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All issues Volume 20 (2025) Math. Model. Nat. Phenom., 20 (2025) 1 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 20, 2025
Article Number 1
Number of page(s) 16
Section Physics
DOI https://doi.org/10.1051/mmnp/2024023
Published online 03 January 2025
  1. B.A. Malomed and D. Mihalache, Nonlinear waves in optical and matter-wave media: a topical survey of recent theoretical and experimental results. Rom. Jo. Phys. 64 (2019) 106. [Google Scholar]
  2. D. Mihalache, Localized structures in optical and matter-wave media: a selection of recent studies. Roman. Rep. Phys. 73 (2021) 403. [Google Scholar]
  3. D. Mihalache, Localized structures in optical media and Bose–Einstein condensates: an overview of recent theoretical and experimental results. Roman. Rep. Phys. 76 (2024) 402. [CrossRef] [Google Scholar]
  4. S.M. Shandarov and E.S. Shandarov, Photorefractive slit waves. Tech. Phys. Lett. 23 (1997) 586–588. [CrossRef] [Google Scholar]
  5. T.H. Zhang, X.K. Ren, B.H. Wang, C.B. Lou, Z.J. Hu, W.W. Shao, Y.H. Xu, H.Z. Kang, J. Yang, D.P. Yang, L. Feng and J.J. Xu, Surface waves with photorefractive nonlinearity. Phys. Rev. A 76 (2007) 013827. [CrossRef] [Google Scholar]
  6. Z. Luo, F. Liu, Y. Xu, H. Liu, T. Zhang, J. Xu and J. Tian, Dark surface waves in self-focusing media with diffusion and photovoltaic nonlinearities. Opt. Express, 21 (2013) 15075–15080. [CrossRef] [Google Scholar]
  7. P.F. Qi, Z.J. Hu, R. Han, T.H. Zhang, J.G. Tian and J.J. Xu, Apodized waveguide arrays induced by photorefractive nonlinear surface waves. Opt. Express 23 (2015) 31144–31149. [CrossRef] [Google Scholar]
  8. L. Chun-Yang, J. Ying, S. De, M. Yi-Ning, Y. Ji-Kai and C. Wei-Jun, Guided modes in thin layer waveguide induced by photorefractive surface waves. Chinese J. Luminescence 39 (2018) 1572–1578. [CrossRef] [Google Scholar]
  9. S.E. Savotchenko, Propagation of surface waves along a dielectric layer in a photorefractive crystal with a diffusion mechanism for the nonlinearity formation. Quant. Electron. 49 (2019) 850–856. [CrossRef] [Google Scholar]
  10. S.E. Savotchenko, Nonlinear surface TM waves in a Kerr defocusing nonlinear slab sandwiched between photorefractive crystals. Solid State Commun. 296 (2019) 32–36. [CrossRef] [Google Scholar]
  11. S.E. Savotchenko, Nonlinear surface waves at the interface between optical media with different nonlinearity induction mechanisms. JETP 129 (2019) 159–167. [CrossRef] [Google Scholar]
  12. S.E. Savotchenko, Effect of the dark illumination intensity on the characteristics of surface waves propagating along the interface between photorefractive and nonlinear Kerr crystals. Russ. Phys. J. 63 (2020) 160–170. [CrossRef] [Google Scholar]
  13. S.E. Savotchenko, Surface waves at the boundary of a photorefractive crystal and a medium with positive Kerr nonlinearity. Phys. Solid State 62 (2020) 1011–1016. [CrossRef] [Google Scholar]
  14. S.E. Savotchenko, Surface waves at the boundary of a medium with a refractive index switching and a crystal with the diffusion-type photorefractive nonlinearity. Phys. Solid State 62 (2020) 1415–1420. [CrossRef] [Google Scholar]
  15. B.A. Usievich, D.Kh. Nurligareev, V.A. Sychugov, L.I. Ivleva, P.A. Lykov and N.V. Bogodaev, Nonlinear surface waves on the boundary of a photorefractive crystal. Quant. Electron. 40 (2010) 437–440. [CrossRef] [Google Scholar]
  16. S.A. Chetkin and I.M. Akhmedzhanov, Optical surface wave in a crystal with diffusion photorefractive nonlinearity. Quant. Electron. 41 (2011) 980–985. [CrossRef] [Google Scholar]
