[go: up one dir, main page]
Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Front-induced transitions

Nature Photonics volume 13, pages 737–748 (2019)Cite this article

Subjects

Abstract

Refractive index fronts propagating in waveguides are special spatiotemporal perturbations. The interaction of light with such fronts can be described in terms of an indirect transition where the frequency and wavenumber of a guided mode both are changed. In recent years, front-induced transitions have been used in dispersion-engineered waveguides for frequency conversion, optical delays, and bandwidth and pulse duration manipulation. These concepts have originated from different research areas of photonics, such as nonlinear fibre optics, slow-light waveguides, plasma physics, moving media and relativistic effects. Here, we discuss these concepts, providing a unifying theoretical description and highlight the potential of this exciting research field for light manipulation in guided optics.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: The refractive index front and the dispersion relation.
Fig. 2: Schematic representation of different photonic transitions.
Fig. 3: Signal transmission through the front.
Fig. 4: Signal reflection from the front.
Fig. 5: Signal trapping inside the front.
Fig. 6: Dynamic pulse delay in a photonic crystal waveguide.

Similar content being viewed by others

References

  1. Snyder, A. W. & Love, J. Optical Waveguide Theory (Springer, 1983).

  2. Vivien, L. & Pavesi, L. Handbook of Silicon Photonics 1st edn (CRC Press, 2013).

  3. Cheben, P., Halir, R., Schmid, J. H., Atwater, H. A. & Smith, D. R. Subwavelength integrated photonics. Nature 560, 565–572 (2018).

    ADS  Google Scholar 

  4. Agrawal, G. P. Nonlinear Fiber Optics 5th edn (Academic Press, 2013).

  5. Baba, T. Slow light in photonic crystals. Nat. Photon. 2, 465–473 (2008).

    ADS  Google Scholar 

  6. Krauss, T. F. Why do we need slow light? Nat. Photon. 2, 448–450 (2008).

    ADS  Google Scholar 

  7. Priolo, F., Gregorkiewicz, T., Galli, M. & Krauss, T. F. Silicon nanostructures for photonics and photovoltaics. Nat. Nanotechnol. 9, 19–32 (2014).

    ADS  Google Scholar 

  8. Stepanov, N. S. Adiabatic transformation of a wave spectrum in a nonstationary medium with dispersion. Radiophys. Quantum Electron. 12, 227–234 (1969).

    ADS  Google Scholar 

  9. Geltner, I., Avitzour, Y. & Suckewer, S. Picosecond pulse frequency upshifting by rapid free-carrier creation in ZnSe. Appl. Phys. Lett. 81, 226–228 (2002).

    ADS  Google Scholar 

  10. Yanik, M. F. & Fan, S. Stopping light all optically. Phys. Rev. Lett. 92, 083901 (2004).

    ADS  Google Scholar 

  11. Notomi, M. & Mitsugi, S. Wavelength conversion via dynamic refractive index tuning of a cavity. Phys. Rev. A 73, 051803 (2006).

    ADS  Google Scholar 

  12. Upham, J., Tanaka, Y., Asano, T. & Noda, S. On-the-fly wavelength conversion of photons by dynamic control of photonic waveguides. Appl. Phys. Express 3, 062001 (2010).

    ADS  Google Scholar 

  13. Castellanos Muñoz, M., Petrov, A. Y. & Eich, M. All-optical on-chip dynamic frequency conversion. Appl. Phys. Lett. 101, 141119 (2012).

    ADS  Google Scholar 

  14. Kim, B. Y., Blake, J. N., Engan, H. E. & Shaw, H. J. All-fiber acousto-optic frequency shifter. Opt. Lett. 11, 389–391 (1986).

    ADS  Google Scholar 

  15. Stolte, R. & Ulrich, R. Integrated-optical gigahertz frequency shifter for 1.5 μm signals. Electron. Lett. 33, 1217–1219 (1997).

    Google Scholar 

  16. Yu, Z. & Fan, S. Complete optical isolation created by indirect interband photonic transitions. Nat. Photon. 3, 91–94 (2009).

    ADS  Google Scholar 

  17. Kittlaus, E. A., Otterstrom, N. T., Kharel, P., Gertler, S. & Rakich, P. T. Non-reciprocal interband Brillouin modulation. Nat. Photon. 12, 613–619 (2018).

