Abstract

We demonstrate that discrete solitons are possible in a micro-fabricated optomechanical structure, which consists of N identical cells. Analyses illustrate that these states originate from photon-phonon interaction or optomechanical effect. In principle, the self-localized entities are capable of exhibiting very slow velocities, depending on the photon hopping rate and phase difference among successive optomechanical cells. The theoretical results pave the way for a new type of on-chip system to observe discrete optical solitons behaviors and may have potential application in on-chip manipulation of photonic information processing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. A. S. Davydov and N. I. Kislukha, “Solitary excitations in one-dimensional molecular chains,” Phys. Status Solidi, B Basic Res. 59(2), 465–470 (1973).
    [Crossref]
  2. W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1971 (1979).
    [Crossref]
  3. A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose-Einstein condensates,” Phys. Rev. Lett. 86(11), 2353–2356 (2001).
    [Crossref] [PubMed]
  4. D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13(9), 794–796 (1988).
    [Crossref] [PubMed]
  5. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
    [Crossref] [PubMed]
  6. S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
    [Crossref] [PubMed]
  7. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
    [Crossref]
  8. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
    [Crossref]
  9. P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B 20(5), 1098–1130 (2003).
    [Crossref]
  10. A. Xuereb and P. Domokos, “Dynamical scattering models in optomechanics: going beyond the coupled cavities model,” New J. Phys. 14(9), 095027 (2012).
    [Crossref]
  11. X. Y. Lü, H. Jing, J. Y. Ma, and Y. Wu, “PT-Symmetry-Breaking Chaos in Optomechanics,” Phys. Rev. Lett. 114(25), 253601 (2015).
    [Crossref] [PubMed]
  12. Y. Wu and P. T. Leung, “Lasing threshold for whispering-gallery-mode microsphere lasers,” Phys. Rev. A 60(1), 630–633 (1999).
    [Crossref]
  13. Y. Wu, X. Yang, and P. T. Leung, “Theory of microcavity-enhanced Raman gain,” Opt. Lett. 24(5), 345–347 (1999).
    [Crossref] [PubMed]
  14. A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
    [Crossref] [PubMed]
  15. S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
    [Crossref] [PubMed]
  16. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
    [Crossref] [PubMed]
  17. G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107(4), 043603 (2011).
    [Crossref] [PubMed]
  18. A. Xuereb, C. Genes, G. Pupillo, M. Paternostro, and A. Dantan, “Reconfigurable long-range phonon dynamics in optomechanical arrays,” Phys. Rev. Lett. 112(13), 133604 (2014).
    [Crossref] [PubMed]
  19. H. Xiong, L. G. Si, X. Yang, and Y. Wu, “Asymmetric optical transmission in an optomechanical array,” Appl. Phys. Lett. 107(9), 91116 (2015).
    [Crossref]
  20. J. H. Gan, H. Xiong, L. G. Si, X. Y. Lü, and Y. Wu, “Solitons in optomechanical arrays,” Opt. Lett. 41(12), 2676–2679 (2016).
    [Crossref] [PubMed]
  21. A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86(3), 33821 (2012).
    [Crossref]
  22. H. Xiong, J. Gan, and Y. Wu, “Kuznetsov-Ma Soliton dynamics based on the mechanical effect of light,” Phys. Rev. Lett. 119(15), 153901 (2017).
    [Crossref] [PubMed]
  23. H. Xiong and Y. Wu, “Optomechanical akhmediev breathers,” Laser Photonics Rev. 12(7), 17003005 (2018).
  24. S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
    [Crossref] [PubMed]
  25. O. Egorov, U. Peschel, and F. Lederer, “Discrete quadratic cavity solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 56612 (2005).
    [Crossref] [PubMed]
  26. O. Egorov, U. Peschel, and F. Lederer, “Mobility of discrete cavity solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066603 (2005).
    [Crossref] [PubMed]
  27. U. Peschel, O. Egorov, and F. Lederer, “Discrete cavity solitons,” Opt. Lett. 29(16), 1909–1911 (2004).
    [Crossref] [PubMed]
  28. O. Egorov, F. Lederer, and K. Staliunas, “Subdiffractive discrete cavity solitons,” Opt. Lett. 32(15), 2106–2108 (2007).
    [Crossref] [PubMed]
  29. O. A. Egorov, F. Lederer, and Y. S. Kivshar, “How does an inclined holding beam affect discrete modulational instability and solitons in nonlinear cavities?” Opt. Express 15(7), 4149–4158 (2007).
    [Crossref] [PubMed]
  30. Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93(14), 143904 (2004).
    [Crossref] [PubMed]
  31. M. Sato, B. E. Hubbard, and A. J. Sievers, “Nonlinear energy localization and its manipulation in micromechanical oscillator arrays,” Rev. Mod. Phys. 78(1), 137–157 (2006).
    [Crossref]

