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Dissipative Solitons in Pattern-Forming Nonlinear Optical Systems: Cavity Solitons and Feedback Solitons

Part of the Lecture Notes in Physics book series (LNP,volume 661)

Abstract

Many dissipative optical systems support patterns. Dissipative solitons are generally found where a pattern coexists with a stable unpatterned state. We consider such phenomena in driven optical cavities containing a nonlinear medium (cavity solitons) and rather similar phenomena (feedback solitons) where a driven nonlinear optical medium is in front of a single feedback mirror. The history, theory, experimental status, and potential application of such solitons are reviewed.

Keywords

  • Saturable Absorber
  • Dark Soliton
  • Optical Bistability
  • Spatial Soliton
  • Dissipative Soliton

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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REFERENCES

  1. N. N. Rosanov,Transverse patterns in wide-aperture nonlinear optical systems. Progress in Optics XXXV, 1–60 (1996).

    Google Scholar 

  2. L. A. Lugiato, M. Brambilla, and A. Gatti Optical pattern formation. Adv. Atom. Mol. Opt. Phys. 40, 229–306 (1999).

    Google Scholar 

  3. F. T. Arecchi, S. Boccaletti, and P. L. Ramazza. Pattern formation and competition in nonlinear optics. Phys. Rep. 318, 1–83 (1999).

    Google Scholar 

  4. C. O. Weiss, M. Vaupel, K. Staliunas, G. Slekys, and V. B. Taranenko. Solitons and Vortices in lasers. Appl. Phys. B 68, 151–168 (1999).

    CrossRef  Google Scholar 

  5. S. Trillo and W. E. Torruellas, editors. Spatial Solitons, volume 82 of Springer Series in Optical Sciences. (Springer, Berlin, 2001).

    Google Scholar 

  6. T. Ackemann and W. Lange. Optical pattern formation in alkali metal vapors: Mechanisms, phenomena and use. Appl. Phys. B 72, 21–34 (2001).

    Google Scholar 

  7. W. J. Firth Theory of Cavity Solitons. In A. D. Boardman and A. P. Sukhorukov, editors, Soliton-Driven Photonics, pages 459–485 (Kluwer Academic Publishers, London, 2001).

    Google Scholar 

  8. W. J. Firth and C. O. Weiss Cavity and feedback solitons. Opt. Photon. News 13(2), 54–58 (2002).

    Google Scholar 

  9. N. N. Rosanov Spatial hysteresis and optical patterns. Springer Series in Synergetics. Springer, Berlin (2002).

    Google Scholar 

  10. U. Peschel, D. Michaelis, and C. O. Weiss Spatial solitons in optical cavities. IEEE J. Quantum Electron. 39, 51–64 (2003).

    Google Scholar 

  11. L. A. Lugiato. {Introduction to the feature section on cavity solitons: An overview}. IEEE J. Quantum Electron. 39(2), 193–196 (2003).

    Google Scholar 

  12. V. B. Taranenko, G. Slekys, C. O. Weiss Dissipative Solitons

    Google Scholar 

  13. N. N. Rosanov Dissipative Solitons.

    Google Scholar 

  14. C. Etrich, U. Peschel, and F. Lederer Solitary Waves in Quadratically Nonlinear Resonators. Phys. Rev. Lett. 79, 2454–2457 (1997).

    CrossRef  Google Scholar 

  15. U. Peschel, D. Michaelis, C. Etrich, and F. Lederer Formation, motion, and decay of vectorial cavity solitons. Phys. Rev. E 58, R2745–R2748 (1998).

    Google Scholar 

  16. D. Michaelis, U. Peschel, C. Etrich, and F. Lederer Quadratic Cavity Solitons – The Up-Conversion Case. IEEE J. Quantum Electron. 39, 255–268 (2003).

    Google Scholar 

  17. S. Longhi Localized structures in optical parametric oscillation. Physica Scripta 56, 611–618 (1997).

    Google Scholar 

  18. K. Staliunas and V. J. Sánchez-Morcillo Localized structures in degenerate optical parametric oscillators. Opt. Commun. 139, 306–312 (1997).

