Abstract

We demonstrate a large tuning of the coupling strength in Photonic Crystal molecules without changing the inter-cavity distance. The key element for the design is the “photonic barrier engineering”, where the “potential barrier” is formed by the air-holes in between the two cavities. This consists in changing the hole radius of the central row in the barrier. As a result we show, both numerically and experimentally, that the wavelength splitting in two evanescently-coupled Photonic Crystal L3 cavities (three holes missing in the ΓK direction of the underlying triangular lattice) can be continuously controlled up to 5× the initial value upon ∼ 30% of hole-size modification in the barrier. Moreover, the sign of the splitting can be reversed in such a way that the fundamental mode can be either the symmetric or the anti-symmetric one without altering neither the cavity geometry nor the inter-cavity distance. Coupling sign inversion is explained in the framework of a Fabry-Perot model with underlying propagating Bloch modes in coupled W1 waveguides.

© 2014 Optical Society of America

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References

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  1. S. Boriskina, “Photonic molecules and spectral engineering,” in Photonic Microresonator Research and Applications, Vol. 156, I. Chremmos, O. Schwelb, N. Uzunoglu, eds. (Springer, 2010) pp. 393–421.
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    [Crossref]
  4. Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
    [Crossref]
  5. X. Yang, M. Yu, D. L. Kwong, C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
    [Crossref] [PubMed]
  6. D. Gerace, H. E. Türeci, A. Imamoglu, V. Giovannetti, R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
    [Crossref]
  7. A. Majumdar, A. Rundquist, M. Bajcsy, J. Vuckovic, “Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule,” Phys. Rev. B 86, 045315 (2012).
    [Crossref]
  8. A. M. Yacomotti, S. Haddadi, S. Barbay, “Self-pulsing nanocavity laser,” Phys. Rev. A 87, 041804(R) (2013).
    [Crossref]
  9. M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch, “Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons,” Nat. Phys. 9, 275–279 (2013).
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    [Crossref]
  12. N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B 86, 035133 (2012).
    [Crossref]
  13. Y. Akahane, T. Asano, B. S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
    [Crossref] [PubMed]
  14. S. Haddadi, L. Le Gratiet, I. Sagnes, F. Raineri, A. Bazin, K. Bencheikh, J. A. Levenson, A. M. Yacomotti, “High quality beaming and efficient free-space coupling in L3 photonic crystal active nanocavities,” Opt. Express 20, 18876–18886 (2012).
    [Crossref] [PubMed]
  15. S. Haddadi, A. M. Yacomotti, I. Sagnes, F. Raineri, G. Beaudoin, L. Le Gratiet, J. A. Levenson, “Photonic crystal coupled cavities with increased beaming and free space coupling efficiency,” Appl. Phys. Lett. 102, 011107 (2013).
    [Crossref]
  16. K. A. Atlasov, K. F. Karlsson, A. Rudra, B. Dwir, E. Kapon, “Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities,” Opt. Express 16, 16255–16264 (2008).
    [Crossref] [PubMed]
  17. S. Ishii, K. Nozaki, T. Baba, “Photonic molecules in photonic crystals,” Jpn. J. Appl. Phys. 45, 6108 (2006).
    [Crossref]
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    [Crossref] [PubMed]
  19. N. Caselli, F. Intonti, F. Riboli, M. Gurioli, “Engineering the mode parity of the ground state in photonic crystal molecules,” Opt. Express 22, 4953–4959 (2014).
    [Crossref] [PubMed]
  20. G. Lecamp, J. P. Hugonin, P. Lalanne, “Theoretical and computational concepts for periodic optical waveguides,” Opt. Express 15, 11042–11060 (2007).
    [Crossref] [PubMed]
  21. The terms symmetric and antisymmetric correspond to the symmetry of the longitudinal electric field component (parallel to the ΓK direction).
  22. C. Sauvan, P. Lalanne, J. P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B 71, 165118 (2005).
    [Crossref]
  23. B. S. Song, S. Noda, T. Asano, Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).
    [Crossref]

2014 (1)

2013 (3)

