Abstract

We investigated experimentally 1D and 2D arrays of coupled L3 photonic crystal cavities. The optical modes of the coupled cavity arrays are fed by a site-controlled quantum wire light source. By performing photoluminescence measurements and relying on near-field calculation of the cavitiy modes, we evidence optical coupling between the cavities as well as supermode delocalization. In particular, for small cavity separations, fabrication induced disorder effects are shown to be negligible compared to optical coupling between cavities.

© 2013 Optical Society of America

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2013 (3)

J. Stajic, “The future of quantum information processing,” Science 339, 1163 (2013).
[Crossref]

M. Bajcsy, A. Majumdar, A. Rundquist, and J. Vukovi, “Photon blockade with a four-level quantum emitter coupled to a photonic-crystal nanocavity,” New J. Phys. 15, 025014 (2013).
[Crossref]

T. Cai, R. Bose, G. S. Solomon, and E. Waks, “Controlled coupling of photonic crystal cavities using photochromic tuning,” Appl. Phys. Lett. 102, 141118 (2013).
[Crossref]

2012 (6)

A. Majumdar, A. Rundquist, M. Bajcsy, V. D. Dasika, S. R. Bank, and J. Vukovi, “Design and analysis of photonic crystal coupled cavity arrays for quantum simulation,” Phys. Rev. B 86, 195312 (2012).
[Crossref]

S. Ritter, C. Nlleke, C. Hahn, A. Reiserer, A. Neuzner, M. Uphoff, M. Mcke, E. Figueroa, J. Bochmann, and G. Rempe, “An elementary quantum network of single atoms in optical cavities,” Nature 484, 195–200 (2012).
[Crossref]

J. I. Cirac and P. Zoller, “Goals and opportunities in quantum simulation,” Nat. Phys. 8, 264–266 (2012).
[Crossref]

D. Englund, A. Majumdar, M. Bajcsy, A. Faraon, P. Petroff, and J. Vučković, “Ultrafast photon-photon interaction in a strongly coupled quantum dot-cavity system,” Phys. Rev. Lett. 108, 093604 (2012).
[Crossref]

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

R. Bose, T. Cai, G. S. Solomon, and E. Waks, “All-optical tuning of a quantum dot in a coupled cavity system,” Appl. Phys. Lett. 100, 231107 (2012).
[Crossref]

2011 (4)

S. Michaelis de Vasconcellos, A. Calvar, A. Dousse, J. Suffczyski, N. Dupuis, A. Lematre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Spatial, spectral, and polarization properties of coupled micropillar cavities,” Appl. Phys. Lett. 99, 101103 (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, and A. M. Fox, “Mode structure of coupled l3 photonic crystal cavities,” Opt. Express 19, 5670–5675 (2011).
[Crossref]

K. A. Atlasov, A. Rudra, B. Dwir, and E. Kapon, “Large mode splitting and lasing in optimally coupled photonic-crystal microcavities,” Opt. Express 19, 2619–2625 (2011).
[Crossref] [PubMed]

M. Calic, P. Gallo, M. Felici, K. A. Atlasov, B. Dwir, A. Rudra, G. Biasiol, L. Sorba, G. Tarel, V. Savona, and E. Kapon, “Phonon-mediated coupling of InGaAs/GaAs quantum-dot excitons to photonic crystal cavities,” Phys. Rev. Lett. 106, 227402 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (5)

J. J. Glennon, R. Tang, W. E. Buhro, R. A. Loomis, D. A. Bussian, H. Htoon, and V. I. Klimov, “Exciton localization and migration in individual CdSe quantum wires at low temperatures,” Phys. Rev. B 80, 081303 (2009).
[Crossref]

C. J. Matthews and R. Seviour, “Effects of disorder on the frequency and field of photonic-crystal cavity resonators,” Appl. Phys. B 94, 381–388 (2009).
[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, 151103 (2009).
[Crossref]

K. A. Atlasov, M. Calic, K. F. Karlsson, P. Gallo, A. Rudra, B. Dwir, and E. Kapon, “Photonic-crystal microcavity laser with site-controlled quantum-wire active medium,” Opt. Express 17, 18178–18183 (2009).
[Crossref]

K. A. Atlasov, P. Gallo, A. Rudra, B. Dwir, and E. Kapon, “Effect of sidewall passivation in BCl3/N2 inductively coupled plasma etching of two-dimensional GaAs photonic crystals,” J. Vac. Sci. Technol. B 27, L21–L24 (2009).
[Crossref]