    Google Scholar 

  19. G.-L. Oppo, A. J. Scroggie, and W. J. Firth From domain walls to localized structures in degenerate optical parametric oscillators. J. Opt. B: Quantum Semiclass. Opt. 1, 133–138 (1999).

    Google Scholar 

  20. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet {Striped and circular domain walls in the DOPO}. J. Opt. B: Quantum Semiclass. Opt. 1, 153–160 (1999).

    Google Scholar 

  21. D. V. Skryabin and W. J. Firth Interaction of cavity solitons in degenerate optical parametric oscillators. Opt. Lett. 24, 1056–1059 (1999).

    Google Scholar 

  22. M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza High-intensity localized structures in the degenerate optical parametric oscillator: Comparisom between the propagation and the mean-field model. Phys. Rev. A 61, 043806 (2000).

    Google Scholar 

  23. G. Izús, M. San Miguel, and M. Santagiustina {Bloch domain walls in type II optical parametric oscillators}. Opt. Lett. {25}, 1454–6 (2000).

    Google Scholar 

  24. G. L. Oppo, A. J. Scroggie, and W. J. Firth Characterization, dynamics and stabilization of diffractive domain walls and dark ring cavity solitons in parametric oscillators. Phys. Rev. E 63, 066209 (2001).

    Google Scholar 

  25. C. Etrich, D. Michaelis, and F. Lederer Bifurcations, stability, and multistability of cavity solitons in parametric downconversion. J. Opt. Soc. Am. B 19, 792–801 (2002).

    Google Scholar 

  26. D. Gomila, P. Colet, M. San Miguel, A. Scroggie, and G. L. Oppo Stable droplets and dark-ring cavity solitons in nonlinear optical devices. IEEE J. Quantum Electron. 39, 238–244 (2003).

    Google Scholar 

  27. R. Vilaseca, M. C. Torrent, J. García-Ojalvo, E. Brambilla, and M. San Miguel Two-photon cavity solitons in active optical media. Phys. Rev. Lett. 87, 083902 (2001).

    Google Scholar 

  28. R. Gallego, M. San Miguel, and R. Toral {Self-similar domain growth, localized structures, and labyrinthine patterns in vectorial Kerr resonators}. Phys. Rev. E 61, 2241–4 (2000).

    Google Scholar 

  29. V. J. Sánchez-Morcillo, I. Pérez-Arjona, Silva F., G. J. Valcárcel, and E. Roldán {Vectorial Kerr cavity solitons}. Opt. Lett. 25, 957–959 (2000).

    Google Scholar 

  30. E. Große Westhoff, V. Kneisel, Yu. A. Logvin, T. Ackemann, and W. Lange Pattern formation in the presence of an intrinsic polarization instability. J. Opt. B: Quantum Semiclass. Opt. 2, 386–392 (2000).

    Google Scholar 

  31. V. B. Taranenko, K. Staliunas, and C. O. Weiss Pattern formation and localized structures in degenerate optical parametric mixing. Phys. Rev. Lett. 81, 2236–2239 (1998).

    Google Scholar 

  32. V. B. Taranenko, M. Zander, P. Wobben, and C. O. Weiss. Stability of localized structures in degenerate wave mixing. Appl. Phys. B 69, 337–339 (1999).

    Google Scholar 

  33. M. Pesch, E. Große Westhoff, T. Ackemann, W. Lange. Vectorial solitons and higher-order localized states in a single-mirror feedback system. In Nonlinear Guided Waves and Their Applications. Toronto, Canada, March 28–31, 2004. Paper TuC24 (2004).

    Google Scholar 

  34. V. Yu. Bazhenov, V. B. Taranenko, and M. V. Vasnetsov. Transverse optical effects in bistable active cavity with nonlinear absorber on bacteriorhodopsin. Proc. SPIE 1840, 183–193 (1992).

