Abstract

A transition from discrete optical modes to 1D photonic bands is experimentally observed and numerically studied in planar photonic-crystal (PhC) LN microcavities of length N. For increasing N the confined modes progressively acquire a well-defined momentum, eventually reconstructing the band dispersion of the corresponding waveguide. Furthermore, photon localization due to disorder is observed experimentally in the membrane PhCs using spatially resolved photoluminescence spectroscopy. Implications on single-photon sources and transfer lines based on quasi-1D PhC structures are discussed.

© 2009 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
    [CrossRef] [PubMed]
  2. V. S. C. Manga Rao and S. Hughes, “"Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: Proposal for an efficient "on chip" single photon gun,” Phys. Rev. Lett. 99, 193101 (2007).
  3. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
    [CrossRef]
  4. A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics 1(4), 215–223 (2007).
    [CrossRef]
  5. W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006).
    [CrossRef] [PubMed]
  6. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
    [CrossRef] [PubMed]
  7. S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
    [CrossRef] [PubMed]
  8. M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, “Room temperature continuous-wave lasing in photonic crystal nanocavity,” Opt. Express 14(13), 6308–6315 (2006).
    [CrossRef] [PubMed]
  9. N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1(3), 165–171 (2007).
    [CrossRef]
  10. 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(16), 3221–3224 (1997).
    [CrossRef]
  11. C. Monroe, “Quantum information processing with atoms and photons,” Nature 416(6877), 238–246 (2002).
    [CrossRef] [PubMed]
  12. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
    [CrossRef]
  13. J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007).
    [CrossRef] [PubMed]
  14. D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vucković, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express 15(9), 5550–5558 (2007).
    [CrossRef] [PubMed]
  15. D. P. Fussell, S. Hughes, and M. M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B 78(14), 144201 (2008).
    [CrossRef]
  16. M. Qiu, “Band gap effects in asymmetric photonic crystal slabs,” Phys. Rev. B 66(3), 331031–331034 (2002).
    [CrossRef]
  17. T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101(11), 113903 (2008).
    [CrossRef] [PubMed]
  18. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
    [CrossRef] [PubMed]
  19. K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90(15), 153107 (2007).
    [CrossRef]
  20. K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 (2005).
    [CrossRef]
  21. M. Felici, K. A. Atlasov, and E. Kapon, in preparation.
  22. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
    [CrossRef] [PubMed]
  23. G. Dasbach, A. A. Dremin, M. Bayer, V. D. Kulakovskii, N. A. Gippius, and A. Forchel, “Oscillations in the differential transmission of a semiconductor microcavity with reduced symmetry,” Phys. Rev. B 65(24), 2453161–2453166 (2002).
    [CrossRef]
  24. Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, R. Raj, G. Roelkens, and D. V. Thourhout, “Hybrid InP-based photonic crystal lasers on silicon on insulators wires,” Appl. Phys. Lett. 95, 201119 (2009).
    [CrossRef]

2009

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, R. Raj, G. Roelkens, and D. V. Thourhout, “Hybrid InP-based photonic crystal lasers on silicon on insulators wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

2008

D. P. Fussell, S. Hughes, and M. M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B 78(14), 144201 (2008).
[CrossRef]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101(11), 113903 (2008).
[CrossRef] [PubMed]

2007

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007).
[CrossRef] [PubMed]

D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vucković, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express 15(9), 5550–5558 (2007).
[CrossRef] [PubMed]

V. S. C. Manga Rao and S. Hughes, “"Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: Proposal for an efficient "on chip" single photon gun,” Phys. Rev. Lett. 99, 193101 (2007).

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[CrossRef]

A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics 1(4), 215–223 (2007).
[CrossRef]

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1(3), 165–171 (2007).
[CrossRef]

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90(15), 153107 (2007).
[CrossRef]

2006

S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
[CrossRef] [PubMed]

M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, “Room temperature continuous-wave lasing in photonic crystal nanocavity,” Opt. Express 14(13), 6308–6315 (2006).
[CrossRef] [PubMed]

W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006).
[CrossRef] [PubMed]

2005

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 (2005).
[CrossRef]

2004

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

2003

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[CrossRef] [PubMed]

2002

G. Dasbach, A. A. Dremin, M. Bayer, V. D. Kulakovskii, N. A. Gippius, and A. Forchel, “Oscillations in the differential transmission of a semiconductor microcavity with reduced symmetry,” Phys. Rev. B 65(24), 2453161–2453166 (2002).
[CrossRef]

M. Qiu, “Band gap effects in asymmetric photonic crystal slabs,” Phys. Rev. B 66(3), 331031–331034 (2002).
[CrossRef]

C. Monroe, “Quantum information processing with atoms and photons,” Nature 416(6877), 238–246 (2002).
[CrossRef] [PubMed]

2001

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

1997

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[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(16), 3221–3224 (1997).
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Andreani, L. C.

