Abstract

We study whispering-gallery-like modes in photonic crystal air-bridge slab micro-cavities having H2 defects using finite-difference time-domain calculations. The defect geometry is optimized to increase the quality factor (Q) of the H2-cavity whispering-gallery mode (WGM). By symmetrically distributing 12 nearest neighbor holes around the defect and controlling size of holes, it is possible to drastically increase the Q of >105 while preserving effective mode volume of the order of the cubic wavelength in material. In addition, we investigate the effect of a dielectric circular post located around the center of the H2 cavity. This post can act as current and heat flow paths that promise electrically-pumped thermally-stable lasing operation. It is interesting to observe that the introduction of the post structure increases the Q of the WGM upto 4×105 and the high Q >105 is still maintained even with large post size. Although diffractive out-coupling through the post is increased, radiated power outside the post is suppressed, which leads to large enhancement of the Q of the H2-cavity WGM.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. H. Yokoyama, �??Physics and Device Application of Optical Microcavities,�?? Science 256, 66-70 (1992).
    [CrossRef] [PubMed]
  2. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O�??Brien, P. D. Dapkus, and I. Kim, �??Two-dimensional photonic band-gap defect mode laser,�?? Science 284, 1819-1821 (1999).
    [CrossRef] [PubMed]
  3. S. Noda, A. Chutinan, and M. Imada, �??Trapping and emission of photons by a single defect in a photonic bandgap structure,�?? Nature 407, 608-610 (2000).
    [CrossRef] [PubMed]
  4. H. Y. Ryu, H. G. Park, and Y. H. Lee, �??Two-Dimensional Photonic Crystal Semiconductor Lasers: Computational Design, Fabrication, and Characterization,�?? IEEE J. Sel. Top. Quantum Electron. 8, 891-908 (2002).
    [CrossRef]
  5. J. Gérard and B. Gayral, �??InAs quantum dots: artificial atoms for solid-state cavity-quantum electrodynamics,�?? Physica E 9, 131-139 (2001).
    [CrossRef]
  6. J. Vu�?kovi�?, M. Lon�?ar, H. Mabuchi, and A. Scherer, �??Design of photonic crystal microcavities for cavity QED,�?? Phys. Rev. E 65, 016608 (2001).
    [CrossRef]
  7. J. Vu�?kovi�?, M. Lon�?ar, H. Mabuchi, and A. Scherer, �??Optimization of the Q Factor in Photonic Crystal Microcavities,�?? IEEE J. Quantum Electron. 38, 850-856 (2002)
    [CrossRef]
  8. K. Srinivasan and O. Painter, �??Momentum space design of high-Q photonic crystal optical cavities,�?? Opt. Express 10, 670-684 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670</a>; K. Srinivasan and O. Painter, �??Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals,�?? Opt. Express 11, 579-593 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-579">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-579</a>.
    [CrossRef] [PubMed]
  9. H. Y. Ryu, S. H. Kim, H. G. Park, J. K. Hwang, Y. H. Lee, and J. S. Kim, �??Square-lattice photonic bandgap single-cell laser operating in the lowest-order whispering gallery mode,�?? Appl. Phys. Lett. 80, 3883-3885 (2002).
    [CrossRef]
  10. H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee, �??Characterization of Modified Single-Defect Two-Dimensional Photonic Crystal Lasers,�?? IEEE J. Quantum Electron. 38, 1353-1365 (2002).