    Google Scholar 

  35. M. Saffman, D. Montgomery, and D. Z. Anderson Collapse of a transverse-mode continuum in a self-imaging photorefractively pumped ring resonator. Opt. Lett. 19, 518–520 (1994).

    Google Scholar 

  36. V. B. Taranenko, K. Staliunas, and C. O. Weiss Spatial soliton laser: localized structures in a laser with a saturable absorber in a self-imaging resonator. Phys. Rev. A 56, 1582–1591 (1997).

    Google Scholar 

  37. D. W. McLaughlin, J. V. Moloney, and A. C. Newell Solitary waves as fixed points of infinite-dimensional maps in an optical bistable ring cavity. Phys. Rev. Lett. 51, 75–78 (1983).

    CrossRef  Google Scholar 

  38. J. V. Moloney and A. C. Newell Nonlinear Optics. Addison-Wesley, Redwood City (1992). Fig. 5.16, p. 225 and associated text.

    Google Scholar 

  39. H. M. Gibbs Optical Bistability: Controlling Light with Light. Academic Press, Orlando (1985).

    Google Scholar 

  40. L. A. Lugiato Theory of optical bistability Progress in Optics XXI pages 70–216 (1984).

    Google Scholar 

  41. W. J. Firth and G. K. Harkness Cavity solitons. Asian J. Phys. 7, 665–677 (1998).

    Google Scholar 

  42. G. S. McDonald and W. J. Firth Spatial solitary-wave optical memory.break J. Opt. Soc. Am. B 7, 1328–1335 (1990).

    Google Scholar 

  43. G. S. McDonald and W. J. Firth Switching dynamics of spatial solitary wave pixels. J. Opt. Soc. Am. B 10, 1081–1089 (1993).

    Google Scholar 

  44. N. N. Rosanov and G. V. Khodova Autosolitons in nonlinear interferometers. Opt. Spectrosc. 65, 449–450 (1988).

    Google Scholar 

  45. N. N. Rosanov and G. V. Khodova Diffractive autosolitons in nonlinear interferometers. J. Opt. Soc. Am. B 7(6), 1057–65 (1990).

    Google Scholar 

  46. W. J. Firth and I. Galbraith Diffusive transverse coupling of bistable elements – switching waves and crosstalk. IEEE J. Quantum Electron. 21, 1399–1403 (1985).

    Google Scholar 

  47. N. B. Abraham and W. J. Firth Overview of transverse effects in nonlinear-optical systems. J. Opt. Soc. Am. B 7, 951–961 (1990).

    Google Scholar 

  48. M. Kreuzer, H. Gottschilk, Th. Tschudi, and R. Neubecker Structure formation and self-organization phenomena in bistable optical elements. Mol. Cryst. Liquid Cryst. 207, 219–230 (1991).

    Google Scholar 

  49. R. Neubecker and T. Tschudi Self-induced mode as a building element of transversal pattern formation. J. Mod. Opt. 41, 885–906 (1994).

    Google Scholar 

  50. G. Giusfredi, J. F. Valley, R. Pon, G. Khitrova, and H. M. Gibbs Optical instabilities in sodium vapor. J. Opt. Soc. Am. B 5, 1181–1191 (1988).

    Google Scholar 

  51. L. A. Lugiato and R. Lefever Spatial dissipative structures in passive optical systems. Phys. Rev. Lett. 58, 2209–2211 (1987).

    CrossRef  Google Scholar 

  52. I. V. Barashenkov, N. V. Alexeeva, and E. V. Zemlyanaya {Two- and three-dimensional oscillons in nonlinear Faraday resonance}. Phys. Rev. Lett. 89, 104101 (2002).

    Google Scholar 

  53. P. B. Umbanhowar, F. Melo, and H. L. Swinney Localized excitations in a vertically vibrated granular layer. Nature 382, 793–796 (1996).

