Abstract

Coupling between photonic-crystal defect microcavities is observed to result in a splitting not only of the mode wavelength but also of the modal loss. It is discussed that the characteristics of the loss splitting may have an important impact on the optical energy transfer between the coupled resonators. The loss splitting — given by the imaginary part of the coupling strength — is found to arise from the difference in diffractive out-of-plane radiation losses of the symmetric and the antisymmetric modes of the coupled system. An approach to control the splitting via coupling barrier engineering is presented.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
    [CrossRef] [PubMed]
  2. H. Altug, D. Englund, and J. Vuckovic, "Ultrafast photonic crystal nanocavity laser," Nat. Physics 2, 484-488 (2006).
    [CrossRef]
  3. D. O'Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. Krauss, "Coupled photonic crystal heterostructure nanocavities," Opt. Express 15, 1228-1233 (2007).
    [CrossRef] [PubMed]
  4. E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, "Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures," IEEE J. Quantum Electron. 38, 837-843 (2002).
    [CrossRef]
  5. S. Mookherjea, and A. Yariv, "Coupled resonator optical waveguides," IEEE J. Sel. Top. Quantum Electron. 8, 448-456 (2002).
    [CrossRef]
  6. S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, "Switchable lasing in multimode microcavities," Phys. Rev. Lett. 99, 073902 (2007).
    [CrossRef] [PubMed]
  7. S. Ishii, A. Nakagawa, and T. Baba, "Modal characteristics and bistability in twin microdisk photonic molecule lasers," IEEE J. Sel. Top. Quantum Electron. 12, 71-77 (2006).
    [CrossRef]
  8. M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
    [CrossRef] [PubMed]
  9. A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, "Quantum Information Processing Using Quantum Dot Spins and Cavity QED," Phys. Rev. Lett. 83, 4204-4207 (1999).
    [CrossRef]
  10. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896-899 (2007).
    [CrossRef] [PubMed]
  11. A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, "Quantum phase transitions of light," Nat. Physics 2, 856-861 (2006).
    [CrossRef]
  12. S. V. Boriskina, "Coupling of whispering-gallery modes in size-mismatched microdisk photonic molecules," Opt. Lett. 32, 1557-1559 (2007).
    [CrossRef] [PubMed]
  13. M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, "Optical modes in photonic molecules," Phys. Rev. Lett. 81, 2582-2585 (1998).
    [CrossRef]
  14. M. Ghulinyan, C. J. Oton, G. Bonetti, Z. Gaburro, and L. Pavesi, "Free-standing porous silicon single and multiple optical cavities," J. Appl. Phys. 93, 9724-9729 (2003).
    [CrossRef]
  15. T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623-4626 (1999).
    [CrossRef]
  16. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
    [CrossRef]
  17. T. D. Happ, M. Kamp, A. Forchel, A. V. Bazhenov, I. I. Tartakovskii, A. Gorbunov, and V. D. Kulakovskii, "Coupling of point-defect microcavities in two-dimensional photonic-crystal slabs," J. Opt. Soc. Am. B 20, 373-378 (2003).
    [CrossRef]
  18. S. Ishii, K. Nozaki, and T. Baba, "Photonic molecules in photonic crystals," Jpn. J. Appl. Phys. 45, 6108-6111 (2006).
    [CrossRef]
  19. D. P. Fussell and M. M. Dignam, "Engineering the quality factors of coupled-cavity modes in photonic crystal slabs," Appl. Phys. Lett. 90, 183121 (2007).
    [CrossRef]
  20. E. Centeno and D. Felbacq, "Rabi oscillations in bidimensional photonic crystals," Phys. Rev. B 62, 10101-10108 (2000).
    [CrossRef]
  21. S. Lam, A. R. Chalcraft, D. Szymanski, R. Oulton, B. D. Jones, D. Sanvitto, D. M. Whittaker, M. Fox, M. S. Skolnick, D. O'Brien, T. F. Krauss, H. Liu, P. W. Fry, and M. Hopkinson, "Coupled Resonant Modes of Dual L3-Defect Planar Photonic Crystal Cavities," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper QFG6. http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2008-QFG6
    [PubMed]
  22. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics (Wiley, New York, 1977).
  23. K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, "Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity," Appl. Phys. Lett. 90, 153107 (2007).
    [CrossRef]
  24. E. Kapon, D. M. Hwang, and R. Bhat, "Stimulated emission in semiconductor quantum wire heterostructures," Phys. Rev. Lett. 63, 430-433 (1989).
    [CrossRef] [PubMed]
  25. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Publishers, 2005).
  26. W. H. Guo, W. J. Li, and Y. Z. Huang, "Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation," IEEE Microwave Wirel. Compon. Lett. 11, 223-225 (2001).
    [CrossRef]
  27. M. Qiu, "Micro-cavities in silicon-on-insulator photonic crystal slabs: Determining resonant frequencies and quality factors accurately," Microwave Opt. Technol. Lett. 45, 381-385 (2005).
    [CrossRef]
  28. J. M. Raimond and S. Haroche, "Atoms in Cavities," in Confined Electrons and Photons: New Physics and Applications, E. Burstein, and C. Weisbuch, eds. (Plenum Press, New York, 1995).
    [CrossRef]
  29. K. Srinivasan, and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670-684 (2002).
    [PubMed]
  30. Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
    [CrossRef] [PubMed]
  31. The flipping is the interference effect between two wave fronts arising from the coupling cavities. Depending on the PhC-lattice geometrical fill-factor, the flipping period does not correspond to nodes (?A = ?S) at an integer number of holes in the barrier, which may accounts for larger splitting in the case of two-hole barrier.
  32. D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vuckovic, "Generation and transfer of single photons on a photonic crystal chip," Opt. Express 15, 5550-5558 (2007).
    [CrossRef] [PubMed]