    [CrossRef]
  11. H. Y. Ryu, J. K. Hwang, and Y. H. Lee, �??The Smallest Possible Whispering-Gallery-Like Mode in the Square Lattice Photonic-Crystal Slab Single-Defect Cavity,�?? IEEE J. Quantum Electron. 39, 314-322 (2003).
    [CrossRef]
  12. J. Vu�?kovi�? and Y. Yamamoto, �??Photonic crystal microcavities for cavity quantum electrodynamics with a single quantum dot,�?? Appl. Phys. Lett. 82, 2374-2376 (2003).
    [CrossRef]
  13. H. Y. Ryu, M. Notomi, and Y. H. Lee, �??Very high quality-factor and small mode-volume hexapole modes in photonic crystal slab nano-cavities,�?? Appl. Phys. Lett. 83, 4294 (2003).
    [CrossRef]
  14. T. Baba, M. Fujita, A. Sakai, M. Kihara, R. Watanabe, �??Lasing Characteristics of GaInAsP-InP Strained Quantum-Well Microdisk Injection Lasers with Diameter of 2-10 m,�?? IEEE Photon. Technol. Lett. 9, 878-880 (1997).
    [CrossRef]
  15. C. Reese, B. Gayral, B. D. Gerardot, A. Imamoglu, P. M. Petroff, and E. Hu, �??High-Q photonic crystal microcavities fabricated in a thin GaAs membrane,�?? J. Vac. Sci. Technol. B 19, 2749-2752 (2001).
    [CrossRef]
  16. C. Monat, C. Seassal, X. Letartre, P. Regreny, P. Rojo-Romeo, P. Viktorovitch, M. L. V. d�??Yerville, D. Cassagne, J. P. Albert, E. Jalaguier, S. Pocas, and B. Aspar, �??Modal Analysis and Engineering on InPBased Two-Dimensional Photonic-Crystal Microlasers on a Si Wafer,�?? IEEE J. Quantum Electron. 39, 419- 425 (2003).
    [CrossRef]
  17. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, �??Whispering-gallery mode microdisk lasers,�?? Appl. Phys. Lett. 60, 289-291 (1991).
    [CrossRef]
  18. M. Fujita, A. Sakai, and T. Baba, �??Ultrasmall and Ultralow Threshold GaInAsP-InP Microdisk Injection Lasers: Design, Fabrication, Lasing Characteristics, and Spontaneous Emission Factor,�?? IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
    [CrossRef]
  19. M. Cai, O. Painter, and K. J. Vahala, �??Observation of critical coupling in a fiber taper to a silicamicrosphere whispering-gallery mode system,�?? Phys. Rev. Lett. 85, 74-77 (2000).
    [CrossRef] [PubMed]
  20. A. F. J. Levi, S. L. McCall, S. J. Pearton, and R. A. Logan, �??Room temperature operation of submicrometer radius disk lasers,�?? Electron. Lett. 29, 1666-1667 (1993).
    [CrossRef]
  21. R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, �??Threshold characteristics of microdisk lasers,�?? Appl. Phys. Lett. 63, 1310-1312 (1993).
    [CrossRef]
  22. S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, �??Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,�?? Appl. Phys. Lett. 78, 3388-3390 (2001).
    [CrossRef]
  23. K. Nozaki, A. Nakagawa, D. Sano, and T. Baba, �??Ultralow Threshold and Single-Mode Lasing in Microgear Lasers and Its Fusion With Quasi-Periodic Photonic Crystals,�?? IEEE J. Sel. Top. Quantum Electron. 9, 1315-1360 (2003).
  24. H. Mabuchi and A. C. Doherty, �??Cavity Quantum Electrodynamics: Coherence in Context,�?? Science 298, 1372-1377 (2002).
    [CrossRef] [PubMed]
  25. H. G. Park, S. K. Kim, S. H. Kwon, G. H. Kim, S. H. Kim, H. Y. Ryu, and Y. H. Lee, �??Single-Mode Operation of Two-Dimensional Photonic Crystal Laser with Central Post,�?? IEEE Photon. Technol. Lett. 15, 1327 (2003).
    [CrossRef]

