EDP Sciences logo
Subscriber Authentication Point
Sciengine logo
Search
Menu
All issues Volume 20 (2025) Math. Model. Nat. Phenom., 20 (2025) 27 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 20, 2025
Article Number 27
Number of page(s) 16
Section Physics
DOI https://doi.org/10.1051/mmnp/2025026
Published online 14 November 2025
  1. P.S. Emeliantsev, N.I. Pyshkov, and S.E. Svyakhovskiy, Designing the Structure of a One-Dimensional Photonic Crystal with a Given Spectrum of the Reflection Coefficient. JETP Lett. 117 (2023) 821–826. [Google Scholar]
  2. Y. Chen, J. Dong, T. Liu, Q. Zhu, and W. Chen, Refractive index sensing performance analysis of photonic crystal containing graphene based on optical Tamm state. Modern Physics Letters B 30 (2016) 1650030. [Google Scholar]
  3. C-L. Chen, Foundations for guided-wave optics (John Wiley & Sons, Inc., 2005) 462. https://doi.org/10.1002/0470042222 [Google Scholar]
  4. A.B. Shvartsburg and A. Maradudin, Waves in gradient metamaterials. World Scientific, Singapore, (2013) 339. https://doi.org/10.1142/8649 [Google Scholar]
  5. M. Azkune, A. Ortega-Gomez, I. Ayesta, and J. Zubia, Refractive-Index Profile Reconstruction in Graded-Index Polymer Optical Fibers Using Raman Spectroscopy. Materials (Basel) 13 (2020) 2251. [Google Scholar]
  6. L. Xue, B.S.M. Timoteo, W. Qiu, Z. Wang, Broadband Circular Polarizer Based on Chirped Double-Helix Chiral Fiber Grating. Materials (Basel) 15 (2022) 3366. [Google Scholar]
  7. P. Pace, S.T. Huntington, K. Lyytikäinen, A. Roberts, and J. Love, Refractive index profiles of Ge-doped optical fibers with nanometer spatial resolution using atomic force microscopy. Optics express 12 (2004) 1452–1457. [Google Scholar]
  8. L.A. Moore and C.M. Smith, Fused silica as an optical material, Opt. Mater. Express 12 (2022) 3043–3059. [Google Scholar]
  9. Y. Yue, Y. Liu, W. Zhao, J. Yang, W. Geng, Y. Wang, Ring-core Fiber Supporting OAM-based Optical Communications, Opto-Electronics and Communications Conference (OECC) (2023) 1-2. https://doi.org/10.1109/OECC56963.2023.10209937 [Google Scholar]
  10. P. Miluski, K. Markowski, M. Kochanowicz, et al. Tm3+/Ho3+ profiled co-doped core area optical fiber for emission in the range of 1.6-2.1 gm. Sci. Rep. 13 (2023) 13963. [Google Scholar]
  11. P.-O. Janvier, C. Matte-Breton, K.J.-J. Monga, L. Wang, L. Rusch, and S. LaRochelle, Optimization criteria and design of few-mode Erbium-doped fibers for cladding-pumped amplifiers. Opt. Express 31 (2023) 14888–14902. [Google Scholar]
  12. M. Adams, An Introduction to Optical Waveguides (Wiley, Chichester, 1981). [Google Scholar]
  13. M. Chung and K. Chang-Min, General eigenvalue equations for optical planar waveguides with arbitrarily graded- index profiles. J. Lightwave Technol. 18 (2000) 878–885. [Google Scholar]
  14. I.C. Goyal, R. Jindal and A.K. Ghatak, Planar optical waveguides with arbitrary index profile: an accurate method of analysis. J. Lightwave Technol. 15 (1997) 2179–2182. [Google Scholar]
  15. A. Sharma and J.-P. Meunier, Cutoff frequencies in planar optical waveguides with arbitrary index profiles: An efficient numerical method. Opt. Quantum Electron 34 (2002) 377–392. [Google Scholar]
  16. A.B. Shvartsburg, Dispersion of electromagnetic waves in stratified and nonstationary media (exactly solvable models). Phys.–Usp. 43 (2000) 1201–1228. [Google Scholar]
  17. T. Touam and F. Yergeau, Analytical solution for a linearly graded-index-profile planar waveguide, Appl. Opt. 32 (1993) 309–312. [Google Scholar]