    ADS  Google Scholar 

  18. Sounas, D. L. & Alù, A. Non-reciprocal photonics based on time modulation. Nat. Photon. 11, 774–783 (2017).

    ADS  Google Scholar 

  19. Zhu, Z., Gauthier, D. J. & Boyd, R. W. Stored light in an optical fiber via stimulated Brillouin scattering. Science 318, 1748–1750 (2007).

    ADS  Google Scholar 

  20. Merklein, M., Stiller, B., Vu, K., Madden, S. J. & Eggleton, B. A chip-integrated coherent photonic–phononic memory. Nat. Commun. 8, 574 (2017).

    ADS  Google Scholar 

  21. Merklein, M., Stiller, B. & Eggleton, B. Brillouin-based light storage and delay techniques. J. Opt. 20, 083003 (2018).

    ADS  Google Scholar 

  22. Dekker, R. et al. Ultrafast Kerr-induced all-optical wavelength conversion in silicon waveguides using 1.55 μm femtosecond pulses. Opt. Express 14, 8336–8346 (2006).

    ADS  Google Scholar 

  23. Hsieh, I. W. et al. Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires. Opt. Express 15, 1135–1146 (2007).

    ADS  Google Scholar 

  24. Philbin, T. G. et al. Fiber-optical analog of the event horizon. Science 319, 1367–1370 (2008).

    ADS  Google Scholar 

  25. Webb, K. E. et al. Nonlinear optics of fibre event horizons. Nat. Commun. 5, 4969 (2014).

    ADS  Google Scholar 

  26. Lobanov, V. E. & Sukhorukov, A. P. Total reflection, frequency, and velocity tuning in optical pulse collision in nonlinear dispersive media. Phys. Rev. A 82, 033809 (2010).

    ADS  Google Scholar 

  27. Rosanov, N. N., Vysotina, N. V. & Shatsev, A. N. Forward light reflection from a moving inhomogeneity. JETP Lett. 93, 308–312 (2011).

    ADS  Google Scholar 

  28. Sukhorukov, A. P., Voitova, T. A., Lobanov, V. E., Bugai, A. N. & Sazonov, S. V. Nonlinear effects upon collisions of optical pulses: tunneling, blocking, and trapping. Bull. Russ. Acad. Sci. Phys. 76, 305–308 (2012).

    Google Scholar 

  29. Choudhary, A. & König, F. Efficient frequency shifting of dispersive waves at solitons. Opt. Express 20, 5538–5546 (2012).

    ADS  Google Scholar 

  30. Eilenberger, F., Kabakova, I. V., de Sterke, C. M., Eggleton, B. & Pertsch, T. Cavity optical pulse extraction: ultra-short pulse generation as seeded Hawking radiation. Sci. Rep. 3, 2607 (2013).

    Google Scholar 

  31. Castellanos Muñoz, M. et al. Optically induced indirect photonic transitions in a slow light photonic crystal waveguide. Phys. Rev. Lett. 112, 053904 (2014).

    ADS  Google Scholar 

  32. Ulchenko, E. A. et al. Pulse compression and broadening by reflection from a moving front of a photonic crystal. Opt. Express 22, 13280–13287 (2014).

    ADS  Google Scholar 

  33. Kondo, K. & Baba, T. Dynamic wavelength conversion in copropagating slow-light pulses. Phys. Rev. Lett. 112, 223904 (2014).

    ADS  Google Scholar 

  34. Plansinis, B. W., Donaldson, W. R. & Agrawal, G. P. What is the temporal analog of reflection and refraction of optical beams? Phys. Rev. Lett. 115, 183901 (2015).

    ADS  Google Scholar 

  35. Ciret, C., Leo, F., Kuyken, B., Roelkens, G. & Gorza, S.-P. Observation of an optical event horizon in a silicon-on-insulator photonic wire waveguide. Opt. Express 24, 114–124 (2016).

    ADS  Google Scholar 

  36. Kanakis, P. & Kamalakis, T. Enabling transistor-like action in photonic crystal waveguides using optical event horizons. Opt. Lett. 41, 1372–1375 (2016).

    ADS  Google Scholar 

  37. Matsuda, N. Deterministic reshaping of single-photon spectra using cross-phase modulation. Sci. Adv. 2, e1501223 (2016).