    Google Scholar 

  54. T. Maggipinto, M. Brambilla, G. K. Harkness, and W. J. Firth {Cavity solitons in semiconductor microresonators: Existence, stability, and dynamical properties}. Phys. Rev. E 62(6), 8726–8739 (2000).

    Google Scholar 

  55. G. K. Harkness, W. J. Firth, G. L. Oppo, and J. M. McSloy Computationally Determined Existence and Stability of Transverse Structures: I. Periodic Optical Patterns. Phys. Rev. E 66, 046605 (2002).

    Google Scholar 

  56. J. M. McSloy, W. J. Firth, G. L. Oppo, and G. K. Harkness Computationally Determined Existence and Stability of Transverse Structures: II. Multi-Peaked Cavity Solitons. Phys. Rev. E 66, 046606 (2002).

    Google Scholar 

  57. T. Maggipinto, M. Brambilla, and W. J. Firth Characterization of stationary patterns and their link with cavity solitons in semiconductor microresonators. IEEE J. Quantum Electron. 39, 206–215 (2003).

    Google Scholar 

  58. W. J. Firth, A. Lord, and A. J. Scroggie Optical bullet holes. Phys. Scr. T67, 12–16 (1996).

    Google Scholar 

  59. W. J. Firth, G. K. Harkness, A. Lord, J. M. McSloy, D. Gomila, and P. Colet {Dynamical properties of two-dimensional Kerr cavity solitons}. J. Opt. Soc. Am. B 19(4), 747–752 (2002).

    Google Scholar 

  60. K. Staliunas {Three-dimensional Turing structures and spatial solitons in optical parametric oscillators}. Phys. Rev. Lett. 81, 81–84 (1998).

    Google Scholar 

  61. M. Tlidi and P. Mandel Three-dimensional optical crystals and localized structures in cavity second harmonic generation. Phys. Rev. Lett. 83, 4995–4998 (1999).

    Google Scholar 

  62. G. Steinmeyer, A. Schwache, and F. Mitschke. Quantitative characterization of turbulence in an optical experiment. Phys. Rev. E 53, 5399–5402 (1996).

    Google Scholar 

  63. S. Wabnitz Suppression of interactions in a phase-locked optical memory. Opt. Lett. 18, 601–603 (1993).

    Google Scholar 

  64. M. Tlidi, P. Mandel, and R. Lefever Localized structures and localized patterns in optical bistability. Phys. Rev. Lett. 73, 640–643 (1994).

    CrossRef  Google Scholar 

  65. W. J. Firth and A. J. Scroggie Optical bullet holes: robust controllable localized states of a nonlinear cavity. Phys. Rev. Lett. 76, 1623–1626 (1996).

    CrossRef  Google Scholar 

  66. W. J. Firth and A. J. Scroggie Spontaneous pattern formation in an absorptive system. Europhys. Lett. 26, 521–526 (1994).

    Google Scholar 

  67. T. Ackemann, S. Barland, J. R. Tredicce, M. Cara, S. Balle, R. Jäger, P. M. Grabherr, M. Miller, and K. J. Ebeling Spatial structure of broad-area vertical-cavity regenerative amplifiers. Opt. Lett. 25, 814–816 (2000).

    Google Scholar 

  68. P. Coullet, C. Riera, and C. Tresser Stable static localized structures in one dimension. Phys. Rev. Lett. 84, 3069–3072 (2000).

    CrossRef  Google Scholar 

  69. P. Coullet, C. Riera, and C. Tresser Qualitative theory of stable stationary localized structures in one dimension. Prog. Theor. Phys. Suppl. 139, 46–58 (2000).

    Google Scholar 

  70. Y. Pomeau Front motion, metastability and subcritical bifurcations in hydrodynamics. Physica D 23, 3–11 (1986).

    Google Scholar 

  71. A. G. Vladimirov, J. M. McSloy, D. V. Skryabin, and W. J. Firth. Two-dimensional clusters of solitary structures in driven optical cavities. Phys. Rev. E 65, 046606 (2002).

