Abstract

We demonstrate both theoretically and experimentally that discrete diffraction resonance can be designed, fabricated, and successfully probed in functionalized – guidonic – coupled waveguide arrays. We evidence that double-barrier patterning of the coupling creates wavelength-independent angular tunnel resonance in the transmitted and the reflected intensity of light beams freely propagating in the plane of the array. Transmission peaks obtained are associated with resonant excitation of the engineered array bound supermodes of the functionalized array, in agreement with accurate and practical numerical modeling based on extended coupled-mode theory. The linear operation of the guidonic resonant tunneling double barrier makes up an original resonator for discrete photonics, suitable for all-optical control of light.

© 2014 Optical Society of America

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References

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  1. D. N. Christodoulides, F. Lederer, Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
    [Crossref] [PubMed]
  2. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
    [Crossref]
  3. J. M. Moison, N. Belabas, C. Minot, J. A. Levenson, “Discrete photonics in waveguide arrays,” Opt. Lett. 34(16), 2462–2464 (2009).
    [Crossref] [PubMed]
  4. A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, A. Tünnermann, “Fresnel’s laws in discrete optical media,” New J. Phys. 10(10), 103020 (2008).
    [Crossref]
  5. H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, A. Bräuer, “Tailoring guided modes in waveguide arrays,” Opt. Express 11(25), 3404–3411 (2003).
    [Crossref] [PubMed]
  6. R. A. Syms, “Approximate solution of eigenmode problems for layered coupled arrays,” IEEE J. Quantum Electron. 23(5), 525–532 (1987).
    [Crossref]
  7. N. Belabas, S. Bouchoule, I. Sagnes, J. A. Levenson, C. Minot, J. M. Moison, “Confining light flow in weakly coupled waveguide arrays by structuring the coupling constant: towards discrete diffractive optics,” Opt. Express 17(5), 3148–3156 (2009).
    [Crossref] [PubMed]
  8. J. M. Moison, N. Belabas, J. A. Levenson, C. Minot, “Light-propagation management in coupled waveguide arrays: quantitative experimental and theoretical assessment from band structures to functional patterns,” Phys. Rev. A 86(3), 033811 (2012).
    [Crossref]
  9. D. N. Christodoulides, E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001).
    [Crossref] [PubMed]
  10. R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, L. L. Buhl, “Narrowband grating resonator filters in InGaAsP/InP waveguides,” Appl. Phys. Lett. 49(3), 125–127 (1986).
    [Crossref]
  11. D. Liang, J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
    [Crossref]
  12. Y. Halioua, A. Bazin, P. Monnier, T. J. Karle, G. Roelkens, I. Sagnes, R. Raj, F. Raineri, “Hybrid III-V semiconductor/silicon nanolaser,” Opt. Express 19(10), 9221–9231 (2011).
    [Crossref] [PubMed]
  13. L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
    [Crossref]
  14. K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
    [Crossref]
  15. A. Shinya, S. Mitsugi, T. Tanabe, M. Notomi, I. Yokohama, H. Takara, S. Kawanishi, “All-optical flip-flop circuit composed of coupled two-port resonant tunneling filter in two-dimensional photonic crystal slab,” Opt. Express 14(3), 1230–1235 (2006).
    [Crossref] [PubMed]
  16. E. Sakat, S. Héron, P. Bouchon, G. Vincent, F. Pardo, S. Collin, J.-L. Pelouard, R. Haïdar, “Metal-dielectric bi-atomic structure for angular-tolerant spectral filtering,” Opt. Lett. 38(4), 425–427 (2013).
    [Crossref] [PubMed]
  17. P. Ghenuche, G. Vincent, M. Laroche, N. Bardou, R. Haïdar, J.-L. Pelouard, S. Collin, “Optical extinction in a single layer of nanorods,” Phys. Rev. Lett. 109(14), 143903 (2012).
    [Crossref] [PubMed]
  18. E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
    [Crossref]
  19. H. S. Nguyen, D. Vishnevsky, C. Sturm, D. Tanese, D. Solnyshkov, E. Galopin, A. Lemaître, I. Sagnes, A. Amo, G. Malpuech, J. Bloch, “Realization of a double-barrier resonant tunneling diode for cavity polaritons,” Phys. Rev. Lett. 110(23), 236601 (2013).
    [Crossref]
  20. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90(5), 053902 (2003).
    [Crossref] [PubMed]
  21. C. E. Rüter, J. Wisniewski, D. Kip, “Prism coupling method to excite and analyze Floquet-Bloch modes in linear and nonlinear waveguide arrays,” Opt. Lett. 31(18), 2768–2770 (2006).
    [Crossref] [PubMed]
  22. T. C. L. G. Sollner, W. D. Goodhue, P. E. Tannenwald, C. D. Parker, D. D. Peck, “Resonant tunneling through quantum wells at frequencies up to 2.5 THz,” Appl. Phys. Lett. 43(6), 588–600 (1983).
    [Crossref]
  23. B. Rico, M. Y. Azbel, “Physics of resonant tunneling. The one-dimensional double-barrier case,” Phys. Rev. B 29(4), 1970–1981 (1984).
    [Crossref]
  24. A. M. Childs, D. Gosset, “Levinson's theorem for graphs II,” J. Math. Phys. 53, 102207 (2012).
  25. Ch. Minot, N. Belabas, J. A. Levenson, J. M. Moison, “Analytical first-order extension of coupled-mode theory for waveguide arrays,” Opt. Express 18(7), 7157–7172 (2010).
    [Crossref] [PubMed]
  26. N. Belabas, Ch. Minot, J. A. Levenson, J. M. Moison, “Ab initio design, experimental validation, and scope of coupling coefficients in waveguide arrays and discrete photonics patterns,” J. Lightwave Technol. 29(19), 3009–3014 (2011).
    [Crossref]
  27. P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006).
    [Crossref]
  28. A. Zeilinger, “General properties of lossless beamsplitters in interferometry,” Am. J. Phys. 49(9), 882–883 (1981).
    [Crossref]

