Abstract

The volume and surface waves supported by a 2D PC slab with termination condition are systematically studied using the rigorous mode-matching method incorporating the Floquet’s solutions. It is interesting to observe that the surface waves are caused by the perturbation of the PC-slab modes from the imposed termination condition, enabling the transition from volume wave to surface wave. The perturbed dispersion curves and electric field strength distribution over the structure are drawn together with the unperturbed ones (without termination condition) to identify the type of bound waves.

© 2007 Optical Society of America

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References

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  1. V. G. Veselago, “The electrodynamics of substance with simultaneously negative values of ε and μ,” Sov. Phy. Usp. 10, 509–514 (1968).
    [Crossref]
  2. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
    [Crossref] [PubMed]
  3. X. S. Rao and C. K. Ong, “Amplification of evanescent waves in a lossy left-handed material slab,” Phys. Rev. B 68, 113103 (2003).
    [Crossref]
  4. X. S. Rao and C. K. Ong, “Subwavelength imaging by a left-handed material superlens,” Phys. Rev. B 68, 067601 (2003).
    [Crossref]
  5. Chiyan Luo, Steven G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystal,” Phys. Rev. B 68, 045115 (2003).
    [Crossref]
  6. Sanshui Xiao, Min Qiu, Zhichao Ruan, and Sailing He, “Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction,” Appl. Phys. Lett. 85, 4269 (2004).
    [Crossref]
  7. Esteban Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
    [Crossref]
  8. P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly Directional Emission from Photonic Crystal Waveguides of Subwavelength Width,” Phys. Rev. Lett. 92, 113909 (2004).
    [Crossref]
  9. X. Wang and K. Kempa, “Effects of disorder on subwavelength lensing in two-dimensional photonic crystal slabs,” Phys. Rev. B 71, 085101 (2005).
    [Crossref]
  10. J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant Transmission of Light Through Finite Chains of Subwavelength Holes in a Metallic Film,” Phys. Rev. Lett. 93, 227401 (2004).
    [Crossref] [PubMed]
  11. R. Moussa, Th. Koschny, and C. M. Soukoulis, “Excitation of surface waves in a photonic crystal with negative refraction: The role of surface termination,” Phys. Rev. B 74, 115111 (2006).
    [Crossref]
  12. S. Enoch, G. Tayeb, and B. Gralak, “The richness of the dispersion relation of electromagnetic bandgap materials,” IEEE Trans. on Antennas and Propagation 51, 2659 (2003).
    [Crossref]
  13. T. Tamir and S. Zhang, “Modal Transmission-Line Theory of Multilayered Grating Structures,” IEEE J. Lightwave Technol. 14, 914 (1996).
    [Crossref]
  14. Ruey Bing Hwang and Cherng Chyi Hsiao, “Frequency-selective transmission by a leaky parallel-plate-like waveguide,” IEEE Trans. on Antennas and Propagation 54, 121 (2006).
    [Crossref]
  15. J. D, Joannopolous, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding theFlow of Light, (Princeton, NJ: Princeton University Press, 1995).

2006 (2)

R. Moussa, Th. Koschny, and C. M. Soukoulis, “Excitation of surface waves in a photonic crystal with negative refraction: The role of surface termination,” Phys. Rev. B 74, 115111 (2006).
[Crossref]

Ruey Bing Hwang and Cherng Chyi Hsiao, “Frequency-selective transmission by a leaky parallel-plate-like waveguide,” IEEE Trans. on Antennas and Propagation 54, 121 (2006).
[Crossref]

2005 (1)

X. Wang and K. Kempa, “Effects of disorder on subwavelength lensing in two-dimensional photonic crystal slabs,” Phys. Rev. B 71, 085101 (2005).
[Crossref]

2004 (4)

J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant Transmission of Light Through Finite Chains of Subwavelength Holes in a Metallic Film,” Phys. Rev. Lett. 93, 227401 (2004).
[Crossref] [PubMed]

Sanshui Xiao, Min Qiu, Zhichao Ruan, and Sailing He, “Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction,” Appl. Phys. Lett. 85, 4269 (2004).
[Crossref]

Esteban Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[Crossref]

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly Directional Emission from Photonic Crystal Waveguides of Subwavelength Width,” Phys. Rev. Lett. 92, 113909 (2004).
[Crossref]

2003 (4)

X. S. Rao and C. K. Ong, “Amplification of evanescent waves in a lossy left-handed material slab,” Phys. Rev. B 68, 113103 (2003).
[Crossref]