2008 (2)

2007 (3)

2006 (3)

A. D. Greentree, C. Tahan, J. H. Cole, and C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).
[Crossref]

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

S. Ishii, A. Nakagawa, and T. Baba, “Modal characteristics and bistability in twin microdisk photonic molecule lasers,” IEEE J. Quantum Electron. 12, 71–77 (2006).
[Crossref]

2005 (1)

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatre, J. Dreiser, and A. Imamolu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87, 021108 (2005).
[Crossref]

2002 (1)

M. Greiner, O. Mandel, T. Esslinger, T. W. Hnsch, and I. Bloch, “Quantum phase transition from a superfluid to a mott insulator in a gas of ultracold atoms,” Nature 415, 39–44 (2002).
[Crossref]

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, 2582–2585 (1998).
[Crossref]

M. Lomascolo, P. Ciccarese, R. Cingolani, R. Rinaldi, and F. K. Reinhart, “Free versus localized exciton in GaAs v-shaped quantum wires,” J. Appl. Phys. 83, 302–305 (1998).
[Crossref]

1997 (1)

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997).
[Crossref]

1991 (2)

U. Bockelmann and G. Bastard, “Interband optical transitions in semiconductor quantum wires: selection rules and absorption spectra,” EPL 15, 215 (1991).
[Crossref]

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79, 1505–1518 (1991).
[Crossref]

1985 (1)

D. Marcuse, “Coupled mode theory of optical resonant cavities,” IEEE J. Quantum Electron. 21, 1819–1826 (1985).
[Crossref]

1982 (1)

R. P. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys. 21, 467–488 (1982).
[Crossref]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Atatre, M.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatre, J. Dreiser, and A. Imamolu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87, 021108 (2005).
[Crossref]

Atlasov, K. A.

M. Calic, P. Gallo, M. Felici, K. A. Atlasov, B. Dwir, A. Rudra, G. Biasiol, L. Sorba, G. Tarel, V. Savona, and E. Kapon, “Phonon-mediated coupling of InGaAs/GaAs quantum-dot excitons to photonic crystal cavities,” Phys. Rev. Lett. 106, 227402 (2011).
[Crossref] [PubMed]

K. A. Atlasov, A. Rudra, B. Dwir, and E. Kapon, “Large mode splitting and lasing in optimally coupled photonic-crystal microcavities,” Opt. Express 19, 2619–2625 (2011).
[Crossref] [PubMed]

K. A. Atlasov, M. Calic, K. F. Karlsson, P. Gallo, A. Rudra, B. Dwir, and E. Kapon, “Photonic-crystal microcavity laser with site-controlled quantum-wire active medium,” Opt. Express 17, 18178–18183 (2009).
[Crossref]

K. A. Atlasov, P. Gallo, A. Rudra, B. Dwir, and E. Kapon, “Effect of sidewall passivation in BCl3/N2 inductively coupled plasma etching of two-dimensional GaAs photonic crystals,” J. Vac. Sci. Technol. B 27, L21–L24 (2009).
[Crossref]

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. Express 16, 16255–16264 (2008).
[Crossref]

Baba, T.

S. Ishii, A. Nakagawa, and T. Baba, “Modal characteristics and bistability in twin microdisk photonic molecule lasers,” IEEE J. Quantum Electron. 12, 71–77 (2006).
[Crossref]

Badolato, A.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatre, J. Dreiser, and A. Imamolu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87, 021108 (2005).
[Crossref]

Bajcsy, M.

M. Bajcsy, A. Majumdar, A. Rundquist, and J. Vukovi, “Photon blockade with a four-level quantum emitter coupled to a photonic-crystal nanocavity,” New J. Phys. 15, 025014 (2013).
[Crossref]

D. Englund, A. Majumdar, M. Bajcsy, A. Faraon, P. Petroff, and J. Vučković, “Ultrafast photon-photon interaction in a strongly coupled quantum dot-cavity system,” Phys. Rev. Lett. 108, 093604 (2012).
[Crossref]

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

A. Majumdar, A. Rundquist, M. Bajcsy, V. D. Dasika, S. R. Bank, and J. Vukovi, “Design and analysis of photonic crystal coupled cavity arrays for quantum simulation,” Phys. Rev. B 86, 195312 (2012).
[Crossref]

Balet, L.

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, 151103 (2009).
[Crossref]

Bank, S. R.