S. Haddadi, A. M. Yacomotti, I. Sagnes, F. Raineri, G. Beaudoin, L. Le Gratiet, J. A. Levenson, “Photonic crystal coupled cavities with increased beaming and free space coupling efficiency,” Appl. Phys. Lett. 102, 011107 (2013).
[Crossref]

A. M. Yacomotti, S. Haddadi, S. Barbay, “Self-pulsing nanocavity laser,” Phys. Rev. A 87, 041804(R) (2013).
[Crossref]

M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch, “Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons,” Nat. Phys. 9, 275–279 (2013).
[Crossref]

2012 (4)

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B 86, 035133 (2012).
[Crossref]

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
[Crossref]

A. Majumdar, A. Rundquist, M. Bajcsy, J. Vuckovic, “Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule,” Phys. Rev. B 86, 045315 (2012).
[Crossref]

S. Haddadi, L. Le Gratiet, I. Sagnes, F. Raineri, A. Bazin, K. Bencheikh, J. A. Levenson, A. M. Yacomotti, “High quality beaming and efficient free-space coupling in L3 photonic crystal active nanocavities,” Opt. Express 20, 18876–18886 (2012).
[Crossref] [PubMed]

2011 (2)

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

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, A. M. Fox, “Mode structure of coupled L3 photonic crystal cavities,” Opt. Express 19, 5670–5675 (2011).
[Crossref] [PubMed]

2009 (2)

X. Yang, M. Yu, D. L. Kwong, C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
[Crossref] [PubMed]

D. Gerace, H. E. Türeci, A. Imamoglu, V. Giovannetti, R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[Crossref]

2008 (3)

2007 (1)

2006 (1)

S. Ishii, K. Nozaki, T. Baba, “Photonic molecules in photonic crystals,” Jpn. J. Appl. Phys. 45, 6108 (2006).
[Crossref]

2005 (2)

C. Sauvan, P. Lalanne, J. P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B 71, 165118 (2005).
[Crossref]

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

2003 (1)

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

Abbarchi, M.

M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch, “Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons,” Nat. Phys. 9, 275–279 (2013).
[Crossref]

Akahane, Y.

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

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

Amo, A.

M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch, “Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons,” Nat. Phys. 9, 275–279 (2013).
[Crossref]

Asano, T.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
[Crossref]

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

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

Atlasov, K. A.

Baba, T.

S. Ishii, K. Nozaki, T. Baba, “Photonic molecules in photonic crystals,” Jpn. J. Appl. Phys. 45, 6108 (2006).
[Crossref]

Bajcsy, M.

A. Majumdar, A. Rundquist, M. Bajcsy, J. Vuckovic, “Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule,” Phys. Rev. B 86, 045315 (2012).
[Crossref]

Balet, L.

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B 86, 035133 (2012).
[Crossref]

Barbay, S.

A. M. Yacomotti, S. Haddadi, S. Barbay, “Self-pulsing nanocavity laser,” Phys. Rev. A 87, 041804(R) (2013).
[Crossref]

Bazin, A.

Beaudoin, G.

S. Haddadi, A. M. Yacomotti, I. Sagnes, F. Raineri, G. Beaudoin, L. Le Gratiet, J. A. Levenson, “Photonic crystal coupled cavities with increased beaming and free space coupling efficiency,” Appl. Phys. Lett. 102, 011107 (2013).
[Crossref]

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

Bencheikh, K.

Bloch, J.

M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch, “Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons,” Nat. Phys. 9, 275–279 (2013).
[Crossref]

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

Boriskina, S.

S. Boriskina, “Photonic molecules and spectral engineering,” in Photonic Microresonator Research and Applications, Vol. 156, I. Chremmos, O. Schwelb, N. Uzunoglu, eds. (Springer, 2010) pp. 393–421.
[Crossref]

Brunstein, M.

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

Caselli, N.

N. Caselli, F. Intonti, F. Riboli, M. Gurioli, “Engineering the mode parity of the ground state in photonic crystal molecules,” Opt. Express 22, 4953–4959 (2014).
[Crossref] [PubMed]

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B 86, 035133 (2012).
[Crossref]

Chalcraft, A. R. A.

Dwir, B.

Fazio, R.