  17. B.A. Usievich, D.Kh. Nurligareev, V.A. Sychugov, L.I. Ivleva, P.A. Lykov and N.V. Bogodaev, Surface photorefractive wave on the boundary of a photorefractive metal-coated crystal. Quant. Electron. 41 (2011) 262–266. [CrossRef] [Google Scholar]
  18. D.Kh. Nurligareev, B.A. Usievich, V.A. Sychugov and L.I. Ivleva, Characteristics of surface photorefractive waves in a nonlinear SBN-75 crystal coated with a metal film. Quant. Electron. 43 (2013) 14–20. [CrossRef] [Google Scholar]
  19. A.B. Shvartsburg and A. Maradudin, Waves in Gradient Metamaterials. World Scientific, Singapore (2013) 339. [Google Scholar]
  20. S.J. Al-Bader and H.A. Jamid, Graded-index optical waveguides with nonlinear cladding. J. Opt. Soc. Am. A 5 (1988) 374–379. [CrossRef] [Google Scholar]
  21. M.J. Adams, An Introduction to Optical Waveguides. Wiley, Chichester (1981). [Google Scholar]
  22. C.-L. Chen, Foundations for Guided-wave Optics. John Wiley & Sons, Inc. (2005) 462. [Google Scholar]
  23. P. D’Ancona, Kato smoothing and strichartz estimates for wave equations with magnetic potentials. Commun. Math. Phys. 335 (2015) 1–16 [CrossRef] [Google Scholar]
  24. F. Cacciafesta, P. D’Ancona and R. Lucà, Renato Helmholtz and dispersive equations with variable coefficients on exterior domains. SIAM J. Math. Anal. 48 (2016) 1798–1832. [CrossRef] [MathSciNet] [Google Scholar]
  25. A.D. Polyanin and A.I. Zhurov, Separation of Variables and Exact Solutions to Nonlinear PDEs. CRC Press, Taylor and Francis Group, LLC, Boca Raton, London (2022) 382. [Google Scholar]
  26. Z. Cao, Y. Jiang, Q. Shen, X. Dou and Y. Chen, Exact analytical method for planar optical waveguides with arbitrary index profile. J. Opt. Soc. Am. A 16 (1999) 2209–2212. [CrossRef] [Google Scholar]
  27. N.A. Kudryashov, Optical solitons of mathematical model with arbitrary refractive index. Optik 224 (2020) 165391. [NASA ADS] [CrossRef] [Google Scholar]
  28. N.A. Kudryashov, Optical solitons of the Chen–Lee–Liu equation with arbitrary refractive index. Optik 247 (2021) 167935. [CrossRef] [Google Scholar]
  29. G. Akram, M. Sadaf and I. Zainab, The dynamical study of Biswas-–Arshed equation via modified auxiliary equation method. Optik 255 (2022) 168614. [CrossRef] [Google Scholar]
  30. N.A. Kudryashov and A. Biswas, Optical solitons of nonlinear Schrödinger’s equation with arbitrary dual-power law parameters. Optik 252 (2022) 168497. [CrossRef] [Google Scholar]
  31. N.A. Kudryashov, Stationary solitons of the model with nonlinear chromatic dispersion and arbitrary refractive index. Optik 259 (2022) 168888. [CrossRef] [Google Scholar]
  32. S.A. Odintsov, E.H. Lock, E.N. Beginin and A.V. Sadovnikov, Nonreciprocal propagation of spin waves in a bilayer magnonic waveguide based on yttrium-iron garnet films. Russ. Technol. J. 10 (2022) 55–64. [CrossRef] [Google Scholar]
  33. Y. Yıldırım, A. Biswas, A.H. Kara, M. Ekici, E.M.E. Zayed, A.K. Alzahrani and M.R. Belic, Optical solitons and conservation law with Kudryashov’s form of arbitrary refractive index. J. Opt. (India) 50 (2021) 542–547. [Google Scholar]
  34. E.M.E. Zayed, A.G. Al-Nowehy, M.E.M. Alngar, A. Biswas, M. Asma, M. Ekici, A.K. Alzahrani and M.R. Belic, Highly dispersive optical solitons in birefringent fibers with four nonlinear forms using Kudryashov’s approach. J. Opt. (India) 50 (2021) 120–131. [CrossRef] [Google Scholar]
  35. J. Vega-Guzman, A. Biswas, M. Asma, A.R. Seadawy, M. Ekici, A.K. Alzahrani and M.R. Belic, Optical soliton perturbation with parabolic–nonlocal combo nonlinearity: undetermined coefficients and semi-inverse variational principle. J. Opt. (India) 51 (2022) 22–28. [CrossRef] [Google Scholar]