2018 (1)

H. Xiong and Y. Wu, “Optomechanical akhmediev breathers,” Laser Photonics Rev. 12(7), 17003005 (2018).

2017 (1)

H. Xiong, J. Gan, and Y. Wu, “Kuznetsov-Ma Soliton dynamics based on the mechanical effect of light,” Phys. Rev. Lett. 119(15), 153901 (2017).
[Crossref] [PubMed]

2016 (1)

J. H. Gan, H. Xiong, L. G. Si, X. Y. Lü, and Y. Wu, “Solitons in optomechanical arrays,” Opt. Lett. 41(12), 2676–2679 (2016).
[Crossref] [PubMed]

2015 (2)

H. Xiong, L. G. Si, X. Yang, and Y. Wu, “Asymmetric optical transmission in an optomechanical array,” Appl. Phys. Lett. 107(9), 91116 (2015).
[Crossref]

X. Y. Lü, H. Jing, J. Y. Ma, and Y. Wu, “PT-Symmetry-Breaking Chaos in Optomechanics,” Phys. Rev. Lett. 114(25), 253601 (2015).
[Crossref] [PubMed]

2014 (2)

A. Xuereb, C. Genes, G. Pupillo, M. Paternostro, and A. Dantan, “Reconfigurable long-range phonon dynamics in optomechanical arrays,” Phys. Rev. Lett. 112(13), 133604 (2014).
[Crossref] [PubMed]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

2012 (2)

A. Xuereb and P. Domokos, “Dynamical scattering models in optomechanics: going beyond the coupled cavities model,” New J. Phys. 14(9), 095027 (2012).
[Crossref]

A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86(3), 33821 (2012).
[Crossref]

2011 (2)

G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107(4), 043603 (2011).
[Crossref] [PubMed]

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

2010 (2)

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
[Crossref] [PubMed]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

2009 (1)

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

2007 (2)

O. Egorov, F. Lederer, and K. Staliunas, “Subdiffractive discrete cavity solitons,” Opt. Lett. 32(15), 2106–2108 (2007).
[Crossref] [PubMed]

O. A. Egorov, F. Lederer, and Y. S. Kivshar, “How does an inclined holding beam affect discrete modulational instability and solitons in nonlinear cavities?” Opt. Express 15(7), 4149–4158 (2007).
[Crossref] [PubMed]

2006 (1)

M. Sato, B. E. Hubbard, and A. J. Sievers, “Nonlinear energy localization and its manipulation in micromechanical oscillator arrays,” Rev. Mod. Phys. 78(1), 137–157 (2006).
[Crossref]

2005 (2)

O. Egorov, U. Peschel, and F. Lederer, “Discrete quadratic cavity solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 56612 (2005).
[Crossref] [PubMed]

O. Egorov, U. Peschel, and F. Lederer, “Mobility of discrete cavity solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066603 (2005).
[Crossref] [PubMed]

2004 (2)

U. Peschel, O. Egorov, and F. Lederer, “Discrete cavity solitons,” Opt. Lett. 29(16), 1909–1911 (2004).
[Crossref] [PubMed]

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93(14), 143904 (2004).
[Crossref] [PubMed]

2003 (2)

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

P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B 20(5), 1098–1130 (2003).
[Crossref]

