Abstract

We study the coupling of cavities defined by the local modulation of the waveguide width using confocal photoluminescence microscopy. We are able to spatially map the profile of the antisymmetric (antibonding) and symmetric (bonding) modes of a pair of strongly coupled cavities (photonic molecule) and follow the coupled cavity system from the strong coupling to the weak coupling regime in the presence of structural disorder. The effect of disorder on this photonic molecule is also investigated numerically with a finite-difference time-domain method and a semi-analytical approach, which enables us to quantify the light localization observed in either cavity as a function of detuning.

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  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(12), 2582–2585 (1998).
    [CrossRef]
  2. S. Ishii and T. Baba, “Bistable lasing in twin microdisk photonic molecules,” Appl. Phys. Lett.87(18), 181102 (2005).
    [CrossRef]
  3. S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett.99(7), 073902 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature432(7014), 206–209 (2004).
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  7. A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature466(7303), 217–220 (2010).
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  14. D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A76(3), 031805 (2007).
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  15. D. O’Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. Krauss, “Coupled photonic crystal heterostructure nanocavities,” Opt. Express15(3), 1228–1233 (2007).
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  16. S. Vignolini, F. Intonti, 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(15), 151103 (2009).
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    [CrossRef]
  23. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
    [CrossRef]
  24. V. A. Mandelshtam and H. S. Taylor, "Harmonic inversion of time signals," J. Chem. Phys.107, 6756-6769 (1997). Erratum, ibid. 109, 4128 (1998).
  25. E. Kuramochi, M. Notomi, M. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett.88(4), 041112 (2006).
    [CrossRef]
  26. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater.4(3), 207–210 (2005).
    [CrossRef]
  27. F. S. F. Brossard, X. L. Xu, D. A. Williams, M. Hadjipanayi, M. Hugues, M. Hopkinson, X. Wang, and R. A. Taylor, “Strongly coupled single quantum dot in a photonic crystal waveguide cavity,” Appl. Phys. Lett.97(11), 111101 (2010).
    [CrossRef]
  28. K. H. Lee, A. M. Green, R. A. Taylor, D. N. Sharp, J. Scrimgeour, O. M. Roche, J. H. Na, A. F. Jarjour, A. J. Turberfield, F. S. F. Brossard, D. A. Williams, and G. A. D. Briggs, “Registration of single quantum dots using cryogenic laser photolithography,” Appl. Phys. Lett.88(19), 193106 (2006).
    [CrossRef]
  29. D. C. Reynolds, K. K. Bajaj, C. W. Litton, G. Peters, P. W. Yu, and J. D. Parsons, “Refractive index, n, and dispersion, −dn/dλ, of GaAs at 2 K determined from Fabry–Perot cavity oscillations,” J. Appl. Phys.61(1), 342–345 (1987).
    [CrossRef]
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    [CrossRef]
  32. A. R. A. Chalcraft, S. Lam, B. D. Jones, D. Szymanski, R. Oulton, A. C. T. Thijssen, M. S. Skolnick, D. M. Whittaker, T. F. Krauss, and A. M. Fox, “Mode structure of coupled L3 photonic crystal cavities,” Opt. Express19(6), 5670–5675 (2011).
    [CrossRef] [PubMed]
  33. C. Kottke, A. Farjadpour, and S. G. Johnson, “Perturbation theory for anisotropic dielectric interfaces, and application to subpixel smoothing of discretized numerical methods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.77(3), 036611 (2008).
    [CrossRef] [PubMed]
  34. N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett.101(21), 211108 (2012).
    [CrossRef]

2012 (4)

A. Majumdar, A. Rundquist, M. Bajcsy, and J. Vuckovic, “Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule,” Phys. Rev. B86(4), 045315 (2012).
[CrossRef]

K. Foubert, B. Cluzel, L. Lalouat, E. Picard, D. Peyrade, F. de Fornel, and E. Hadji, “Influence of dimensional fluctuations on the optical coupling between nanobeam twin cavities,” Phys. Rev. B85(23), 235454 (2012).
[CrossRef]

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B86(3), 035133 (2012).
[CrossRef]

N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett.101(21), 211108 (2012).
[CrossRef]

2011 (4)

A. R. A. Chalcraft, S. Lam, B. D. Jones, D. Szymanski, R. Oulton, A. C. T. Thijssen, M. S. Skolnick, D. M. Whittaker, T. F. Krauss, and A. M. Fox, “Mode structure of coupled L3 photonic crystal cavities,” Opt. Express19(6), 5670–5675 (2011).
[CrossRef] [PubMed]