2013 (2)

H. S. Nguyen, D. Vishnevsky, C. Sturm, D. Tanese, D. Solnyshkov, E. Galopin, A. Lemaître, I. Sagnes, A. Amo, G. Malpuech, J. Bloch, “Realization of a double-barrier resonant tunneling diode for cavity polaritons,” Phys. Rev. Lett. 110(23), 236601 (2013).
[Crossref]

E. Sakat, S. Héron, P. Bouchon, G. Vincent, F. Pardo, S. Collin, J.-L. Pelouard, R. Haïdar, “Metal-dielectric bi-atomic structure for angular-tolerant spectral filtering,” Opt. Lett. 38(4), 425–427 (2013).
[Crossref] [PubMed]

2012 (4)

A. M. Childs, D. Gosset, “Levinson's theorem for graphs II,” J. Math. Phys. 53, 102207 (2012).

J. M. Moison, N. Belabas, J. A. Levenson, C. Minot, “Light-propagation management in coupled waveguide arrays: quantitative experimental and theoretical assessment from band structures to functional patterns,” Phys. Rev. A 86(3), 033811 (2012).
[Crossref]

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[Crossref]

P. Ghenuche, G. Vincent, M. Laroche, N. Bardou, R. Haïdar, J.-L. Pelouard, S. Collin, “Optical extinction in a single layer of nanorods,” Phys. Rev. Lett. 109(14), 143903 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (4)

Ch. Minot, N. Belabas, J. A. Levenson, J. M. Moison, “Analytical first-order extension of coupled-mode theory for waveguide arrays,” Opt. Express 18(7), 7157–7172 (2010).
[Crossref] [PubMed]

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

D. Liang, J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
[Crossref]

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

2009 (2)

2008 (2)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[Crossref]

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, A. Tünnermann, “Fresnel’s laws in discrete optical media,” New J. Phys. 10(10), 103020 (2008).
[Crossref]

2006 (3)

2003 (3)

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90(5), 053902 (2003).
[Crossref] [PubMed]

D. N. Christodoulides, F. Lederer, Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, A. Bräuer, “Tailoring guided modes in waveguide arrays,” Opt. Express 11(25), 3404–3411 (2003).
[Crossref] [PubMed]

2001 (1)

D. N. Christodoulides, E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001).
[Crossref] [PubMed]

1987 (1)

R. A. Syms, “Approximate solution of eigenmode problems for layered coupled arrays,” IEEE J. Quantum Electron. 23(5), 525–532 (1987).
[Crossref]

1986 (1)

R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, L. L. Buhl, “Narrowband grating resonator filters in InGaAsP/InP waveguides,” Appl. Phys. Lett. 49(3), 125–127 (1986).
[Crossref]

1984 (1)

B. Rico, M. Y. Azbel, “Physics of resonant tunneling. The one-dimensional double-barrier case,” Phys. Rev. B 29(4), 1970–1981 (1984).
[Crossref]

1983 (1)

T. C. L. G. Sollner, W. D. Goodhue, P. E. Tannenwald, C. D. Parker, D. D. Peck, “Resonant tunneling through quantum wells at frequencies up to 2.5 THz,” Appl. Phys. Lett. 43(6), 588–600 (1983).
[Crossref]

1981 (1)

A. Zeilinger, “General properties of lossless beamsplitters in interferometry,” Am. J. Phys. 49(9), 882–883 (1981).
[Crossref]

Aitchison, J. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90(5), 053902 (2003).
[Crossref] [PubMed]

Alferness, R. C.