X. S. Rao and C. K. Ong, “Subwavelength imaging by a left-handed material superlens,” Phys. Rev. B 68, 067601 (2003).
[Crossref]

Chiyan Luo, Steven G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystal,” Phys. Rev. B 68, 045115 (2003).
[Crossref]

S. Enoch, G. Tayeb, and B. Gralak, “The richness of the dispersion relation of electromagnetic bandgap materials,” IEEE Trans. on Antennas and Propagation 51, 2659 (2003).
[Crossref]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[Crossref] [PubMed]

1996 (1)

T. Tamir and S. Zhang, “Modal Transmission-Line Theory of Multilayered Grating Structures,” IEEE J. Lightwave Technol. 14, 914 (1996).
[Crossref]

1968 (1)

V. G. Veselago, “The electrodynamics of substance with simultaneously negative values of ε and μ,” Sov. Phy. Usp. 10, 509–514 (1968).
[Crossref]

Agio, M.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly Directional Emission from Photonic Crystal Waveguides of Subwavelength Width,” Phys. Rev. Lett. 92, 113909 (2004).
[Crossref]

Birner, A.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly Directional Emission from Photonic Crystal Waveguides of Subwavelength Width,” Phys. Rev. Lett. 92, 113909 (2004).
[Crossref]

Bravo-Abad, J.

J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant Transmission of Light Through Finite Chains of Subwavelength Holes in a Metallic Film,” Phys. Rev. Lett. 93, 227401 (2004).
[Crossref] [PubMed]

Enoch, S.

S. Enoch, G. Tayeb, and B. Gralak, “The richness of the dispersion relation of electromagnetic bandgap materials,” IEEE Trans. on Antennas and Propagation 51, 2659 (2003).
[Crossref]

Garcia-Vidal, F. J.

Esteban Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[Crossref]

García-Vidal, F. J.

J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant Transmission of Light Through Finite Chains of Subwavelength Holes in a Metallic Film,” Phys. Rev. Lett. 93, 227401 (2004).
[Crossref] [PubMed]

Gösele, U.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly Directional Emission from Photonic Crystal Waveguides of Subwavelength Width,” Phys. Rev. Lett. 92, 113909 (2004).
[Crossref]

Gralak, B.

S. Enoch, G. Tayeb, and B. Gralak, “The richness of the dispersion relation of electromagnetic bandgap materials,” IEEE Trans. on Antennas and Propagation 51, 2659 (2003).
[Crossref]

He, Sailing

Sanshui Xiao, Min Qiu, Zhichao Ruan, and Sailing He, “Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction,” Appl. Phys. Lett. 85, 4269 (2004).
[Crossref]

Hsiao, Cherng Chyi

Ruey Bing Hwang and Cherng Chyi Hsiao, “Frequency-selective transmission by a leaky parallel-plate-like waveguide,” IEEE Trans. on Antennas and Propagation 54, 121 (2006).
[Crossref]

Hwang, Ruey Bing

Ruey Bing Hwang and Cherng Chyi Hsiao, “Frequency-selective transmission by a leaky parallel-plate-like waveguide,” IEEE Trans. on Antennas and Propagation 54, 121 (2006).
[Crossref]

Joannopolous, J. D,

J. D, Joannopolous, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding theFlow of Light, (Princeton, NJ: Princeton University Press, 1995).

Joannopoulos, J. D.

Chiyan Luo, Steven G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystal,” Phys. Rev. B 68, 045115 (2003).
[Crossref]

Johnson, Steven G.

Chiyan Luo, Steven G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystal,” Phys. Rev. B 68, 045115 (2003).
[Crossref]

Kempa, K.

X. Wang and K. Kempa, “Effects of disorder on subwavelength lensing in two-dimensional photonic crystal slabs,” Phys. Rev. B 71, 085101 (2005).
[Crossref]

Koschny, Th.

R. Moussa, Th. Koschny, and C. M. Soukoulis, “Excitation of surface waves in a photonic crystal with negative refraction: The role of surface termination,” Phys. Rev. B 74, 115111 (2006).
[Crossref]

Kramper, P.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly Directional Emission from Photonic Crystal Waveguides of Subwavelength Width,” Phys. Rev. Lett. 92, 113909 (2004).
[Crossref]

Luo, Chiyan

Chiyan Luo, Steven G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystal,” Phys. Rev. B 68, 045115 (2003).
[Crossref]

Martin-Moreno, L.