2002 (1)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

2001 (1)

A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose-Einstein condensates,” Phys. Rev. Lett. 86(11), 2353–2356 (2001).
[Crossref] [PubMed]

1999 (2)

Y. Wu and P. T. Leung, “Lasing threshold for whispering-gallery-mode microsphere lasers,” Phys. Rev. A 60(1), 630–633 (1999).
[Crossref]

Y. Wu, X. Yang, and P. T. Leung, “Theory of microcavity-enhanced Raman gain,” Opt. Lett. 24(5), 345–347 (1999).
[Crossref] [PubMed]

1998 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

1988 (1)

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13(9), 794–796 (1988).
[Crossref] [PubMed]

1979 (1)

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1971 (1979).
[Crossref]

1973 (1)

A. S. Davydov and N. I. Kislukha, “Solitary excitations in one-dimensional molecular chains,” Phys. Status Solidi, B Basic Res. 59(2), 465–470 (1973).
[Crossref]

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Alegre, T. P. M.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Arcizet, O.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
[Crossref] [PubMed]

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

Balle, S.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

Barland, S.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

Bartelt, H.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Brambilla, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Chan, J.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Chang, D. E.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Christodoulides, D. N.

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

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13(9), 794–796 (1988).
[Crossref] [PubMed]

Dantan, A.

A. Xuereb, C. Genes, G. Pupillo, M. Paternostro, and A. Dantan, “Reconfigurable long-range phonon dynamics in optomechanical arrays,” Phys. Rev. Lett. 112(13), 133604 (2014).
[Crossref] [PubMed]

Davydov, A. S.

A. S. Davydov and N. I. Kislukha, “Solitary excitations in one-dimensional molecular chains,” Phys. Status Solidi, B Basic Res. 59(2), 465–470 (1973).
[Crossref]

Deléglise, S.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
[Crossref] [PubMed]

Deng, L.

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93(14), 143904 (2004).
[Crossref] [PubMed]

Diehl, S.

A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86(3), 33821 (2012).
[Crossref]

Domokos, P.

A. Xuereb and P. Domokos, “Dynamical scattering models in optomechanics: going beyond the coupled cavities model,” New J. Phys. 14(9), 095027 (2012).
[Crossref]

P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B 20(5), 1098–1130 (2003).
[Crossref]

Egorov, O.

O. Egorov, F. Lederer, and K. Staliunas, “Subdiffractive discrete cavity solitons,” Opt. Lett. 32(15), 2106–2108 (2007).
[Crossref] [PubMed]

O. Egorov, U. Peschel, and F. Lederer, “Discrete quadratic cavity solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 56612 (2005).
[Crossref] [PubMed]

O. Egorov, U. Peschel, and F. Lederer, “Mobility of discrete cavity solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066603 (2005).
[Crossref] [PubMed]

U. Peschel, O. Egorov, and F. Lederer, “Discrete cavity solitons,” Opt. Lett. 29(16), 1909–1911 (2004).
[Crossref] [PubMed]

Egorov, O. A.

O. A. Egorov, F. Lederer, and Y. S. Kivshar, “How does an inclined holding beam affect discrete modulational instability and solitons in nonlinear cavities?” Opt. Express 15(7), 4149–4158 (2007).
[Crossref] [PubMed]

Eichenfield, M.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Eilenberger, F.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Gan, J.

H. Xiong, J. Gan, and Y. Wu, “Kuznetsov-Ma Soliton dynamics based on the mechanical effect of light,” Phys. Rev. Lett. 119(15), 153901 (2017).
[Crossref] [PubMed]

Gan, J. H.

J. H. Gan, H. Xiong, L. G. Si, X. Y. Lü, and Y. Wu, “Solitons in optomechanical arrays,” Opt. Lett. 41(12), 2676–2679 (2016).
[Crossref] [PubMed]

Gavartin, E.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
[Crossref] [PubMed]

Genes, C.

A. Xuereb, C. Genes, G. Pupillo, M. Paternostro, and A. Dantan, “Reconfigurable long-range phonon dynamics in optomechanical arrays,” Phys. Rev. Lett. 112(13), 133604 (2014).
[Crossref] [PubMed]

Giudici, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

Heeger, A. J.