2007 (7)

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, "Switchable lasing in multimode microcavities," Phys. Rev. Lett. 99, 073902 (2007).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896-899 (2007).
[CrossRef] [PubMed]

D. P. Fussell and M. M. Dignam, "Engineering the quality factors of coupled-cavity modes in photonic crystal slabs," Appl. Phys. Lett. 90, 183121 (2007).
[CrossRef]

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, "Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity," Appl. Phys. Lett. 90, 153107 (2007).
[CrossRef]

D. O'Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. Krauss, "Coupled photonic crystal heterostructure nanocavities," Opt. Express 15, 1228-1233 (2007).
[CrossRef] [PubMed]

D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vuckovic, "Generation and transfer of single photons on a photonic crystal chip," Opt. Express 15, 5550-5558 (2007).
[CrossRef] [PubMed]

S. V. Boriskina, "Coupling of whispering-gallery modes in size-mismatched microdisk photonic molecules," Opt. Lett. 32, 1557-1559 (2007).
[CrossRef] [PubMed]

2006 (4)

H. Altug, D. Englund, and J. Vuckovic, "Ultrafast photonic crystal nanocavity laser," Nat. Physics 2, 484-488 (2006).
[CrossRef]

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, "Quantum phase transitions of light," Nat. Physics 2, 856-861 (2006).
[CrossRef]

S. Ishii, K. Nozaki, and T. Baba, "Photonic molecules in photonic crystals," Jpn. J. Appl. Phys. 45, 6108-6111 (2006).
[CrossRef]

S. Ishii, A. Nakagawa, and T. Baba, "Modal characteristics and bistability in twin microdisk photonic molecule lasers," IEEE J. Sel. Top. Quantum Electron. 12, 71-77 (2006).
[CrossRef]

2005 (1)

M. Qiu, "Micro-cavities in silicon-on-insulator photonic crystal slabs: Determining resonant frequencies and quality factors accurately," Microwave Opt. Technol. Lett. 45, 381-385 (2005).
[CrossRef]

2004 (1)

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

2003 (4)

M. Ghulinyan, C. J. Oton, G. Bonetti, Z. Gaburro, and L. Pavesi, "Free-standing porous silicon single and multiple optical cavities," J. Appl. Phys. 93, 9724-9729 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

