Abstract

Some particular geometries are discussed in which the transmission spectrum is different for light traveling from right to left or from left to right. The conditions that allow this transmission asymmetry are discussed.

© 2007 Optical Society of America

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References

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  1. E. Yablonovich, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2061 (1987).
    [Crossref]
  2. J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).
  3. C. M. Soukoulis, Photonic Band Gap Materials (Kluwer Academic, 1996).
  4. Ph. Russell, T. Birks, and F. D. Lloyd-Lucas, Photonic Block Waves and Photonic Band Gaps (Plenum, 1995).
  5. J. Rarity and C. Weisbuch, Microcavities and Photonic Band-Gaps: Physics and Applications, NATO Advanced Study Institute Series E: Applied Sciences (Kluwer, 1996) Vol. 324.
  6. A. Scherer, T. Doll, E. Yablonovitch, H. O. Everitt, and J. A. Higgins, eds., "Special section on electromagnetic crystal structures, design, synthesis, and applications," J. Lightwave Technol. 17, 1928-2207 (1999).
    [Crossref]
  7. M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Effect of the magnetic permeability on photonic band gaps," Phys. Rev. B 56, 959-962 (1997).
    [Crossref]
  8. C.-S. Kee, J.-E. Kim, H. Y. Park, I. Park, and H. Lim, "Two-dimensional tunable magnetic photonic crystals," Phys. Rev. B 61, 15523-15525 (2000).
    [Crossref]
  9. M. Inoue and T. Fujii, "A theoretical analysis of magneto-optical Faraday effect of YIG films with random multilayer structures," J. Appl. Phys. 81, 5659-5661 (1997).
    [Crossref]
  10. M. Inoue, K. Arai, and T. Fujii, "Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers," J. Appl. Phys. 83, 6768-6770 (1997).
    [Crossref]
  11. I. Abduhalim, "Analytic propagation matrix method for anisotropic magneto-optic layered media," J. Opt. A 2, 557-564 (2000).
    [Crossref]
  12. R. Fuchs, "Wave propagation in a magnetoelectric medium," Philos. Mag. 11, 647-649 (1965).
    [Crossref]
  13. A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
    [Crossref]
  14. V. V. Konotop and V. Kuzmiak, "Nonreciprocal frequency doubler of electromagnetic waves based on a photonic crystal," Phys. Rev. B 66, 235208 (2002).
    [Crossref]
  15. H. Dammann and E. Klotz, "Coherent optical generation and inspection of two-dimensional periodic structure," J. Mod. Opt. 24, 505-515 (1977).

2002 (1)

V. V. Konotop and V. Kuzmiak, "Nonreciprocal frequency doubler of electromagnetic waves based on a photonic crystal," Phys. Rev. B 66, 235208 (2002).
[Crossref]

2001 (1)

A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
[Crossref]

2000 (2)

I. Abduhalim, "Analytic propagation matrix method for anisotropic magneto-optic layered media," J. Opt. A 2, 557-564 (2000).
[Crossref]

C.-S. Kee, J.-E. Kim, H. Y. Park, I. Park, and H. Lim, "Two-dimensional tunable magnetic photonic crystals," Phys. Rev. B 61, 15523-15525 (2000).
[Crossref]

1999 (1)

A. Scherer, T. Doll, E. Yablonovitch, H. O. Everitt, and J. A. Higgins, eds., "Special section on electromagnetic crystal structures, design, synthesis, and applications," J. Lightwave Technol. 17, 1928-2207 (1999).
[Crossref]

1997 (3)

M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Effect of the magnetic permeability on photonic band gaps," Phys. Rev. B 56, 959-962 (1997).
[Crossref]

M. Inoue and T. Fujii, "A theoretical analysis of magneto-optical Faraday effect of YIG films with random multilayer structures," J. Appl. Phys. 81, 5659-5661 (1997).
[Crossref]

M. Inoue, K. Arai, and T. Fujii, "Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers," J. Appl. Phys. 83, 6768-6770 (1997).
[Crossref]

1987 (1)

E. Yablonovich, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2061 (1987).
[Crossref]

1977 (1)

H. Dammann and E. Klotz, "Coherent optical generation and inspection of two-dimensional periodic structure," J. Mod. Opt. 24, 505-515 (1977).