    ADS  Google Scholar 

  38. Kondo, K. & Baba, T. Slow-light-induced Doppler shift in photonic-crystal waveguides. Phys. Rev. A 93, 011802 (2016).

    ADS  Google Scholar 

  39. Kondo, K., Ishikura, N., Tamura, T. & Baba, T. Temporal pulse compression by dynamic slow-light tuning in photonic-crystal waveguides. Phys. Rev. A 91, 023831 (2015).

    ADS  Google Scholar 

  40. Gaafar, M. A., Petrov, A. Y. & Eich, M. Free carrier front induced indirect photonic transitions: a new paradigm for frequency manipulation on chip. ACS Photon. 4, 2751–2758 (2017).

    Google Scholar 

  41. Kondo, K. & Baba, T. Adiabatic wavelength redshift by dynamic carrier depletion using p-i-n-diode-loaded photonic crystal waveguides. Phys. Rev. A 97, 033818 (2018).

    ADS  Google Scholar 

  42. Marest, T. et al. Collision between a dark soliton and a linear wave in an optical fiber. Opt. Express 26, 23480–23491 (2018).

    ADS  Google Scholar 

  43. Gaafar, M. A. et al. Reflection from a free carrier front via an intraband indirect photonic transition. Nat. Commun. 9, 1447 (2018).

    ADS  Google Scholar 

  44. Semenova, V. I. Reflection of electromagnetic waves from an ionization front. Radiophys. Quantum Electron. 10, 599–604 (1967).

    ADS  Google Scholar 

  45. Lai, C. H., Katsouleas, T. C., Mori, W. B. & Whittum, D. Frequency upshifting by an ionization front in a magnetized plasma. IEEE Trans. Plasma Sci. 21, 45–52 (1993).

    ADS  Google Scholar 

  46. Lampe, M., Ott, E. & Walker, J. H. Interaction of electromagnetic waves with a moving ionization front. Phys. Fluids 21, 42–54 (1978).

    ADS  Google Scholar 

  47. Meng, F., Thomson, M. D. & Roskos, H. G. Relativistic Doppler frequency upconversion of terahertz pulses reflecting from a photoinduced plasma front in silicon. Phys. Rev. B 90, 155207 (2014).

    ADS  Google Scholar 

  48. Biancalana, F., Amann, A., Uskov, A. V. & O’Reilly, E. P. Dynamics of light propagation in spatiotemporal dielectric structures. Phys. Rev. E 75, 046607 (2007).

    ADS  Google Scholar 

  49. Savage, R. L., Joshi, C. & Mori, W. B. Frequency upconversion of electromagnetic radiation upon transmission into an ionization front. Phys. Rev. Lett. 68, 946–949 (1992).

    ADS  Google Scholar 

  50. Savage, R. L., Brogle, R. P., Mori, W. B. & Joshi, C. Frequency upshifting and pulse compression via underdense relativistic ionization fronts. IEEE Trans. Plasma Sci. 21, 5–19 (1993).

    ADS  Google Scholar 

  51. Gaafar, M. A., Renner, H., Petrov, A. Y. & Eich, E. Linear Schrödinger equation with temporal evolution for front induced transitions. Opt. Express 27, 21273–21284 (2019).

    ADS  Google Scholar 

  52. de Sterke, C. M. Optical push broom. Opt. Lett. 17, 914–916 (1992).

    ADS  Google Scholar 

  53. Broderick, N. G. R., Taverner, D., Richardson, D. J., Ibsen, M. & Laming, R. I. Optical pulse compression in fiber Bragg gratings. Phys. Rev. Lett. 79, 4566–4569 (1997).

    ADS  Google Scholar 

  54. Kondo, K. et al. Ultrafast slow-light tuning beyond the carrier lifetime using photonic crystal waveguides. Phys. Rev. Lett. 110, 053902 (2013).

    ADS  Google Scholar 

  55. Beggs, D. M. et al. Ultrafast tunable optical delay line based on indirect photonic transitions. Phys. Rev. Lett. 108, 213901 (2012).

    ADS  Google Scholar 

  56. Beggs, D. M., Krauss, T. F., Kuipers, L. & Kampfrath, T. Ultrafast tilting of the dispersion of a photonic crystal and adiabatic spectral compression of light pulses. Phys. Rev. Lett. 108, 033902 (2012).