S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
[CrossRef] [PubMed]

Arakawa, Y.

Asano, T.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Atature, M.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 (2005).
[CrossRef]

Atlasov, K. A.

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90(15), 153107 (2007).
[CrossRef]

Badolato, A.

S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 (2005).
[CrossRef]

Bartolini, P.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[CrossRef]

Bayer, M.

G. Dasbach, A. A. Dremin, M. Bayer, V. D. Kulakovskii, N. A. Gippius, and A. Forchel, “Oscillations in the differential transmission of a semiconductor microcavity with reduced symmetry,” Phys. Rev. B 65(24), 2453161–2453166 (2002).
[CrossRef]

Bouwmeester, D.

S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
[CrossRef] [PubMed]

Chang, H. S.

W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006).
[CrossRef] [PubMed]

Chang, W. H.

W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006).
[CrossRef] [PubMed]

Chen, W. Y.

W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006).
[CrossRef] [PubMed]

Choi, Y. S.

S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
[CrossRef] [PubMed]

Chyi, J. I.

W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006).
[CrossRef] [PubMed]

Cirac, J. I.

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(16), 3221–3224 (1997).
[CrossRef]

Dasbach, G.

G. Dasbach, A. A. Dremin, M. Bayer, V. D. Kulakovskii, N. A. Gippius, and A. Forchel, “Oscillations in the differential transmission of a semiconductor microcavity with reduced symmetry,” Phys. Rev. B 65(24), 2453161–2453166 (2002).
[CrossRef]

Deichsel, E.

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90(15), 153107 (2007).
[CrossRef]

Deppe, D. G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Dignam, M. M.

D. P. Fussell, S. Hughes, and M. M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B 78(14), 144201 (2008).
[CrossRef]

Dreiser, J.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 (2005).
[CrossRef]

Dremin, A. A.

G. Dasbach, A. A. Dremin, M. Bayer, V. D. Kulakovskii, N. A. Gippius, and A. Forchel, “Oscillations in the differential transmission of a semiconductor microcavity with reduced symmetry,” Phys. Rev. B 65(24), 2453161–2453166 (2002).
[CrossRef]

Dwir, B.

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90(15), 153107 (2007).
[CrossRef]

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Englund, D.

Faraon, A.

Forchel, A.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101(11), 113903 (2008).
[CrossRef] [PubMed]

G. Dasbach, A. A. Dremin, M. Bayer, V. D. Kulakovskii, N. A. Gippius, and A. Forchel, “Oscillations in the differential transmission of a semiconductor microcavity with reduced symmetry,” Phys. Rev. B 65(24), 2453161–2453166 (2002).
[CrossRef]

Fujita, M.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[CrossRef]

Fussell, D. P.

D. P. Fussell, S. Hughes, and M. M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B 78(14), 144201 (2008).
[CrossRef]

Gibbs, H. M.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Gippius, N. A.

G. Dasbach, A. A. Dremin, M. Bayer, V. D. Kulakovskii, N. A. Gippius, and A. Forchel, “Oscillations in the differential transmission of a semiconductor microcavity with reduced symmetry,” Phys. Rev. B 65(24), 2453161–2453166 (2002).
[CrossRef]

Gisin, N.

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1(3), 165–171 (2007).
[CrossRef]

Halioua, Y.

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, R. Raj, G. Roelkens, and D. V. Thourhout, “Hybrid InP-based photonic crystal lasers on silicon on insulators wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Hennessy, K.

S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 (2005).
[CrossRef]

Hsieh, T. P.

W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006).
[CrossRef] [PubMed]

Hsu, T. M.

W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006).
[CrossRef] [PubMed]

Hu, E.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 (2005).
[CrossRef]

Hu, E. L.

S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
[CrossRef] [PubMed]

Hughes, S.

D. P. Fussell, S. Hughes, and M. M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B 78(14), 144201 (2008).
[CrossRef]

V. S. C. Manga Rao and S. Hughes, “"Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: Proposal for an efficient "on chip" single photon gun,” Phys. Rev. Lett. 99, 193101 (2007).

Ilic, B.

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007).
[CrossRef] [PubMed]

Imamoglu, A.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 (2005).
[CrossRef]

Ishida, S.