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1971 (1979).
[Crossref]

Heinrich, G.

G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107(4), 043603 (2011).
[Crossref] [PubMed]

Hill, J. T.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Hubbard, B. E.

M. Sato, B. E. Hubbard, and A. J. Sievers, “Nonlinear energy localization and its manipulation in micromechanical oscillator arrays,” Rev. Mod. Phys. 78(1), 137–157 (2006).
[Crossref]

Jäger, R.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

Jing, H.

X. Y. Lü, H. Jing, J. Y. Ma, and Y. Wu, “PT-Symmetry-Breaking Chaos in Optomechanics,” Phys. Rev. Lett. 114(25), 253601 (2015).
[Crossref] [PubMed]

Joseph, R. I.

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13(9), 794–796 (1988).
[Crossref] [PubMed]

Kartashov, Y. V.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Kippenberg, T. J.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
[Crossref] [PubMed]

Kislukha, N. I.

A. S. Davydov and N. I. Kislukha, “Solitary excitations in one-dimensional molecular chains,” Phys. Status Solidi, B Basic Res. 59(2), 465–470 (1973).
[Crossref]

Kivshar, Y. S.

O. A. Egorov, F. Lederer, and Y. S. Kivshar, “How does an inclined holding beam affect discrete modulational instability and solitons in nonlinear cavities?” Opt. Express 15(7), 4149–4158 (2007).
[Crossref] [PubMed]

Knödl, T.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

Kobelke, J.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Kubala, B.

G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107(4), 043603 (2011).
[Crossref] [PubMed]

Lederer, F.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

O. A. Egorov, F. Lederer, and Y. S. Kivshar, “How does an inclined holding beam affect discrete modulational instability and solitons in nonlinear cavities?” Opt. Express 15(7), 4149–4158 (2007).
[Crossref] [PubMed]

O. Egorov, F. Lederer, and K. Staliunas, “Subdiffractive discrete cavity solitons,” Opt. Lett. 32(15), 2106–2108 (2007).
[Crossref] [PubMed]

O. Egorov, U. Peschel, and F. Lederer, “Discrete quadratic cavity solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 56612 (2005).
[Crossref] [PubMed]

O. Egorov, U. Peschel, and F. Lederer, “Mobility of discrete cavity solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066603 (2005).
[Crossref] [PubMed]

U. Peschel, O. Egorov, and F. Lederer, “Discrete cavity solitons,” Opt. Lett. 29(16), 1909–1911 (2004).
[Crossref] [PubMed]

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

Leung, P. T.

Y. Wu and P. T. Leung, “Lasing threshold for whispering-gallery-mode microsphere lasers,” Phys. Rev. A 60(1), 630–633 (1999).
[Crossref]

Y. Wu, X. Yang, and P. T. Leung, “Theory of microcavity-enhanced Raman gain,” Opt. Lett. 24(5), 345–347 (1999).
[Crossref] [PubMed]

Lin, Q.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Lü, X. Y.

J. H. Gan, H. Xiong, L. G. Si, X. Y. Lü, and Y. Wu, “Solitons in optomechanical arrays,” Opt. Lett. 41(12), 2676–2679 (2016).
[Crossref] [PubMed]

X. Y. Lü, H. Jing, J. Y. Ma, and Y. Wu, “PT-Symmetry-Breaking Chaos in Optomechanics,” Phys. Rev. Lett. 114(25), 253601 (2015).
[Crossref] [PubMed]

Ludwig, M.

G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107(4), 043603 (2011).
[Crossref] [PubMed]

Lugiato, L. A.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

Lukin, M. D.

A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86(3), 33821 (2012).
[Crossref]

Ma, J. Y.

X. Y. Lü, H. Jing, J. Y. Ma, and Y. Wu, “PT-Symmetry-Breaking Chaos in Optomechanics,” Phys. Rev. Lett. 114(25), 253601 (2015).
[Crossref] [PubMed]

Maggipinto, T.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

Marquardt, F.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107(4), 043603 (2011).
[Crossref] [PubMed]

Miller, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

Minardi, S.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Nolte, S.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Painter, O.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Paternostro, M.