T. D. Happ, M. Kamp, A. Forchel, A. V. Bazhenov, I. I. Tartakovskii, A. Gorbunov, and V. D. Kulakovskii, "Coupling of point-defect microcavities in two-dimensional photonic-crystal slabs," J. Opt. Soc. Am. B 20, 373-378 (2003).
[CrossRef]

2002 (3)

K. Srinivasan, and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670-684 (2002).
[PubMed]

E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, "Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures," IEEE J. Quantum Electron. 38, 837-843 (2002).
[CrossRef]

S. Mookherjea, and A. Yariv, "Coupled resonator optical waveguides," IEEE J. Sel. Top. Quantum Electron. 8, 448-456 (2002).
[CrossRef]

2001 (1)

W. H. Guo, W. J. Li, and Y. Z. Huang, "Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation," IEEE Microwave Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

2000 (1)

E. Centeno and D. Felbacq, "Rabi oscillations in bidimensional photonic crystals," Phys. Rev. B 62, 10101-10108 (2000).
[CrossRef]

1999 (2)

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623-4626 (1999).
[CrossRef]

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, "Quantum Information Processing Using Quantum Dot Spins and Cavity QED," Phys. Rev. Lett. 83, 4204-4207 (1999).
[CrossRef]

1998 (1)

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, "Optical modes in photonic molecules," Phys. Rev. Lett. 81, 2582-2585 (1998).
[CrossRef]

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

1989 (1)

E. Kapon, D. M. Hwang, and R. Bhat, "Stimulated emission in semiconductor quantum wire heterostructures," Phys. Rev. Lett. 63, 430-433 (1989).
[CrossRef] [PubMed]

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Altug, H.

H. Altug, D. Englund, and J. Vuckovic, "Ultrafast photonic crystal nanocavity laser," Nat. Physics 2, 484-488 (2006).
[CrossRef]

Asano, T.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Atatüre, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896-899 (2007).
[CrossRef] [PubMed]

Atlasov, K. A.

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, "Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity," Appl. Phys. Lett. 90, 153107 (2007).
[CrossRef]

Awschalom, D. D.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, "Quantum Information Processing Using Quantum Dot Spins and Cavity QED," Phys. Rev. Lett. 83, 4204-4207 (1999).
[CrossRef]

Baba, T.

S. Ishii, A. Nakagawa, and T. Baba, "Modal characteristics and bistability in twin microdisk photonic molecule lasers," IEEE J. Sel. Top. Quantum Electron. 12, 71-77 (2006).
[CrossRef]

S. Ishii, K. Nozaki, and T. Baba, "Photonic molecules in photonic crystals," Jpn. J. Appl. Phys. 45, 6108-6111 (2006).
[CrossRef]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896-899 (2007).
[CrossRef] [PubMed]

Bayer, M.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, "Optical modes in photonic molecules," Phys. Rev. Lett. 81, 2582-2585 (1998).
[CrossRef]

Bayindir, M.

E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, "Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures," IEEE J. Quantum Electron. 38, 837-843 (2002).
[CrossRef]

Bazhenov, A. V.

Bhat, R.

E. Kapon, D. M. Hwang, and R. Bhat, "Stimulated emission in semiconductor quantum wire heterostructures," Phys. Rev. Lett. 63, 430-433 (1989).
[CrossRef] [PubMed]

Binsma, H.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Bonetti, G.

M. Ghulinyan, C. J. Oton, G. Bonetti, Z. Gaburro, and L. Pavesi, "Free-standing porous silicon single and multiple optical cavities," J. Appl. Phys. 93, 9724-9729 (2003).
[CrossRef]

Boriskina, S. V.

Bulu, I.

E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, "Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures," IEEE J. Quantum Electron. 38, 837-843 (2002).
[CrossRef]

Burkard, G.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, "Quantum Information Processing Using Quantum Dot Spins and Cavity QED," Phys. Rev. Lett. 83, 4204-4207 (1999).
[CrossRef]

Centeno, E.