Iwamoto, S.

Julsgaard, B.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101(11), 113903 (2008).
[CrossRef] [PubMed]

Kamp, M.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101(11), 113903 (2008).
[CrossRef] [PubMed]

Kapon, E.

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90(15), 153107 (2007).
[CrossRef]

Karle, T. J.

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, R. Raj, G. Roelkens, and D. V. Thourhout, “Hybrid InP-based photonic crystal lasers on silicon on insulators wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

Karlsson, K. F.

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90(15), 153107 (2007).
[CrossRef]

Khitrova, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Kimble, H. J.

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(16), 3221–3224 (1997).
[CrossRef]

Kulakovskii, V. D.

G. Dasbach, A. A. Dremin, M. Bayer, V. D. Kulakovskii, N. A. Gippius, and A. Forchel, “Oscillations in the differential transmission of a semiconductor microcavity with reduced symmetry,” Phys. Rev. B 65(24), 2453161–2453166 (2002).
[CrossRef]

Kumagai, N.

Lagendijk, A.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[CrossRef]

Lodahl, P.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101(11), 113903 (2008).
[CrossRef] [PubMed]

Lund-Hansen, T.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101(11), 113903 (2008).
[CrossRef] [PubMed]

Mabuchi, H.

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(16), 3221–3224 (1997).
[CrossRef]

Manga Rao, V. S. C.

V. S. C. Manga Rao and S. Hughes, “"Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: Proposal for an efficient "on chip" single photon gun,” Phys. Rev. Lett. 99, 193101 (2007).

Monnier, P.

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, R. Raj, G. Roelkens, and D. V. Thourhout, “Hybrid InP-based photonic crystal lasers on silicon on insulators wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

Monroe, C.

C. Monroe, “Quantum information processing with atoms and photons,” Nature 416(6877), 238–246 (2002).
[CrossRef] [PubMed]

Nakata, Y.

Noda, S.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Nomura, M.

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Petroff, P. M.

S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 (2005).
[CrossRef]

Qiu, M.

M. Qiu, “Band gap effects in asymmetric photonic crystal slabs,” Phys. Rev. B 66(3), 331031–331034 (2002).
[CrossRef]

Raineri, F.

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, R. Raj, G. Roelkens, and D. V. Thourhout, “Hybrid InP-based photonic crystal lasers on silicon on insulators wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

Raj, R.

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, R. Raj, G. Roelkens, and D. V. Thourhout, “Hybrid InP-based photonic crystal lasers on silicon on insulators wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

Rakher, M. T.

S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
[CrossRef] [PubMed]

Righini, R.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[CrossRef]

Roelkens, G.

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, R. Raj, G. Roelkens, and D. V. Thourhout, “Hybrid InP-based photonic crystal lasers on silicon on insulators wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

Rudra, A.

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90(15), 153107 (2007).
[CrossRef]

Rupper, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Sagnes, I.

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, R. Raj, G. Roelkens, and D. V. Thourhout, “Hybrid InP-based photonic crystal lasers on silicon on insulators wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

Scherer, A.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Shchekin, O. B.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Shields, A. J.

A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics 1(4), 215–223 (2007).
[CrossRef]

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Song, B. S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Stobbe, S.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101(11), 113903 (2008).
[CrossRef] [PubMed]

Strauf, S.

S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
[CrossRef] [PubMed]

Sünner, T.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101(11), 113903 (2008).
[CrossRef] [PubMed]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Tamboli, A.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 (2005).
[CrossRef]

Thew, R.

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1(3), 165–171 (2007).
[CrossRef]

Thourhout, D. V.

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, R. Raj, G. Roelkens, and D. V. Thourhout, “Hybrid InP-based photonic crystal lasers on silicon on insulators wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

Thyrrestrup, H.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101(11), 113903 (2008).
[CrossRef] [PubMed]

Topolancik, J.

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007).
[CrossRef] [PubMed]

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[CrossRef] [PubMed]

Vollmer, F.

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007).
[CrossRef] [PubMed]

Vuckovic, J.

Watanabe, K.

Wiersma, D. S.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[CrossRef]

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Yamamoto, Y.

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Yoshie, T.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Zhang, B.

Zoller, P.

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(16), 3221–3224 (1997).
[CrossRef]

Appl. Phys. Lett.