1965 (1)

R. Fuchs, "Wave propagation in a magnetoelectric medium," Philos. Mag. 11, 647-649 (1965).
[Crossref]

Abduhalim, I.

I. Abduhalim, "Analytic propagation matrix method for anisotropic magneto-optic layered media," J. Opt. A 2, 557-564 (2000).
[Crossref]

Arai, K.

M. Inoue, K. Arai, and T. Fujii, "Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers," J. Appl. Phys. 83, 6768-6770 (1997).
[Crossref]

Birks, T.

Ph. Russell, T. Birks, and F. D. Lloyd-Lucas, Photonic Block Waves and Photonic Band Gaps (Plenum, 1995).

Biswas, R.

M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Effect of the magnetic permeability on photonic band gaps," Phys. Rev. B 56, 959-962 (1997).
[Crossref]

Dammann, H.

H. Dammann and E. Klotz, "Coherent optical generation and inspection of two-dimensional periodic structure," J. Mod. Opt. 24, 505-515 (1977).

Doll, T.

A. Scherer, T. Doll, E. Yablonovitch, H. O. Everitt, and J. A. Higgins, eds., "Special section on electromagnetic crystal structures, design, synthesis, and applications," J. Lightwave Technol. 17, 1928-2207 (1999).
[Crossref]

Everitt, H. O.

A. Scherer, T. Doll, E. Yablonovitch, H. O. Everitt, and J. A. Higgins, eds., "Special section on electromagnetic crystal structures, design, synthesis, and applications," J. Lightwave Technol. 17, 1928-2207 (1999).
[Crossref]

Figotin, A.

A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
[Crossref]

Fuchs, R.

R. Fuchs, "Wave propagation in a magnetoelectric medium," Philos. Mag. 11, 647-649 (1965).
[Crossref]

Fujii, T.

M. Inoue, K. Arai, and T. Fujii, "Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers," J. Appl. Phys. 83, 6768-6770 (1997).
[Crossref]

M. Inoue and T. Fujii, "A theoretical analysis of magneto-optical Faraday effect of YIG films with random multilayer structures," J. Appl. Phys. 81, 5659-5661 (1997).
[Crossref]

Higgins, J. A.

A. Scherer, T. Doll, E. Yablonovitch, H. O. Everitt, and J. A. Higgins, eds., "Special section on electromagnetic crystal structures, design, synthesis, and applications," J. Lightwave Technol. 17, 1928-2207 (1999).
[Crossref]

Ho, K. M.

M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Effect of the magnetic permeability on photonic band gaps," Phys. Rev. B 56, 959-962 (1997).
[Crossref]

Inoue, M.

M. Inoue, K. Arai, and T. Fujii, "Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers," J. Appl. Phys. 83, 6768-6770 (1997).
[Crossref]

M. Inoue and T. Fujii, "A theoretical analysis of magneto-optical Faraday effect of YIG films with random multilayer structures," J. Appl. Phys. 81, 5659-5661 (1997).
[Crossref]

Joannopoulos, J.

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Kee, C.-S.

C.-S. Kee, J.-E. Kim, H. Y. Park, I. Park, and H. Lim, "Two-dimensional tunable magnetic photonic crystals," Phys. Rev. B 61, 15523-15525 (2000).
[Crossref]

Kim, J.-E.

C.-S. Kee, J.-E. Kim, H. Y. Park, I. Park, and H. Lim, "Two-dimensional tunable magnetic photonic crystals," Phys. Rev. B 61, 15523-15525 (2000).
[Crossref]

Klotz, E.

H. Dammann and E. Klotz, "Coherent optical generation and inspection of two-dimensional periodic structure," J. Mod. Opt. 24, 505-515 (1977).

Konotop, V. V.

V. V. Konotop and V. Kuzmiak, "Nonreciprocal frequency doubler of electromagnetic waves based on a photonic crystal," Phys. Rev. B 66, 235208 (2002).
[Crossref]

Kuzmiak, V.