  18. S.-Y. Huang and S. Wang, Ray optics of a planar waveguide with an exponential index profile. J. Appl. Phys. 55 (1984) 647–651. [Google Scholar]
  19. R.L. Lachance and P.-A. Belanger, Modes in divergent parabolic graded-index optical fibers, J. Light. Technol. 9 (1991) 1425–1430. [Google Scholar]
  20. S.E. Savotchenko, Surface waves propagating along the interface between a parabolic graded-index medium and a self-focusing nonlinear medium: exact analytical solution. J. Opt. 24 (2022) 105501. [Google Scholar]
  21. V.W. Biricik, Hyperbolic tangent graded-index antireflection coatings, Optical Society of America Annual Meeting, Technical Digest Series. (1991), ThMM52. https://doi.org/10.1364/OAM.1991.ThMM52 [Google Scholar]
  22. M. Dalarsson, Y. Ivanenko and S. Nordebo, Wave propagation in waveguides with graded plasmonic obstacles. J. Opt. Soc. Am. B 38 (2021) 104–113. [Google Scholar]
  23. B. Rana, B.B. Svendsen and M. Dalarsson, TE-Wave Propagation Over an Impedance-Matched RHM to LHM Transition in a Hollow Waveguide, Prog. Electromagn. Res. M 110 (2022) 1–10. [Google Scholar]
  24. 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]
  25. N.A. Kudryashov, Optical solitons of mathematical model with arbitrary refractive index. Optik 224, (2020) 165391. [NASA ADS] [CrossRef] [Google Scholar]
  26. N.A. Kudryashov, Stationary solitons of the model with nonlinear chromatic dispersion and arbitrary refractive index. Optik 259 (2022) 168888. [CrossRef] [Google Scholar]
  27. 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]
  28. E. Garmire, Nonlinear Optics in Semiconductors. Phys. Today 47 (1994) 42–48. [Google Scholar]
  29. H.E. Ruda and N. Matsuura, A Properties and Applications of Photonic Crystals, In: Optical Properties of Materials and Their Applications, J. Singh ed. (John Wiley & Sons Ltd., Hoboken, New Jersey, 2019) 251-268. https://doi.org/10.1002/9781119506003.ch9 [Google Scholar]
  30. D. Dragoman and M. Dragoman, Advanced Optoelectronic devices (Springer, Berlin, 1999) 424. [Google Scholar]
  31. R.W. Boyd, A.L. Gaeta and E. Giese, Nonlinear optics. In Springer Handbook of Atomic, Molecular, and Optical Physics (Cham: Springer International Publishing, 2008) 1097-1110. [Google Scholar]
  32. V.R. Bilyk, K.A. Brekhov, M.B. Agranat and E.D. Mishina, Dispersion of optical constants of Si:PbGeO crystal in the terahertz range. Russ. Technolo. J. 11 (2023) 38–45. [Google Scholar]
  33. A.S.L. Gomes, C.L.A.V. Campos, C.B. de Araújo, M. Maldonado, M.L. da Silva-Neto, A.M. Jawaid, R. Busch and R.A. Vaia, Intensity-Dependent Optical Response of 2D LTMDs Suspensions: From Thermal to Electronic Nonlinearities. Nanomaterials 13 (2023) 2267. [Google Scholar]
  34. S.A. Taya, H.M. Kullab and I.M. Qadoura, Dispersion properties of slab waveguides with double negative material guiding layer and nonlinear substrate, J. Opt. Soc. Am. B 30 (2013) 2008–2013. [Google Scholar]
  35. A.H.M. Almawgani, S.A. Taya and A.J. Hussein, I. Colak, Dispersion properties of a slab waveguide with a graded- index core layer and a nonlinear cladding using the WKB approximation method, J. Opt. Soc. Am., B39 (2022) 1606-1613. https://doi.org/10.1364/JOSAB.458569. [Google Scholar]
  36. J.M. Kubica, Analysis of planar waveguides with a thin overlayer and nonlinear cladding. Opt. Quant. Electron. 55 (2023) 137. [Google Scholar]
  37. S. Leble, Waveguide Propagation of Nonlinear Waves, Springer (2019) 288. [Google Scholar]
  38. M.J. Goodwin, Nonlinear Waveguides. In: Miller, L.S., Mullin, J.B. (eds) Electron. Mater. (Springer, Boston, MA. 1991). https://doi.org/10.1007/978-1-4615-3818-9_22. [Google Scholar]