M. Brunstein, T. J. Karle, I. Sagnes, F. Raineri, J. Bloch, Y. Halioua, G. Beaudoin, L. Le Gratiet, J. A. Levenson, and A. M. Yacomotti, “Radiation patterns from coupled photonic crystal nanocavities,” Appl. Phys. Lett.99(11), 111101 (2011).
[CrossRef]

M. Bamba, A. Imamoğlu, I. Carusotto, and C. Ciuti, “Origin of strong photon antibunching in weakly nonlinear photonic molecules,” Phys. Rev. A83(2), 021802 (2011).
[CrossRef]

M. Bamba and C. Ciuti, “Counter-polarized single-photon generation from the auxiliary cavity of a weakly nonlinear photonic molecule,” Appl. Phys. Lett.99(17), 171111 (2011).
[CrossRef]

2010 (5)

E. I. Simakov, L. M. Earley, C. E. Heath, D. Yu. Shchegolkov, and B. D. Schultz, “First experimental demonstration of a photonic band gap channel-drop filter at 240 GHz,” Rev. Sci. Instrum.81(10), 104701 (2010).
[CrossRef] [PubMed]

A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature466(7303), 217–220 (2010).
[CrossRef] [PubMed]

T. C. H. Liew and V. Savona, “Single photons from coupled quantum modes,” Phys. Rev. Lett.104(18), 183601 (2010).
[CrossRef] [PubMed]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

F. S. F. Brossard, X. L. Xu, D. A. Williams, M. Hadjipanayi, M. Hugues, M. Hopkinson, X. Wang, and R. A. Taylor, “Strongly coupled single quantum dot in a photonic crystal waveguide cavity,” Appl. Phys. Lett.97(11), 111101 (2010).
[CrossRef]

2009 (1)

S. Vignolini, F. Intonti, 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(15), 151103 (2009).
[CrossRef]

2008 (3)

C. Kottke, A. Farjadpour, and S. G. Johnson, “Perturbation theory for anisotropic dielectric interfaces, and application to subpixel smoothing of discretized numerical methods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.77(3), 036611 (2008).
[CrossRef] [PubMed]

K. A. Atlasov, K. F. Karlsson, A. Rudra, B. Dwir, and E. Kapon, “Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities,” Opt. Express16(20), 16255–16264 (2008).
[CrossRef] [PubMed]

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics2(12), 741–747 (2008).
[CrossRef]

2007 (3)

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A76(3), 031805 (2007).
[CrossRef]

D. O’Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. Krauss, “Coupled photonic crystal heterostructure nanocavities,” Opt. Express15(3), 1228–1233 (2007).
[CrossRef] [PubMed]

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett.99(7), 073902 (2007).
[CrossRef] [PubMed]

2006 (3)

K. H. Lee, A. M. Green, R. A. Taylor, D. N. Sharp, J. Scrimgeour, O. M. Roche, J. H. Na, A. F. Jarjour, A. J. Turberfield, F. S. F. Brossard, D. A. Williams, and G. A. D. Briggs, “Registration of single quantum dots using cryogenic laser photolithography,” Appl. Phys. Lett.88(19), 193106 (2006).
[CrossRef]

E. Kuramochi, M. Notomi, M. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett.88(4), 041112 (2006).
[CrossRef]

M. J. Hartmann, F. G. S. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys.2(12), 849–855 (2006).
[CrossRef]

2005 (3)

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater.4(3), 207–210 (2005).
[CrossRef]

L. C. Andreani, D. Gerace, and M. Agio, “Exciton-polaritons and nanoscale cavities in photonic crystal slabs,” Phys. Stat. Sol. B242(11), 2197–2209 (2005).
[CrossRef]

S. Ishii and T. Baba, “Bistable lasing in twin microdisk photonic molecules,” Appl. Phys. Lett.87(18), 181102 (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. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature432(7014), 206–209 (2004).
[CrossRef] [PubMed]

2003 (1)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature425(6961), 944–947 (2003).
[CrossRef] [PubMed]

1998 (2)

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(12), 2582–2585 (1998).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express3(1), 4–11 (1998).
[CrossRef] [PubMed]

1997 (1)

V. A. Mandelshtam and H. S. Taylor, "Harmonic inversion of time signals," J. Chem. Phys.107, 6756-6769 (1997). Erratum, ibid. 109, 4128 (1998).

