef]

D. Felbacq and R. Smaâli, Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef] [PubMed]

B. Guizal, D. Barchiesi, and D. Felbacq, J. Opt. Soc. Am. A 20, 2274 (2003).
[CrossRef]

R. Smaâli, D. Felbacq, and G. Granet, Physica E (Amsterdam) 18, 443 (2003).
[CrossRef]

D. Felbacq, B. Guizal, and F. Zolla, J. Opt. A Pure Appl. Opt. 2, L30 (2000).
[CrossRef]

D. Felbacq, B. Guizal, and F. Zolla, Opt. Commun. 152, 119 (1998).
[CrossRef]

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq, Foundations of Photonic Crystal Fibers (Imperial College Press, 2005).
[CrossRef]

B. Guizal, D. Felbacq, and R. Smaâli, arXiv.org e-print archive, arXiv:0801.3161, January 21, 2008, http://arXiv.org/abs/0801.3161 (submited to Phys. Rev. E).

Granet, G.

R. Smaâli, D. Felbacq, and G. Granet, Physica E (Amsterdam) 18, 443 (2003).
[CrossRef]

Guenneau, S.

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq, Foundations of Photonic Crystal Fibers (Imperial College Press, 2005).
[CrossRef]

Guizal, B.

B. Guizal, D. Barchiesi, and D. Felbacq, J. Opt. Soc. Am. A 20, 2274 (2003).
[CrossRef]

D. Felbacq, B. Guizal, and F. Zolla, J. Opt. A Pure Appl. Opt. 2, L30 (2000).
[CrossRef]

D. Felbacq, B. Guizal, and F. Zolla, Opt. Commun. 152, 119 (1998).
[CrossRef]

B. Guizal, D. Felbacq, and R. Smaâli, arXiv.org e-print archive, arXiv:0801.3161, January 21, 2008, http://arXiv.org/abs/0801.3161 (submited to Phys. Rev. E).

Kuhlmey, B.

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq, Foundations of Photonic Crystal Fibers (Imperial College Press, 2005).
[CrossRef]

Matsumoto, T.

Nicolet, A.

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq, Foundations of Photonic Crystal Fibers (Imperial College Press, 2005).
[CrossRef]

Notomi, M.

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

Renversez, G.

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq, Foundations of Photonic Crystal Fibers (Imperial College Press, 2005).
[CrossRef]

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2005).

Smaâli, R.

D. Felbacq and R. Smaâli, Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef] [PubMed]

R. Smaâli, D. Felbacq, and G. Granet, Physica E (Amsterdam) 18, 443 (2003).
[CrossRef]

B. Guizal, D. Felbacq, and R. Smaâli, arXiv.org e-print archive, arXiv:0801.3161, January 21, 2008, http://arXiv.org/abs/0801.3161 (submited to Phys. Rev. E).

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 2005).

Zolla, F.

D. Felbacq and F. Zolla, Wave Motion 42, 75 (2005).
[CrossRef]

D. Felbacq, B. Guizal, and F. Zolla, J. Opt. A Pure Appl. Opt. 2, L30 (2000).
[CrossRef]

D. Felbacq, B. Guizal, and F. Zolla, Opt. Commun. 152, 119 (1998).
[CrossRef]

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq, Foundations of Photonic Crystal Fibers (Imperial College Press, 2005).
[CrossRef]

Am. J. Phys. (1)

A. Bers, Am. J. Phys. 68, 482 (2000).
[CrossRef]

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

D. Felbacq, B. Guizal, and F. Zolla, J. Opt. A Pure Appl. Opt. 2, L30 (2000).
[CrossRef]

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

Opt. Commun. (1)

D. Felbacq, B. Guizal, and F. Zolla, Opt. Commun. 152, 119 (1998).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

D. Felbacq and R. Smaâli, Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef] [PubMed]

Physica E (Amsterdam) (1)

R. Smaâli, D. Felbacq, and G. Granet, Physica E (Amsterdam) 18, 443 (2003).
[CrossRef]

Wave Motion (1)

D. Felbacq and F. Zolla, Wave Motion 42, 75 (2005).
[CrossRef]

Other (4)

B. Guizal, D. Felbacq, and R. Smaâli, arXiv.org e-print archive, arXiv:0801.3161, January 21, 2008, http://arXiv.org/abs/0801.3161 (submited to Phys. Rev. E).

P. Yeh, Optical Waves in Layered Media (Wiley, 2005).

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq, Foundations of Photonic Crystal Fibers (Imperial College Press, 2005).
[CrossRef]

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2005).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the studied structure. The inset shows the basic cell.

Fig. 2
Fig. 2

Sketch of the propagation of the beam inside the structure. The multiple scattering of rays is shown for the first two beams.

Fig. 3
Fig. 3

Renormalized Bloch diagram; the arrows represent the normals (direct orientation) to the curves.

Fig. 4
Fig. 4

Nonrenormalized Bloch diagram. The thin curve corresponds to λ = 3 d x , and the thick curve corresponds to λ = 2.9 d x . The arrows are oriented in the direction of the decreasing wavelength.

Equations (7)

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

G i = ( x u i ( x , 0 ) 2 d x ) ( u i ( x , 0 ) 2 d x ) ,
G t = ( x u t ( x , N d y ) 2 d x ) ( u t ( x , N d y ) 2 d x ) .
r N ( k x ) = ( γ 2 1 ) f γ 2 g 1 f , t N ( k x ) = γ ( 1 g 1 f ) γ 2 g 1 f ,
t N = ( 1 g 2 ) γ p = 0 + γ 2 p g 2 p .
u t ( x , N d y ) = A ( k x ) ( 1 g 2 ) e i N d y k y e i k x x d k x .
G t = i γ d γ d k x = N d y d k y d k x
T = [ cos ( k y h ) μ k y sin ( k y h ) k y μ sin ( k y h ) cos ( k y h ) ] .

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