E. Centeno and D. Felbacq, "Rabi oscillations in bidimensional photonic crystals," Phys. Rev. B 62, 10101-10108 (2000).
[CrossRef]

Chigrin, D. N.

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, "Switchable lasing in multimode microcavities," Phys. Rev. Lett. 99, 073902 (2007).
[CrossRef] [PubMed]

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Cole, J. H.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, "Quantum phase transitions of light," Nat. Physics 2, 856-861 (2006).
[CrossRef]

Cubukcu, E.

E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, "Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures," IEEE J. Quantum Electron. 38, 837-843 (2002).
[CrossRef]

De Vries, T.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Deichsel, E.

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, "Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity," Appl. Phys. Lett. 90, 153107 (2007).
[CrossRef]

Den Besten, J. H.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Dignam, M. M.

D. P. Fussell and M. M. Dignam, "Engineering the quality factors of coupled-cavity modes in photonic crystal slabs," Appl. Phys. Lett. 90, 183121 (2007).
[CrossRef]

DiVincenzo, D. P.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, "Quantum Information Processing Using Quantum Dot Spins and Cavity QED," Phys. Rev. Lett. 83, 4204-4207 (1999).
[CrossRef]

Dorren, H. J. S.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Dremin, A. A.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, "Optical modes in photonic molecules," Phys. Rev. Lett. 81, 2582-2585 (1998).
[CrossRef]

Dwir, B.

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, "Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity," Appl. Phys. Lett. 90, 153107 (2007).
[CrossRef]

Englund, D.

Fält, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896-899 (2007).
[CrossRef] [PubMed]

Faraon, A.

Felbacq, D.

E. Centeno and D. Felbacq, "Rabi oscillations in bidimensional photonic crystals," Phys. Rev. B 62, 10101-10108 (2000).
[CrossRef]

Forchel, A.

T. D. Happ, M. Kamp, A. Forchel, A. V. Bazhenov, I. I. Tartakovskii, A. Gorbunov, and V. D. Kulakovskii, "Coupling of point-defect microcavities in two-dimensional photonic-crystal slabs," J. Opt. Soc. Am. B 20, 373-378 (2003).
[CrossRef]

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, "Optical modes in photonic molecules," Phys. Rev. Lett. 81, 2582-2585 (1998).
[CrossRef]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Fussell, D. P.

D. P. Fussell and M. M. Dignam, "Engineering the quality factors of coupled-cavity modes in photonic crystal slabs," Appl. Phys. Lett. 90, 183121 (2007).
[CrossRef]

Gaburro, Z.

M. Ghulinyan, C. J. Oton, G. Bonetti, Z. Gaburro, and L. Pavesi, "Free-standing porous silicon single and multiple optical cavities," J. Appl. Phys. 93, 9724-9729 (2003).
[CrossRef]

Gerace, D.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896-899 (2007).
[CrossRef] [PubMed]

Ghulinyan, M.

M. Ghulinyan, C. J. Oton, G. Bonetti, Z. Gaburro, and L. Pavesi, "Free-standing porous silicon single and multiple optical cavities," J. Appl. Phys. 93, 9724-9729 (2003).
[CrossRef]

Gorbunov, A.

Greentree, A. D.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, "Quantum phase transitions of light," Nat. Physics 2, 856-861 (2006).
[CrossRef]

Gulde, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896-899 (2007).
[CrossRef] [PubMed]

Guo, W. H.

W. H. Guo, W. J. Li, and Y. Z. Huang, "Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation," IEEE Microwave Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

Gutbrod, T.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, "Optical modes in photonic molecules," Phys. Rev. Lett. 81, 2582-2585 (1998).
[CrossRef]

Happ, T. D.

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Hennessy, K.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896-899 (2007).
[CrossRef] [PubMed]

Hill, M. T.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Hollenberg, L. C. L.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, "Quantum phase transitions of light," Nat. Physics 2, 856-861 (2006).
[CrossRef]

Hu, E. L.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896-899 (2007).
[CrossRef] [PubMed]

Huang, Y. Z.