A. Majumdar, A. Rundquist, M. Bajcsy, V. D. Dasika, S. R. Bank, and J. Vukovi, “Design and analysis of photonic crystal coupled cavity arrays for quantum simulation,” Phys. Rev. B 86, 195312 (2012).
[Crossref]

Bastard, G.

U. Bockelmann and G. Bastard, “Interband optical transitions in semiconductor quantum wires: selection rules and absorption spectra,” EPL 15, 215 (1991).
[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, 2582–2585 (1998).
[Crossref]

Biasiol, G.

M. Calic, P. Gallo, M. Felici, K. A. Atlasov, B. Dwir, A. Rudra, G. Biasiol, L. Sorba, G. Tarel, V. Savona, and E. Kapon, “Phonon-mediated coupling of InGaAs/GaAs quantum-dot excitons to photonic crystal cavities,” Phys. Rev. Lett. 106, 227402 (2011).
[Crossref] [PubMed]

Bloch, I.

M. Greiner, O. Mandel, T. Esslinger, T. W. Hnsch, and I. Bloch, “Quantum phase transition from a superfluid to a mott insulator in a gas of ultracold atoms,” Nature 415, 39–44 (2002).
[Crossref]

Bloch, J.

S. Michaelis de Vasconcellos, A. Calvar, A. Dousse, J. Suffczyski, N. Dupuis, A. Lematre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Spatial, spectral, and polarization properties of coupled micropillar cavities,” Appl. Phys. Lett. 99, 101103 (2011).
[Crossref]

Bochmann, J.

S. Ritter, C. Nlleke, C. Hahn, A. Reiserer, A. Neuzner, M. Uphoff, M. Mcke, E. Figueroa, J. Bochmann, and G. Rempe, “An elementary quantum network of single atoms in optical cavities,” Nature 484, 195–200 (2012).
[Crossref]

Bockelmann, U.

U. Bockelmann and G. Bastard, “Interband optical transitions in semiconductor quantum wires: selection rules and absorption spectra,” EPL 15, 215 (1991).
[Crossref]

Bose, R.

T. Cai, R. Bose, G. S. Solomon, and E. Waks, “Controlled coupling of photonic crystal cavities using photochromic tuning,” Appl. Phys. Lett. 102, 141118 (2013).
[Crossref]

R. Bose, T. Cai, G. S. Solomon, and E. Waks, “All-optical tuning of a quantum dot in a coupled cavity system,” Appl. Phys. Lett. 100, 231107 (2012).
[Crossref]

Brando, F. G. S. L.

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

Buhro, W. E.

J. J. Glennon, R. Tang, W. E. Buhro, R. A. Loomis, D. A. Bussian, H. Htoon, and V. I. Klimov, “Exciton localization and migration in individual CdSe quantum wires at low temperatures,” Phys. Rev. B 80, 081303 (2009).
[Crossref]

Bussian, D. A.

J. J. Glennon, R. Tang, W. E. Buhro, R. A. Loomis, D. A. Bussian, H. Htoon, and V. I. Klimov, “Exciton localization and migration in individual CdSe quantum wires at low temperatures,” Phys. Rev. B 80, 081303 (2009).
[Crossref]

Cai, T.

T. Cai, R. Bose, G. S. Solomon, and E. Waks, “Controlled coupling of photonic crystal cavities using photochromic tuning,” Appl. Phys. Lett. 102, 141118 (2013).
[Crossref]

R. Bose, T. Cai, G. S. Solomon, and E. Waks, “All-optical tuning of a quantum dot in a coupled cavity system,” Appl. Phys. Lett. 100, 231107 (2012).
[Crossref]

Calic, M.

M. Calic, P. Gallo, M. Felici, K. A. Atlasov, B. Dwir, A. Rudra, G. Biasiol, L. Sorba, G. Tarel, V. Savona, and E. Kapon, “Phonon-mediated coupling of InGaAs/GaAs quantum-dot excitons to photonic crystal cavities,” Phys. Rev. Lett. 106, 227402 (2011).
[Crossref] [PubMed]

K. A. Atlasov, M. Calic, K. F. Karlsson, P. Gallo, A. Rudra, B. Dwir, and E. Kapon, “Photonic-crystal microcavity laser with site-controlled quantum-wire active medium,” Opt. Express 17, 18178–18183 (2009).
[Crossref]

Calleja, J. M.

Calvar, A.

S. Michaelis de Vasconcellos, A. Calvar, A. Dousse, J. Suffczyski, N. Dupuis, A. Lematre, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Spatial, spectral, and polarization properties of coupled micropillar cavities,” Appl. Phys. Lett. 99, 101103 (2011).
[Crossref]

Chalcraft, A. R. A.