    ADS  Google Scholar 

  57. Jacquet, M. & König, F. Quantum vacuum emission from a refractive-index front. Phys. Rev. A 92, 023851 (2015).

    ADS  Google Scholar 

  58. Bermudez, D. & Leonhardt, U. Hawking spectrum for a fiber-optical analog of the event horizon. Phys. Rev. A 93, 053820 (2016).

    ADS  Google Scholar 

  59. Steel, M. J., Jackson, D. G. A. & de Sterke, C. M. Approximate model for optical pulse compression by cross-phase modulation in Bragg gratings. Phys. Rev. A 50, 3447–3452 (1994).

    ADS  Google Scholar 

  60. Gordon, J. P. Dispersive perturbations of solitons of the nonlinear Schrödinger equation. J. Opt. Soc. Am. B 9, 91–97 (1992).

    ADS  Google Scholar 

  61. Yulin, A. V., Skryabin, D. V. & Russell, P. S. J. Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion. Opt. Lett. 29, 2411–2413 (2004).

    ADS  Google Scholar 

  62. Skryabin, D. V. & Yulin, A. V. Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers. Phys. Rev. E 72, 016619 (2005).

    ADS  MathSciNet  Google Scholar 

  63. de Sterke, C. M., Broderick, N. G. R., Eggleton, B. & Steel, M. J. Nonlinear optics in fiber gratings. Opt. Fiber Technol. 2, 253–268 (1996).

    ADS  Google Scholar 

  64. Reed, E. J., Soljačić, M. & Joannopoulos, J. D. Color of shock waves in photonic crystals. Phys. Rev. Lett. 90, 203904 (2003).

    ADS  Google Scholar 

  65. Reed, E. J., Soljačić, M. & Joannopoulos, J. D. Reversed Doppler effect in photonic crystals. Phys. Rev. Lett. 91, 133901 (2003).

    ADS  Google Scholar 

  66. Stepanov, N. S. Waves in nonstationary media. Radiophys. Quantum Electron. 36, 401–409 (1993).

    ADS  Google Scholar 

  67. Plansinis, B. W., Donaldson, W. R. & Agrawal, G. P. Temporal waveguides for optical pulses. J. Opt. Soc. Am. B 33, 1112–1119 (2016).

    ADS  Google Scholar 

  68. Tanabe, T. et al. Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities. Appl. Phys. Lett. 90, 031115 (2007).

    ADS  Google Scholar 

  69. Zhang, Y. et al. Non-degenerate two-photon absorption in silicon waveguides: analytical and experimental study. Opt. Express 23, 17101–17110 (2015).

    ADS  Google Scholar 

  70. Joannopoulos, J. D. Photonic Crystals, Molding the Flow of Light (Princeton University Press, 2008).

  71. Yanik, M. F. & Fan, S. Stopping and storing light coherently. Phys. Rev. A 71, 013803 (2005).

    ADS  Google Scholar 

  72. Preble, S. F., Xu, Q. & Lipson, M. Changing the colour of light in a silicon resonator. Nat. Photon. 1, 293–296 (2007).

    ADS  Google Scholar 

  73. Kampfrath, T. et al. Ultrafast adiabatic manipulation of slow light in a photonic crystal. Phys. Rev. A 81, 043837 (2010).

    ADS  Google Scholar 

  74. Munoz, M. C., Kanchana, A., Petrov, A. Y. & Eich, M. Dynamic light storage in slow light waveguides. IEEE J. Quantum Electron. 48, 862–866 (2012).

    ADS  Google Scholar 

  75. Verbist, M., Bogaerts, W. & Thourhout, D. V. Design of weak 1-D Bragg grating filters in SOI waveguides using volume holography techniques. J. Lightwave Technol. 32, 1915–1920 (2014).

    ADS  Google Scholar 

  76. Li, J., White, T. P., O’Faolain, L., Gomez-Iglesias, A. & Krauss, T. F. Systematic design of flat band slow light in photonic crystal waveguides. Opt. Express 16, 6227–6232 (2008).

    ADS  Google Scholar 

  77. Dudley, J. M., Genty, G. & Coen, S. Supercontinuum generation in photonic crystal fiber. Rev. Mod. Phys. 78, 1135–1184 (2006).

    ADS  Google Scholar 

  78. Meltz, G., Morey, W. W. & Glenn, W. H. Formation of Bragg gratings in optical fibers by a transverse holographic method. Opt. Lett. 14, 823–825 (1989).