1987 (1)

D. C. Reynolds, K. K. Bajaj, C. W. Litton, G. Peters, P. W. Yu, and J. D. Parsons, “Refractive index, n, and dispersion, −dn/dλ, of GaAs at 2 K determined from Fabry–Perot cavity oscillations,” J. Appl. Phys.61(1), 342–345 (1987).
[CrossRef]

Agio, M.

L. C. Andreani, D. Gerace, and M. Agio, “Exciton-polaritons and nanoscale cavities in photonic crystal slabs,” Phys. Stat. Sol. B242(11), 2197–2209 (2005).
[CrossRef]

Akahane, Y.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater.4(3), 207–210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Andreani, L. C.

L. C. Andreani, D. Gerace, and M. Agio, “Exciton-polaritons and nanoscale cavities in photonic crystal slabs,” Phys. Stat. Sol. B242(11), 2197–2209 (2005).
[CrossRef]

Angelakis, D. G.

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A76(3), 031805 (2007).
[CrossRef]

Asano, T.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater.4(3), 207–210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Atlasov, K. A.

Baba, T.

S. Ishii and T. Baba, “Bistable lasing in twin microdisk photonic molecules,” Appl. Phys. Lett.87(18), 181102 (2005).
[CrossRef]

Bajaj, K. K.

D. C. Reynolds, K. K. Bajaj, C. W. Litton, G. Peters, P. W. Yu, and J. D. Parsons, “Refractive index, n, and dispersion, −dn/dλ, of GaAs at 2 K determined from Fabry–Perot cavity oscillations,” J. Appl. Phys.61(1), 342–345 (1987).
[CrossRef]

Bajcsy, M.

A. Majumdar, A. Rundquist, M. Bajcsy, and J. Vuckovic, “Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule,” Phys. Rev. B86(4), 045315 (2012).
[CrossRef]

Balet, L.

N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett.101(21), 211108 (2012).
[CrossRef]

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B86(3), 035133 (2012).
[CrossRef]

S. Vignolini, F. Intonti, 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(15), 151103 (2009).
[CrossRef]

Bamba, M.

M. Bamba, A. Imamoğlu, I. Carusotto, and C. Ciuti, “Origin of strong photon antibunching in weakly nonlinear photonic molecules,” Phys. Rev. A83(2), 021802 (2011).
[CrossRef]

M. Bamba and C. Ciuti, “Counter-polarized single-photon generation from the auxiliary cavity of a weakly nonlinear photonic molecule,” Appl. Phys. Lett.99(17), 171111 (2011).
[CrossRef]

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(12), 2582–2585 (1998).
[CrossRef]

Beaudoin, G.

M. Brunstein, T. J. Karle, I. Sagnes, F. Raineri, J. Bloch, Y. Halioua, G. Beaudoin, L. Le Gratiet, J. A. Levenson, and A. M. Yacomotti, “Radiation patterns from coupled photonic crystal nanocavities,” Appl. Phys. Lett.99(11), 111101 (2011).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Beveratos, A.

A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature466(7303), 217–220 (2010).
[CrossRef] [PubMed]

Bianchi, C.

N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett.101(21), 211108 (2012).
[CrossRef]

Binsma, H.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature432(7014), 206–209 (2004).
[CrossRef] [PubMed]

Bloch, J.

M. Brunstein, T. J. Karle, I. Sagnes, F. Raineri, J. Bloch, Y. Halioua, G. Beaudoin, L. Le Gratiet, J. A. Levenson, and A. M. Yacomotti, “Radiation patterns from coupled photonic crystal nanocavities,” Appl. Phys. Lett.99(11), 111101 (2011).
[CrossRef]

A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature466(7303), 217–220 (2010).
[CrossRef] [PubMed]

Bose, S.

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A76(3), 031805 (2007).
[CrossRef]

Brandão, F. G. S.

M. J. Hartmann, F. G. S. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys.2(12), 849–855 (2006).
[CrossRef]

Briggs, G. A. D.

K. H. Lee, A. M. Green, R. A. Taylor, D. N. Sharp, J. Scrimgeour, O. M. Roche, J. H. Na, A. F. Jarjour, A. J. Turberfield, F. S. F. Brossard, D. A. Williams, and G. A. D. Briggs, “Registration of single quantum dots using cryogenic laser photolithography,” Appl. Phys. Lett.88(19), 193106 (2006).
[CrossRef]

Brossard, F. S. F.