    Google Scholar 

  72. W. J. Firth Optical Memory and Spatial Chaos. Phys. Rev. Lett. 61, 329–332 (1988).

    Google Scholar 

  73. P. Coullet, C. Riera, and C. Tresser A new approach to data storage using localized structures. Chaos 14, 193–198 (2004).

    Google Scholar 

  74. M. Tlidi and P. Mandel. Spatial patterns in nascent optical bistability. Chaos, Solitons & Fractals 4, 1475–1486 (1994).

    Google Scholar 

  75. M. Brambilla, L. A. Lugiato, and M. Stefani Interaction and control of optical localized structures. Europhys. Lett. 34, 109–114 (1996).

    CrossRef  Google Scholar 

  76. M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth Spatial soliton pixels in semiconductor devices. Phys. Rev. Lett. 79, 2042–2045 (1997).

    CrossRef  Google Scholar 

  77. L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato Spatial solitons in semiconductor microcavities. Phys. Rev. A 58, 2542–2559 (1998).

    CrossRef  Google Scholar 

  78. M. Tlidi, M. Georgiou, and P. Mandel Transverse patterns in nascent optical bistability. Phys. Rev. A 48, 4605–4609 (1993).

    Google Scholar 

  79. M. C. Cross and P. C. Hohenberg Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112 (1993).

    CrossRef  Google Scholar 

  80. S. Hoogland, J. J. Baumberg, S. Coyle, J. Baggett, M. J. Coles, and H. J. Coles Self-organized patterns and spatial solitons in liquid-crystal microcavities. Phys. Rev. A 66, 055801 (2002).

    Google Scholar 

  81. G. Tissoni, L. Spinelli, M. Brambilla, I. Perrini, T. Maggipinto, and L. A. Lugiato Cavity solitons in bulk semiconductor microcavities: dynamical properties and control. J. Opt. Soc. Am. B 16, 2095–2105 (1999).

    Google Scholar 

  82. L. Spinelli, G. Tissoni, M. Tarenghi, and M. Brambilla First principle theory for cavity solitons in semiconductor microresonators. Eur. Phys. J. D 15, 257–266 (2001).

    CrossRef  Google Scholar 

  83. S. Barbay, J. Koehler, R. Kuszelewicz, T. Maggipinto, I. M. Perrini, and M. Brambilla Optical patterns and cavity solitons in quantum-dot microresonators. IEEE J. Quantum Electron. 39, 245–254 (2003).

    Google Scholar 

  84. D. Michaelis, U. Peschel, and F. Lederer Multistable localized structures and superlattices in semiconductor optical resonators. Phys. Rev. A 56, R3366–R3369 (1997).

    Google Scholar 

  85. V. B. Taranenko and C. O. Weiss Incoherent optical switching of semiconductor resonator solitons. Appl. Phys. B 72(7), 893–895 (2001).

    Google Scholar 

  86. S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödel, M. Miller, and R. Jäger Cavity solitons as pixels in semiconductors. Nature 419, 699–702 (2002).

    CrossRef  Google Scholar 

  87. V. B. Taranenko, C. O. Weiss, and B. Schäpers From coherent to incoherent hexagonal patterns in semiconductor resonators. Phys. Rev. A 65, 13812 (2002).

    Google Scholar 

  88. V. B. Taranenko, F. J. Ahlers, and K. Pierz. Coherent switching of semiconductor resonator solitons. Appl. Phys. B 75, 75–77 (2002).

    Google Scholar 

  89. I. Ganne, G. Slekys, I. Sagnes, and R. Kuszelewicz. Precursor forms of cavity solitons in nonlinear semiconductor microresonators. Phys. Rev. E 66, 066613 (2002).

    Google Scholar 

  90. X. Hachair, S. Barland, L. Furfaro, M. Giudici, S. Balle, J. Tredicce, M.break Brambilla, T. Maggipinto, I. M. Perrini, G. Tissoni, and L. Lugiato Cavity solitons in broad-area vertical-cavity surface-emitting lasers below threshold. Phys. Rev. A 69, 043817 (2004).

