Abstract

Light transmission through a slab of two-dimensional photonic crystal is known to present forbidden gaps. By a particular choice of he surface cut of the slab, it is possible to introduce modes guided in the vicinity of the crystal surface, which can have propagation constants lying inside the forbidden gap. These modes can be excited using additional diffraction gratings positioned onto the surfaces. This resonant excitation introduces defects in the gap that can lead to a narrow-band transmission with a 100% maximum. By working near normal incidence, it is possible to use the flattening of the mode dispersion curve near the Bragg cell boundaries and to reduce the requirements for beam parallelism, while preserving the strong spectral selectivity.

© 2005 Optical Society of America

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References

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  1. J. Joannopoulos, R. Meade, and J. Winn, Photonic crystals: Molding the flow of light, Princeton University Press,1995
  2. K.M. Ho, C.T. Chan, and C.M. Soukoulis, “Existence of photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990)
    [Crossref] [PubMed]
  3. E. Popov, B. Bozhkov, and M. Neviére, “Almost perfect blazing by photonic crystal rod gratings,” Appl. Opt. 40, 2417–2422 (2001)
    [Crossref]
  4. D. Maystre. “Photonic crystal diffraction gratings,” Opt. Express 8, 290–216 (2001)
    [Crossref]
  5. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, R10961 (1991)
    [Crossref]
  6. F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112 (1999)
    [Crossref]
  7. L. Mashev and E. Popov, “Zero Order Anomaly of Dielectric Coated Grating,” Opt. Commun. 55, 377–380 (1985)
    [Crossref]
  8. E. Popov, L. Mashev, and D. Maystr, “Theoretical Study of the Anomalies of Coated Dielectric Gratings,” Opt. Acta 33, 607 (1986)
    [Crossref]
  9. S. S. Wang, R. Magnusson, J. S. Bagby, and M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990)
    [Crossref]
  10. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993)
    [Crossref] [PubMed]
  11. A. Sentenac and A.-L. Fehrembach, “Angular tolerant resonant grating filtes under oblique incidence,” J. Opt. Soc. Am. A 22, 475–480 (2005)
    [Crossref]
  12. A.-L. Fehrembach and A. Sentenac , “Unpolarized narrow-band filtering with resonant gratings,” Appl. Phys. Lett. 86, 121105 (2005)
    [Crossref]
  13. M. Nevière and E. Popov; Light Propagation in Periodic Media, Marcel Dekker, New York,2003
  14. D. Maystre, “General study of grating anomalies from electromagnetic surface modes,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (John Wiley,1982), ch.17
  15. A. Hessel and A.A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4, 1275–1297 (1965)
    [Crossref]
  16. E. Popov and B. Bozhkov, “Corrugated waveguides as resonance optical filters - advantages and limitations,” J. Opt. Soc. Am. A 18, 1758–1764 (2001)
    [Crossref]

2005 (2)

A. Sentenac and A.-L. Fehrembach, “Angular tolerant resonant grating filtes under oblique incidence,” J. Opt. Soc. Am. A 22, 475–480 (2005)
[Crossref]

A.-L. Fehrembach and A. Sentenac , “Unpolarized narrow-band filtering with resonant gratings,” Appl. Phys. Lett. 86, 121105 (2005)
[Crossref]

2001 (3)

1999 (1)

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112 (1999)
[Crossref]

1993 (1)

1991 (1)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, R10961 (1991)
[Crossref]

1990 (2)

S. S. Wang, R. Magnusson, J. S. Bagby, and M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990)
[Crossref]

K.M. Ho, C.T. Chan, and C.M. Soukoulis, “Existence of photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990)
[Crossref] [PubMed]

1986 (1)

E. Popov, L. Mashev, and D. Maystr, “Theoretical Study of the Anomalies of Coated Dielectric Gratings,” Opt. Acta 33, 607 (1986)
[Crossref]

1985 (1)

L. Mashev and E. Popov, “Zero Order Anomaly of Dielectric Coated Grating,” Opt. Commun. 55, 377–380 (1985)
[Crossref]

1965 (1)

Bagby, J. S.

Bozhkov, B.

Brommer, K. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, R10961 (1991)
[Crossref]

Chan, C.T.

K.M. Ho, C.T. Chan, and C.M. Soukoulis, “Existence of photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990)
[Crossref] [PubMed]

Fehrembach, A.-L.

A.-L. Fehrembach and A. Sentenac , “Unpolarized narrow-band filtering with resonant gratings,” Appl. Phys. Lett. 86, 121105 (2005)
[Crossref]

A. Sentenac and A.-L. Fehrembach, “Angular tolerant resonant grating filtes under oblique incidence,” J. Opt. Soc. Am. A 22, 475–480 (2005)
[Crossref]

Halevi, P.

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112 (1999)
[Crossref]

Hessel, A.

Ho, K.M.

K.M. Ho, C.T. Chan, and C.M. Soukoulis, “Existence of photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990)
[Crossref] [PubMed]

Joannopoulos, J.

J. Joannopoulos, R. Meade, and J. Winn, Photonic crystals: Molding the flow of light, Princeton University Press,1995

Joannopoulos, J. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, R10961 (1991)
[Crossref]

Magnusson, R.

Mashev, L.

E. Popov, L. Mashev, and D. Maystr, “Theoretical Study of the Anomalies of Coated Dielectric Gratings,” Opt. Acta 33, 607 (1986)
[Crossref]

L. Mashev and E. Popov, “Zero Order Anomaly of Dielectric Coated Grating,” Opt. Commun. 55, 377–380 (1985)
[Crossref]

Maystr, D.