Ciccarese, P.

M. Lomascolo, P. Ciccarese, R. Cingolani, R. Rinaldi, and F. K. Reinhart, “Free versus localized exciton in GaAs v-shaped quantum wires,” J. Appl. Phys. 83, 302–305 (1998).
[Crossref]

Cingolani, R.

M. Lomascolo, P. Ciccarese, R. Cingolani, R. Rinaldi, and F. K. Reinhart, “Free versus localized exciton in GaAs v-shaped quantum wires,” J. Appl. Phys. 83, 302–305 (1998).
[Crossref]

Cirac, J. I.

J. I. Cirac and P. Zoller, “Goals and opportunities in quantum simulation,” Nat. Phys. 8, 264–266 (2012).
[Crossref]

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997).
[Crossref]

Cole, J. H.

A. D. Greentree, C. Tahan, J. H. Cole, and C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).
[Crossref]

Dasika, V. D.

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A. Majumdar, A. Rundquist, M. Bajcsy, V. D. Dasika, S. R. Bank, and J. Vukovi, “Design and analysis of photonic crystal coupled cavity arrays for quantum simulation,” Phys. Rev. B 86, 195312 (2012).
[Crossref]

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[Crossref]

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Figures (5)

Fig. 1
Fig. 1

Schematics of 1D (a) and 2D (b) arrays of coupled PhC L3 nanocavities on a slab membrane; and (c) cross-sectional view of the stacked QWRs light sources integrated in the central cavity of the PhC arrays. (d) Measured spectrum of isolated QWRs (no cavities) linearly resolved in polarization along the directions V and H indicated in (b). The corresponding degree of polarization (DOP) is shown in grey (inset).

Fig. 2
Fig. 2

Computed near-field distributions for the modes of the 3 coupled cavities. (a)–(f) Cavities separated by 3 rows : (a)–(c) y component of the field for M01, M02 and M03 ; (d)–(f) x component of the field for M01, M02 and M03. (g)–(l) Cavities separated by 1 row : (g)–(i) y component of the field for M01, M02 and M03 ; (j)–(l) x component of the field for M01, M02 and M03. For clarity reasons, the positions of the cavities are indicated in figures (a) and (g). The white horizontal line indicates the position of the QWR light source. The directions x and y are analogue to the directions V and H defined in Fig. 1(b).

Fig. 3
Fig. 3

Measured PL spectra of three diagonally coupled L3 cavities, resolved in linear polarization along the directions V and H; QWR light source inserted in center cavity only: (a) spectra for 3 rows separation, (b) spectra for 1 row separation. The DOP is indicated for both spectra. Insets: SEM image of the corresponding structure. The dark line indicates the position of the QWRs. (c) Calculated M02 Ey field distribution for 3-row cavity separation; the PhC hole size follows a normal distribution with standard deviation of σd = 3 nm to mimic fabrication induced disorder. (d) Near-field intensity of the M02 mode integrated along the QWR within the central cavity as a function of σd.

Fig. 4
Fig. 4

Measured energies of the M01, M02 and M03 supermodes as a function of their mean energy value (dotted lines) for three cavity CCAs with a cavity separation of 3 rows (a) and 1 row (b). The vertical yellow lines indicate the set of points belonging to the same structure. The mean value of the supermodes energy separation Δ̄ as well as its standard deviation σ are indicated in (c) and (d) for respectively the 3 rows and 1 row separations. Δ̄ is compared to the values computed using 3D FDTD.

Fig. 5
Fig. 5

(a) PL spectra linearly resolved in linear polarization along the directions defined in Fig. 1 for a structure consisting of 5 coupled cavities (refer to inset for design). Inset: SEM image of the structure. The dark horizontal line indicates the nominal position of the QWR light source. (b)–(f) Calculated intensity distributions for the M01, M02, M03, M04 and M05 supermodes.

Tables (2)

Tables Icon

Table 1 Calculated mode energies associated to the modes of Fig. 2 for three coupled cavities separated by 3 rows (top) and 1 row (bottom). The energy separations Δ12 and Δ32 are the energy differences between the modes M02 and M01, and M03 and M02.

Tables Icon

Table 2 Calculated and experimental mode splitting for the five-cavity 2D CCA.

Equations (2)

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

DOP = I V I H I V + I H
Δ = Δ 0 2 + 4 g 2

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