W. H. Guo, W. J. Li, and Y. Z. Huang, "Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation," IEEE Microwave Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

Hwang, D. M.

E. Kapon, D. M. Hwang, and R. Bhat, "Stimulated emission in semiconductor quantum wire heterostructures," Phys. Rev. Lett. 63, 430-433 (1989).
[CrossRef] [PubMed]

Imamoglu, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896-899 (2007).
[CrossRef] [PubMed]

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, "Quantum Information Processing Using Quantum Dot Spins and Cavity QED," Phys. Rev. Lett. 83, 4204-4207 (1999).
[CrossRef]

Ishii, S.

S. Ishii, A. Nakagawa, and T. Baba, "Modal characteristics and bistability in twin microdisk photonic molecule lasers," IEEE J. Sel. Top. Quantum Electron. 12, 71-77 (2006).
[CrossRef]

S. Ishii, K. Nozaki, and T. Baba, "Photonic molecules in photonic crystals," Jpn. J. Appl. Phys. 45, 6108-6111 (2006).
[CrossRef]

Jimba, Y.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623-4626 (1999).
[CrossRef]

Kamp, M.

Kapon, E.

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, "Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity," Appl. Phys. Lett. 90, 153107 (2007).
[CrossRef]

E. Kapon, D. M. Hwang, and R. Bhat, "Stimulated emission in semiconductor quantum wire heterostructures," Phys. Rev. Lett. 63, 430-433 (1989).
[CrossRef] [PubMed]

Karle, T.

Karlsson, K. F.

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, "Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity," Appl. Phys. Lett. 90, 153107 (2007).
[CrossRef]

Khoe, G. D.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Knipp, P. A.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, "Optical modes in photonic molecules," Phys. Rev. Lett. 81, 2582-2585 (1998).
[CrossRef]

Krauss, T. F.

Kroha, J.

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, "Switchable lasing in multimode microcavities," Phys. Rev. Lett. 99, 073902 (2007).
[CrossRef] [PubMed]

Kulakovskii, V. D.

T. D. Happ, M. Kamp, A. Forchel, A. V. Bazhenov, I. I. Tartakovskii, A. Gorbunov, and V. D. Kulakovskii, "Coupling of point-defect microcavities in two-dimensional photonic-crystal slabs," J. Opt. Soc. Am. B 20, 373-378 (2003).
[CrossRef]

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, "Optical modes in photonic molecules," Phys. Rev. Lett. 81, 2582-2585 (1998).
[CrossRef]

Kuwata-Gonokami, M.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623-4626 (1999).
[CrossRef]

Laine, J. P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Lavrinenko, A. V.

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, "Switchable lasing in multimode microcavities," Phys. Rev. Lett. 99, 073902 (2007).
[CrossRef] [PubMed]

Leijtens, X. J. M.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Li, W. J.

W. H. Guo, W. J. Li, and Y. Z. Huang, "Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation," IEEE Microwave Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Loss, D.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, "Quantum Information Processing Using Quantum Dot Spins and Cavity QED," Phys. Rev. Lett. 83, 4204-4207 (1999).
[CrossRef]

Michaeli, A.

Miyazaki, H.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623-4626 (1999).
[CrossRef]

Mookherjea, S.

S. Mookherjea, and A. Yariv, "Coupled resonator optical waveguides," IEEE J. Sel. Top. Quantum Electron. 8, 448-456 (2002).
[CrossRef]

Mukaiyama, T.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623-4626 (1999).
[CrossRef]

Nakagawa, A.

S. Ishii, A. Nakagawa, and T. Baba, "Modal characteristics and bistability in twin microdisk photonic molecule lasers," IEEE J. Sel. Top. Quantum Electron. 12, 71-77 (2006).
[CrossRef]

Noda, S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Nozaki, K.

S. Ishii, K. Nozaki, and T. Baba, "Photonic molecules in photonic crystals," Jpn. J. Appl. Phys. 45, 6108-6111 (2006).
[CrossRef]

O'Brien, D.

Oel, Y. S.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Oton, C. J.