R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, L. L. Buhl, “Narrowband grating resonator filters in InGaAsP/InP waveguides,” Appl. Phys. Lett. 49(3), 125–127 (1986).
[Crossref]

Amo, A.

H. S. Nguyen, D. Vishnevsky, C. Sturm, D. Tanese, D. Solnyshkov, E. Galopin, A. Lemaître, I. Sagnes, A. Amo, G. Malpuech, J. Bloch, “Realization of a double-barrier resonant tunneling diode for cavity polaritons,” Phys. Rev. Lett. 110(23), 236601 (2013).
[Crossref]

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[Crossref]

Azbel, M. Y.

B. Rico, M. Y. Azbel, “Physics of resonant tunneling. The one-dimensional double-barrier case,” Phys. Rev. B 29(4), 1970–1981 (1984).
[Crossref]

Baets, R.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

Bardou, N.

P. Ghenuche, G. Vincent, M. Laroche, N. Bardou, R. Haïdar, J.-L. Pelouard, S. Collin, “Optical extinction in a single layer of nanorods,” Phys. Rev. Lett. 109(14), 143903 (2012).
[Crossref] [PubMed]

Bazin, A.

Belabas, N.

Bloch, J.

H. S. Nguyen, D. Vishnevsky, C. Sturm, D. Tanese, D. Solnyshkov, E. Galopin, A. Lemaître, I. Sagnes, A. Amo, G. Malpuech, J. Bloch, “Realization of a double-barrier resonant tunneling diode for cavity polaritons,” Phys. Rev. Lett. 110(23), 236601 (2013).
[Crossref]

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Bouchon, P.

Bouchoule, S.

Bowers, J. E.

D. Liang, J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
[Crossref]

Bräuer, A.

Buhl, L. L.

R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, L. L. Buhl, “Narrowband grating resonator filters in InGaAsP/InP waveguides,” Appl. Phys. Lett. 49(3), 125–127 (1986).
[Crossref]

Childs, A. M.

A. M. Childs, D. Gosset, “Levinson's theorem for graphs II,” J. Math. Phys. 53, 102207 (2012).

Christodoulides, D. N.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[Crossref]

D. N. Christodoulides, F. Lederer, Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

D. N. Christodoulides, E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001).
[Crossref] [PubMed]

Collin, S.

E. Sakat, S. Héron, P. Bouchon, G. Vincent, F. Pardo, S. Collin, J.-L. Pelouard, R. Haïdar, “Metal-dielectric bi-atomic structure for angular-tolerant spectral filtering,” Opt. Lett. 38(4), 425–427 (2013).
[Crossref] [PubMed]

P. Ghenuche, G. Vincent, M. Laroche, N. Bardou, R. Haïdar, J.-L. Pelouard, S. Collin, “Optical extinction in a single layer of nanorods,” Phys. Rev. Lett. 109(14), 143903 (2012).
[Crossref] [PubMed]

de Vries, T.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

Divino, M. D.

R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, L. L. Buhl, “Narrowband grating resonator filters in InGaAsP/InP waveguides,” Appl. Phys. Lett. 49(3), 125–127 (1986).
[Crossref]

Dreisow, F.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, A. Tünnermann, “Fresnel’s laws in discrete optical media,” New J. Phys. 10(10), 103020 (2008).
[Crossref]

Eisenberg, H. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90(5), 053902 (2003).
[Crossref] [PubMed]

Eugenieva, E. D.

D. N. Christodoulides, E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001).
[Crossref] [PubMed]

Ferrier, L.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Galopin, E.

H. S. Nguyen, D. Vishnevsky, C. Sturm, D. Tanese, D. Solnyshkov, E. Galopin, A. Lemaître, I. Sagnes, A. Amo, G. Malpuech, J. Bloch, “Realization of a double-barrier resonant tunneling diode for cavity polaritons,” Phys. Rev. Lett. 110(23), 236601 (2013).
[Crossref]

Geluk, E.-J.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

Ghenuche, P.