Esteban Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[Crossref]

Martín-Moreno, L.

J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant Transmission of Light Through Finite Chains of Subwavelength Holes in a Metallic Film,” Phys. Rev. Lett. 93, 227401 (2004).
[Crossref] [PubMed]

Meade, R. D.

J. D, Joannopolous, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding theFlow of Light, (Princeton, NJ: Princeton University Press, 1995).

Moreno, Esteban

Esteban Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[Crossref]

Moussa, R.

R. Moussa, Th. Koschny, and C. M. Soukoulis, “Excitation of surface waves in a photonic crystal with negative refraction: The role of surface termination,” Phys. Rev. B 74, 115111 (2006).
[Crossref]

Müller, F.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly Directional Emission from Photonic Crystal Waveguides of Subwavelength Width,” Phys. Rev. Lett. 92, 113909 (2004).
[Crossref]

Ong, C. K.

X. S. Rao and C. K. Ong, “Subwavelength imaging by a left-handed material superlens,” Phys. Rev. B 68, 067601 (2003).
[Crossref]

X. S. Rao and C. K. Ong, “Amplification of evanescent waves in a lossy left-handed material slab,” Phys. Rev. B 68, 113103 (2003).
[Crossref]

Pendry, J. B.

Chiyan Luo, Steven G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystal,” Phys. Rev. B 68, 045115 (2003).
[Crossref]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[Crossref] [PubMed]

Qiu, Min

Sanshui Xiao, Min Qiu, Zhichao Ruan, and Sailing He, “Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction,” Appl. Phys. Lett. 85, 4269 (2004).
[Crossref]

Rao, X. S.

X. S. Rao and C. K. Ong, “Amplification of evanescent waves in a lossy left-handed material slab,” Phys. Rev. B 68, 113103 (2003).
[Crossref]

X. S. Rao and C. K. Ong, “Subwavelength imaging by a left-handed material superlens,” Phys. Rev. B 68, 067601 (2003).
[Crossref]

Ruan, Zhichao

Sanshui Xiao, Min Qiu, Zhichao Ruan, and Sailing He, “Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction,” Appl. Phys. Lett. 85, 4269 (2004).
[Crossref]

Sandoghdar, V.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly Directional Emission from Photonic Crystal Waveguides of Subwavelength Width,” Phys. Rev. Lett. 92, 113909 (2004).
[Crossref]

Soukoulis, C. M.

R. Moussa, Th. Koschny, and C. M. Soukoulis, “Excitation of surface waves in a photonic crystal with negative refraction: The role of surface termination,” Phys. Rev. B 74, 115111 (2006).
[Crossref]

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly Directional Emission from Photonic Crystal Waveguides of Subwavelength Width,” Phys. Rev. Lett. 92, 113909 (2004).
[Crossref]

Tamir, T.

T. Tamir and S. Zhang, “Modal Transmission-Line Theory of Multilayered Grating Structures,” IEEE J. Lightwave Technol. 14, 914 (1996).
[Crossref]

Tayeb, G.

S. Enoch, G. Tayeb, and B. Gralak, “The richness of the dispersion relation of electromagnetic bandgap materials,” IEEE Trans. on Antennas and Propagation 51, 2659 (2003).
[Crossref]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substance with simultaneously negative values of ε and μ,” Sov. Phy. Usp. 10, 509–514 (1968).
[Crossref]

Wang, X.

X. Wang and K. Kempa, “Effects of disorder on subwavelength lensing in two-dimensional photonic crystal slabs,” Phys. Rev. B 71, 085101 (2005).
[Crossref]

Wehrspohn, R. B.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly Directional Emission from Photonic Crystal Waveguides of Subwavelength Width,” Phys. Rev. Lett. 92, 113909 (2004).
[Crossref]

Winn, J. N.

J. D, Joannopolous, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding theFlow of Light, (Princeton, NJ: Princeton University Press, 1995).

Xiao, Sanshui

Sanshui Xiao, Min Qiu, Zhichao Ruan, and Sailing He, “Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction,” Appl. Phys. Lett. 85, 4269 (2004).
[Crossref]

Zhang, S.