M. Ghulinyan, C. J. Oton, G. Bonetti, Z. Gaburro, and L. Pavesi, "Free-standing porous silicon single and multiple optical cavities," J. Appl. Phys. 93, 9724-9729 (2003).
[CrossRef]

Ozbay, E.

E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, "Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures," IEEE J. Quantum Electron. 38, 837-843 (2002).
[CrossRef]

Painter, O.

Pavesi, L.

M. Ghulinyan, C. J. Oton, G. Bonetti, Z. Gaburro, and L. Pavesi, "Free-standing porous silicon single and multiple optical cavities," J. Appl. Phys. 93, 9724-9729 (2003).
[CrossRef]

Qiu, M.

M. Qiu, "Micro-cavities in silicon-on-insulator photonic crystal slabs: Determining resonant frequencies and quality factors accurately," Microwave Opt. Technol. Lett. 45, 381-385 (2005).
[CrossRef]

Reinecke, T. L.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, "Optical modes in photonic molecules," Phys. Rev. Lett. 81, 2582-2585 (1998).
[CrossRef]

Reithmaier, J. P.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, "Optical modes in photonic molecules," Phys. Rev. Lett. 81, 2582-2585 (1998).
[CrossRef]

Rudra, A.

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, "Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity," Appl. Phys. Lett. 90, 153107 (2007).
[CrossRef]

Salib, M.

Settle, M. D.

Sherwin, M.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, "Quantum Information Processing Using Quantum Dot Spins and Cavity QED," Phys. Rev. Lett. 83, 4204-4207 (1999).
[CrossRef]

Smalbrugge, B.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Small, A.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, "Quantum Information Processing Using Quantum Dot Spins and Cavity QED," Phys. Rev. Lett. 83, 4204-4207 (1999).
[CrossRef]

Smit, M. K.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Song, B. S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Srinivasan, K.

Tahan, C.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, "Quantum phase transitions of light," Nat. Physics 2, 856-861 (2006).
[CrossRef]

Takeda, K.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623-4626 (1999).
[CrossRef]

Tartakovskii, I. I.

Vahala, K. J.

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

Vuckovic, J.

Winger, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896-899 (2007).
[CrossRef] [PubMed]

Yamamoto, Y.

Yariv, A.

S. Mookherjea, and A. Yariv, "Coupled resonator optical waveguides," IEEE J. Sel. Top. Quantum Electron. 8, 448-456 (2002).
[CrossRef]

Zhang, B.

Zhukovsky, S. V.

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, "Switchable lasing in multimode microcavities," Phys. Rev. Lett. 99, 073902 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

D. P. Fussell and M. M. Dignam, "Engineering the quality factors of coupled-cavity modes in photonic crystal slabs," Appl. Phys. Lett. 90, 183121 (2007).
[CrossRef]

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, "Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity," Appl. Phys. Lett. 90, 153107 (2007).
[CrossRef]

IEEE J. Quantum Electron. (1)

E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, "Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures," IEEE J. Quantum Electron. 38, 837-843 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

S. Mookherjea, and A. Yariv, "Coupled resonator optical waveguides," IEEE J. Sel. Top. Quantum Electron. 8, 448-456 (2002).
[CrossRef]

S. Ishii, A. Nakagawa, and T. Baba, "Modal characteristics and bistability in twin microdisk photonic molecule lasers," IEEE J. Sel. Top. Quantum Electron. 12, 71-77 (2006).
[CrossRef]

IEEE Microwave Wirel. Compon. Lett. (1)

W. H. Guo, W. J. Li, and Y. Z. Huang, "Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation," IEEE Microwave Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

J. Appl. Phys. (1)

M. Ghulinyan, C. J. Oton, G. Bonetti, Z. Gaburro, and L. Pavesi, "Free-standing porous silicon single and multiple optical cavities," J. Appl. Phys. 93, 9724-9729 (2003).
[CrossRef]

J. Lightwave Technol. (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (1)

S. Ishii, K. Nozaki, and T. Baba, "Photonic molecules in photonic crystals," Jpn. J. Appl. Phys. 45, 6108-6111 (2006).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

