Abstract

We investigate the energy splitting, quality factor and polarization of the fundamental modes of coupled L3 photonic crystal cavities. Four different geometries are evaluated theoretically, before experimentally investigating coupling in a direction at 30° to the line of the cavities. In this geometry, a smooth variation of the energy splitting with the cavity separation is predicted and observed, together with significant differences between the polarizations of the bonding and anti-bonding states. The controlled splitting of the coupled states is potentially useful for applications that require simultaneous resonant enhancement of two transitions.

© 2011 Optical Society of America

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  1. 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]
  2. S. V. Boriskina, Photonic molecules and spectral engineering in Photonic microresonator research and applications, I. Chremmos, O. Schwelb, and N. Uzonoglu, eds. (Springer, New York, 2010), pp 393–421.
    [CrossRef]
  3. 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]
  4. S. Ishii, K. Nozaki, and T. Baba, “Photonic Molecules in Photonic Crystals,” Jpn. J. Appl. Phys. 45, 6108–6111 (2006).
    [CrossRef]
  5. 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]
  6. K. Atlasov, K. F. Karlsson, A. Rudra, B. Dwir, and E. Kapon, “Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities,” Opt. Express 16, 16255–16264 (2008).
    [CrossRef] [PubMed]
  7. S. Vignolini, F. Intonit, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94, 151103 (2009).
    [CrossRef]
  8. M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
    [CrossRef]
  9. H. Lin, J.-H. Chen, S.-S. Chao, M.-C. Lo, S.-D. Lin, and W.-H. Chang, “Strong coupling of different cavity modes in photonic molecules formed by two adjacent microdisk microcavities,” Opt. Express 18, 23948–23956 (2010).
    [CrossRef] [PubMed]
  10. B. M. Möller, U. Woggon, M. V. Artemyev, and R. Wannemacher, “Photonic molecules doped with semiconductor nanocrystals,” Phys. Rev. B 70, 115323 (2004).
    [CrossRef]
  11. A. Dousse, J. Suffczynski, O. Krebs, A. Beveratos, A. Lemaitre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature 466, 217–220 (2010).
    [CrossRef] [PubMed]
  12. A. Dousse, J. Suffczyński, A. Beveratos, and O. Krebs, “A. Lemaˆıtre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “A quantum dot based bright source of entangled photon pairs operating at 53 K,” Appl. Phys. Lett. 97, 081104 (2010).
    [CrossRef]
  13. J. Cho, D. G. Angelakis, and S. Bose, “Heralded generation of entanglement with coupled cavities,” Phys. Rev. A 78, 022323 (2008).
    [CrossRef]
  14. D. Gerace, H. E. Tŭreci, A. Imamoğlu, V. Giovanetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
    [CrossRef]
  15. D. M. Whittaker, I. S. Culshaw, V. N. Astratov, and M. S. Skolnick, “Photonic band structure of patterned waveguides with dielectric and metallic cladding,” Phys. Rev. B 65, 073102 (2002).
    [CrossRef]
  16. L. C. Andreani and M. Agio, “Photonic bands and gap maps in a photonic crystal slab,” IEEE J. Quantum Electron. 38, 891–898 (2002).
    [CrossRef]
  17. L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).
    [CrossRef]
  18. A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
    [CrossRef]
  19. The modal volumes are similar for B and AB modes, and vary by less than 10% over the range of separations considered. For example, at smallest separation, the B and AB values are 1.64(⌊ /n)3 and 1.77(⌊ /n)3 respectively. This compares with V = 0.76(⌊ /n)3 for an isolated cavity in the same lattice.
  20. Three other modes exist between the _ + −1_ and _−−2_ modes. Unfortunately, the close spacings and low qualityfactors of these other modes [18] make it impractical to identify their peaks unambiguosly in Fig. 3. It is, however,likely that the predicted 1.5 meV splitting of the _ + + 1_ mode is responsible for the most prominent features; thepredicted splittings of the other two modes are insufficient to explain the peak around 1.32 eV.21.
  21. Note that the results for the FDTD simluations become inaccurate for the largest cavity separation, since theintensity above the center of the double cavity becomes very low.
  22. E. Gallardo, L. J. Martínez, A. K. Nowak, H. P. van der Meulen, J. M. Calleja, C. Tejedor, I. Prieto, D. Granados, A. G. Taboada, J. M. García, and P. A. Postigo, “Emission polarization control in semiconductor quantum dots coupled to a photonic crystal microcavity,” Opt. Express 18, 13301–13308 (2010).
    [CrossRef] [PubMed]

