Abstract

The parametric analysis of the electromagnetic properties of 2D guided wave photonic band gap structures is reported with the aim of providing a valid tool for the optimal design. The modelling approach is based on the Bloch-Floquet method. Different lattice configurations and geometrical parameters are considered. An optimum value for the ratio between the hole (or rod) radius and the lattice constant does exist and the calculation demonstrated that it is almost independent from the etching depth, only depending on the lattice type. The results are suitable for the design optimisation of photonic crystal reflectors to be used in integrated optical devices.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. N. Ikeda, Y. Sugimoto, Y. Tanaka, K. Inoue, and K. Asakawa, “Low propagation posses in single-line-defect photonic crystal waveguides on GaAs membranes,” IEEE J. Sel. Areas Commun. 23, 1315-1320 (2005).
    [CrossRef]
  2. Y. Tanaka, T. Asano, R. Hatsuta, and S. Noda, “Analysis of a line-defect waveguide on a silicon-on-insulator two-dimensional photonic-crystal slab,” J. Lightwave Technol. 22, 2787-2792 (2004).
    [CrossRef]
  3. M. Koshiba, “Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers,” J. Lightwave Technol. 19, 1970-1975 (2001).
    [CrossRef]
  4. J. Smajic, C. Hafner, and D. Erni, “On the design of photonic crystal multiplexers,” Opt. Express 11, 566-571 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-566">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-566<a/>.
    [CrossRef] [PubMed]
  5. M. Loncar, T. Yoshie, Y. Qiu, P. Gogna, and A. Scherer, “Low-threshold photonic crystal laser,” Proc. SPIE 5000, 16-26 (2003).
    [CrossRef]
  6. M. Rattier, T. F. Krauss, J.-F. Carlin, R. Stanley, U. Oesterle, R. Houdrè, C. J. M. Smith, R. M. De La Rue, H. Benisty, and C. Weisbuch, “High extraction efficiency, laterally injected, light emitting diodes combining microcavities and photonic crystals,” Opt. and Quantum Electron. 34, 79-89 (2002).
    [CrossRef]
  7. H.-Y. Ryu, S.-H. Kwon, Y.-J. Lee, Y.-H. Lee, and J.-S. Kim, “Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs,” Appl. Phys. Lett. 80, 3476-3478 (2002).
    [CrossRef]
  8. K. Sakoda, “Low-threshold laser oscillation due to group-velocity anomaly peculiar to two- and three-dimensional photonic crystals,” Opt. Express 4, 481-489 (1999), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-12-481">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-12-481</a>.
    [CrossRef] [PubMed]
  9. A. Lupu, E. Cassan, S. Laval, L. El Melhaoui, P. Lyan, and J. M. Fedeli, “Experimental evidence for superprism phenomena in SOI photonic crystals,” Opt. Express 23, 5690-5696 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-23-5690">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-23-5690</a>.
    [CrossRef]
  10. T. Baba, and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron. 38, 909-914 (2002).
    [CrossRef]
  11. R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, “Negative refraction and superlens behaviuor in a two-dimensional photonic crystal,” Phys. Rev. B 71, 085106 (2005).
    [CrossRef]
  12. E. Cubukcu, K. Aydin, and E. Ozbay, “Subwavelength resolution in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. Lett. 91, 207401 (2003).
    [CrossRef] [PubMed]
  13. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751-5758 (1999).
    [CrossRef]
  14. C. Ciminelli, F. Peluso and M. N. Armenise, “Modeling and design of two-dimensional guided-wave photonic band-gap devices,” J. Lightwave Technol. 23, 886-901 (2005).
    [CrossRef]
  15. C. Ciminelli, F. Peluso, M. N. Armenise and R. M. De La Rue, “Variable oblique incidence for tunability in a 2D guided wave photonic band gap filter,” J. Lightwave Technol. (to be published).
  16. T. D. Happ, A. Markard, M. Kamp, J.-L. Genter, and A. Forchel, “InP-based short cavity with 2D photonic crystal mirror,” Electron. Lett. 37, 428-429 (2001).
    [CrossRef]
  17. C. Ciminelli, F. Peluso, and M. N. Armenise, “2D guided-wave photonic band gap single and multiple cavity filters” in Proceedings of 2005 IEEE/LEOS Workshop on Fibres and Optical Passive Components, 404–409.
  18. K. Sakoda, “Transmittance and Bragg reflectivity of two-dimensional photonic lattices,” Phys. Rev. B 52, 8992-9002 (1995).
    [CrossRef]
  19. D. Labilloy et al., “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045-1052 (1999).
    [CrossRef]
  20. W. Bogaerts, P. Bienstmann, D. Taillaert, R. Baets and D. De Zutter, “Out-of-plane scattering in photonic crystal slabs,” IEEE Photon. Technol. Lett. 13, 565-567 (2001).
    [CrossRef]
  21. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, New Jersey, 1995).
  22. C. Ciminelli, H. M. H. Chong, F. Peluso, M. N. Armenise and R. M. De La Rue, “High Q guided-wave photonic crystal extended microcavity” in Proceedings of ECOC 2004, Post deadline paper Th 4.2.6, 26-27.