V. V. Konotop and V. Kuzmiak, "Nonreciprocal frequency doubler of electromagnetic waves based on a photonic crystal," Phys. Rev. B 66, 235208 (2002).
[Crossref]

Lim, H.

C.-S. Kee, J.-E. Kim, H. Y. Park, I. Park, and H. Lim, "Two-dimensional tunable magnetic photonic crystals," Phys. Rev. B 61, 15523-15525 (2000).
[Crossref]

Lloyd-Lucas, F. D.

Ph. Russell, T. Birks, and F. D. Lloyd-Lucas, Photonic Block Waves and Photonic Band Gaps (Plenum, 1995).

Meade, R.

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Park, H. Y.

C.-S. Kee, J.-E. Kim, H. Y. Park, I. Park, and H. Lim, "Two-dimensional tunable magnetic photonic crystals," Phys. Rev. B 61, 15523-15525 (2000).
[Crossref]

Park, I.

C.-S. Kee, J.-E. Kim, H. Y. Park, I. Park, and H. Lim, "Two-dimensional tunable magnetic photonic crystals," Phys. Rev. B 61, 15523-15525 (2000).
[Crossref]

Rarity, J.

J. Rarity and C. Weisbuch, Microcavities and Photonic Band-Gaps: Physics and Applications, NATO Advanced Study Institute Series E: Applied Sciences (Kluwer, 1996) Vol. 324.

Russell, Ph.

Ph. Russell, T. Birks, and F. D. Lloyd-Lucas, Photonic Block Waves and Photonic Band Gaps (Plenum, 1995).

Scherer, A.

A. Scherer, T. Doll, E. Yablonovitch, H. O. Everitt, and J. A. Higgins, eds., "Special section on electromagnetic crystal structures, design, synthesis, and applications," J. Lightwave Technol. 17, 1928-2207 (1999).
[Crossref]

Sigalas, M. M.

M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Effect of the magnetic permeability on photonic band gaps," Phys. Rev. B 56, 959-962 (1997).
[Crossref]

Soukoulis, C. M.

M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Effect of the magnetic permeability on photonic band gaps," Phys. Rev. B 56, 959-962 (1997).
[Crossref]

C. M. Soukoulis, Photonic Band Gap Materials (Kluwer Academic, 1996).

Vitebsky, I.

A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
[Crossref]

Weisbuch, C.

J. Rarity and C. Weisbuch, Microcavities and Photonic Band-Gaps: Physics and Applications, NATO Advanced Study Institute Series E: Applied Sciences (Kluwer, 1996) Vol. 324.

Winn, J.

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Yablonovich, E.

E. Yablonovich, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2061 (1987).
[Crossref]

Yablonovitch, E.

A. Scherer, T. Doll, E. Yablonovitch, H. O. Everitt, and J. A. Higgins, eds., "Special section on electromagnetic crystal structures, design, synthesis, and applications," J. Lightwave Technol. 17, 1928-2207 (1999).
[Crossref]

J. Appl. Phys. (2)

M. Inoue and T. Fujii, "A theoretical analysis of magneto-optical Faraday effect of YIG films with random multilayer structures," J. Appl. Phys. 81, 5659-5661 (1997).
[Crossref]

M. Inoue, K. Arai, and T. Fujii, "Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers," J. Appl. Phys. 83, 6768-6770 (1997).
[Crossref]

J. Lightwave Technol. (1)

A. Scherer, T. Doll, E. Yablonovitch, H. O. Everitt, and J. A. Higgins, eds., "Special section on electromagnetic crystal structures, design, synthesis, and applications," J. Lightwave Technol. 17, 1928-2207 (1999).
[Crossref]

J. Mod. Opt. (1)

H. Dammann and E. Klotz, "Coherent optical generation and inspection of two-dimensional periodic structure," J. Mod. Opt. 24, 505-515 (1977).