2010

A. Dousse, J. Suffczynski, O. Krebs, A. Beveratos, A. Lemaitre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature 466, 217–220 (2010).
[CrossRef] [PubMed]

A. Dousse, J. Suffczyński, A. Beveratos, and O. Krebs, “A. Lemaˆıtre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “A quantum dot based bright source of entangled photon pairs operating at 53 K,” Appl. Phys. Lett. 97, 081104 (2010).
[CrossRef]

E. Gallardo, L. J. Martínez, A. K. Nowak, H. P. van der Meulen, J. M. Calleja, C. Tejedor, I. Prieto, D. Granados, A. G. Taboada, J. M. García, and P. A. Postigo, “Emission polarization control in semiconductor quantum dots coupled to a photonic crystal microcavity,” Opt. Express 18, 13301–13308 (2010).
[CrossRef] [PubMed]

H. Lin, J.-H. Chen, S.-S. Chao, M.-C. Lo, S.-D. Lin, and W.-H. Chang, “Strong coupling of different cavity modes in photonic molecules formed by two adjacent microdisk microcavities,” Opt. Express 18, 23948–23956 (2010).
[CrossRef] [PubMed]

2009

S. Vignolini, F. Intonit, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94, 151103 (2009).
[CrossRef]

D. Gerace, H. E. Tŭreci, A. Imamoğlu, V. Giovanetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

2008

J. Cho, D. G. Angelakis, and S. Bose, “Heralded generation of entanglement with coupled cavities,” Phys. Rev. A 78, 022323 (2008).
[CrossRef]

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
[CrossRef]

K. Atlasov, K. F. Karlsson, A. Rudra, B. Dwir, and E. Kapon, “Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities,” Opt. Express 16, 16255–16264 (2008).
[CrossRef] [PubMed]

2007

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]

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

2006

L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).
[CrossRef]

S. Ishii, K. Nozaki, and T. Baba, “Photonic Molecules in Photonic Crystals,” Jpn. J. Appl. Phys. 45, 6108–6111 (2006).
[CrossRef]

2004

B. M. Möller, U. Woggon, M. V. Artemyev, and R. Wannemacher, “Photonic molecules doped with semiconductor nanocrystals,” Phys. Rev. B 70, 115323 (2004).
[CrossRef]

2003

2002

D. M. Whittaker, I. S. Culshaw, V. N. Astratov, and M. S. Skolnick, “Photonic band structure of patterned waveguides with dielectric and metallic cladding,” Phys. Rev. B 65, 073102 (2002).
[CrossRef]

L. C. Andreani and M. Agio, “Photonic bands and gap maps in a photonic crystal slab,” IEEE J. Quantum Electron. 38, 891–898 (2002).
[CrossRef]

Agio, M.

L. C. Andreani and M. Agio, “Photonic bands and gap maps in a photonic crystal slab,” IEEE J. Quantum Electron. 38, 891–898 (2002).
[CrossRef]

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]

Andreani, L. C.

L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).
[CrossRef]

L. C. Andreani and M. Agio, “Photonic bands and gap maps in a photonic crystal slab,” IEEE J. Quantum Electron. 38, 891–898 (2002).
[CrossRef]

Angelakis, D. G.

