Light propagation along a helical waveguide: variational approach


We investigate numerically and analytically light propagation in a single spiral waveguide formed in a nonlinear dielectric medium, in the regime of low spatial frequency of the waveguide rotation. We present a general variational approach for computing soliton parameters analytically, which includes various types of nonlinearity. In the particular case of media with cubic-quintic nonlinearity, analytical expressions found are in very good agreement with the numerical findings.

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  1. Aleksić, N., Petrović, M., Strinić, A., Belić, M.: Solitons in highly nonlocal nematic liquid crystals: variational approach. Phys. Rev. A 85, 033826 (2012)

    ADS  Article  Google Scholar 

  2. Cuevas, J., Malomed, B., Kevrekidis, P.G.: Two-dimensional discrete solitons in rotating lattices. Phys. Rev. E 76, 046608 (2007)

    ADS  MathSciNet  Article  Google Scholar 

  3. Henneberger, W.C.: Perturbation method for atoms in intense light beams. Phys. Rev. Lett. 21, 838–841 (1968)

    ADS  Article  Google Scholar 

  4. Jia, S., Fleischer, J.: Nonlinear light propagation in rotating waveguide arrays. Phys. Rev. A 79, 041804 (R) (2009)

    ADS  Article  Google Scholar 

  5. Kivshar, Y.S., Agrawal, G.: Optical Solitons: From Fibers to Photonic Crystals. Academic, San Diego (2003)

    Google Scholar 

  6. Longhi, S.: Wave packet dynamics in a helical optical waveguide. Phys. Rev. A 71, 055402 (2005)

    ADS  Article  Google Scholar 

  7. Longhi, S.: Bloch dynamics of light waves in helical optical waveguide arrays. Phys. Rev. B 76, 195119 (2007)

    ADS  Article  Google Scholar 

  8. Longhi, S., Janner, D., Marano, M., Laporta, P.: Quantum-mechanical analogy of beam propagation in waveguides with a bent axis: dynamic-mode stabilization and radiation-loss suppression. Phys. Rev. E 67, 036601 (2003)

    ADS  Article  Google Scholar 

  9. Lumer, Y., Plotnik, Y., Rechtsman, M., Segev, M.: Self-localized states in photonic topological insulators. Phys. Rev. Lett. 111, 243905 (2013)

    ADS  Article  Google Scholar 

  10. Milián, C., Kartashov, Y.V., Torner, L.: Robust ultrashort light bullets in strongly twisted waveguide arrays. Phys. Rev. Lett. 123, 133902 (2019)

    ADS  Article  Google Scholar 

  11. Parto, M., Lopez-Aviles, H., Antonio-Lopez, J.E., Khajavikhan, M., Amezcua-Correa, R., Christodoulides, D.N.: Observation of twist-induced geometric phases and inhibition of optical tunneling via Aharonov–Bohm effects. Sci. Adv. 5, 1–5 (2019)

    Article  Google Scholar 

  12. Petrović, M.S., Strinić, A.I., Aleksić, N.B., Belić, M.R.: Rotating solitons supported by a spiral waveguide. Phys. Rev. A 98, 063822 (2018)

    ADS  Article  Google Scholar 

  13. Rechtsman, M., Zeuner, J., Plotnik, Y., Lumer, Y., Podolsky, D., Dreisow, F., Nolte, S., Segev, M., Szameit, A.: Photonic Floquet topological insulators. Nature 496, 196–200 (2013)

    ADS  Article  Google Scholar 

  14. Sakaguchi, H., Malomed, B.: Solitary vortices and gap solitons in rotating optical lattices. Phys. Rev. A 79, 043606 (2009)

    ADS  Article  Google Scholar 

  15. Strinić, A.I., Petrović, M.S., Aleksić, N.B., Belić, M.R.: Quasi-stable rotating solitons supported by a single spiraling waveguide. Opt. Quant. Electron. 50, 126 (2018)

    Article  Google Scholar 

  16. Zhang, X., Ye, F., Kartashov, Y., Vysloukh, V., Chen, X.: Localized waves supported by the rotating waveguide array. Opt. Lett. 41, 4106–4109 (2016)

    ADS  Article  Google Scholar 

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This work was supported by the Ministry of Science of the Republic of Serbia under the Projects OI 171033 and 171006, by the NPRP 11S-1126-170033 project of the Qatar National Research Fund, and the Russian Science Foundation Project No. 18-11-00247. Authors acknowledge supercomputer time provided by the IT Research Computing group of Texas A&M University at Qatar. MRB acknowledges support by the Al Sraiya Holding Group.

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Correspondence to Aleksandra I. Strinić.

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This article is part of the Topical Collection on Advanced Photonics Meets Machine Learning.

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Strinić, A.I., Aleksić, N.B., Belić, M.R. et al. Light propagation along a helical waveguide: variational approach. Opt Quant Electron 52, 310 (2020).

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  • Light propagation
  • Spiral waveguide
  • Variational approach