    ADS  Google Scholar 

  79. Yanik, M. F. & Fan, S. Time reversal of light with linear optics and modulators. Phys. Rev. Lett. 93, 173903 (2004).

    ADS  Google Scholar 

  80. Sivan, Y. & Pendry, J. B. Time reversal in dynamically tuned zero-gap periodic systems. Phys. Rev. Lett. 106, 193902 (2011).

    ADS  Google Scholar 

  81. Yachini, M., Malomed, B. & Bahabad, A. Envelope time reversal of optical pulses following frequency conversion with accelerating quasi-phase-matching. ACS Photon. 3, 2017–2021 (2016).

    Google Scholar 

  82. Minkov, M. & Fan, S. Localization and time-reversal of light through dynamic modulation. Phys. Rev. B 97, 060301 (2018).

    ADS  Google Scholar 

  83. Konoike, R., Asano, T. & Noda, S. On-chip dynamic time reversal of light in a coupled-cavity system. APL Photon. 4, 030806 (2019).

    ADS  Google Scholar 

  84. Colman, P., Combrié, S., Lehoucq, G., de Rossi, A. & Trillo, S. Blue self-frequency shift of slow solitons and radiation locking in a line-defect waveguide. Phys. Rev. Lett. 109, 093901 (2012).

    ADS  Google Scholar 

  85. Blanco-Redondo, A. et al. Observation of soliton compression in silicon photonic crystals. Nat. Commun. 5, 3160 (2014).

    ADS  Google Scholar 

  86. Bhat, N. A. R. & Sipe, J. E. Optical pulse propagation in nonlinear photonic crystals. Phys. Rev E 64, 056604 (2001).

    ADS  Google Scholar 

  87. Yulin, A. V. & Skryabin, D. V. Slowing down of solitons by intrapulse Raman scattering in fibers with frequency cutoff. Opt. Lett. 31, 3092–3094 (2006).

    ADS  Google Scholar 

  88. Demircan, A., Amiranashvili, S. & Steinmeyer, G. Controlling light by light with an optical event horizon. Phys. Rev. Lett. 106, 163901 (2011).

    ADS  Google Scholar 

  89. Belgiorno, F. et al. Hawking radiation from ultrashort laser pulse filaments. Phys. Rev. Lett. 105, 203901 (2010).

    ADS  Google Scholar 

  90. Plansinis, B. W., Donaldson, W. R. & Agrawal, G. P. Cross-phase-modulation-induced temporal reflection and waveguiding of optical pulses. J. Opt. Soc. Am. B 35, 436–445 (2018).

    ADS  Google Scholar 

  91. Gaeta, A. L., Lipson, M. & Kippenberg, T. J. Photonic-chip-based frequency combs. Nat. Photon. 13, 158–169 (2019).

    ADS  Google Scholar 

  92. Köttig, F. et al. Mid-infrared dispersive wave generation in gas-filled photonic crystal fibre by transient ionization-driven changes in dispersion. Nat. Commun. 8, 813 (2017).

    ADS  Google Scholar 

  93. Maier, S. A. Plasmonics: Fundamentals and Applications (Springer US, 2007).

  94. Stockman, M. I. Nanofocusing of optical energy in tapered plasmonic waveguides. Phys. Rev. Lett. 93, 137404 (2004).

    ADS  Google Scholar 

  95. Gramotnev, D. K. & Bozhevolnyi, S. I. Nanofocusing of electromagnetic radiation. Nat. Photon. 8, 13–22 (2014).

    ADS  Google Scholar 

  96. Willner, A. E., Khaleghi, S., Chitgarha, M. R. & Yilmaz, O. F. All-optical signal processing. J. Lightwave Technol. 32, 660–680 (2014).

    ADS  Google Scholar 

  97. Wengerowsky, S., Joshi, S. K., Steinlechner, F., Hübel, H. & Ursin, R. An entanglement-based wavelength-multiplexed quantum communication network. Nature 564, 225–228 (2018).

    ADS  Google Scholar 

  98. Leuthold, J., Koos, C. & Freude, W. Nonlinear silicon photonics. Nat. Photon. 4, 535–544 (2010).

    ADS  Google Scholar 

  99. Morichetti, F. et al. Travelling-wave resonant four-wave mixing breaks the limits of cavity-enhanced all-optical wavelength conversion. Nat. Commun. 2, 296 (2011).