J. Cho, D. G. Angelakis, and S. Bose, “Heralded generation of entanglement with coupled cavities,” Phys. Rev. A 78, 022323 (2008).
[CrossRef]

Artemyev, M. V.

B. M. Möller, U. Woggon, M. V. Artemyev, and R. Wannemacher, “Photonic molecules doped with semiconductor nanocrystals,” Phys. Rev. B 70, 115323 (2004).
[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]

Astratov, V. N.

D. M. Whittaker, I. S. Culshaw, V. N. Astratov, and M. S. Skolnick, “Photonic band structure of patterned waveguides with dielectric and metallic cladding,” Phys. Rev. B 65, 073102 (2002).
[CrossRef]

Atlasov, K.

Baba, T.

S. Ishii, K. Nozaki, and T. Baba, “Photonic Molecules in Photonic Crystals,” Jpn. J. Appl. Phys. 45, 6108–6111 (2006).
[CrossRef]

Balet, L.

S. Vignolini, F. Intonit, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94, 151103 (2009).
[CrossRef]

Bazhenov, A. V.

Benyoucef, M.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Beveratos, A.

A. Dousse, J. Suffczyński, A. Beveratos, and O. Krebs, “A. Lemaˆıtre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “A quantum dot based bright source of entangled photon pairs operating at 53 K,” Appl. Phys. Lett. 97, 081104 (2010).
[CrossRef]

A. Dousse, J. Suffczynski, O. Krebs, A. Beveratos, A. Lemaitre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature 466, 217–220 (2010).
[CrossRef] [PubMed]

Bloch, J.

A. Dousse, J. Suffczynski, O. Krebs, A. Beveratos, A. Lemaitre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature 466, 217–220 (2010).
[CrossRef] [PubMed]

Bose, S.

J. Cho, D. G. Angelakis, and S. Bose, “Heralded generation of entanglement with coupled cavities,” Phys. Rev. A 78, 022323 (2008).
[CrossRef]

Calleja, J. M.

Chalcraft, A. R. A.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Chang, W.-H.

Chao, S.-S.

Chen, J.-H.

Cho, J.

J. Cho, D. G. Angelakis, and S. Bose, “Heralded generation of entanglement with coupled cavities,” Phys. Rev. A 78, 022323 (2008).
[CrossRef]

Culshaw, I. S.

D. M. Whittaker, I. S. Culshaw, V. N. Astratov, and M. S. Skolnick, “Photonic band structure of patterned waveguides with dielectric and metallic cladding,” Phys. Rev. B 65, 073102 (2002).
[CrossRef]

Dousse, A.

A. Dousse, J. Suffczynski, O. Krebs, A. Beveratos, A. Lemaitre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature 466, 217–220 (2010).
[CrossRef] [PubMed]

A. Dousse, J. Suffczyński, A. Beveratos, and O. Krebs, “A. Lemaˆıtre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “A quantum dot based bright source of entangled photon pairs operating at 53 K,” Appl. Phys. Lett. 97, 081104 (2010).
[CrossRef]

Dwir, B.

Fazio, R.

D. Gerace, H. E. Tŭreci, A. Imamoğlu, V. Giovanetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

Fiore, A.

S. Vignolini, F. Intonit, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94, 151103 (2009).
[CrossRef]

Forchel, A.

Fox, A. M.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Francardi, M.

S. Vignolini, F. Intonit, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94, 151103 (2009).
[CrossRef]

Gallardo, E.

García, J. M.

Gerace, D.

D. Gerace, H. E. Tŭreci, A. Imamoğlu, V. Giovanetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).
[CrossRef]

Gerardino, A.

S. Vignolini, F. Intonit, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94, 151103 (2009).
[CrossRef]

Giovanetti, V.

D. Gerace, H. E. Tŭreci, A. Imamoğlu, V. Giovanetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

Gorbunov, A.

Granados, D.

Gurioli, M.

S. Vignolini, F. Intonit, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94, 151103 (2009).
[CrossRef]

Happ, T. D.