P. Ghenuche, G. Vincent, M. Laroche, N. Bardou, R. Haïdar, J.-L. Pelouard, S. Collin, “Optical extinction in a single layer of nanorods,” Phys. Rev. Lett. 109(14), 143903 (2012).
[Crossref] [PubMed]

Goodhue, W. D.

T. C. L. G. Sollner, W. D. Goodhue, P. E. Tannenwald, C. D. Parker, D. D. Peck, “Resonant tunneling through quantum wells at frequencies up to 2.5 THz,” Appl. Phys. Lett. 43(6), 588–600 (1983).
[Crossref]

Gosset, D.

A. M. Childs, D. Gosset, “Levinson's theorem for graphs II,” J. Math. Phys. 53, 102207 (2012).

Grousson, R.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Haïdar, R.

E. Sakat, S. Héron, P. Bouchon, G. Vincent, F. Pardo, S. Collin, J.-L. Pelouard, R. Haïdar, “Metal-dielectric bi-atomic structure for angular-tolerant spectral filtering,” Opt. Lett. 38(4), 425–427 (2013).
[Crossref] [PubMed]

P. Ghenuche, G. Vincent, M. Laroche, N. Bardou, R. Haïdar, J.-L. Pelouard, S. Collin, “Optical extinction in a single layer of nanorods,” Phys. Rev. Lett. 109(14), 143903 (2012).
[Crossref] [PubMed]

Halioua, Y.

Heinrich, M.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, A. Tünnermann, “Fresnel’s laws in discrete optical media,” New J. Phys. 10(10), 103020 (2008).
[Crossref]

Héron, S.

Huybrechts, K.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

Johne, R.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Joyner, C. H.

R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, L. L. Buhl, “Narrowband grating resonator filters in InGaAsP/InP waveguides,” Appl. Phys. Lett. 49(3), 125–127 (1986).
[Crossref]

Karle, T. J.

Kavokin, A. V.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Kawaguchi, Y.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[Crossref]

Kawanishi, S.

Kip, D.

Kumar, R.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

Laroche, M.

P. Ghenuche, G. Vincent, M. Laroche, N. Bardou, R. Haïdar, J.-L. Pelouard, S. Collin, “Optical extinction in a single layer of nanorods,” Phys. Rev. Lett. 109(14), 143903 (2012).
[Crossref] [PubMed]

Lederer, F.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, A. Tünnermann, “Fresnel’s laws in discrete optical media,” New J. Phys. 10(10), 103020 (2008).
[Crossref]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[Crossref]

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, A. Bräuer, “Tailoring guided modes in waveguide arrays,” Opt. Express 11(25), 3404–3411 (2003).
[Crossref] [PubMed]

D. N. Christodoulides, F. Lederer, Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

Lemaître, A.

H. S. Nguyen, D. Vishnevsky, C. Sturm, D. Tanese, D. Solnyshkov, E. Galopin, A. Lemaître, I. Sagnes, A. Amo, G. Malpuech, J. Bloch, “Realization of a double-barrier resonant tunneling diode for cavity polaritons,” Phys. Rev. Lett. 110(23), 236601 (2013).
[Crossref]

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Levenson, J. A.

Liang, D.

D. Liang, J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
[Crossref]

Liu, L.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

Malpuech, G.

H. S. Nguyen, D. Vishnevsky, C. Sturm, D. Tanese, D. Solnyshkov, E. Galopin, A. Lemaître, I. Sagnes, A. Amo, G. Malpuech, J. Bloch, “Realization of a double-barrier resonant tunneling diode for cavity polaritons,” Phys. Rev. Lett. 110(23), 236601 (2013).
[Crossref]

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Mandelik, D.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90(5), 053902 (2003).
[Crossref] [PubMed]

Martyak, M. J. R.

R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, L. L. Buhl, “Narrowband grating resonator filters in InGaAsP/InP waveguides,” Appl. Phys. Lett. 49(3), 125–127 (1986).
[Crossref]

Matsuo, S.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[Crossref]

Michaelis, D.

Minot, C.

Minot, Ch.

Mitsugi, S.

Moison, J. M.

Monnier, P.

Morandotti, R.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90(5), 053902 (2003).
[Crossref] [PubMed]

Morthier, G.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

Nguyen, H. S.