  36. A. Jawad and M. Abu-Al Shaeer, Highly dispersive optical solitons with cubic law and cubic-quintic-septic law nonlinearities by two methods. Rafidain J. Eng. Sci. 1 (2023) 1–8. [Google Scholar]
  37. M. Jawad A. Jafar, Y. Yildirim, A. Biswas, I.K. Ibraheem and A.S. Alshomrani, Highly dispersive optical solitons with differential group delay for kerr law of self-phase modulation by Sardar sub-equation approach. Contemp. Math. 5 (2024) 3839–383957. [Google Scholar]
  38. A.J.M. Jawad, A. Biswas, Y. Yildirim and A.S. Alshomrani, Highly dispersive optical solitons with quadratic-cubic nonlinear form of self-phase modulation by Sardar sub-equation approach. Contemp. Math. 5 (2024) 1300–1322. [Google Scholar]
  39. N. Jihad and M. Abd Almuhsan, Evaluation of impairment mitigations for optical fiber communications using dispersion compensation techniques. Rafidain J. Eng. Sci. 1 (2023) 81–92. [CrossRef] [Google Scholar]
  40. A.J.M. Jawad, A. Biswas, Y. Yildirim and A.S. Alshomrani, A fresh perspective on the concatenation model in optical fibers with Kerr law of self-phase modulation. Eng. Sci. Technol. 5 (2024) 195–208. [CrossRef] [Google Scholar]
  41. A.J.M. Jawad, A. Biswas, Y. Yildirim and A.S. Alshomrani, Dark-singular straddled optical solitons for the dispersive concatenation model with power-law of self-phase modulation by Tanh-Coth approach. Contemp. Math. 5 (2024) 3198–3214. [CrossRef] [Google Scholar]
  42. A. Jawad and A. Biswas, Solutions of resonant nonlinear Schrödinger’s equation with exotic non-Kerr law nonlinearities. Rafidain J. Eng. Sci. 2 (2023) 43–50. [Google Scholar]
  43. T. Aytug, A. Lupini, G. Jellison, P.C. Joshi, I. Ivanov, T. Liu, P. Wang, R. Menon, R. Trejo, E. Lara-Curzio, S. Hunter, J. Simpson, P. Paranthaman and D. Christen, Monolithic graded-refractive-index glass-based antireflective coatings: broadband/omnidirectional light harvesting and self cleaning characteristics. J. Mater. Chem. C 3 (2015) 5440. [CrossRef] [Google Scholar]
  44. J. Zheng, W. Zhao, B. Zhao, C. Hou, Z. Li, G. Li, Q. Gao, P. Ju, W. Gao, S. She, P. Wu and W. Li, 4.62 kW excellent beam quality laser output with a low-loss Yb/Ce co-doped fiber fabricated by chelate gas phase deposition technique. Opt. Mater. Express 7 (2017) 1259–1266. [CrossRef] [Google Scholar]
  45. F. Gaufillet and E. Akmansoy, Design and experimental evidence of a flat graded-index photonic crystal lens. J. Appl. Phys. 114 (2013) 083105. [CrossRef] [Google Scholar]
  46. H. Rauh, G.I. Yampolskaya and S.V. Yampolskii, Optical transmittance of photonic structures with linearly graded dielectric constituents. New J. Phys. 12 (2010) 073033. [CrossRef] [Google Scholar]
  47. K. Ratra, M. Singh and A.K. Goyal, Design and analysis of omni-directional solar spectrum reflector using one-dimensional photonic crystal. J. Nanophoton. 14 (2020) 026005. [CrossRef] [Google Scholar]
  48. Y.B. Kim, J.W. Cho, Y.J. Lee, B. Dukkyu and S.-K. Kim, High-index-contrast photonic structures: a versatile platform for photon manipulation. Light Sci. Appl. 11 (2022) 316. [CrossRef] [Google Scholar]
  49. B.K. Singh, A. Bijalwan, P.C. Pandey and V. Rastogi, Photonic bandgaps engineering in double graded hyperbolic, exponential and linear index materials embedded one-dimensional photonic crystals. Eng. Res. Express 1 (2019) 025004. [CrossRef] [Google Scholar]