Hopkinson, M.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Imamoglu, A.

D. Gerace, H. E. Tŭreci, A. Imamoğlu, V. Giovanetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

Intonit, F.

S. Vignolini, F. Intonit, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94, 151103 (2009).
[CrossRef]

Ishii, S.

S. Ishii, K. Nozaki, and T. Baba, “Photonic Molecules in Photonic Crystals,” Jpn. J. Appl. Phys. 45, 6108–6111 (2006).
[CrossRef]

Kamp, M.

Kapon, E.

Karle, T.

Karlsson, K. F.

Kiravittaya, S.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Krauss, T. F.

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]

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Krebs, O.

A. Dousse, J. Suffczyński, A. Beveratos, and O. Krebs, “A. Lemaˆıtre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “A quantum dot based bright source of entangled photon pairs operating at 53 K,” Appl. Phys. Lett. 97, 081104 (2010).
[CrossRef]

A. Dousse, J. Suffczynski, O. Krebs, A. Beveratos, A. Lemaitre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature 466, 217–220 (2010).
[CrossRef] [PubMed]

Kulakovskii, V. D.

Lam, S.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Lemaitre, A.

A. Dousse, J. Suffczynski, O. Krebs, A. Beveratos, A. Lemaitre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature 466, 217–220 (2010).
[CrossRef] [PubMed]

Li, L. H.

S. Vignolini, F. Intonit, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94, 151103 (2009).
[CrossRef]

Lin, H.

Lin, S.-D.

Liu, H.-Y.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Lo, M.-C.

Martínez, L. J.

Mei, Y. F.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Michaeli, A.

Möller, B. M.

B. M. Möller, U. Woggon, M. V. Artemyev, and R. Wannemacher, “Photonic molecules doped with semiconductor nanocrystals,” Phys. Rev. B 70, 115323 (2004).
[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]

Nowak, A. K.

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.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

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A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
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Prieto, I.

Rastelli, A.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
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S. Vignolini, F. Intonit, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94, 151103 (2009).
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Sagnes, I.

A. Dousse, J. Suffczynski, O. Krebs, A. Beveratos, A. Lemaitre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature 466, 217–220 (2010).
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A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
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Sanvitto, D.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
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Schmidt, O. G.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
[CrossRef]

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A. Dousse, J. Suffczynski, O. Krebs, A. Beveratos, A. Lemaitre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature 466, 217–220 (2010).
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Skolnick, M. S.

A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
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D. M. Whittaker, I. S. Culshaw, V. N. Astratov, and M. S. Skolnick, “Photonic band structure of patterned waveguides with dielectric and metallic cladding,” Phys. Rev. B 65, 073102 (2002).
[CrossRef]

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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).
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Suffczynski, J.

A. Dousse, J. Suffczyński, A. Beveratos, and O. Krebs, “A. Lemaˆıtre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “A quantum dot based bright source of entangled photon pairs operating at 53 K,” Appl. Phys. Lett. 97, 081104 (2010).
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A. Dousse, J. Suffczynski, O. Krebs, A. Beveratos, A. Lemaitre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature 466, 217–220 (2010).
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A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
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S. Vignolini, F. Intonit, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94, 151103 (2009).
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Voisin, P.

A. Dousse, J. Suffczynski, O. Krebs, A. Beveratos, A. Lemaitre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature 466, 217–220 (2010).
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A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
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D. M. Whittaker, I. S. Culshaw, V. N. Astratov, and M. S. Skolnick, “Photonic band structure of patterned waveguides with dielectric and metallic cladding,” Phys. Rev. B 65, 073102 (2002).
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S. Vignolini, F. Intonit, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94, 151103 (2009).
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B. M. Möller, U. Woggon, M. V. Artemyev, and R. Wannemacher, “Photonic molecules doped with semiconductor nanocrystals,” Phys. Rev. B 70, 115323 (2004).
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S. Vignolini, F. Intonit, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94, 151103 (2009).
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A. Dousse, J. Suffczyński, A. Beveratos, and O. Krebs, “A. Lemaˆıtre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “A quantum dot based bright source of entangled photon pairs operating at 53 K,” Appl. Phys. Lett. 97, 081104 (2010).
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A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H.-Y. Liu, and M. Hopkinson, “Mode structure of the L3 photonic crystal cavity,” Appl. Phys. Lett. 90, 241117 (2007).
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S. Vignolini, F. Intonit, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94, 151103 (2009).
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Nature