F. S. F. Brossard, X. L. Xu, D. A. Williams, M. Hadjipanayi, M. Hugues, M. Hopkinson, X. Wang, and R. A. Taylor, “Strongly coupled single quantum dot in a photonic crystal waveguide cavity,” Appl. Phys. Lett.97(11), 111101 (2010).
[CrossRef]

K. H. Lee, A. M. Green, R. A. Taylor, D. N. Sharp, J. Scrimgeour, O. M. Roche, J. H. Na, A. F. Jarjour, A. J. Turberfield, F. S. F. Brossard, D. A. Williams, and G. A. D. Briggs, “Registration of single quantum dots using cryogenic laser photolithography,” Appl. Phys. Lett.88(19), 193106 (2006).
[CrossRef]

Brunstein, M.

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[CrossRef]

Oulton, R.

Parsons, J. D.

D. C. Reynolds, K. K. Bajaj, C. W. Litton, G. Peters, P. W. Yu, and J. D. Parsons, “Refractive index, n, and dispersion, −dn/dλ, of GaAs at 2 K determined from Fabry–Perot cavity oscillations,” J. Appl. Phys.61(1), 342–345 (1987).
[CrossRef]

Peters, G.

D. C. Reynolds, K. K. Bajaj, C. W. Litton, G. Peters, P. W. Yu, and J. D. Parsons, “Refractive index, n, and dispersion, −dn/dλ, of GaAs at 2 K determined from Fabry–Perot cavity oscillations,” J. Appl. Phys.61(1), 342–345 (1987).
[CrossRef]

Peyrade, D.

K. Foubert, B. Cluzel, L. Lalouat, E. Picard, D. Peyrade, F. de Fornel, and E. Hadji, “Influence of dimensional fluctuations on the optical coupling between nanobeam twin cavities,” Phys. Rev. B85(23), 235454 (2012).
[CrossRef]

Picard, E.

K. Foubert, B. Cluzel, L. Lalouat, E. Picard, D. Peyrade, F. de Fornel, and E. Hadji, “Influence of dimensional fluctuations on the optical coupling between nanobeam twin cavities,” Phys. Rev. B85(23), 235454 (2012).
[CrossRef]

Plenio, M. B.

M. J. Hartmann, F. G. S. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys.2(12), 849–855 (2006).
[CrossRef]

Raineri, F.

M. Brunstein, T. J. Karle, I. Sagnes, F. Raineri, J. Bloch, Y. Halioua, G. Beaudoin, L. Le Gratiet, J. A. Levenson, and A. M. Yacomotti, “Radiation patterns from coupled photonic crystal nanocavities,” Appl. Phys. Lett.99(11), 111101 (2011).
[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(12), 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(12), 2582–2585 (1998).
[CrossRef]

Reynolds, D. C.

D. C. Reynolds, K. K. Bajaj, C. W. Litton, G. Peters, P. W. Yu, and J. D. Parsons, “Refractive index, n, and dispersion, −dn/dλ, of GaAs at 2 K determined from Fabry–Perot cavity oscillations,” J. Appl. Phys.61(1), 342–345 (1987).
[CrossRef]

Riboli, F.

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B86(3), 035133 (2012).
[CrossRef]

N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett.101(21), 211108 (2012).
[CrossRef]

S. Vignolini, F. Intonti, 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(15), 151103 (2009).
[CrossRef]

Roche, O. M.

K. H. Lee, A. M. Green, R. A. Taylor, D. N. Sharp, J. Scrimgeour, O. M. Roche, J. H. Na, A. F. Jarjour, A. J. Turberfield, F. S. F. Brossard, D. A. Williams, and G. A. D. Briggs, “Registration of single quantum dots using cryogenic laser photolithography,” Appl. Phys. Lett.88(19), 193106 (2006).
[CrossRef]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Rudra, A.

Rundquist, A.

A. Majumdar, A. Rundquist, M. Bajcsy, and J. Vuckovic, “Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule,” Phys. Rev. B86(4), 045315 (2012).
[CrossRef]

Sagnes, I.

M. Brunstein, T. J. Karle, I. Sagnes, F. Raineri, J. Bloch, Y. Halioua, G. Beaudoin, L. Le Gratiet, J. A. Levenson, and A. M. Yacomotti, “Radiation patterns from coupled photonic crystal nanocavities,” Appl. Phys. Lett.99(11), 111101 (2011).
[CrossRef]

A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature466(7303), 217–220 (2010).
[CrossRef] [PubMed]

Salib, M.

Santos, M. F.

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A76(3), 031805 (2007).
[CrossRef]

Savona, V.