H. S. Nguyen, D. Vishnevsky, C. Sturm, D. Tanese, D. Solnyshkov, E. Galopin, A. Lemaître, I. Sagnes, A. Amo, G. Malpuech, J. Bloch, “Realization of a double-barrier resonant tunneling diode for cavity polaritons,” Phys. Rev. Lett. 110(23), 236601 (2013).
[Crossref]

Nolte, S.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, A. Tünnermann, “Fresnel’s laws in discrete optical media,” New J. Phys. 10(10), 103020 (2008).
[Crossref]

Notomi, M.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[Crossref]

A. Shinya, S. Mitsugi, T. Tanabe, M. Notomi, I. Yokohama, H. Takara, S. Kawanishi, “All-optical flip-flop circuit composed of coupled two-port resonant tunneling filter in two-dimensional photonic crystal slab,” Opt. Express 14(3), 1230–1235 (2006).
[Crossref] [PubMed]

Nozaki, K.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[Crossref]

Pardo, F.

Parker, C. D.

T. C. L. G. Sollner, W. D. Goodhue, P. E. Tannenwald, C. D. Parker, D. D. Peck, “Resonant tunneling through quantum wells at frequencies up to 2.5 THz,” Appl. Phys. Lett. 43(6), 588–600 (1983).
[Crossref]

Peck, D. D.

T. C. L. G. Sollner, W. D. Goodhue, P. E. Tannenwald, C. D. Parker, D. D. Peck, “Resonant tunneling through quantum wells at frequencies up to 2.5 THz,” Appl. Phys. Lett. 43(6), 588–600 (1983).
[Crossref]

Pelouard, J.-L.

E. Sakat, S. Héron, P. Bouchon, G. Vincent, F. Pardo, S. Collin, J.-L. Pelouard, R. Haïdar, “Metal-dielectric bi-atomic structure for angular-tolerant spectral filtering,” Opt. Lett. 38(4), 425–427 (2013).
[Crossref] [PubMed]

P. Ghenuche, G. Vincent, M. Laroche, N. Bardou, R. Haïdar, J.-L. Pelouard, S. Collin, “Optical extinction in a single layer of nanorods,” Phys. Rev. Lett. 109(14), 143903 (2012).
[Crossref] [PubMed]

Pertsch, T.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, A. Tünnermann, “Fresnel’s laws in discrete optical media,” New J. Phys. 10(10), 103020 (2008).
[Crossref]

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, A. Bräuer, “Tailoring guided modes in waveguide arrays,” Opt. Express 11(25), 3404–3411 (2003).
[Crossref] [PubMed]

Peschel, U.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, A. Tünnermann, “Fresnel’s laws in discrete optical media,” New J. Phys. 10(10), 103020 (2008).
[Crossref]

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, A. Bräuer, “Tailoring guided modes in waveguide arrays,” Opt. Express 11(25), 3404–3411 (2003).
[Crossref] [PubMed]

Raineri, F.

Raj, R.

Regreny, P.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

Rico, B.

B. Rico, M. Y. Azbel, “Physics of resonant tunneling. The one-dimensional double-barrier case,” Phys. Rev. B 29(4), 1970–1981 (1984).
[Crossref]

Roelkens, G.

Y. Halioua, A. Bazin, P. Monnier, T. J. Karle, G. Roelkens, I. Sagnes, R. Raj, F. Raineri, “Hybrid III-V semiconductor/silicon nanolaser,” Opt. Express 19(10), 9221–9231 (2011).
[Crossref] [PubMed]

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

Russell, P. St. J.

Rüter, C. E.

Sagnes, I.

H. S. Nguyen, D. Vishnevsky, C. Sturm, D. Tanese, D. Solnyshkov, E. Galopin, A. Lemaître, I. Sagnes, A. Amo, G. Malpuech, J. Bloch, “Realization of a double-barrier resonant tunneling diode for cavity polaritons,” Phys. Rev. Lett. 110(23), 236601 (2013).
[Crossref]

Y. Halioua, A. Bazin, P. Monnier, T. J. Karle, G. Roelkens, I. Sagnes, R. Raj, F. Raineri, “Hybrid III-V semiconductor/silicon nanolaser,” Opt. Express 19(10), 9221–9231 (2011).
[Crossref] [PubMed]

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

N. Belabas, S. Bouchoule, I. Sagnes, J. A. Levenson, C. Minot, J. M. Moison, “Confining light flow in weakly coupled waveguide arrays by structuring the coupling constant: towards discrete diffractive optics,” Opt. Express 17(5), 3148–3156 (2009).
[Crossref] [PubMed]

Sakat, E.