D. Gerace, H. E. Türeci, A. Imamoglu, V. Giovannetti, R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[Crossref]

Ferrier, L.

M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch, “Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons,” Nat. Phys. 9, 275–279 (2013).
[Crossref]

Fiore, A.

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B 86, 035133 (2012).
[Crossref]

Flayac, H.

M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch, “Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons,” Nat. Phys. 9, 275–279 (2013).
[Crossref]

Fox, A. M.

Francardi, M.

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B 86, 035133 (2012).
[Crossref]

Galopin, E.

M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch, “Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons,” Nat. Phys. 9, 275–279 (2013).
[Crossref]

Gerace, D.

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B 86, 035133 (2012).
[Crossref]

D. Gerace, H. E. Türeci, A. Imamoglu, V. Giovannetti, R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[Crossref]

Gerardino, A.

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B 86, 035133 (2012).
[Crossref]

Giovannetti, V.

D. Gerace, H. E. Türeci, A. Imamoglu, V. Giovannetti, R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[Crossref]

Gurioli, M.

N. Caselli, F. Intonti, F. Riboli, M. Gurioli, “Engineering the mode parity of the ground state in photonic crystal molecules,” Opt. Express 22, 4953–4959 (2014).
[Crossref] [PubMed]

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B 86, 035133 (2012).
[Crossref]

Haddadi, S.

S. Haddadi, A. M. Yacomotti, I. Sagnes, F. Raineri, G. Beaudoin, L. Le Gratiet, J. A. Levenson, “Photonic crystal coupled cavities with increased beaming and free space coupling efficiency,” Appl. Phys. Lett. 102, 011107 (2013).
[Crossref]

A. M. Yacomotti, S. Haddadi, S. Barbay, “Self-pulsing nanocavity laser,” Phys. Rev. A 87, 041804(R) (2013).
[Crossref]

S. Haddadi, L. Le Gratiet, I. Sagnes, F. Raineri, A. Bazin, K. Bencheikh, J. A. Levenson, A. M. Yacomotti, “High quality beaming and efficient free-space coupling in L3 photonic crystal active nanocavities,” Opt. Express 20, 18876–18886 (2012).
[Crossref] [PubMed]

Halioua, Y.

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

Hugonin, J. P.

G. Lecamp, J. P. Hugonin, P. Lalanne, “Theoretical and computational concepts for periodic optical waveguides,” Opt. Express 15, 11042–11060 (2007).
[Crossref] [PubMed]

C. Sauvan, P. Lalanne, J. P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B 71, 165118 (2005).
[Crossref]

Imamoglu, A.

D. Gerace, H. E. Türeci, A. Imamoglu, V. Giovannetti, R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[Crossref]

Intonti, F.

N. Caselli, F. Intonti, F. Riboli, M. Gurioli, “Engineering the mode parity of the ground state in photonic crystal molecules,” Opt. Express 22, 4953–4959 (2014).
[Crossref] [PubMed]

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B 86, 035133 (2012).
[Crossref]

Ishii, S.

S. Ishii, K. Nozaki, T. Baba, “Photonic molecules in photonic crystals,” Jpn. J. Appl. Phys. 45, 6108 (2006).
[Crossref]

Jones, B. D.

Kapon, E.

Karle, T. J.

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

Karlsson, K. F.

Krauss, T. F.

Kuramochi, E.

M. Notomi, E. Kuramochi, T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photon. 2, 741 (2008).
[Crossref]

Kwong, D. L.

X. Yang, M. Yu, D. L. Kwong, C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
[Crossref] [PubMed]

Lalanne, P.

G. Lecamp, J. P. Hugonin, P. Lalanne, “Theoretical and computational concepts for periodic optical waveguides,” Opt. Express 15, 11042–11060 (2007).
[Crossref] [PubMed]

C. Sauvan, P. Lalanne, J. P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B 71, 165118 (2005).
[Crossref]

Lam, S.

Le Gratiet, L.