T. C. H. Liew and V. Savona, “Single photons from coupled quantum modes,” Phys. Rev. Lett.104(18), 183601 (2010).
[CrossRef] [PubMed]

Schultz, B. D.

E. I. Simakov, L. M. Earley, C. E. Heath, D. Yu. Shchegolkov, and B. D. Schultz, “First experimental demonstration of a photonic band gap channel-drop filter at 240 GHz,” Rev. Sci. Instrum.81(10), 104701 (2010).
[CrossRef] [PubMed]

Scrimgeour, J.

K. H. Lee, A. M. Green, R. A. Taylor, D. N. Sharp, J. Scrimgeour, O. M. Roche, J. H. Na, A. F. Jarjour, A. J. Turberfield, F. S. F. Brossard, D. A. Williams, and G. A. D. Briggs, “Registration of single quantum dots using cryogenic laser photolithography,” Appl. Phys. Lett.88(19), 193106 (2006).
[CrossRef]

Senellart, P.

A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature466(7303), 217–220 (2010).
[CrossRef] [PubMed]

Settle, M. D.

Sharp, D. N.

K. H. Lee, A. M. Green, R. A. Taylor, D. N. Sharp, J. Scrimgeour, O. M. Roche, J. H. Na, A. F. Jarjour, A. J. Turberfield, F. S. F. Brossard, D. A. Williams, and G. A. D. Briggs, “Registration of single quantum dots using cryogenic laser photolithography,” Appl. Phys. Lett.88(19), 193106 (2006).
[CrossRef]

Shchegolkov, D. Yu.

E. I. Simakov, L. M. Earley, C. E. Heath, D. Yu. Shchegolkov, and B. D. Schultz, “First experimental demonstration of a photonic band gap channel-drop filter at 240 GHz,” Rev. Sci. Instrum.81(10), 104701 (2010).
[CrossRef] [PubMed]

Shinya, A.

E. Kuramochi, M. Notomi, M. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett.88(4), 041112 (2006).
[CrossRef]

Simakov, E. I.

E. I. Simakov, L. M. Earley, C. E. Heath, D. Yu. Shchegolkov, and B. D. Schultz, “First experimental demonstration of a photonic band gap channel-drop filter at 240 GHz,” Rev. Sci. Instrum.81(10), 104701 (2010).
[CrossRef] [PubMed]

Skolnick, M. S.

Smalbrugge, B.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature432(7014), 206–209 (2004).
[CrossRef] [PubMed]

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. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature432(7014), 206–209 (2004).
[CrossRef] [PubMed]

Song, B. S.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater.4(3), 207–210 (2005).
[CrossRef]

Song, B.-S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Suffczynski, J.

A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature466(7303), 217–220 (2010).
[CrossRef] [PubMed]

Szymanski, D.

Tanabe, T.

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics2(12), 741–747 (2008).
[CrossRef]

E. Kuramochi, M. Notomi, M. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett.88(4), 041112 (2006).
[CrossRef]

Taylor, H. S.

V. A. Mandelshtam and H. S. Taylor, "Harmonic inversion of time signals," J. Chem. Phys.107, 6756-6769 (1997). Erratum, ibid. 109, 4128 (1998).

Taylor, R. A.

F. S. F. Brossard, X. L. Xu, D. A. Williams, M. Hadjipanayi, M. Hugues, M. Hopkinson, X. Wang, and R. A. Taylor, “Strongly coupled single quantum dot in a photonic crystal waveguide cavity,” Appl. Phys. Lett.97(11), 111101 (2010).
[CrossRef]

K. H. Lee, A. M. Green, R. A. Taylor, D. N. Sharp, J. Scrimgeour, O. M. Roche, J. H. Na, A. F. Jarjour, A. J. Turberfield, F. S. F. Brossard, D. A. Williams, and G. A. D. Briggs, “Registration of single quantum dots using cryogenic laser photolithography,” Appl. Phys. Lett.88(19), 193106 (2006).
[CrossRef]

Thijssen, A. C. T.

Turberfield, A. J.

K. H. Lee, A. M. Green, R. A. Taylor, D. N. Sharp, J. Scrimgeour, O. M. Roche, J. H. Na, A. F. Jarjour, A. J. Turberfield, F. S. F. Brossard, D. A. Williams, and G. A. D. Briggs, “Registration of single quantum dots using cryogenic laser photolithography,” Appl. Phys. Lett.88(19), 193106 (2006).
[CrossRef]

Vignolini, S.