Sanvitto, D.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Sato, T.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[Crossref]

Segawa, T.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[Crossref]

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[Crossref]

Senellart, P.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Shinya, A.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[Crossref]

A. Shinya, S. Mitsugi, T. Tanabe, M. Notomi, I. Yokohama, H. Takara, S. Kawanishi, “All-optical flip-flop circuit composed of coupled two-port resonant tunneling filter in two-dimensional photonic crystal slab,” Opt. Express 14(3), 1230–1235 (2006).
[Crossref] [PubMed]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[Crossref]

D. N. Christodoulides, F. Lederer, Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90(5), 053902 (2003).
[Crossref] [PubMed]

Sollner, T. C. L. G.

T. C. L. G. Sollner, W. D. Goodhue, P. E. Tannenwald, C. D. Parker, D. D. Peck, “Resonant tunneling through quantum wells at frequencies up to 2.5 THz,” Appl. Phys. Lett. 43(6), 588–600 (1983).
[Crossref]

Solnyshkov, D.

H. S. Nguyen, D. Vishnevsky, C. Sturm, D. Tanese, D. Solnyshkov, E. Galopin, A. Lemaître, I. Sagnes, A. Amo, G. Malpuech, J. Bloch, “Realization of a double-barrier resonant tunneling diode for cavity polaritons,” Phys. Rev. Lett. 110(23), 236601 (2013).
[Crossref]

Solnyshkov, D. D.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Spuesens, T.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[Crossref]

Streppel, U.

Sturm, C.

H. S. Nguyen, D. Vishnevsky, C. Sturm, D. Tanese, D. Solnyshkov, E. Galopin, A. Lemaître, I. Sagnes, A. Amo, G. Malpuech, J. Bloch, “Realization of a double-barrier resonant tunneling diode for cavity polaritons,” Phys. Rev. Lett. 110(23), 236601 (2013).
[Crossref]

Suzaki, Y.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[Crossref]

Syms, R. A.

R. A. Syms, “Approximate solution of eigenmode problems for layered coupled arrays,” IEEE J. Quantum Electron. 23(5), 525–532 (1987).
[Crossref]

Szameit, A.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, A. Tünnermann, “Fresnel’s laws in discrete optical media,” New J. Phys. 10(10), 103020 (2008).
[Crossref]

Takahashi, R.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[Crossref]

Takara, H.

Tanabe, T.

Tanese, D.

H. S. Nguyen, D. Vishnevsky, C. Sturm, D. Tanese, D. Solnyshkov, E. Galopin, A. Lemaître, I. Sagnes, A. Amo, G. Malpuech, J. Bloch, “Realization of a double-barrier resonant tunneling diode for cavity polaritons,” Phys. Rev. Lett. 110(23), 236601 (2013).
[Crossref]

Tannenwald, P. E.

T. C. L. G. Sollner, W. D. Goodhue, P. E. Tannenwald, C. D. Parker, D. D. Peck, “Resonant tunneling through quantum wells at frequencies up to 2.5 THz,” Appl. Phys. Lett. 43(6), 588–600 (1983).
[Crossref]

Trompeter, H.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, A. Tünnermann, “Fresnel’s laws in discrete optical media,” New J. Phys. 10(10), 103020 (2008).
[Crossref]

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, A. Bräuer, “Tailoring guided modes in waveguide arrays,” Opt. Express 11(25), 3404–3411 (2003).
[Crossref] [PubMed]

Tünnermann, A.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, A. Tünnermann, “Fresnel’s laws in discrete optical media,” New J. Phys. 10(10), 103020 (2008).
[Crossref]

Van Thourhout, D.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

Vincent, G.

E. Sakat, S. Héron, P. Bouchon, G. Vincent, F. Pardo, S. Collin, J.-L. Pelouard, R. Haïdar, “Metal-dielectric bi-atomic structure for angular-tolerant spectral filtering,” Opt. Lett. 38(4), 425–427 (2013).
[Crossref] [PubMed]

P. Ghenuche, G. Vincent, M. Laroche, N. Bardou, R. Haïdar, J.-L. Pelouard, S. Collin, “Optical extinction in a single layer of nanorods,” Phys. Rev. Lett. 109(14), 143903 (2012).
[Crossref] [PubMed]

Vishnevsky, D.

H. S. Nguyen, D. Vishnevsky, C. Sturm, D. Tanese, D. Solnyshkov, E. Galopin, A. Lemaître, I. Sagnes, A. Amo, G. Malpuech, J. Bloch, “Realization of a double-barrier resonant tunneling diode for cavity polaritons,” Phys. Rev. Lett. 110(23), 236601 (2013).
[Crossref]

Wertz, E.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Wisniewski, J.

Yokohama, I.

Zeilinger, A.