E. Popov, L. Mashev, and D. Maystr, “Theoretical Study of the Anomalies of Coated Dielectric Gratings,” Opt. Acta 33, 607 (1986)
[Crossref]

Maystre, D.

D. Maystre. “Photonic crystal diffraction gratings,” Opt. Express 8, 290–216 (2001)
[Crossref]

D. Maystre, “General study of grating anomalies from electromagnetic surface modes,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (John Wiley,1982), ch.17

Meade, R.

J. Joannopoulos, R. Meade, and J. Winn, Photonic crystals: Molding the flow of light, Princeton University Press,1995

Meade, R. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, R10961 (1991)
[Crossref]

Moharam, M. G.

Neviére, M.

Nevière, M.

M. Nevière and E. Popov; Light Propagation in Periodic Media, Marcel Dekker, New York,2003

Oliner, A.A.

Popov, E.

E. Popov, B. Bozhkov, and M. Neviére, “Almost perfect blazing by photonic crystal rod gratings,” Appl. Opt. 40, 2417–2422 (2001)
[Crossref]

E. Popov and B. Bozhkov, “Corrugated waveguides as resonance optical filters - advantages and limitations,” J. Opt. Soc. Am. A 18, 1758–1764 (2001)
[Crossref]

E. Popov, L. Mashev, and D. Maystr, “Theoretical Study of the Anomalies of Coated Dielectric Gratings,” Opt. Acta 33, 607 (1986)
[Crossref]

L. Mashev and E. Popov, “Zero Order Anomaly of Dielectric Coated Grating,” Opt. Commun. 55, 377–380 (1985)
[Crossref]

M. Nevière and E. Popov; Light Propagation in Periodic Media, Marcel Dekker, New York,2003

Ramos-Mendieta, F.

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112 (1999)
[Crossref]

Rappe, A. M.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, R10961 (1991)
[Crossref]

Sentenac, A.

A.-L. Fehrembach and A. Sentenac , “Unpolarized narrow-band filtering with resonant gratings,” Appl. Phys. Lett. 86, 121105 (2005)
[Crossref]

A. Sentenac and A.-L. Fehrembach, “Angular tolerant resonant grating filtes under oblique incidence,” J. Opt. Soc. Am. A 22, 475–480 (2005)
[Crossref]

Soukoulis, C.M.

K.M. Ho, C.T. Chan, and C.M. Soukoulis, “Existence of photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990)
[Crossref] [PubMed]

Wang, S. S.

Winn, J.

J. Joannopoulos, R. Meade, and J. Winn, Photonic crystals: Molding the flow of light, Princeton University Press,1995

Appl. Opt. (3)

Appl. Phys. Lett. (1)

A.-L. Fehrembach and A. Sentenac , “Unpolarized narrow-band filtering with resonant gratings,” Appl. Phys. Lett. 86, 121105 (2005)
[Crossref]

J. Opt. Soc. Am. A (3)

Opt. Acta (1)

E. Popov, L. Mashev, and D. Maystr, “Theoretical Study of the Anomalies of Coated Dielectric Gratings,” Opt. Acta 33, 607 (1986)
[Crossref]

Opt. Commun. (1)

L. Mashev and E. Popov, “Zero Order Anomaly of Dielectric Coated Grating,” Opt. Commun. 55, 377–380 (1985)
[Crossref]

Opt. Express (1)

Phys. Rev. B (2)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, R10961 (1991)
[Crossref]

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112 (1999)
[Crossref]

Phys. Rev. Lett. (1)

K.M. Ho, C.T. Chan, and C.M. Soukoulis, “Existence of photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990)
[Crossref] [PubMed]

Other (3)

J. Joannopoulos, R. Meade, and J. Winn, Photonic crystals: Molding the flow of light, Princeton University Press,1995

M. Nevière and E. Popov; Light Propagation in Periodic Media, Marcel Dekker, New York,2003

D. Maystre, “General study of grating anomalies from electromagnetic surface modes,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (John Wiley,1982), ch.17

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Figures (7)

Fig. 1.
Fig. 1.

Schematic representation of a two-dimensional photonic crystal slab and its optogeometrical parameters

Fig. 2.
Fig. 2.

The band-gap structure of the photonic crystal presented in Fig. 1 and the dispersion curve of the guided surface-induced TM mode. The parameter kx is the normalized x-component of the wavevector k⃗: k x = 2 π d k · x = λ d sin θ (for θ, see Fig. 3). The thin ligh presents the light cone and the thick line, the mode dispersion curve

Fig. 3.
Fig. 3.

Schematic representation of the in-coupling gratings having twice the period D = 2d and thickness t, made of the same dielectric material as the crystal. Incident wave comes from the left and generates a reflected and a transmitted waves

Fig. 4.
Fig. 4.

Resonances in the spectral (a) and angular (b) responses of the system presented in Fig. 3 with t/d = 0.002 and working in non-normal incidence. The wavelength and angular parameters are indicated in the figure.

Fig. 5.
Fig. 5.

As in Fig. 4 but working close to normal incidence. The thin curve in Fig. 5(a) corresponds to different thicknesses of the supplementary gratings in Fig. 3, the left grating is 0.002d thick, while the right grating is twice thinner.

Fig. 6.
Fig. 6.

As in Fig. 5 but with thicker supplementary gratings, t/d = 0.0048 instead of 0.002

Fig. 7.
Fig. 7.

As in Fig. 6(b), but for different in-coupling grating parameters

Equations (3)

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sin θ + n λ D = α g
α g = k g k 0 .
A n = c n α α n z α α p

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