A. Dousse, J. Suffczynski, O. Krebs, A. Beveratos, A. Lemaitre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature 466, 217–220 (2010).
[CrossRef] [PubMed]

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).
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J. Cho, D. G. Angelakis, and S. Bose, “Heralded generation of entanglement with coupled cavities,” Phys. Rev. A 78, 022323 (2008).
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B. M. Möller, U. Woggon, M. V. Artemyev, and R. Wannemacher, “Photonic molecules doped with semiconductor nanocrystals,” Phys. Rev. B 70, 115323 (2004).
[CrossRef]

D. M. Whittaker, I. S. Culshaw, V. N. Astratov, and M. S. Skolnick, “Photonic band structure of patterned waveguides with dielectric and metallic cladding,” Phys. Rev. B 65, 073102 (2002).
[CrossRef]

L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).
[CrossRef]

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, “Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances,” Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Other

S. V. Boriskina, Photonic molecules and spectral engineering in Photonic microresonator research and applications, I. Chremmos, O. Schwelb, and N. Uzonoglu, eds. (Springer, New York, 2010), pp 393–421.
[CrossRef]

The modal volumes are similar for B and AB modes, and vary by less than 10% over the range of separations considered. For example, at smallest separation, the B and AB values are 1.64(⌊ /n)3 and 1.77(⌊ /n)3 respectively. This compares with V = 0.76(⌊ /n)3 for an isolated cavity in the same lattice.

Three other modes exist between the _ + −1_ and _−−2_ modes. Unfortunately, the close spacings and low qualityfactors of these other modes [18] make it impractical to identify their peaks unambiguosly in Fig. 3. It is, however,likely that the predicted 1.5 meV splitting of the _ + + 1_ mode is responsible for the most prominent features; thepredicted splittings of the other two modes are insufficient to explain the peak around 1.32 eV.21.

Note that the results for the FDTD simluations become inaccurate for the largest cavity separation, since theintensity above the center of the double cavity becomes very low.

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Figures (5)

Fig. 1
Fig. 1

Theoretical plots of the energies and quality factors of the split fundamental modes of parallel L3 cavities coupled along lines defined relative to those of the cavities. Green lines represent bonding (B) states, red lines represent anti-bonding (AB) states.

Fig. 2
Fig. 2

Theoretical in-plane electric fields at the center of the slab for the bonding (a–c) and anti-bonding (d–f) states. (a,d) |E|2; (b,e) Ex; (c,f) Ey. Color scales run from blue (low) to red (high). In (a) and (d), blue and red represent zero and high intensity respectively, while in (b), (c), (e) and (f), blue is negative and red positive.

Fig. 3
Fig. 3

Comparison of an experimental PL spectrum from (a) an isolated cavity, and (b) a photonic molecule with a pair of cavities separated by 2 3 a. The inset shows the experimental geometry with 30° diagonal coupling.

Fig. 4
Fig. 4

Energies (a) and quality factors (b) of the split fundamental modes of coupled L3 cavities in the 30° geometry. The theoretical results for the modes energies from Section 2 are included for comparison in (a).

Fig. 5
Fig. 5

Experimental (solid circles) and theoretical (open circles) polarization angles for the 30° geometry as a function of cavity separation. The inset shows the polar plot for a cavity separation of 2 3 a. The line at 30° indicates the coupling axis.

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