    Google Scholar 

  91. L. Spinelli, G. Tissoni, L. Lugiato, and M. Brambilla Thermal effects and transverse structures in semiconductor microcavities with population inversion. Phys. Rev. A 66, 023817 (2002).

    CrossRef  Google Scholar 

  92. A. J. Scroggie, J. M. McSloy, and W. J. Firth Self-Propelled Cavity Solitons in Semiconductor Microresonators. Phys. Rev. E 66, 036607 (2002).

    Google Scholar 

  93. S. Barland, O. Piro, M. Giudici, J. R. Tredicce, and S. Balle {Experimental evidence of van der Pol–Fitzhugh–Nagumo dynamics in semiconductor optical amplifiers}. Phys. Rev. E 68, 036209 (2003).

    CrossRef  Google Scholar 

  94. P. Coullet, J. Lega, B. Houchmanzadeh, and J. Lajzerowics Breaking chirality in nonequilibrium systems. Phys. Rev. Lett. 65, 1352–1355 (1990).

    Google Scholar 

  95. D. Michaelis, U. Peschel, F. Lederer, D. V. Skryabin, and W. J. Firth {Universal criterion and amplitude equation for a nonequilibrium Ising-Bloch transition}. Phys. Rev. E 63, 066602 (2001).

    Google Scholar 

  96. D. V. Skryabin, A. Yulin, D. Michaelis, W. J. Firth, G.-L. Oppo, U. Peschel, and F. Lederer. Perturbation theory for domain walls in the parametric Ginzburg-Landau equation. Phys. Rev. E 64, 056618 (2001).

    Google Scholar 

  97. C. Degen, I. Fischer, W. Elsäßer, L. Fratta, P. Debernardi, G. Bava, M. Brunner, R. Hövel, M. Moser, and K. Gulden Transverse modes in thermally detuned oxide-confined vertical-cavity surface-emitting lasers. Phys. Rev. A 63, 23817 (2001).

    Google Scholar 

  98. T. Rössler, R. A. Indik, G. K. Harkness, and J. V. Moloney Modeling the interplay of thermal effects and transverse mode behavior in native-oxide confined vertical-cavity surface-emitting lasers. Phys. Rev. A 58, 3279–3292 (1998).

    Google Scholar 

  99. M. Bode {Pattern formation in dissipative systems: A particle approach}. Adv. in Solid State Phys. 41, 369–381 (2001).

    Google Scholar 

  100. H. U. Bödeker, M. C. Röttger, A. W. Liehr, Frank. T. D., R. Friedrich, and H. G. Purwins Noise-covered drift bifurcation of dissipative solitons in a planar gas-discharge system. Phys. Rev. E 67, 056220 (2003).

    Google Scholar 

  101. W. J. Firth Spatial instabilities in a {Kerr} medium with single feedback mirror. J. Mod. Opt. 37, 151–153 (1990).

    Google Scholar 

  102. G. D’Alessandro and W. J. Firth Spontaneous hexagon formation in a nonlinear optical medium with feedback mirror. Phys. Rev. Lett. 66, 2597–2600 (1991).

    Google Scholar 

  103. G. D’Alessandro and W. J. Firth Hexagonal spatial pattern for a {Kerr} slice with a feedback mirror. Phys. Rev. A 46, 537–548 (1992).

    Google Scholar 

  104. M. Kreuzer, A. Schreiber, and B. Thüring Evolution and switching dynamics of solitary spots in nonlinear optical feedback systems. Mol. Cryst. Liq. Cryst. 282, 91–105 (1996).

    Google Scholar 

  105. A. Schreiber, M. Kreuzer, B. Thüring, and T. Tschudi Experimental investigation of solitary structures in a nonlinear optical feedback system Opt. Commun. 136, 415–418 (1997).