A. Zeilinger, “General properties of lossless beamsplitters in interferometry,” Am. J. Phys. 49(9), 882–883 (1981).
[Crossref]

Am. J. Phys. (1)

A. Zeilinger, “General properties of lossless beamsplitters in interferometry,” Am. J. Phys. 49(9), 882–883 (1981).
[Crossref]

Appl. Phys. Lett. (2)

T. C. L. G. Sollner, W. D. Goodhue, P. E. Tannenwald, C. D. Parker, D. D. Peck, “Resonant tunneling through quantum wells at frequencies up to 2.5 THz,” Appl. Phys. Lett. 43(6), 588–600 (1983).
[Crossref]

R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, L. L. Buhl, “Narrowband grating resonator filters in InGaAsP/InP waveguides,” Appl. Phys. Lett. 49(3), 125–127 (1986).
[Crossref]

IEEE J. Quantum Electron. (1)

R. A. Syms, “Approximate solution of eigenmode problems for layered coupled arrays,” IEEE J. Quantum Electron. 23(5), 525–532 (1987).
[Crossref]

J. Lightwave Technol. (2)

J. Math. Phys. (1)

A. M. Childs, D. Gosset, “Levinson's theorem for graphs II,” J. Math. Phys. 53, 102207 (2012).

Nat. Photonics (3)

D. Liang, J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
[Crossref]

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[Crossref]

Nat. Phys. (1)

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Nature (1)

D. N. Christodoulides, F. Lederer, Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

New J. Phys. (1)

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, A. Tünnermann, “Fresnel’s laws in discrete optical media,” New J. Phys. 10(10), 103020 (2008).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
[Crossref]

Phys. Rev. A (1)

J. M. Moison, N. Belabas, J. A. Levenson, C. Minot, “Light-propagation management in coupled waveguide arrays: quantitative experimental and theoretical assessment from band structures to functional patterns,” Phys. Rev. A 86(3), 033811 (2012).
[Crossref]

Phys. Rev. B (1)

B. Rico, M. Y. Azbel, “Physics of resonant tunneling. The one-dimensional double-barrier case,” Phys. Rev. B 29(4), 1970–1981 (1984).
[Crossref]

Phys. Rev. Lett. (4)

D. N. Christodoulides, E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87(23), 233901 (2001).
[Crossref] [PubMed]

P. Ghenuche, G. Vincent, M. Laroche, N. Bardou, R. Haïdar, J.-L. Pelouard, S. Collin, “Optical extinction in a single layer of nanorods,” Phys. Rev. Lett. 109(14), 143903 (2012).
[Crossref] [PubMed]

H. S. Nguyen, D. Vishnevsky, C. Sturm, D. Tanese, D. Solnyshkov, E. Galopin, A. Lemaître, I. Sagnes, A. Amo, G. Malpuech, J. Bloch, “Realization of a double-barrier resonant tunneling diode for cavity polaritons,” Phys. Rev. Lett. 110(23), 236601 (2013).
[Crossref]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90(5), 053902 (2003).
[Crossref] [PubMed]

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Figures (9)