Appl. Phys. Lett. (1)

H.-Y. Ryu, S.-H. Kwon, Y.-J. Lee, Y.-H. Lee, and J.-S. Kim, “Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs,” Appl. Phys. Lett. 80, 3476-3478 (2002).
[CrossRef]

Electron. Lett. (1)

T. D. Happ, A. Markard, M. Kamp, J.-L. Genter, and A. Forchel, “InP-based short cavity with 2D photonic crystal mirror,” Electron. Lett. 37, 428-429 (2001).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. Labilloy et al., “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045-1052 (1999).
[CrossRef]

T. Baba, and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron. 38, 909-914 (2002).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

N. Ikeda, Y. Sugimoto, Y. Tanaka, K. Inoue, and K. Asakawa, “Low propagation posses in single-line-defect photonic crystal waveguides on GaAs membranes,” IEEE J. Sel. Areas Commun. 23, 1315-1320 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

W. Bogaerts, P. Bienstmann, D. Taillaert, R. Baets and D. De Zutter, “Out-of-plane scattering in photonic crystal slabs,” IEEE Photon. Technol. Lett. 13, 565-567 (2001).
[CrossRef]

J. Lightwave Technol. (4)

Opt. and Quantum Electron. (1)

M. Rattier, T. F. Krauss, J.-F. Carlin, R. Stanley, U. Oesterle, R. Houdrè, C. J. M. Smith, R. M. De La Rue, H. Benisty, and C. Weisbuch, “High extraction efficiency, laterally injected, light emitting diodes combining microcavities and photonic crystals,” Opt. and Quantum Electron. 34, 79-89 (2002).
[CrossRef]

Opt. Express (3)

Phys. Rev. B (3)

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, “Negative refraction and superlens behaviuor in a two-dimensional photonic crystal,” Phys. Rev. B 71, 085106 (2005).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

K. Sakoda, “Transmittance and Bragg reflectivity of two-dimensional photonic lattices,” Phys. Rev. B 52, 8992-9002 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

E. Cubukcu, K. Aydin, and E. Ozbay, “Subwavelength resolution in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

Proc. SPIE 5000 (2003) (1)

M. Loncar, T. Yoshie, Y. Qiu, P. Gogna, and A. Scherer, “Low-threshold photonic crystal laser,” Proc. SPIE 5000, 16-26 (2003).
[CrossRef]

Proceedings of 2005 IEEE/LEOS Workshop (1)

C. Ciminelli, F. Peluso, and M. N. Armenise, “2D guided-wave photonic band gap single and multiple cavity filters” in Proceedings of 2005 IEEE/LEOS Workshop on Fibres and Optical Passive Components, 404–409.

Proceedings of ECOC 2004 (1)

C. Ciminelli, H. M. H. Chong, F. Peluso, M. N. Armenise and R. M. De La Rue, “High Q guided-wave photonic crystal extended microcavity” in Proceedings of ECOC 2004, Post deadline paper Th 4.2.6, 26-27.

Other (1)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, New Jersey, 1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1.
Fig. 1.

Two different lattices. (a) periodic repetition of holes; (b) periodic repetition of rods.

Fig. 2.
Fig. 2.

Two different unit cell symmetries. (a) triangular; (b) square.

Fig. 3.
Fig. 3.

BW/λ0 versus R/a (a) and αmax versus R/a (b) for different photonic crystal structure in a 100 nm thick AlxOy/GaAs slab waveguide.

Fig. 4.
Fig. 4.

Reflectance (a) and transmittance (b) at the centre of the stop band (λ0 = 1.55 μm) versus R/a for different photonic crystal structures in a 100 nm thick AlxOy /GaAs slab waveguide (15 hole/rod rows).

Fig. 5.
Fig. 5.

0 - λc,rad)/λ0 (a) and relative percentage (b) versus R/a for different photonic crystal structures in a 100 nm thick AlxOy/GaAs slab waveguide.

Fig. 6.
Fig. 6.

BW/λ0 % (a) and BW/[2 - (λ0 - λc,rad)] (b) versus etching depth for different photonic crystal structure in a 100 nm thick AlxOy/GaAs slab waveguide.

Fig. 7.
Fig. 7.

Peak attenuation coefficient in the forbidden band (a), reflectance at λ0 (15 hole/rod rows) (b), transmittance at λ0 (15 hole/rod rows) (c) as function of the etching depth tg/tf for different photonic crystal structures in a 100 nm thick AlxOy/GaAs slab waveguide.

Fig. 8.
Fig. 8.

BW/λ0 % (a), (λ0 - λc,rad)/λ0 (b), reflectance at λ0 = 1.55 μm (15 hole rows) (c), transmittance at λ0 (15 hole rows) (d) as functions of the ratio R/a at different etching depths tg/tf for a triangular lattice of holes in a 100 nm thick AlxOy/GaAs slab waveguide.

Fig. 9.
Fig. 9.

BW/λ0 % (a), (λ0 - λc,rad)/λ0 (b), reflectance at λ0 = 1.55 μm (15 rod rows) (c), transmittance at λ0 (15 rod rows) (d) as functions of the ratio R/a at different etching depths tg/tf for a triangular lattice of rods in a 100 nm thick AlxOy/GaAs slab waveguide.

Fig. 10.
Fig. 10.

BW/λ0 % (a), (λ0 - λc,rad)/λ0 (b), reflectance at λ0 = 1.55 μm (15 hole rows) (c), transmittance at λ0 (15 hole rows) (d) as functions of the ratio R/a at different etching depths tg/tf for a square lattice of holes in a 100 nm thick AlxOy/GaAs slab waveguide.

Fig. 11.
Fig. 11.

BW/λ0 % (a), (λ0 - λc,rad)/λ0 (b), reflectance at λ0 = 1.55 μm (15 rod rows) (c), transmittance at λ0 (15 rod rows) (d) as functions of the ratio R/a at different etching depths tg/tf for a square lattice of rods in a 100 nm thick AlxOy/GaAs slab waveguide.

Fig. 12.
Fig. 12.

Dispersion curves of photonic crystals consisting on a square pattern of holes, evaluated along the ΓX direction for four different etching depths. The ratio R/a is equal to 0.35 and the lattice constant a is adjusted to have a centre wavelength λ0 = 1.55 μm in each case: (a) phase constant; (b) attenuation coefficient.

Tables (1)

Tables Icon

Table 1. Optimum value of the ratio R/a, corresponding filling factor, fopt relative width BW/λ0 of the bandgap and peak attenuation coefficient αmax for different types of photonic crystals

Equations (4)

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

E , H = i , G E , H i , G ( x ) a i e j ( k + G ) · ρ
G = m 1 b 1 + m 2 b 2
ψ x ρ = a ψ + x ρ + x ρ
β y , p = p 2 π Λ y

Metrics