    CrossRef  Google Scholar 

  106. B. A. Samson and M. A. Vorontsov Localized states in a nonlinear optical system with a binary-phase slice and a feedback mirror. Phys. Rev. A 56, 1621–1626 (1997).

    Google Scholar 

  107. B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange Interaction of localized structures in an optical pattern forming system. Phys. Rev. Lett. 85, 748–751 (2000).

    CrossRef  Google Scholar 

  108. P. L. Ramazza, S. Ducci, S. Boccaletti, and F. T. Arecchi Localized versus delocalized patterns in a nonlinear optical interferometer. J. Opt. B: Quantum Semiclass. Opt. 2(3), 399–405 (2000).

    Google Scholar 

  109. M. G. Clerc, S. Residori, and C. S. Riera {First-order Frédericksz transition in the presence of light-driven feedback in nematic liquid cyrstals}. Phys. Rev. E 63, 060701(R) (2001).

    Google Scholar 

  110. B. Schäpers, T. Ackemann, and W. Lange Characteristics and possible applications of localized structures in an optical pattern–forming system. Proc. SPIE 4271, 130–137 (2001).

    Google Scholar 

  111. B. Schäpers, T. Ackemann, and W. Lange Robust control of switching of localized structures and its dynamics in a single-mirror feedback scheme.break J. Opt. Soc. Am. B 19(4), 707–715 (2002).

    Google Scholar 

  112. P. L. Ramazza, E. Benkler, U. Bortolozzo, S. Boccaletti, S. Ducci, and F. T. Arecchi Taloiring the profile and interactions of optical localized structures. Phys. Rev. E 65, 066204 (2002).

    Google Scholar 

  113. B. Gütlich, M. Kreuzer, R. Neubecker, and T. Tschudi Manipulation of solitary structures in a nonlinear optical single feedback experiment. Mol. Cryst. Liq. Cryst. 375, 281–289 (2002).

    Google Scholar 

  114. B. Schäpers, T. Ackemann, and W. Lange Properties of feedback solitons in a single-mirror experiment. IEEE J. Quantum Electron. 39(2), 227–237 (2003).

    Google Scholar 

  115. B. Gütlich, R. Neubecker, M. Kreuzer, and T. Tschudi Control and manipulation of solitary structures in a nonlinear optical single feedback experiment. Chaos 13, 239–246 (2003).

    Google Scholar 

  116. S. Rankin, E. Yao, and F. Papoff Traveling waves and counterpropagating bright droplets as a result of tailoring the transverse dispersion relation in a multistable optical system. Phys. Rev. A 68, 013821 (2003).

    Google Scholar 

  117. W. H. F. Talbot {Facts relating to optical science. No. IV}. Philos. Mag. 9(Third series), 401–407 (1836).

    Google Scholar 

  118. E. Ciaramella, M. Tamburrini, and E. Santamato Talbot assisted hexagonal beam patterning in a thin liquid crystal film with a single feedback mirror at negative distance. Appl. Phys. Lett. 63, 1604–1606 (1993).

    Google Scholar 

  119. T. Ackemann, B. Giese, B. Schäpers, and W. Lange {Investigation of pattern forming mechanisms by Fourier filtering: properties of hexagons and the transition to stripes in an anisotropic system}. J. Opt. B: Quantum Semiclass. Opt. 1, 70–76 (1999).

    Google Scholar 

  120. S. G. Odoulov, M. Yu. Goulkov, and O. A. Shinkarenko Threshold behavior in formation of optical hexagons and first order optical phase transition. Phys. Rev. Lett. 83, 3637–3640 (1999).

    CrossRef  Google Scholar 

  121. S. A. Akhmanov, M. A. Vorontsov, V. Yu. Ivanov, A. V. Larichev, and N. I. Zheleynykh Controlling transverse-wave interactions in nonlinear optics: generation and interaction of spatiotemporal structures. J. Opt. Soc. Am. B 9, 78–90 (1992).