S. Haddadi, A. M. Yacomotti, I. Sagnes, F. Raineri, G. Beaudoin, L. Le Gratiet, J. A. Levenson, “Photonic crystal coupled cavities with increased beaming and free space coupling efficiency,” Appl. Phys. Lett. 102, 011107 (2013).
[Crossref]

S. Haddadi, L. Le Gratiet, I. Sagnes, F. Raineri, A. Bazin, K. Bencheikh, J. A. Levenson, A. M. Yacomotti, “High quality beaming and efficient free-space coupling in L3 photonic crystal active nanocavities,” Opt. Express 20, 18876–18886 (2012).
[Crossref] [PubMed]

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

Lecamp, G.

Lemaître, A.

M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch, “Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons,” Nat. Phys. 9, 275–279 (2013).
[Crossref]

Levenson, J. A.

S. Haddadi, A. M. Yacomotti, I. Sagnes, F. Raineri, G. Beaudoin, L. Le Gratiet, J. A. Levenson, “Photonic crystal coupled cavities with increased beaming and free space coupling efficiency,” Appl. Phys. Lett. 102, 011107 (2013).
[Crossref]

S. Haddadi, L. Le Gratiet, I. Sagnes, F. Raineri, A. Bazin, K. Bencheikh, J. A. Levenson, A. M. Yacomotti, “High quality beaming and efficient free-space coupling in L3 photonic crystal active nanocavities,” Opt. Express 20, 18876–18886 (2012).
[Crossref] [PubMed]

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

Li, L. H.

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B 86, 035133 (2012).
[Crossref]

Liu, L.

Majumdar, A.

A. Majumdar, A. Rundquist, M. Bajcsy, J. Vuckovic, “Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule,” Phys. Rev. B 86, 045315 (2012).
[Crossref]

Malpuech, G.

M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch, “Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons,” Nat. Phys. 9, 275–279 (2013).
[Crossref]

Noda, S.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
[Crossref]

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

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

Notomi, M.

M. Notomi, E. Kuramochi, T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photon. 2, 741 (2008).
[Crossref]

Nozaki, K.

S. Ishii, K. Nozaki, T. Baba, “Photonic molecules in photonic crystals,” Jpn. J. Appl. Phys. 45, 6108 (2006).
[Crossref]

Oulton, R.

Raineri, F.

S. Haddadi, A. M. Yacomotti, I. Sagnes, F. Raineri, G. Beaudoin, L. Le Gratiet, J. A. Levenson, “Photonic crystal coupled cavities with increased beaming and free space coupling efficiency,” Appl. Phys. Lett. 102, 011107 (2013).
[Crossref]

S. Haddadi, L. Le Gratiet, I. Sagnes, F. Raineri, A. Bazin, K. Bencheikh, J. A. Levenson, A. M. Yacomotti, “High quality beaming and efficient free-space coupling in L3 photonic crystal active nanocavities,” Opt. Express 20, 18876–18886 (2012).
[Crossref] [PubMed]

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

Riboli, F.

N. Caselli, F. Intonti, F. Riboli, M. Gurioli, “Engineering the mode parity of the ground state in photonic crystal molecules,” Opt. Express 22, 4953–4959 (2014).
[Crossref] [PubMed]

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B 86, 035133 (2012).
[Crossref]

Rudra, A.

Rundquist, A.

A. Majumdar, A. Rundquist, M. Bajcsy, J. Vuckovic, “Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule,” Phys. Rev. B 86, 045315 (2012).
[Crossref]

Sagnes, I.

M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch, “Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons,” Nat. Phys. 9, 275–279 (2013).
[Crossref]

S. Haddadi, A. M. Yacomotti, I. Sagnes, F. Raineri, G. Beaudoin, L. Le Gratiet, J. A. Levenson, “Photonic crystal coupled cavities with increased beaming and free space coupling efficiency,” Appl. Phys. Lett. 102, 011107 (2013).
[Crossref]

S. Haddadi, L. Le Gratiet, I. Sagnes, F. Raineri, A. Bazin, K. Bencheikh, J. A. Levenson, A. M. Yacomotti, “High quality beaming and efficient free-space coupling in L3 photonic crystal active nanocavities,” Opt. Express 20, 18876–18886 (2012).
[Crossref] [PubMed]

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

Sala, V. G.

M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch, “Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons,” Nat. Phys. 9, 275–279 (2013).
[Crossref]

Sato, Y.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
[Crossref]

Sauvan, C.