Fig. 1
Fig. 1 Top left: the RTDB, a set of identical waveguides identically coupled almost everywhere (blue) except in two barriers (purple) where the coupling constant is lowered by a factor of 2 i.e. CH/CL = 2. A guidonic beam is sent across the array with an angle of incidence characterized by its wavevector component kx. Bottom middle: confinement in-between the barriers results in a set of bound quasi-modes at the band edges (red solid line) and at mid-band (red dashed line). Bottom right: CMT diffraction relations in the barriers and elsewhere (solid line), with evanescent continuations (dash-dotted line) plotted vs. ikx since they correspond to pure imaginary values of kx ; all zones here have the same array period. Top right (resp. bottom left): kx (resp. Kz) controls the transmission of the RTDB.
Fig. 2
Fig. 2 Left: incident (blue), reflected (red) and transmitted (green) plane waves in the typical RTDB, with phase fronts (dashed lines) and wavevectors ( ± Kx,Kz). Center: field modulus as a function of kx and waveguide index m, calculated by CMT for an incident wave of unit amplitude. Right: same as center but m is considered as a continuous variable. This distorted view displays more clearly the bound supermodes and the transmitted and stationary waves.
Fig. 3
Fig. 3 Eigenmodes of the eCMT propagation matrix for the typical RTDB in a 400-waveguide array. Left: eigenvalues Kz labeled by kx (line) nearly perfectly overlap the diffraction relation of the high-C regions. Selected values (dots) correspond to the 7 bound modes. Middle: map of eigenvectors I(kx,X/S), zoomed in X around the RTDB; eigenvector profiles have been convoluted with the single-waveguide mode profile to smooth the picture. Right: selected eigenvector profiles I(X/S) corresponding to the 7 bound modes, also zoomed; symbol colors are matched with those on the diffraction relation (left) and the eigenvector map (middle).
Fig. 4
Fig. 4 Transmission of the typical RTDB. Orange: eCMT reflectivity of CHCL interface. Red: eCMT reflectivity of single barrier CHCLCH. Green: plane wave Fabry-Pérot model for the CHCLCHCLCH double barrier using red curve as mirror reflectivity. Blue line: same as green with broadening by the finite beam width W = 100µm. Blue dots: eCMT simulation for the same RTDB and width. Vertical dashed lines: kx of eCMT eigenmodes of the double barrier.
Fig. 5
Fig. 5 Left: propagation of a guidonic beam (W = 100µm, kx = 0.35π, L = 50 mm) across the typical RTDB. Middle: guidonic signature. The input beam is rotated around mid-length and mid-structure to scan kx and the output intensity profile along X is monitored. Right: model signature I(kx,X/L). The vertical line indicates the 0.35 π abscissa used in the left-hand figure.
Fig. 6
Fig. 6 Influence of W and L parameters on the model guidonic signature of Fig. 5. Leftmost sequence: decreasing propagation length; due to the choice of a X/L deviation ordinate, decreasing the length increases the apparent size of the RTDB. Middle sequence: influence of beam waist. Rightmost signature: combination corresponding to the experimental case.
Fig. 7
Fig. 7 Left: experimental signature of the B1C6B1 RTDB with an injected beam of waist W = 23µm and TE polarization. SB = 8.0µm and L ~10 mm. Middle: eCMT simulation. Right: superposition of the experimental signature with the model signature shown as contours lines.
Fig. 8
Fig. 8 Left: part of experimental signature of B1C6B1 (Fig. 7) between 0 and π. Traces of the center deviation of transmitted and reflected beams T and R are shown respectively as green and red lines. Right: transmission curves, calculated for plane waves (dashed line), and obtained along traces from the eCMT model (full line) and experimental signatures (dots).
Fig. 9
Fig. 9 Left: variation of relative barrier height δ with the wavelength λ for various barrier periods SB, for 9, 8, and 7 µm top to bottom. Right: plane-wave transmission of the typical single (dashed line) and double (solid line) barrier for SB = 8 µm and λ = 1.5 (blue), 1.55 (green), and 1.6 (red) µm.

Equations (15)

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tan N k x = f M = 1 ( k x ) δ 2 sin 2 k x 1 δ 2 cos 2 k x
a n z =iC( a n-1 + a n+1 ),
a n e iK z Z e in k x .
K Z =2 C p-1 cos k x p1 =2 C p cos k x p .
A p e in k x p + B p e -in k x p = A p (n)+ B p (n).
a n p z =i( C p1 a n p 1 + C p a n p +1 ),
1 2isin k x p [ e -i k x p C p1 C p e i k x p-1 e -i k x p C p1 C p e -i k x p-1 ( e i k x p C p1 C p e i k x p-1 ) ( e i k x p C p1 C p e -i k x p-1 ) ].
[ A p ( n p+1 ) B p ( n p+1 ) ]=[ e i( n p+1 n p ) k x p 0 0 e -i( n p+1 n p ) k x p ][ A p ( n p ) B p ( n p ) ],
r NM = T NM 21 T NM 22 , =2iα β * sinM k x B ( | α | 2 e iM k x B | β | 2 e iM k x B )+( | α | 2 e iM k x B | β | 2 e iM k x B ) e 2iN k x ( | α | 2 e iM k x B | β | 2 e iM k x B ) 2 +4 | α | 2 | β | 2 sin 2 M k x B e 2iN k x ,
α= e i k x B δ e i k x β= e i k x B δ e i k x ,
tanN k x =cotM k x B | α | 2 | β | 2 | α | 2 + | β | 2
tanN k x = T M ( δcos k x ) U M-1 ( δcos k x ) 2δsin k x 1 δ 2 cos2 k x f M ( k x ),
tanN k x = f M=1 ( k x ) δ 2 sin2 k x 1 δ 2 cos2 k x .
tanN k x = f M ( k x ) 2δsin k x δ 2 cos 2 k x 1 1 δ 2 cos2 k x
tanN k x f M ( k x )=± δ 2 1 δ 2 1 U M1 2 ( δcos k x )cosN k x 1cos2 k x 1 δ 2 cos2 k x

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