Appl. Phys. Lett.

J. Vu�?kovi�? and Y. Yamamoto, �??Photonic crystal microcavities for cavity quantum electrodynamics with a single quantum dot,�?? Appl. Phys. Lett. 82, 2374-2376 (2003).
[CrossRef]

H. Y. Ryu, M. Notomi, and Y. H. Lee, �??Very high quality-factor and small mode-volume hexapole modes in photonic crystal slab nano-cavities,�?? Appl. Phys. Lett. 83, 4294 (2003).
[CrossRef]

H. Y. Ryu, S. H. Kim, H. G. Park, J. K. Hwang, Y. H. Lee, and J. S. Kim, �??Square-lattice photonic bandgap single-cell laser operating in the lowest-order whispering gallery mode,�?? Appl. Phys. Lett. 80, 3883-3885 (2002).
[CrossRef]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, �??Whispering-gallery mode microdisk lasers,�?? Appl. Phys. Lett. 60, 289-291 (1991).
[CrossRef]

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, �??Threshold characteristics of microdisk lasers,�?? Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, �??Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,�?? Appl. Phys. Lett. 78, 3388-3390 (2001).
[CrossRef]

Electron. Lett.

A. F. J. Levi, S. L. McCall, S. J. Pearton, and R. A. Logan, �??Room temperature operation of submicrometer radius disk lasers,�?? Electron. Lett. 29, 1666-1667 (1993).
[CrossRef]

IEEE J. Quantum Electron.

C. Monat, C. Seassal, X. Letartre, P. Regreny, P. Rojo-Romeo, P. Viktorovitch, M. L. V. d�??Yerville, D. Cassagne, J. P. Albert, E. Jalaguier, S. Pocas, and B. Aspar, �??Modal Analysis and Engineering on InPBased Two-Dimensional Photonic-Crystal Microlasers on a Si Wafer,�?? IEEE J. Quantum Electron. 39, 419- 425 (2003).
[CrossRef]

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee, �??Characterization of Modified Single-Defect Two-Dimensional Photonic Crystal Lasers,�?? IEEE J. Quantum Electron. 38, 1353-1365 (2002).
[CrossRef]

H. Y. Ryu, J. K. Hwang, and Y. H. Lee, �??The Smallest Possible Whispering-Gallery-Like Mode in the Square Lattice Photonic-Crystal Slab Single-Defect Cavity,�?? IEEE J. Quantum Electron. 39, 314-322 (2003).
[CrossRef]

J. Vu�?kovi�?, M. Lon�?ar, H. Mabuchi, and A. Scherer, �??Optimization of the Q Factor in Photonic Crystal Microcavities,�?? IEEE J. Quantum Electron. 38, 850-856 (2002)
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

H. Y. Ryu, H. G. Park, and Y. H. Lee, �??Two-Dimensional Photonic Crystal Semiconductor Lasers: Computational Design, Fabrication, and Characterization,�?? IEEE J. Sel. Top. Quantum Electron. 8, 891-908 (2002).
[CrossRef]

M. Fujita, A. Sakai, and T. Baba, �??Ultrasmall and Ultralow Threshold GaInAsP-InP Microdisk Injection Lasers: Design, Fabrication, Lasing Characteristics, and Spontaneous Emission Factor,�?? IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
[CrossRef]

K. Nozaki, A. Nakagawa, D. Sano, and T. Baba, �??Ultralow Threshold and Single-Mode Lasing in Microgear Lasers and Its Fusion With Quasi-Periodic Photonic Crystals,�?? IEEE J. Sel. Top. Quantum Electron. 9, 1315-1360 (2003).

IEEE Photon. Technol. Lett.

H. G. Park, S. K. Kim, S. H. Kwon, G. H. Kim, S. H. Kim, H. Y. Ryu, and Y. H. Lee, �??Single-Mode Operation of Two-Dimensional Photonic Crystal Laser with Central Post,�?? IEEE Photon. Technol. Lett. 15, 1327 (2003).
[CrossRef]

T. Baba, M. Fujita, A. Sakai, M. Kihara, R. Watanabe, �??Lasing Characteristics of GaInAsP-InP Strained Quantum-Well Microdisk Injection Lasers with Diameter of 2-10 m,�?? IEEE Photon. Technol. Lett. 9, 878-880 (1997).
[CrossRef]

J. Vac. Sci. Technol. B

C. Reese, B. Gayral, B. D. Gerardot, A. Imamoglu, P. M. Petroff, and E. Hu, �??High-Q photonic crystal microcavities fabricated in a thin GaAs membrane,�?? J. Vac. Sci. Technol. B 19, 2749-2752 (2001).
[CrossRef]

Nature

S. Noda, A. Chutinan, and M. Imada, �??Trapping and emission of photons by a single defect in a photonic bandgap structure,�?? Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. E

J. Vu�?kovi�?, M. Lon�?ar, H. Mabuchi, and A. Scherer, �??Design of photonic crystal microcavities for cavity QED,�?? Phys. Rev. E 65, 016608 (2001).
[CrossRef]

Phys. Rev. Lett.