J. Opt. A (1)

I. Abduhalim, "Analytic propagation matrix method for anisotropic magneto-optic layered media," J. Opt. A 2, 557-564 (2000).
[Crossref]

Philos. Mag. (1)

R. Fuchs, "Wave propagation in a magnetoelectric medium," Philos. Mag. 11, 647-649 (1965).
[Crossref]

Phys. Rev. B (3)

V. V. Konotop and V. Kuzmiak, "Nonreciprocal frequency doubler of electromagnetic waves based on a photonic crystal," Phys. Rev. B 66, 235208 (2002).
[Crossref]

M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Effect of the magnetic permeability on photonic band gaps," Phys. Rev. B 56, 959-962 (1997).
[Crossref]

C.-S. Kee, J.-E. Kim, H. Y. Park, I. Park, and H. Lim, "Two-dimensional tunable magnetic photonic crystals," Phys. Rev. B 61, 15523-15525 (2000).
[Crossref]

Phys. Rev. E (1)

A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
[Crossref]

Phys. Rev. Lett. (1)

E. Yablonovich, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2061 (1987).
[Crossref]

Other (4)

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

C. M. Soukoulis, Photonic Band Gap Materials (Kluwer Academic, 1996).

Ph. Russell, T. Birks, and F. D. Lloyd-Lucas, Photonic Block Waves and Photonic Band Gaps (Plenum, 1995).

J. Rarity and C. Weisbuch, Microcavities and Photonic Band-Gaps: Physics and Applications, NATO Advanced Study Institute Series E: Applied Sciences (Kluwer, 1996) Vol. 324.

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Figures (11)

Fig. 1
Fig. 1

Representation of a simple 2D system with one input plane wave and three plane waves at the output.

Fig. 2
Fig. 2

System built by a one-dimensional layer coupled to one grating. Two equal semispaces are at the sides. The input is from left to right.

Fig. 3
Fig. 3

System built by a one-dimensional layer coupled to one grating. Two equal semispaces are at the sides. The input is from right to left.

Fig. 4
Fig. 4

Two-dimensional system with a 1D layer connected with a grating.

Fig. 5
Fig. 5

Comparison between the two average power spectra; the first one (dashed curve) refers to a plane wave traveling from right to left, the second one (solid curve) refers to a plane wave traveling from left to right.

Fig. 6
Fig. 6

Comparison between the transmissions of the zero order (dashed curve), with that of the +1 order obtained by incidence from right (dotted curve) and from left (solid curve).

Fig. 7
Fig. 7

Two-dimensional system where the 1D layers are needed to generate a gap while the 2D layers generate the asymmetric behavior for the output field.

Fig. 8
Fig. 8

Average power spectrum for a plane wave that comes from the right.

Fig. 9
Fig. 9

Average power spectrum for a plane wave that comes from the left (note the change of scale).

Fig. 10
Fig. 10

Comparison between the two average power spectra; the first one (dashed curve) refers to a plane wave traveling from right to left, the second one (solid curve) refers to a plane wave traveling from left to right.

Fig. 11
Fig. 11

Comparison between the transmissions of the zeroth order (dashed curve), with that of the +1 order obtained by incidence from right (dotted curve) and from left (solid curve).

Equations (13)

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τ ( x ) = m = + τ m e 2 π i m ( x d ) , τ m = 1 d ( 0 ) ( d ) τ ( x ) e 2 π i m ( x d ) d x ,
E u ( x , z ) = m = τ m e i ( k m x x + t m z ) ,
E r ( x , z ) = m = τ m e i ( k m x x + r m z ) ,
t m = n 0 2 k 0 2 k m x 2 ,
r m = n i 2 k 0 2 k m x 2 ,
n 0 2 k 0 2 k m x 2 0 .
m n 0 d λ .
m n 0 d λ < m + 1 .
E u ( x , z ) = m = τ m ( k x ) exp { i [ ( m k d + k x ) x + n 0 2 k 0 2 ( m k d + k x ) 2 z ] } E i ( k x ) d k x .
E u ( x , z ) = τ ( k x , x , z ) E i ( k x ) e i k x x d k x ,
τ ( k x , x , z ) = m = τ m ( k x ) exp { i [ m k d x + n 0 2 k 0 2 ( m k d + k x ) 2 z ] } .
1 < n 0 d λ < 2 .
0 < n 1 D d λ < 1 .

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