C. Sauvan, P. Lalanne, J. P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B 71, 165118 (2005).
[Crossref]

Shang, L.

Skolnick, M. S.

Solnyshkov, D. D.

M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch, “Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons,” Nat. Phys. 9, 275–279 (2013).
[Crossref]

Song, B. S.

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

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

Szymanski, D.

Takahashi, Y.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
[Crossref]

Tanabe, T.

M. Notomi, E. Kuramochi, T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photon. 2, 741 (2008).
[Crossref]

Tanaka, Y.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
[Crossref]

Thijssen, A. C. T.

Türeci, H. E.

D. Gerace, H. E. Türeci, A. Imamoglu, V. Giovannetti, R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[Crossref]

Upham, J.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
[Crossref]

Vinattieri, A.

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B 86, 035133 (2012).
[Crossref]

Vuckovic, J.

A. Majumdar, A. Rundquist, M. Bajcsy, J. Vuckovic, “Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule,” Phys. Rev. B 86, 045315 (2012).
[Crossref]

Whittaker, D. M.

Wong, C. W.

X. Yang, M. Yu, D. L. Kwong, C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
[Crossref] [PubMed]

Xu, L.

Yacomotti, A. M.

A. M. Yacomotti, S. Haddadi, S. Barbay, “Self-pulsing nanocavity laser,” Phys. Rev. A 87, 041804(R) (2013).
[Crossref]

S. Haddadi, A. M. Yacomotti, I. Sagnes, F. Raineri, G. Beaudoin, L. Le Gratiet, J. A. Levenson, “Photonic crystal coupled cavities with increased beaming and free space coupling efficiency,” Appl. Phys. Lett. 102, 011107 (2013).
[Crossref]

S. Haddadi, L. Le Gratiet, I. Sagnes, F. Raineri, A. Bazin, K. Bencheikh, J. A. Levenson, A. M. Yacomotti, “High quality beaming and efficient free-space coupling in L3 photonic crystal active nanocavities,” Opt. Express 20, 18876–18886 (2012).
[Crossref] [PubMed]

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

Yang, X.

X. Yang, M. Yu, D. L. Kwong, C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
[Crossref] [PubMed]

Yu, M.

X. Yang, M. Yu, D. L. Kwong, C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

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

S. Haddadi, A. M. Yacomotti, I. Sagnes, F. Raineri, G. Beaudoin, L. Le Gratiet, J. A. Levenson, “Photonic crystal coupled cavities with increased beaming and free space coupling efficiency,” Appl. Phys. Lett. 102, 011107 (2013).
[Crossref]

Jpn. J. Appl. Phys. (1)

S. Ishii, K. Nozaki, T. Baba, “Photonic molecules in photonic crystals,” Jpn. J. Appl. Phys. 45, 6108 (2006).
[Crossref]

Nat. Mater. (1)

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

Nat. Photon. (2)

M. Notomi, E. Kuramochi, T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photon. 2, 741 (2008).
[Crossref]

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
[Crossref]

Nat. Phys. (2)

D. Gerace, H. E. Türeci, A. Imamoglu, V. Giovannetti, R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[Crossref]

M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch, “Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons,” Nat. Phys. 9, 275–279 (2013).
[Crossref]

Nature (1)

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

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. A (1)

A. M. Yacomotti, S. Haddadi, S. Barbay, “Self-pulsing nanocavity laser,” Phys. Rev. A 87, 041804(R) (2013).
[Crossref]

Phys. Rev. B (3)

C. Sauvan, P. Lalanne, J. P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B 71, 165118 (2005).
[Crossref]

N. Caselli, F. Intonti, F. Riboli, A. Vinattieri, D. Gerace, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, M. Gurioli, “Antibonding ground state in photonic crystal molecules,” Phys. Rev. B 86, 035133 (2012).
[Crossref]

A. Majumdar, A. Rundquist, M. Bajcsy, J. Vuckovic, “Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule,” Phys. Rev. B 86, 045315 (2012).
[Crossref]

Phys. Rev. Lett. (1)

X. Yang, M. Yu, D. L. Kwong, C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
[Crossref] [PubMed]

Other (3)

B. A. Malomed, ed., Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations (Springer, 2013).
[Crossref]

S. Boriskina, “Photonic molecules and spectral engineering,” in Photonic Microresonator Research and Applications, Vol. 156, I. Chremmos, O. Schwelb, N. Uzunoglu, eds. (Springer, 2010) pp. 393–421.
[Crossref]

The terms symmetric and antisymmetric correspond to the symmetry of the longitudinal electric field component (parallel to the ΓK direction).