M. Cai, O. Painter, and K. J. Vahala, �??Observation of critical coupling in a fiber taper to a silicamicrosphere whispering-gallery mode system,�?? Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

Physica E

J. Gérard and B. Gayral, �??InAs quantum dots: artificial atoms for solid-state cavity-quantum electrodynamics,�?? Physica E 9, 131-139 (2001).
[CrossRef]

Science

H. Yokoyama, �??Physics and Device Application of Optical Microcavities,�?? Science 256, 66-70 (1992).
[CrossRef] [PubMed]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O�??Brien, P. D. Dapkus, and I. Kim, �??Two-dimensional photonic band-gap defect mode laser,�?? Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

H. Mabuchi and A. C. Doherty, �??Cavity Quantum Electrodynamics: Coherence in Context,�?? Science 298, 1372-1377 (2002).
[CrossRef] [PubMed]

Supplementary Material (6)

» Media 1: GIF (332 KB)     
» Media 2: GIF (89 KB)     
» Media 3: GIF (370 KB)     
» Media 4: GIF (336 KB)     
» Media 5: GIF (309 KB)     
» Media 6: GIF (295 KB)     

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 (13)

Fig. 1.
Fig. 1.

Whispering-gallery mode (WGM) in photonic crystal hexagonal disk cavities. (a) H2-cavity WGM, (b) H3-cavity WGM, (c) H4-cavity WGM.

Fig. 2.
Fig. 2.

Quality factor (Q) of the WGM for H2, H3, and H4 disk cavities versus radius of air holes.

Fig. 3.
Fig. 3.

(a) Fourier-space electric field intensity distribution. Black circle represents light line. (b) Side-view electric field intensity of the WGM in Fig. 1(a). A color map of relative intensity scale is shown at the right of (b).

Fig. 4.
Fig. 4.

(a) Configuration of the modified H2 cavity. Here, nearest neighbor holes along the Γ-M direction are pushed away along the radial direction by the displacement parameter, p. (b) Quality factor as a function of p when radius of holes is 0.3 a. The blue dotted line indicates the position where nearest neighbor holes are symmetrically distributed.

Fig. 5.
Fig. 5.

Electric field intensity (|E|2) distribution of the WGM in a structure shown in Fig. 4(a).. A color map of relative intensity scale is shown at the bottom of figures. (a) |E|2 at the center plane of the slab. Circles represent air holes (b) Side view of the |E|2, (c) Fourier space representation. The black circle near center indicates light line.

Fig. 6.
Fig. 6.

(a) Configuration of the modified H2 cavity from the structure in Fig. 4(a) with p=(2-√3) a. Here, radius of nearest neighbor holes is modified from r to rm . (b) Quality factor as a function of rm for three r values.

Fig. 7.
Fig. 7.

(a) Quality factors as a function of rm for three r values in the structure, Fig. 6(a). (b) Effective mode volume of the WGM as a function of rm when radius of holes is 0.3 a.

Fig. 8.
Fig. 8.

(a) (330kB) Movie of electric field intensity of the modified H2-cavity WGM (b) (90kB) Movie of magnetic field amplitude of the modified H2-cavity WGM. Regular hole radius and modified hole radius are 0.3 a and 0.225 a, respectively. Black circles represent air holes.

Fig. 9.
Fig. 9.

Side -view of dielectric post structures. dP means post diameter. Here, dP is about 1.0 a. (a) Symmetric slab, (b) Asymmetric slab.

Fig. 10.
Fig. 10.

Quality factors of the WGM with the symmetric post plotted as a function of post diameter. Regular hole radius and modified hole radius are 0.3 a and 0.225 a, respectively.

Fig. 11.
Fig. 11.

(a) (340kB) Movie of the Poynting vector calculated at z=2.3 a when there is no post. (b) (270kB) Movie of the Poynting vector when the post diameter is 1.0 a. A dotted circle near the center indicates the post.

Fig. 12.
Fig. 12.

(a) Quality factor of the WGM with asymmetric posts versus post diameter. (b) Quality factor decomposed into the top and the bottom components. Each represents optical loss into the top air region and the bottom post region, respectively.

Fig. 13.
Fig. 13.

(a) (300kB) Movie of the Poynting vector calculated at z=2.3 a where there is no post. (b) (310kB) Movie of the Poynting vector calculated at z=-2.3 a where there is a post with diameter of 1.0 a. A dotted circle near the center indicates the post.

Metrics