A. Xuereb, C. Genes, G. Pupillo, M. Paternostro, and A. Dantan, “Reconfigurable long-range phonon dynamics in optomechanical arrays,” Phys. Rev. Lett. 112(13), 133604 (2014).
[Crossref] [PubMed]

Pertsch, T.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Peschel, U.

O. Egorov, U. Peschel, and F. Lederer, “Mobility of discrete cavity solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066603 (2005).
[Crossref] [PubMed]

O. Egorov, U. Peschel, and F. Lederer, “Discrete quadratic cavity solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 56612 (2005).
[Crossref] [PubMed]

U. Peschel, O. Egorov, and F. Lederer, “Discrete cavity solitons,” Opt. Lett. 29(16), 1909–1911 (2004).
[Crossref] [PubMed]

Pupillo, G.

A. Xuereb, C. Genes, G. Pupillo, M. Paternostro, and A. Dantan, “Reconfigurable long-range phonon dynamics in optomechanical arrays,” Phys. Rev. Lett. 112(13), 133604 (2014).
[Crossref] [PubMed]

Qian, J.

G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107(4), 043603 (2011).
[Crossref] [PubMed]

Rabl, P.

A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86(3), 33821 (2012).
[Crossref]

Ritsch, H.

P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B 20(5), 1098–1130 (2003).
[Crossref]

Rivière, R.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
[Crossref] [PubMed]

Röpke, U.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Sato, M.

M. Sato, B. E. Hubbard, and A. J. Sievers, “Nonlinear energy localization and its manipulation in micromechanical oscillator arrays,” Rev. Mod. Phys. 78(1), 137–157 (2006).
[Crossref]

Schliesser, A.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
[Crossref] [PubMed]

Schrieffer, J. R.

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1971 (1979).
[Crossref]

Schuster, K.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Si, L. G.

J. H. Gan, H. Xiong, L. G. Si, X. Y. Lü, and Y. Wu, “Solitons in optomechanical arrays,” Opt. Lett. 41(12), 2676–2679 (2016).
[Crossref] [PubMed]

H. Xiong, L. G. Si, X. Yang, and Y. Wu, “Asymmetric optical transmission in an optomechanical array,” Appl. Phys. Lett. 107(9), 91116 (2015).
[Crossref]

Sievers, A. J.

M. Sato, B. E. Hubbard, and A. J. Sievers, “Nonlinear energy localization and its manipulation in micromechanical oscillator arrays,” Rev. Mod. Phys. 78(1), 137–157 (2006).
[Crossref]

Silberberg, Y.

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

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Smerzi, A.

A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose-Einstein condensates,” Phys. Rev. Lett. 86(11), 2353–2356 (2001).
[Crossref] [PubMed]

Spinelli, L.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

Staliunas, K.

O. Egorov, F. Lederer, and K. Staliunas, “Subdiffractive discrete cavity solitons,” Opt. Lett. 32(15), 2106–2108 (2007).
[Crossref] [PubMed]

Su, W. P.

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1971 (1979).
[Crossref]

Szameit, A.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Tissoni, G.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

Tomadin, A.

A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86(3), 33821 (2012).
[Crossref]

Torner, L.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Tredicce, J. R.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

Trombettoni, A.

A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose-Einstein condensates,” Phys. Rev. Lett. 86(11), 2353–2356 (2001).
[Crossref] [PubMed]

Tünnermann, A.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-dimensional light bullets in arrays of waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Vahala, K. J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Weis, S.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
[Crossref] [PubMed]

Winger, M.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Wu, Y.