N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett.101(21), 211108 (2012).
[CrossRef]

S. Vignolini, F. Intonti, 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(15), 151103 (2009).
[CrossRef]

Villeneuve, P. R.

Vinattieri, A.

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B86(3), 035133 (2012).
[CrossRef]

Voisin, P.

A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature466(7303), 217–220 (2010).
[CrossRef] [PubMed]

Vuckovic, J.

A. Majumdar, A. Rundquist, M. Bajcsy, and J. Vuckovic, “Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule,” Phys. Rev. B86(4), 045315 (2012).
[CrossRef]

Wang, X.

F. S. F. Brossard, X. L. Xu, D. A. Williams, M. Hadjipanayi, M. Hugues, M. Hopkinson, X. Wang, and R. A. Taylor, “Strongly coupled single quantum dot in a photonic crystal waveguide cavity,” Appl. Phys. Lett.97(11), 111101 (2010).
[CrossRef]

Watanabe, T.

E. Kuramochi, M. Notomi, M. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett.88(4), 041112 (2006).
[CrossRef]

Whittaker, D. M.

Wiersma, D. S.

S. Vignolini, F. Intonti, 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(15), 151103 (2009).
[CrossRef]

Williams, D. A.

F. S. F. Brossard, X. L. Xu, D. A. Williams, M. Hadjipanayi, M. Hugues, M. Hopkinson, X. Wang, and R. A. Taylor, “Strongly coupled single quantum dot in a photonic crystal waveguide cavity,” Appl. Phys. Lett.97(11), 111101 (2010).
[CrossRef]

K. H. Lee, A. M. Green, R. A. Taylor, D. N. Sharp, J. Scrimgeour, O. M. Roche, J. H. Na, A. F. Jarjour, A. J. Turberfield, F. S. F. Brossard, D. A. Williams, and G. A. D. Briggs, “Registration of single quantum dots using cryogenic laser photolithography,” Appl. Phys. Lett.88(19), 193106 (2006).
[CrossRef]

Xu, X. L.

F. S. F. Brossard, X. L. Xu, D. A. Williams, M. Hadjipanayi, M. Hugues, M. Hopkinson, X. Wang, and R. A. Taylor, “Strongly coupled single quantum dot in a photonic crystal waveguide cavity,” Appl. Phys. Lett.97(11), 111101 (2010).
[CrossRef]

Yacomotti, A. M.

M. Brunstein, T. J. Karle, I. Sagnes, F. Raineri, J. Bloch, Y. Halioua, G. Beaudoin, L. Le Gratiet, J. A. Levenson, and A. M. Yacomotti, “Radiation patterns from coupled photonic crystal nanocavities,” Appl. Phys. Lett.99(11), 111101 (2011).
[CrossRef]

Yu, P. W.

D. C. Reynolds, K. K. Bajaj, C. W. Litton, G. Peters, P. W. Yu, and J. D. Parsons, “Refractive index, n, and dispersion, −dn/dλ, of GaAs at 2 K determined from Fabry–Perot cavity oscillations,” J. Appl. Phys.61(1), 342–345 (1987).
[CrossRef]

Zani, M.

S. Vignolini, F. Intonti, 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(15), 151103 (2009).
[CrossRef]

Zhukovsky, S. V.

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett.99(7), 073902 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett. (8)

S. Ishii and T. Baba, “Bistable lasing in twin microdisk photonic molecules,” Appl. Phys. Lett.87(18), 181102 (2005).
[CrossRef]

M. Bamba and C. Ciuti, “Counter-polarized single-photon generation from the auxiliary cavity of a weakly nonlinear photonic molecule,” Appl. Phys. Lett.99(17), 171111 (2011).
[CrossRef]

S. Vignolini, F. Intonti, 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(15), 151103 (2009).
[CrossRef]

M. Brunstein, T. J. Karle, I. Sagnes, F. Raineri, J. Bloch, Y. Halioua, G. Beaudoin, L. Le Gratiet, J. A. Levenson, and A. M. Yacomotti, “Radiation patterns from coupled photonic crystal nanocavities,” Appl. Phys. Lett.99(11), 111101 (2011).
[CrossRef]

E. Kuramochi, M. Notomi, M. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett.88(4), 041112 (2006).
[CrossRef]

F. S. F. Brossard, X. L. Xu, D. A. Williams, M. Hadjipanayi, M. Hugues, M. Hopkinson, X. Wang, and R. A. Taylor, “Strongly coupled single quantum dot in a photonic crystal waveguide cavity,” Appl. Phys. Lett.97(11), 111101 (2010).
[CrossRef]