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90(15), 153107 (2007).
[CrossRef]

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 (2005).
[CrossRef]

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, R. Raj, G. Roelkens, and D. V. Thourhout, “Hybrid InP-based photonic crystal lasers on silicon on insulators wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

Nat. Photonics

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[CrossRef]

A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics 1(4), 215–223 (2007).
[CrossRef]

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1(3), 165–171 (2007).
[CrossRef]

Nature

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[CrossRef] [PubMed]

C. Monroe, “Quantum information processing with atoms and photons,” Nature 416(6877), 238–246 (2002).
[CrossRef] [PubMed]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. B

D. P. Fussell, S. Hughes, and M. M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B 78(14), 144201 (2008).
[CrossRef]

M. Qiu, “Band gap effects in asymmetric photonic crystal slabs,” Phys. Rev. B 66(3), 331031–331034 (2002).
[CrossRef]

G. Dasbach, A. A. Dremin, M. Bayer, V. D. Kulakovskii, N. A. Gippius, and A. Forchel, “Oscillations in the differential transmission of a semiconductor microcavity with reduced symmetry,” Phys. Rev. B 65(24), 2453161–2453166 (2002).
[CrossRef]

Phys. Rev. Lett.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101(11), 113903 (2008).
[CrossRef] [PubMed]

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007).
[CrossRef] [PubMed]

V. S. C. Manga Rao and S. Hughes, “"Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: Proposal for an efficient "on chip" single photon gun,” Phys. Rev. Lett. 99, 193101 (2007).

W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006).
[CrossRef] [PubMed]

S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96(12), 127404 (2006).
[CrossRef] [PubMed]

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(16), 3221–3224 (1997).
[CrossRef]

Other

M. Felici, K. A. Atlasov, and E. Kapon, in preparation.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

(Color online) (a) Sketch of a GaAs-air 2D PhC W1 waveguide, (b) Band diagram computed using effective index neff=3.223 (as estimated from 3D FDTD) and corrected for the infrared dispersion of nGaAs. The PhC continuum and radiative (above the light line) leaky modes are shaded in gray. The band parity notation follows the full 3D field distributions [16] (verified by 3D FDTD analysis). The odd band (red symbols) is well-defined up to the anticrossing point with the upper PhC bands. (c) SEM top-view of a fabricated L11 cavity.

Fig. 2
Fig. 2

(Color online) Simulations and experiments for LN cavity modes with increasing cavity length N. (a) Calculated spectra (insets show the Ey field-component distributions). The “mode weight” is related to the out-of-plane cavity losses [18], and it is calculated as the inverse of the Fourier transform of a given field integrated within the light-cone area normalized to that integrated over the full domain. (b) Calculated mode frequencies vs. N for the first 5 lowest-order modes (continuous lines are guides to the eye; inset shows a magnified view near saturation); (c) Measured micro-PL spectra. For L3 and L6 cavities r/a ≈ 0.24 while for L11,21,35 r/a ≈ 0.265 was chosen in order to overlap with the QWR emission. The resulting spectral offset (Δλ ≈ 8 nm) is taken into account in the figure; (d) Same as (b), but with measured values superimposed on calculated trends [the 13-nm offset is taken into account (see text)].

Fig. 3
Fig. 3

(Color online) Comparison of the W1 dispersion (black line) with the 1D Fourier transform FT { E y m , N ( x ) } (colormap) of the confined modes of the L3, L11, L21 and L35 cavities (for the latter, only the first 16 modes are shown). PhC bands are shown as grey-shaded regions, and the light line is in green.

Fig. 4
Fig. 4

(Color online) (a) Top-view SEM image of the measured L35 cavity (close-up of the cavity termination). (b) Mode patterns (Ey component) obtained from 2D-FD computations using the SEM image shown in panel (a) (lowest-order modes shown). (c) Same as Fig. 3, for the first 14 modes of the measured L35 cavity. The zoomed part shows the lowest-order states compared to an ideal L35-cavity structure (both with a=196 nm).

Fig. 5
Fig. 5

(Color online) (a) Micro-PL intensity profile of the first 6 cavity modes across the measured L35 cavity. (b) Representative micro-PL spectra excited by a ~1.5µm wide laser spot at different positions in the cavity. The spectra are vertically shifted for clarity. Excitation conditions: pulsed (3 ps, 78 MHz), 700 nm, 12.5 μW. T=50K. (c) Top-view SEM image of the measured L35 cavity [this image was used to compute the modes shown in Fig. 4(a)].

Equations (2)

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

E N m ( x , y ) = 1 V k x 0 , 2 π a c w k x m , N E w k x ( x , y ) e i k x x .
c w k x m , N = G FT { E y m , N ( x ) } | k x + G × ( W G w k x ) * .

Metrics