H. Xiong and Y. Wu, “Optomechanical akhmediev breathers,” Laser Photonics Rev. 12(7), 17003005 (2018).

H. Xiong, J. Gan, and Y. Wu, “Kuznetsov-Ma Soliton dynamics based on the mechanical effect of light,” Phys. Rev. Lett. 119(15), 153901 (2017).
[Crossref] [PubMed]

J. H. Gan, H. Xiong, L. G. Si, X. Y. Lü, and Y. Wu, “Solitons in optomechanical arrays,” Opt. Lett. 41(12), 2676–2679 (2016).
[Crossref] [PubMed]

H. Xiong, L. G. Si, X. Yang, and Y. Wu, “Asymmetric optical transmission in an optomechanical array,” Appl. Phys. Lett. 107(9), 91116 (2015).
[Crossref]

X. Y. Lü, H. Jing, J. Y. Ma, and Y. Wu, “PT-Symmetry-Breaking Chaos in Optomechanics,” Phys. Rev. Lett. 114(25), 253601 (2015).
[Crossref] [PubMed]

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93(14), 143904 (2004).
[Crossref] [PubMed]

Y. Wu and P. T. Leung, “Lasing threshold for whispering-gallery-mode microsphere lasers,” Phys. Rev. A 60(1), 630–633 (1999).
[Crossref]

Y. Wu, X. Yang, and P. T. Leung, “Theory of microcavity-enhanced Raman gain,” Opt. Lett. 24(5), 345–347 (1999).
[Crossref] [PubMed]

Xiong, H.

H. Xiong and Y. Wu, “Optomechanical akhmediev breathers,” Laser Photonics Rev. 12(7), 17003005 (2018).

H. Xiong, J. Gan, and Y. Wu, “Kuznetsov-Ma Soliton dynamics based on the mechanical effect of light,” Phys. Rev. Lett. 119(15), 153901 (2017).
[Crossref] [PubMed]

J. H. Gan, H. Xiong, L. G. Si, X. Y. Lü, and Y. Wu, “Solitons in optomechanical arrays,” Opt. Lett. 41(12), 2676–2679 (2016).
[Crossref] [PubMed]

H. Xiong, L. G. Si, X. Yang, and Y. Wu, “Asymmetric optical transmission in an optomechanical array,” Appl. Phys. Lett. 107(9), 91116 (2015).
[Crossref]

Xuereb, A.

A. Xuereb, C. Genes, G. Pupillo, M. Paternostro, and A. Dantan, “Reconfigurable long-range phonon dynamics in optomechanical arrays,” Phys. Rev. Lett. 112(13), 133604 (2014).
[Crossref] [PubMed]

A. Xuereb and P. Domokos, “Dynamical scattering models in optomechanics: going beyond the coupled cavities model,” New J. Phys. 14(9), 095027 (2012).
[Crossref]

Yang, X.

H. Xiong, L. G. Si, X. Yang, and Y. Wu, “Asymmetric optical transmission in an optomechanical array,” Appl. Phys. Lett. 107(9), 91116 (2015).
[Crossref]

Y. Wu, X. Yang, and P. T. Leung, “Theory of microcavity-enhanced Raman gain,” Opt. Lett. 24(5), 345–347 (1999).
[Crossref] [PubMed]

Zoller, P.

A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86(3), 33821 (2012).
[Crossref]

Appl. Phys. Lett. (1)

H. Xiong, L. G. Si, X. Yang, and Y. Wu, “Asymmetric optical transmission in an optomechanical array,” Appl. Phys. Lett. 107(9), 91116 (2015).
[Crossref]

J. Opt. Soc. Am. B (1)

P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B 20(5), 1098–1130 (2003).
[Crossref]

Laser Photonics Rev. (1)

H. Xiong and Y. Wu, “Optomechanical akhmediev breathers,” Laser Photonics Rev. 12(7), 17003005 (2018).

Nature (4)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419(6908), 699–702 (2002).
[Crossref] [PubMed]

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

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

New J. Phys. (1)

A. Xuereb and P. Domokos, “Dynamical scattering models in optomechanics: going beyond the coupled cavities model,” New J. Phys. 14(9), 095027 (2012).
[Crossref]

Opt. Express (1)

O. A. Egorov, F. Lederer, and Y. S. Kivshar, “How does an inclined holding beam affect discrete modulational instability and solitons in nonlinear cavities?” Opt. Express 15(7), 4149–4158 (2007).
[Crossref] [PubMed]