    Google Scholar 

  122. A. Kastler Optical methods of atomic orientation and of magnetic resonance. J. Opt. Soc. Am. 47, 460–465 (1957).

    Google Scholar 

  123. F. Mitschke, R. Deserno, W. Lange, and J. Mlynek Magnetically induced optical self-pulsing in a nonlinear resonator. Phys. Rev. A 33, 3219–3231 (1986).

    Google Scholar 

  124. T. Ackemann, A. Heuer, Yu. A. Logvin, and W. Lange Light-shift induced level crossing and resonatorless optical bistability in sodium vapor. Phys. Rev. A 56, 2321–2326 (1997).

    Google Scholar 

  125. D. N. Maywar, G. P. Agrawal, and Y. Nakano Robust optical control of an optical-amplifier-based flip-flop. Opt. Express 6, 75–80 (2000).

    Google Scholar 

  126. W. Lange, Yu. A. Logvin, and T. Ackemann Spontaneous optical patterns in an atomic vapor: observation and simulation. Physica D 96, 230–241 (1996).

    Google Scholar 

  127. B. Schäpers {Lokalisierte Strukturen in einem atomaren Dampf mit optischer Rückkopplung}. Phd thesis, Westfälische Wilhelms-Universität Münster (2001).

    Google Scholar 

  128. M. Kreuzer {Grundlagen und Anwendungen von Füssigkristallen in der optischen Informations- und Kommunikationstechnologie}. PhD thesis, Darmstadt (1994).

    Google Scholar 

  129. T. Ackemann (2002) Unpublished.

    Google Scholar 

  130. G. Grynberg, A. Petrossian, M. Pinard, and M. Vallet. Phase-contrast mirror based on four-wave mixing. Europhys. Lett. 17, 213 (1992).

    Google Scholar 

  131. G. Grynberg Roll and hexagonal patterns in a phase-contrast oscillator.break J. Phys. III 3, 1345–1355 (1993).

    Google Scholar 

  132. M. Tlidi, A. G. Vladimirov, and P. Mandel. Interaction and Stability of Periodic and Localized Structures in Optical Bistable Systems. IEEE J. Quantum Electron. 39, 216–226 (2003).

    Google Scholar 

  133. Yu. A. Logvin, B. Schäpers, and T. Ackemann Stationary and drifting localized structures near a multiple bifurcation point. Phys. Rev. E 61, 4622–4625 (2000).

    Google Scholar 

  134. S. Mêtens, G. Dewel, P. Borckmanns, and R. Engelhardt Pattern selection in bistable systems. Europhys. Lett. 37, 109–114 (1997).

    Google Scholar 

  135. W. J. Firth Processing Information with Arrays of Spatial Solitons. Proc. SPIE 4016, 388–394 (2000).

    Google Scholar 

  136. E. Lugagne Delpon, J. L. Oudar, and H. Lootvoet Operation of a 4×1 optical register as a fast access optical buffer memory. Electron. Lett. 33, 1161–1162 (1997).

    Google Scholar 

  137. P. Mandel Scaling properties of switching pulses. Opt. Commun. 55, 293–296 (1985).

    Google Scholar 

  138. B. Segard, J. Zemmouri, and B. Macke Noncritical slowing down in optical bistability. Opt. Commun. 63, 339–343 (1987).

    Google Scholar 

  139. J. Y. Bigot, A. Daunois, and P. Mandel Slowing down far from the limit points in optical bistability. Phys. Lett. A 123, 123–127 (1987).

    Google Scholar 

  140. F. Mitschke, C. Boden, W. Lange, and P. Mandel Exploring the dynamics of the unstable branch of bistable systems. Opt. Commun. 71, 385–392 (1989).

    Google Scholar 

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Ackemann, T., Firth, W. Dissipative Solitons in Pattern-Forming Nonlinear Optical Systems: Cavity Solitons and Feedback Solitons. In: Akhmediev, N., Ankiewicz, A. (eds) Dissipative Solitons. Lecture Notes in Physics, vol 661. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10928028_4

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