M. Qiu, "Micro-cavities in silicon-on-insulator photonic crystal slabs: Determining resonant frequencies and quality factors accurately," Microwave Opt. Technol. Lett. 45, 381-385 (2005).
[CrossRef]

Nat. Physics (2)

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, "Quantum phase transitions of light," Nat. Physics 2, 856-861 (2006).
[CrossRef]

H. Altug, D. Englund, and J. Vuckovic, "Ultrafast photonic crystal nanocavity laser," Nat. Physics 2, 484-488 (2006).
[CrossRef]

Nature (4)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896-899 (2007).
[CrossRef] [PubMed]

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (1)

E. Centeno and D. Felbacq, "Rabi oscillations in bidimensional photonic crystals," Phys. Rev. B 62, 10101-10108 (2000).
[CrossRef]

Phys. Rev. Lett. (5)

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, "Quantum Information Processing Using Quantum Dot Spins and Cavity QED," Phys. Rev. Lett. 83, 4204-4207 (1999).
[CrossRef]

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, "Switchable lasing in multimode microcavities," Phys. Rev. Lett. 99, 073902 (2007).
[CrossRef] [PubMed]

E. Kapon, D. M. Hwang, and R. Bhat, "Stimulated emission in semiconductor quantum wire heterostructures," Phys. Rev. Lett. 63, 430-433 (1989).
[CrossRef] [PubMed]

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, "Optical modes in photonic molecules," Phys. Rev. Lett. 81, 2582-2585 (1998).
[CrossRef]

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623-4626 (1999).
[CrossRef]

Other (5)

The flipping is the interference effect between two wave fronts arising from the coupling cavities. Depending on the PhC-lattice geometrical fill-factor, the flipping period does not correspond to nodes (?A = ?S) at an integer number of holes in the barrier, which may accounts for larger splitting in the case of two-hole barrier.

J. M. Raimond and S. Haroche, "Atoms in Cavities," in Confined Electrons and Photons: New Physics and Applications, E. Burstein, and C. Weisbuch, eds. (Plenum Press, New York, 1995).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Publishers, 2005).

S. Lam, A. R. Chalcraft, D. Szymanski, R. Oulton, B. D. Jones, D. Sanvitto, D. M. Whittaker, M. Fox, M. S. Skolnick, D. O'Brien, T. F. Krauss, H. Liu, P. W. Fry, and M. Hopkinson, "Coupled Resonant Modes of Dual L3-Defect Planar Photonic Crystal Cavities," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper QFG6. http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2008-QFG6
[PubMed]

C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics (Wiley, New York, 1977).

Supplementary Material (1)

» Media 1: MOV (4034 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 (7)

Fig. 1.
Fig. 1.

Illustration to the loss splitting and the energy transfer. (a) one-dimensional envelope functions (amplitudes) of the supermodes in space. (b) Time evolution of the supermode amplitudes (upper panel; note, AS(t) curve is shifted downwards for clarity) and the intensity in the coupled system within the “cavity 1” (|AS+AA|2) and within the “cavity 2” (|AS-AA|2) in the case of ΓS =ΓA. (c) time evolution in the case of ΓS ΓA

Fig. 2.
Fig. 2.

Experimental arrangement. (a) Schematics of the fabricated structure: free-standing membrane with V-groove QWRs integrated into two coupled PhC L3 cavities, (b) Low-temperature (T=10K) micro-PL spectrum of a “bare” QWR located outside the membrane, (c,d) SEM top-views of the measured samples, (e) schematics of the selective pumping configuration.

Fig. 3.
Fig. 3.

Evidence for direct coupling of PhC L3 microcavities. (a) Micro-PL spectrum acquired for different pump locations as shown in Fig. 2(e) for a single- hole barrier structure [Fig. 2(c)]. (b) 3D FDTD simulation of the cavity spectrum using the imported SEM top view of Fig. 2(c). (c) Near-field patterns of the symmetric (MS) and the antisymmetric (MA) supermodes inferred from computed stationary mode distributions (Ey components) for the single-hole barrier structure. (d) Position-dependent micro-PL spectra for the three-hole barrier structure [Fig. 2(d)]. (e) near-field patterns for the three-hole structure showing virtually complete localization (Ey components).