Opt. Lett. (5)

U. Peschel, O. Egorov, and F. Lederer, “Discrete cavity solitons,” Opt. Lett. 29(16), 1909–1911 (2004).
[Crossref] [PubMed]

O. Egorov, F. Lederer, and K. Staliunas, “Subdiffractive discrete cavity solitons,” Opt. Lett. 32(15), 2106–2108 (2007).
[Crossref] [PubMed]

J. H. Gan, H. Xiong, L. G. Si, X. Y. Lü, and Y. Wu, “Solitons in optomechanical arrays,” Opt. Lett. 41(12), 2676–2679 (2016).
[Crossref] [PubMed]

Y. Wu, X. Yang, and P. T. Leung, “Theory of microcavity-enhanced Raman gain,” Opt. Lett. 24(5), 345–347 (1999).
[Crossref] [PubMed]

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13(9), 794–796 (1988).
[Crossref] [PubMed]

Phys. Rev. A (2)

Y. Wu and P. T. Leung, “Lasing threshold for whispering-gallery-mode microsphere lasers,” Phys. Rev. A 60(1), 630–633 (1999).
[Crossref]

A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86(3), 33821 (2012).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

O. Egorov, U. Peschel, and F. Lederer, “Discrete quadratic cavity solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 56612 (2005).
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S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
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Figures (3)

Fig. 1
Fig. 1 (a) Schematic diagram of an optomechanical cell that consists of a cavity, in which one mirror is fixed, and another is movable; (b) schematic diagram of the optomechanical array consists of N coupled optomechanical cells. The excitation and probe of the optical mode can be achieved by using atapered and dimpled optical fiber.
Fig. 2
Fig. 2 Schematic diagram of discrete soliton propagating along a chain of coupled optomechanical cells at a group speed ν e .
Fig. 3
Fig. 3 The evolution of the discrete optomechanical solitons in a coupled optomechanical cells for different phase difference q. The parameters we take here are g 0 = 10 4 , x 0 =10,J = 2, Ω=1,n = 100. (a) for q=0, (b) q=π/6, (c) q=π/2, (d) q=π/6.

Equations (11)

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H ^ = n [Ω β ^ n β ^ n + ω c α ^ n α ^ n g 0 α ^ n α ^ n ( β ^ n + β ^ n )] 1 2 n (J α ^ n α ^ n+1 +H.C.)
a ˙ n =γ a n +i g 0 a n ( b n + b n )+i J 2 ( a n+1 + a n1 2 a n )
b ˙ n =(ΓiΩ) b n +i g 0 | a n | 2
b n (t)=exp(iΩt) b n (0)+i g 0 0 t exp[iΩ(t t ' )]| a n ( t ' ) | 2 d t '
a ˙ n =i J 2 ( a n+1 + a n1 2 a n )+i g 0 α n (2 g 0 0 t sin[Ω(t t ' )]| a n ( t ' ) | 2 d t ' )
i a ˙ n + J 2 ( a n+1 + a n1 2 a n )+ 2 g 0 2 a n | a n | 2 Ω 2 g 0 2 a n | a n | 2 Ω cosΩt=0
i a ˙ n + J 2 ( a n+1 + a n1 2 a n )+ 2 g 0 2 a n | a n | 2 Ω =0
i[ Ψ ˙ +ΨiJ(cosq1)]+ 2 g 0 2 Ω | Ψ | 2 Ψ + J 2 [(Ψ+d Ψ x + d 2 2 2 Ψ x 2 ) e iq +(Ψd Ψ x + d 2 2 2 Ψ x 2 ) e iq 2Ψ]=0
i Ψ ˙ +iJd Ψ x sinq+ J d 2 2 2 Ψ x 2 cosq+ 2 g 0 2 Ω | Ψ | 2 Ψ=0
Ψ= Ψ peak sech( x ν e t x 0 )exp(iλt)
( v e Jd ) 2 + ( 2 g 0 2 x 0 2 P JΩ d 2 ) 2 =1

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