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Figures (7)

Fig. 1
Fig. 1 Barrier engineering: 2D model. (a) Schematics of two coupled L3 cavities with modified barrier. Refractive index is n = 2.77, lattice period a = 0.430nm, hole radius of the PhC triangular lattice r0 = 0.266a (white holes), size of shifted holes r1 = r0 − 0.06a (red holes), and the radius of modified holes within the barrier (black holes) is r2 = r0(1 + x). (b) Numerical results of resonant wavelengths for symmetric (red) and antisymmetric (black) modes, as a function of the barrier hole size x. Filled squares: results from the Fabry-Perot model; open circles: direct numerical calculation of resonant wavelengths.
Fig. 2
Fig. 2 Building-up the Fabry-Perot model. (a) An optical defect is composed by a “free propagation” cavity region of length L = 3a surrounded by two PhC mirrors; the boundary between the cavity region and the mirror is given by the dashed lines. (b) Phase of the modal reflection [ϕr(λ)] of the Bloch modes of two coupled W1 waveguides on a PhC mirror. (c) Effective index of symmetric (red) and anti-symmetric (black) Bloch modes. The values of the effective index are taken at the resonance wavelengths of the cavities. (d) Idem as in (c) for the reflectivity phases at resonance.
Fig. 3
Fig. 3 (a) Wavelength splitting as a function of the hole size in the barrier. Filled squares: F-P model from Eq. (2); open circles: exact calculations. (b) Index (blue) and phase (green) contributions for the wavelength splitting. Degeneracy is achieved at the intersection of these two curves [see Eq. (3)].
Fig. 4
Fig. 4 (a) 3D-FDTD simulation results of wavelength splitting Δ λ = λ 0 a s λ 0 s as a function of the hole size in the barrier. (b) Modulus of (a) in log scale; red line is the initial splitting [Δλ (x = 0)]. (c) and (d) Experimental results. Target parameters for the fabrication are the same as the theoretical ones, a = 390nm, r0 = 0.232a, s=0.16a and r1 = r0 − 0.06a.
Fig. 5
Fig. 5 Dependence of wavelength splitting upon the underlying hole radius r0. Black: r0 = 0.232a, red: r0 = 0.266a and blue: r0 = 0.3a. (a) 3D-FDTD simulations and (b) Experimental results. Inset: calculated Q-factors.
Fig. 6
Fig. 6 Far field images from the shortest wavelength mode (λ<, left), and the largest wavelength one (λ>, right), for different hole sizes in the barrier. (a)–(c) 3D-FDTD simulations, (d)–(f) Experimental results with mean pump power ∼ 35μW on the sample. (a) and (d): x = −0.15; (b) and (e): x = 0; (c) and (f): x = 0.15. Other parameters are the same as in Fig. 4.
Fig. 7
Fig. 7 (a) SEM images of coupled L3 cavities on a suspended membrane with barrier engineering, for three hole sizes in the barrier. (b) Measured resonant wavelengths of splitted modes (λ<:filled squares, and λ>: empty squares) as a function of the barrier modification. Inset: PL spectra showing mode splitting. Pump power is ∼ 30μW. Target fabrication parameters are those of Fig. 4.

Equations (3)

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( 2 π / λ 0 ( s ) , ( a s ) ) n eff ( s ) , ( a s ) ( λ 0 ( s ) , ( a s ) ) L + ϕ r ( s ) , ( a s ) ( λ 0 ( s ) , ( a s ) ) = p π
Δ λ = ( p ϕ ¯ r π ) 1 ( 2 L Δ n eff + Δ ϕ r π λ ¯ ) .
Δ n eff = Δ ϕ r λ 0 2 π L ,

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