  50. B.K. Singh, A. Bijalwan, P.C. Pandey and V. Rastogi, Multi-channel photonic bandgap consequences in one-dimensional linear, exponential, and hyperbolic graded-index photonic crystals. J. Opt. Soc. Am. B 37 (2020) 523. [CrossRef] [Google Scholar]
  51. D. Dash and J. Saini, Hyperbolic graded index biophotonic cholesterol sensor with improved sensitivity. Progr. Electromagnet. Res. M 116 (2023) 165–176. [CrossRef] [Google Scholar]
  52. P. Yeh, Optical Wave in Layered Media. Wiley, New Jersey (1988). [Google Scholar]
  53. S.E. Savotchenko, The surface waves propagating along the contact between the layer with the constant gradient of refractive index and photorefractive crystal. J. Opt. 24 (2022) 045501. [Google Scholar]
  54. S.E. Savotchenko, Waveguide properties of interface separating a photorefractive crystal with diffusion nonlinearity and an exponential graded-index medium. Phys. Lett. A 455 (2022) 128516. [CrossRef] [Google Scholar]
  55. S.E. Savotchenko, Surface waves propagating along the interface between parabolic graded-index medium and photorefractive crystal with diffusion nonlinearity. Physica B: Condensed Matter 648 (2023) 414434. [CrossRef] [Google Scholar]
  56. S.E. Savotchenko, Temperature controlled waveguide properties of the linearly graded-index film in semiconductor crystal with the photorefractive nonlinearity. Appl. Phys. B: Lasers Opt. 129 (2023) 7. [CrossRef] [Google Scholar]
  57. S.E. Savotchenko, The effect of dielectric slab between photorefractive crystal and graded-index medium on the surface wave properties. Physica E 147 (2023) 115622. [CrossRef] [Google Scholar]
  58. S.E. Savotchenko, Nonlinear waves in a composite optical structure containing a dielectric layer between a photorefractive crystal and a medium with an exponential index profile. Waves in Random and Complex Media (2023). [Google Scholar]
  59. S.E. Savotchenko, Nonlinear surface waves propagating along an interface between the Kerr nonlinear and hyperbolic graded-index crystals. J. Opt. (India) 53 (2024). [Google Scholar]
  60. S.E. Savotchenko, Features of the surface wave propagation along the interface between the hyperbolic graded-index layer and nonlinear medium with a step change in the dielectric constant. Phys. Lett. A 524 (2024) 129822. [CrossRef] [Google Scholar]
  61. S.E. Savotchenko, Effect of the temperature on the redistribution of an energy flux carried by surface waves along the interface between crystals with different mechanisms of formation of a nonlinear response. JETP Lett. 109 (2019) 744–748. [CrossRef] [Google Scholar]
  62. W. Van Assche, Ordinary Special Functions. Encyclopedia of Mathematical Physics edited by J.-P. Françoise, G. L. Naber and T.S. Tsun. Academic Press, New York (2006) 637–645. [CrossRef] [Google Scholar]
  63. V.K. Chaubey, K.K. Dey and P. Khastgir, Field intensity and power confinement of four-layer slab waveguides with various refractive index profiles in the guiding region. J. Opt. Commun. 15 (1994) 95–100. [CrossRef] [Google Scholar]
  64. L.V. Fedorov and K.D. Ljahomskaja, Nonlinear surface waves with allowance for the saturation effect. Tech. Phys. Lett. 23 (1997) 915–916. [CrossRef] [Google Scholar]
  65. O.V. Korovai and P.I. Khadzhi, Nonlinear asymmetric waves induced in a symmetrical three-layer structure by the generation of excitons and biexcitons in semiconductors. Phys. Solid State 50 (2008) 1116–1120. [Google Scholar]
  66. O.V. Korovai, Nonlinear s-polarized quasi-surface waves in the symmetric structure with a metamaterial core. Phys. Solid State 57 (2015) 1456–1462. [CrossRef] [Google Scholar]

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