T. Tamir and S. Zhang, “Modal Transmission-Line Theory of Multilayered Grating Structures,” IEEE J. Lightwave Technol. 14, 914 (1996).
[Crossref]

Appl. Phys. Lett. (1)

Sanshui Xiao, Min Qiu, Zhichao Ruan, and Sailing He, “Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction,” Appl. Phys. Lett. 85, 4269 (2004).
[Crossref]

IEEE J. Lightwave Technol. (1)

T. Tamir and S. Zhang, “Modal Transmission-Line Theory of Multilayered Grating Structures,” IEEE J. Lightwave Technol. 14, 914 (1996).
[Crossref]

IEEE Trans. on Antennas and Propagation (2)

Ruey Bing Hwang and Cherng Chyi Hsiao, “Frequency-selective transmission by a leaky parallel-plate-like waveguide,” IEEE Trans. on Antennas and Propagation 54, 121 (2006).
[Crossref]

S. Enoch, G. Tayeb, and B. Gralak, “The richness of the dispersion relation of electromagnetic bandgap materials,” IEEE Trans. on Antennas and Propagation 51, 2659 (2003).
[Crossref]

Phys. Rev. B (6)

R. Moussa, Th. Koschny, and C. M. Soukoulis, “Excitation of surface waves in a photonic crystal with negative refraction: The role of surface termination,” Phys. Rev. B 74, 115111 (2006).
[Crossref]

Esteban Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[Crossref]

X. Wang and K. Kempa, “Effects of disorder on subwavelength lensing in two-dimensional photonic crystal slabs,” Phys. Rev. B 71, 085101 (2005).
[Crossref]

X. S. Rao and C. K. Ong, “Amplification of evanescent waves in a lossy left-handed material slab,” Phys. Rev. B 68, 113103 (2003).
[Crossref]

X. S. Rao and C. K. Ong, “Subwavelength imaging by a left-handed material superlens,” Phys. Rev. B 68, 067601 (2003).
[Crossref]

Chiyan Luo, Steven G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystal,” Phys. Rev. B 68, 045115 (2003).
[Crossref]

Phys. Rev. Lett. (3)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[Crossref] [PubMed]

J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant Transmission of Light Through Finite Chains of Subwavelength Holes in a Metallic Film,” Phys. Rev. Lett. 93, 227401 (2004).
[Crossref] [PubMed]

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly Directional Emission from Photonic Crystal Waveguides of Subwavelength Width,” Phys. Rev. Lett. 92, 113909 (2004).
[Crossref]

Sov. Phy. Usp. (1)

V. G. Veselago, “The electrodynamics of substance with simultaneously negative values of ε and μ,” Sov. Phy. Usp. 10, 509–514 (1968).
[Crossref]

Other (1)

J. D, Joannopolous, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding theFlow of Light, (Princeton, NJ: Princeton University Press, 1995).

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Figures (9)

Fig. 1.
Fig. 1.

Structure configuration: a 2D PBG structure with termination condition (left-hand side), a 2D PBG structure with defect in its central layer (right-hand side)

Fig. 2.
Fig. 2.

Dispersion relation of the 2D PBG structure with termination conditions; the black curves represent the dispersion relation of the case with open-circuit termination (h=0.01), and the red ones stand for the case without termination.

Fig. 3.
Fig. 3.

Distribution of the electric field strength along the y-direction at the normalized frequency 0.25.

Fig. 4.
Fig. 4.

Dispersion relation of the 2D PBG structure with termination conditions; the black curves represent the dispersion relation of the case with short-circuit termination (h=0.01), and the red ones stand for the case without termination.

Fig. 5.
Fig. 5.

Dispersion relation of the 2D PBG structure with termination conditions; the black curves represent the dispersion relation of the case with open-circuit termination (h=0.1), and the red ones stand for the case without termination.

Fig. 6.
Fig. 6.

Dispersion relation of the 2D PBG structure with termination conditions; the black curves represent the dispersion relation of the case with open-circuit termination (h=0.245), and the red ones stand for the case without termination

Fig. 7.
Fig. 7.

the distribution of the electric field strength Ey at the normalized frequency 0.25, the left-hand side picture is for OC termination (with effective refraction index 1.1972) and the right-hand side one is for un-terminated case (with effective refractive index 1.1542).

Fig. 8.
Fig. 8.

the distribution of the electric field strength Ey at the normalized frequency 0.25, the left-hand side picture is for OC termination (with effective refraction index 1.3872) and the right-hand side one is for un-terminated case (with effective refractive index 1.3449).

Fig. 9.
Fig. 9.

the distribution of the electric field strength Ey at the normalized frequency 0.25, the left-hand side picture is for OC termination (with effective refraction index 1.4779) and the right-hand side one is for un-terminated case (with effective refractive index 1.4532).

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