    ADS  Google Scholar 

  100. Monat, C. et al. Four-wave mixing in slow light engineered silicon photonic crystal waveguides. Opt. Express 18, 22915–22927 (2010).

    ADS  Google Scholar 

  101. Suchowski, H., Porat, G. & Arie, A. Adiabatic processes in frequency conversion. Laser Photon. Rev. 8, 333–367 (2014).

    ADS  Google Scholar 

  102. Tan, D. T. H., Agarwal, A. M. & Kimerling, L. C. Nonlinear photonic waveguides for on-chip optical pulse compression. Laser Photon. Rev. 9, 294–308 (2015).

    ADS  Google Scholar 

  103. Foster, M. A. et al. Ultrafast waveform compression using a time-domain telescope. Nat. Photon. 3, 581–585 (2009).

    ADS  Google Scholar 

  104. Karpiński, M., Jachura, M., Wright, L. J. & Smith, B. J. Bandwidth manipulation of quantum light by an electro-optic time lens. Nat. Photon. 11, 53–57 (2016).

    ADS  Google Scholar 

  105. Xu, Q., Dong, P. & Lipson, M. Breaking the delay-bandwidth limit in a photonic structure. Nat. Phys. 3, 406–410 (2007).

    Google Scholar 

  106. Phillips, D. F., Fleischhauer, A., Mair, A., Walsworth, R. L. & Lukin, M. D. Storage of light in atomic vapor. Phys. Rev. Lett. 86, 783–786 (2001).

    ADS  Google Scholar 

  107. Liu, C., Dutton, Z., Behroozi, C. H. & Hau, L. V. Observation of coherent optical information storage in an atomic medium using halted light pulses. Nature 409, 490–493 (2001).

    ADS  Google Scholar 

  108. Tanaka, Y. et al. Dynamic control of the Q factor in a photonic crystal nanocavity. Nat. Mater. 6, 862–865 (2007).

    ADS  Google Scholar 

  109. Tanabe, T., Notomi, M., Taniyama, H. & Kuramochi, E. Dynamic release of trapped light from an ultrahigh-Q nanocavity via adiabatic frequency tuning. Phys. Rev. Lett. 102, 043907 (2009).

    ADS  Google Scholar 

  110. Elshaari, A. W., Aboketaf, A. & Preble, S. F. Controlled storage of light in silicon cavities. Opt. Express 18, 3014–3022 (2010).

    ADS  Google Scholar 

  111. Upham, J. et al. Pulse capture without carrier absorption in dynamic Q photonic crystal nanocavities. Opt. Express 22, 15459–15466 (2014).

    ADS  Google Scholar 

  112. Drori, J., Rosenberg, Y., Bermudez, D., Silberberg, Y. & Leonhardt, U. Observation of stimulated Hawking radiation in an optical analogue. Phys. Rev. Lett. 122, 010404 (2019).

    ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge the support of the German Research Foundation (DFG) under grant no. 392102174. We further acknowledge discussions with H. Renner.

Author information

Authors and Affiliations

  1. Institute of Optical and Electronic Materials, Hamburg University of Technology, Hamburg, Germany

    Mahmoud A. Gaafar, Manfred Eich & Alexander Yu. Petrov

  2. Department of Physics, Faculty of Science, Menoufia University, Menoufia, Egypt

    Mahmoud A. Gaafar

  3. Department of Electrical and Computer Engineering, Yokohama National University, Hodogayaku, Yokohama, Japan

    Toshihiko Baba

  4. Institute of Materials Research, Helmholtz-Zentrum Geesthacht, Geesthacht, Germany

    Manfred Eich

  5. ITMO University, St. Petersburg, Russia

    Alexander Yu. Petrov

Authors
  1. Mahmoud A. Gaafar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Toshihiko Baba
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Manfred Eich
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alexander Yu. Petrov
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

M.A.G. performed the LSE simulations and wrote the first version of the manuscript with A.Y.P. All authors discussed and edited the content in the manuscript.

Corresponding authors

Correspondence to Mahmoud A. Gaafar or Alexander Yu. Petrov.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gaafar, M.A., Baba, T., Eich, M. et al. Front-induced transitions. Nat. Photonics 13, 737–748 (2019). https://doi.org/10.1038/s41566-019-0511-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-019-0511-6

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing