Abstract

The geometry of photonic crystal waveguides with ring-shaped holes is optimized to minimize dispersion in the slow light regime. We found geometries with a nearly constant group index in excess of 20 over a wavelength range of 8 nm. The origin of the low dispersion is related to the widening of the propagating mode close to the lower band gap edge.

© 2007 Optical Society of America

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References

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  1. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef] [PubMed]
  2. X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, "Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes," Appl. Phys. Lett. 79, 2312-2314 (2001).
    [CrossRef]
  3. M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H-Y. Ryu, "Waveguides, resonators and their coupled elements in photonic crystal slabs," Opt. Express 12, 1551-1561 (2004).
    [CrossRef] [PubMed]
  4. H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss and L. Kuipers, "Real-Space Observation of Ultraslow Light in Photonic Crystal Waveguides," Phys. Rev. Lett. 94, 073903 (2005).
    [CrossRef] [PubMed]
  5. Y. A. Vlasov, M. O’Boyle, H. F. Hamann and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
    [CrossRef] [PubMed]
  6. M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, "Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth," Opt. Express 15, 219-226 (2007).
    [CrossRef] [PubMed]
  7. L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, "Photonic crystal waveguides with semi-slow light and tailored dispersion properties," Opt. Express 14, 9444-9450 (2006).
    [CrossRef] [PubMed]
  8. A. Jafarpour, A. Adibi, Y. Xu and R. K. Lee, "Mode dispersion in biperiodic photonic crystal waveguides," Phys. Rev. B 68, 233102 (2003).
    [CrossRef]
  9. M. Mulot, A. Säynätjoki, S. Arpiainen, H. Lipsanen and J. Ahopelto, "Photonic crystal slabs with ring-shaped holes in a triangular lattice," proceedings of the 3rd European Symposium on Photonic Crystals (ESPC 2005), Barcelona, Spain, 3-7 July, 2005.
  10. H. Kurt and D. S. Citrin, "Annular Photonic Crystals," Opt. Express 13, 10316-10326 (2005).
    [CrossRef] [PubMed]
  11. M. Mulot, A. Säynätjoki, S. Arpiainen, H. Lipsanen, J. Ahopelto, "Slow light propagation in photonic crystal waveguides with ring-shaped holes," accepted for publication in J. Opt. A : Pure and Appl. Opt
  12. A. Säynätjoki, M. Mulot, S. Arpiainen, J. Ahopelto, and H. Lipsanen, "Photonic crystals with ring-shaped holes," PECS VII conference, Monterey, USA, 8-11 April, 2007.
  13. S. Johnson, and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001).
    [CrossRef] [PubMed]
  14. R. P. Feynman, "Forces in molecules," Phys. Rev. 56, 340-343 (1939).
    [CrossRef]
  15. M. Qiu, F2P software, http://www.imit.kth.se/info/FOFU/PC/F2P/

2007 (1)

2006 (1)

2005 (3)

H. Kurt and D. S. Citrin, "Annular Photonic Crystals," Opt. Express 13, 10316-10326 (2005).
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss and L. Kuipers, "Real-Space Observation of Ultraslow Light in Photonic Crystal Waveguides," Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (1)

A. Jafarpour, A. Adibi, Y. Xu and R. K. Lee, "Mode dispersion in biperiodic photonic crystal waveguides," Phys. Rev. B 68, 233102 (2003).
[CrossRef]

2001 (3)

S. Johnson, and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, "Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes," Appl. Phys. Lett. 79, 2312-2314 (2001).
[CrossRef]

1939 (1)

R. P. Feynman, "Forces in molecules," Phys. Rev. 56, 340-343 (1939).
[CrossRef]

Appl. Phys. Lett. (1)

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, "Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes," Appl. Phys. Lett. 79, 2312-2314 (2001).
[CrossRef]

Nature (1)

Y. A. Vlasov, M. O’Boyle, H. F. Hamann and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Opt. Express (5)

Phys. Rev. (1)

R. P. Feynman, "Forces in molecules," Phys. Rev. 56, 340-343 (1939).
[CrossRef]

Phys. Rev. B (1)

A. Jafarpour, A. Adibi, Y. Xu and R. K. Lee, "Mode dispersion in biperiodic photonic crystal waveguides," Phys. Rev. B 68, 233102 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss and L. Kuipers, "Real-Space Observation of Ultraslow Light in Photonic Crystal Waveguides," Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Other (4)

M. Qiu, F2P software, http://www.imit.kth.se/info/FOFU/PC/F2P/

M. Mulot, A. Säynätjoki, S. Arpiainen, H. Lipsanen and J. Ahopelto, "Photonic crystal slabs with ring-shaped holes in a triangular lattice," proceedings of the 3rd European Symposium on Photonic Crystals (ESPC 2005), Barcelona, Spain, 3-7 July, 2005.

M. Mulot, A. Säynätjoki, S. Arpiainen, H. Lipsanen, J. Ahopelto, "Slow light propagation in photonic crystal waveguides with ring-shaped holes," accepted for publication in J. Opt. A : Pure and Appl. Opt

A. Säynätjoki, M. Mulot, S. Arpiainen, J. Ahopelto, and H. Lipsanen, "Photonic crystals with ring-shaped holes," PECS VII conference, Monterey, USA, 8-11 April, 2007.

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Figures (7)

Fig. 1.
Fig. 1.

Scanning electron micrograph of a RPhCW fabricated by electron beam lithography and reactive ion etching [11].

Fig. 2.
Fig. 2.

Dispersion relation and group index of a W1 RPhCW with a = 430 nm, Rout = 0.344a and Rin = 0.203a in comparison with those of a conventional W1 PhCW with a = 415 nm and R = 0.278a.

Fig. 3.
Fig. 3.

Change of band gap edge and waveguide mode frequencies with the change of ring radius. The width of the ring Rout Rin is kept constant at 0.14a.

Fig. 4.
Fig. 4.

Electric field energy densities for the slow mode in a RPhCW with Rout =0.38a and Rin =0.24a with three different propagation constants.

Fig. 5.
Fig. 5.

Dispersion relation and group index of a W1 RPhCW with a =430nm,Rout = 0.38a and Rin = 0.24a. The scatter plot shows the results of the FDTD simulations. The light line of SiO2 is shown in red in the dispersion relation.

Fig. 6.
Fig. 6.

Dispersion relation and group index of a W1 RPhCW with a = 392 nm, Rout = 0.385a and Rin = 0.235a etched into a 400 nm thick silicon layer on silica. The light line of SiO2 is shown in red in the dispersion relation.

Fig. 7.
Fig. 7.

Group velocity dispersion calculated from the group index spectra of three waveguides. RPhCW A: Rout = 0.38a, Rin = 0.24a, a = 430 nm and h = 240 nm, RPhCW B: Rout = 0.385a, Rin = 0.235a, a = 392 nm and h = 400 nm. The curve with closed dots corresponds to a conventional PhCW with R = 0.278a, a = 400 nm and h = 240 nm. Lattice constants are chosen so that the cut-off wavelength is 1575 nm for all three waveguides.

Equations (3)

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v g = ω β = 2 π c a u β .
n g = c v g = a 2 π β u .
D = 1 c . d n g d λ .

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