Fig. 4.
Fig. 4.

Calculated complex-frequency splitting vs detuning. The Splitting curves are computed from Eq. (1) where the coupling strength g is estimated from the Fig. 3(a).

Fig. 5.
Fig. 5.

3D-FDTD simulated spectral response and Ey field distributions of the intentionally detuned L3 cavities (at fixed detuning). Note that the coupling strength is greatly reduced already for the triple-hole barrier, and the mode separation is marginally larger than for an infinite barrier (cavities computed separately). The Ey -field distributions in the case of the 3-hole barrier show slight mode delocalization, which indicates a very weak, but finite, coupling.

Fig. 6.
Fig. 6.

Diffractive losses of the coupled-cavity system (3D FDTD analysis applied to disorder-free PhC structures). (a) E-fields of the symmetric (MS) and the antisymmetric (MA) modes in the reciprocal k-space (Fourier transforms at the reference plane above the membrane), for two coupled-cavity structures with different (one-hole, five-hole) barriers schematically illustrated on the right. The corresponding field pattern for the single L3 cavity is also shown, at the bottom. Leaky field components are situated within the air light cone (encircled area). Calculated from Eq. (3), the percentage of the integrated field intensity with k-vectors located inside the light cone is shown in the insets. (b) Real-space E-field patterns (absolute value) in the plane perpendicular to the membrane and along the symmetry axis (X) of the cavities for the structures of part (a), visualizing the radiation responsible for loss. The Q-factors, shown in the insets, were extracted directly from the 3D FDTD temporal response.

Fig. 7.
Fig. 7.

Coupling and energy transfer design by PhC barrier engineering (3D FDTD analysis on disorder-free PhC structures). (a) Spectral response of the two coupled L3 cavities with increasing barrier length by adding holes. Geometry: the (normalized) radius of PhC holes is r/a=0.255, the lattice constant is a=210 nm. The field distributions (Ey ) of the symmetric (MS, red) and the antisymmetric (MA, blue) modes are fully delocalized being essentially similar to the ones shown e.g. in the Fig. 3(c). (b) Adiabatic modification of the single-hole barrier by varying the radius of the separating hole from r/a=0 to 0.4. The trends are shown for both the mode frequencies (MA and MS solid curves, left axis) and their Q-factors (dashed curves, right axis). Crossing point ΓSA is indicated. The horizontal straight lines indicate the wavelength (solid) and the Q-factor (dashed) of an unperturbed L3 cavity. Vertical straight line indicates the close-to “experimental” case [i.e. compared to Fig. 3(a)]. (c) Calculated from Eq. (2), the time evolution of the field intensities in each cavity showing the energy transfer in the coupled system. The “experimental” case with loss splitting (upper panel) is compared to an optimized case (lower panel) where the losses can equalize (ΓSA). (d) 3D FDTD simulation of the PhC system that shows ΓSA : (left) time evolution of the probed field intensities (Hz component extracted from the two probes at the membrane center laterally positioned as shown on the sketch to the right); (right, bottom) cut by mirror symmetry, the in-plane near-field distributions (recorded in lg(1+|He|2) scale) corresponding to different moments in time (Media 1).

Equations (4)

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

Ω s , A + i Γ s , A = 1 2 [ ω 1 + ω 2 i ( γ 1 + γ 2 ) ] ± 1 2 [ ω 1 ω 2 i ( γ 1 γ 2 ) ] 2 + 4 g 2 ,
e 2 Γ s t e i ( Ω A Ω s ) t e ( Γ A Γ s ) t ± 1 2 .
η diff = k 2 π λ F T ( E ) 2 d k x d k y k F T ( E ) 2 d k x d k y 100 % ,
F T ( E ) 2 = F T ( E x ) 2 + F T ( E y ) 2 + F T ( E z ) 2

Metrics