K. H. Lee, A. M. Green, R. A. Taylor, D. N. Sharp, J. Scrimgeour, O. M. Roche, J. H. Na, A. F. Jarjour, A. J. Turberfield, F. S. F. Brossard, D. A. Williams, and G. A. D. Briggs, “Registration of single quantum dots using cryogenic laser photolithography,” Appl. Phys. Lett.88(19), 193106 (2006).
[CrossRef]

N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett.101(21), 211108 (2012).
[CrossRef]

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Harmonic inversion of time signals (1)

V. A. Mandelshtam and H. S. Taylor, "Harmonic inversion of time signals," J. Chem. Phys.107, 6756-6769 (1997). Erratum, ibid. 109, 4128 (1998).

J. Appl. Phys. (1)

D. C. Reynolds, K. K. Bajaj, C. W. Litton, G. Peters, P. W. Yu, and J. D. Parsons, “Refractive index, n, and dispersion, −dn/dλ, of GaAs at 2 K determined from Fabry–Perot cavity oscillations,” J. Appl. Phys.61(1), 342–345 (1987).
[CrossRef]

Nat. Mater. (1)

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater.4(3), 207–210 (2005).
[CrossRef]

Nat. Photonics (1)

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics2(12), 741–747 (2008).
[CrossRef]

Nat. Phys. (1)

M. J. Hartmann, F. G. S. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys.2(12), 849–855 (2006).
[CrossRef]

Nature (3)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature425(6961), 944–947 (2003).
[CrossRef] [PubMed]

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature432(7014), 206–209 (2004).
[CrossRef] [PubMed]

A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature466(7303), 217–220 (2010).
[CrossRef] [PubMed]

Opt. Express (4)

Phys. Rev. A (2)

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A76(3), 031805 (2007).
[CrossRef]

M. Bamba, A. Imamoğlu, I. Carusotto, and C. Ciuti, “Origin of strong photon antibunching in weakly nonlinear photonic molecules,” Phys. Rev. A83(2), 021802 (2011).
[CrossRef]

Phys. Rev. B (3)

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B86(3), 035133 (2012).
[CrossRef]

A. Majumdar, A. Rundquist, M. Bajcsy, and J. Vuckovic, “Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule,” Phys. Rev. B86(4), 045315 (2012).
[CrossRef]

K. Foubert, B. Cluzel, L. Lalouat, E. Picard, D. Peyrade, F. de Fornel, and E. Hadji, “Influence of dimensional fluctuations on the optical coupling between nanobeam twin cavities,” Phys. Rev. B85(23), 235454 (2012).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

C. Kottke, A. Farjadpour, and S. G. Johnson, “Perturbation theory for anisotropic dielectric interfaces, and application to subpixel smoothing of discretized numerical methods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.77(3), 036611 (2008).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

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(12), 2582–2585 (1998).
[CrossRef]

T. C. H. Liew and V. Savona, “Single photons from coupled quantum modes,” Phys. Rev. Lett.104(18), 183601 (2010).
[CrossRef] [PubMed]

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett.99(7), 073902 (2007).
[CrossRef] [PubMed]

Phys. Stat. Sol. B (1)

L. C. Andreani, D. Gerace, and M. Agio, “Exciton-polaritons and nanoscale cavities in photonic crystal slabs,” Phys. Stat. Sol. B242(11), 2197–2209 (2005).
[CrossRef]

Rev. Sci. Instrum. (1)

E. I. Simakov, L. M. Earley, C. E. Heath, D. Yu. Shchegolkov, and B. D. Schultz, “First experimental demonstration of a photonic band gap channel-drop filter at 240 GHz,” Rev. Sci. Instrum.81(10), 104701 (2010).
[CrossRef] [PubMed]

Other (2)

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

C. Cohen-Tannoudji, B. Diu, and F. Lalöe, Quantum Mechanics (Wiley-Interscience, Paris, 1977), Chap. 4.

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Figures (7)

Fig. 1
Fig. 1

Calculated mode profiles for two-coupled and a single PhCWG cavity defined by the local modulation of the waveguide width. The waveguide width outside the cavity is given by W=0.98 3 a where a is the lattice constant. (a) Top: SEM image of the PM. Scale bar: 1 µm. The holes are shifted within each dashed hexagon by (red arrows) dy = 12 nm, (yellow arrows) 8 nm (2dy/3), and (blue arrows) 4 nm (dy/3) in a 330 nm PhC lattice with hole size ~180 nm. Bottom: Schematic band diagram of the PM showing the stop gap in red. (b-c) Ey Electric field distribution of the supermodes and their profile along the waveguide direction. The dashed lines indicate the centre of each cavity. The S mode is shown in (b) and AS mode in (c). The profile in black is obtained from 3D FDTD calculations on the PM, that in red superimposed from φ(x) + φ(x-6a) for the S mode and φ(x)-φ(x-6a) for the AS mode where φ(x) corresponds to the 3D FDTD mode profile of a single cavity and 6a the centre-to-centre distance between cavities. (d) Same as (a) but for a single cavity. (e) Ey Electric field distribution of the first order mode of a single cavity and its profile φ(x) along the waveguide direction. (f) Same as (e) but for the second order mode of the single cavity.

Fig. 2
Fig. 2

(a) Integrated PL mapping of a PhCWG without cavity. (b) SEM image of the PhCWG. The PL mapping is obtained by scanning the laser spot pumping the QDs along the direction of the waveguide defined by the X axis then translated along the Y axis.

Fig. 3
Fig. 3

Experimental demonstration of a strongly coupled system in a PM involving the first order mode of a PhCWG cavity. (a) PL spectra of a single cavity collected along the waveguide showing the first and second order bound mode of the cavity. (b) Predicted mode profile for the first and second order bound mode of a single cavity as obtained from 3D FDTD calculations. The time averaged electric field energy distribution is shown in black. The convoluted profile with a Gaussian beam of 1.2 µm size is shown by the envelope. (c) PL spectra of two-coupled cavities collected along the waveguide showing the first order S and AS supermodes. (d) Predicted time averaged electric field energy distribution and convoluted mode profile for the first order S and AS supermodes of two-coupled cavities as obtained from 3D FDTD calculations.

Fig. 4
Fig. 4

Effect of random structural variations in fabricated PMs on the profile of the supermodes of two-coupled PhCWG cavities. (a) High and low energy supermodes of a batch of nominally identical coupled cavity systems measured from the PL spectra. (b-d) PL spectra of coupled cavities obtained along the waveguide direction for each device and presented in increasing order of splitting ΔΩ = 1.8 nm, 2.2 nm and 2.8 nm, respectively.

Fig. 5
Fig. 5

Calculated splitting as a function of detuning for two-coupled PhCWG cavities. (a) Schematic band diagram showing the variation in the modulation width of the left cavity C2. In this process the holes indicated by the red arrows in Fig. 1 are spatially shifted by a few nm in the y direction. The other holes of the left cavity are shifted accordingly as to maintain the ratio described in Fig. 1.(b) Calculated detuning with 3D FDTD as a function of the variation in the modulation width (spatial detuning) of the left cavity. (c) Calculated splitting ΔΩ as a function of detuning Δλ. Results from the full 3D FDTD computation on the detuned system (plain squares) are compared with that obtained from a semi-analytic approach (circles). The straight lines correspond to the difference in the resonant wavelength between isolated (or uncoupled) cavities, hence ΔΩ = Δλ where one of them experiences the same variation in the modulation width as C2.

Fig. 6
Fig. 6

Evolution of the calculated mode profile of the S (black) and AS (blue) supermodes as a function of detuning for two-coupled PhCWG cavities showing the time averaged electric field energy distribution and the envelope resulting from the convolution with a Gaussian beam of spot size 1.2 µm. The detuning from left to right corresponds to Δλ = 0 nm, 0.6 nm, 1.2 nm, and 2.3 nm, respectively. (a-d) Results obtained from full 3D FDTD computation on the detuned system (e-h) Results obtained from the semi-analytic approach.

Fig. 7
Fig. 7

Calculated supermode delocalization factor Γ as a function of detuning Δλ for two-coupled PhCWG cavities. Results from the semi-analytical approach (circles) are compared with results from the full 3D FDTD on the detuned system for the high (plain squares) and low (empty squares) energy modes. A mechanism to explain the difference between the mode delocalization of the high and low energy modes with detuning is shown schematically in the inset.

Equations (3)

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ΔΩ= (Δλ) 2 +4 J 2 Δλ= λ 1 λ 2
ψ + (r)=( sin θ 2 ) φ 2 (r)+( cos θ 2 ) φ 1 (r) ψ - (r)=( cos θ 2 ) φ 2 (r)( sin θ 2 ) φ 1 (r) tanθ= 2J Δλ
Γ= ( sin θ 2 ) 2 ( cos θ 2 ) 2

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