  39. A.J. Hussein, Z.M. Nassar and S.A. Taya, Dispersion properties of slab waveguides with a linear graded-index film and a nonlinear substrate. Microsyst. Technol. 27 (2021) 2589–2594. [Google Scholar]
  40. A.J. Hussein, S.A. Taya, D. Vigneswaran, R. Udiayakumar, A. Upadhyay, T. Anwar and I.S. Amiri, Universal dispersion curves of a planar waveguide with an exponential graded-index guiding layer and a nonlinear cladding. Results Phys. 20 (2021) 103734. [Google Scholar]
  41. S.A. Taya, A.J. Hussein, O.M. Ramahi, I. Colak and Y.B. Chaouche, Dispersion curves of a slab waveguide with a nonlinear covering medium and an exponential graded-index thin film (transverse magnetic case). J. Opt. Soc. Am. B 38 (2021) 3237–3243. [Google Scholar]
  42. S.E. Savotchenko, Light localization near the interface between two crystals with sign-change nonlinearity and the index gradient. Phys. Lett. A 538 (2025) 130339. [Google Scholar]
  43. S.E. Savotchenko, Nonlinear waves in a waveguide with a linear spatial profile of the refractive index and a nearsurface layer with disappearing nonlinearity. Optik 272 (2023) 170373. [Google Scholar]
  44. S.E. Savotchenko, Analytical solutions describing new features of guided wave modes in a circular fiber consisting of a constant-index core and a graded-index cladding with saturation, Rom. J. Phys. 69 (2024) 202. [Google Scholar]
  45. P. Yeh, Optical wave in layered media (Wiley, New Jersey, 1988). [Google Scholar]
  46. H. Kurt and D.S. Citrin, Graded index photonic crystals, Opt. Express 15, (2007) 1240-1253. [Google Scholar]
  47. Q. Zhu, L. Jin and Y. Fu, Graded index photonic crystals: A review, Ann. Phys. 527 (2015) 205–218. [Google Scholar]
  48. 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]
  49. B.K. Singh, V. Bambole, V. Rastogi and P.C. Pandey, Multi-channel photonic bandgap engineering in hyperbolic graded index materials embedded one-dimensional photonic crystals, Opt. Laser Technol. 129 (2020) 106293. [Google Scholar]
  50. D. Dash and J. Saini, Hyperbolic Graded Index Biophotonic Cholesterol Sensor with Improved Sensitivity, Prog. Electromagn. Res. M 116 (2023) 165–176. [Google Scholar]
  51. S.E. Savotchenko, Modes of appearance of a defocusing nonlinear response with increasing electric field in the surface layer of a crystal covered with a fully shielding film. Rom. J. Phys. 66 (2021) 203. [Google Scholar]
  52. S.E. Savotchenko, Influence of an increase in the electric field on the appearance of positive nonlinearity in the near-surface region in a crystal with a fully screening coating. Rom. Rep. Phys. 74 (2022) 407. [Google Scholar]
  53. S.E. Savotchenko, The composite planar waveguide structure consisting of the linearly graded-index layer and the nonlinear layer formed with an increasing the electric field. Optik 252 (2022) 168542. [Google Scholar]
  54. S.E. Savotchenko, Surface waves propagating along an interface between media with an exponential spatial profile of the dielectric function and an abruptly appearance of a self-focusing nonlinear response in a near-surface layer at the strong light intensity. Opt. Quantum Electron 55 (2023) 580. [Google Scholar]
  55. S.E. Savotchenko, New surface waves in a hyperbolic graded-index crystal, Rom. Rep. Phys. 76 (2024) 406. [Google Scholar]
  56. J.W. You, S.R. Bongu, Q. Bao and N.C. Panoiu, Nonlinear optical properties and applications of 2D materials: theoretical and experimental aspects. Nanophotonics 8 (2019) 63–97. [Google Scholar]
  57. A.E. Kaplan, Multistable self-trapping of light and multistable soliton pulse propagation, IEEE J. Quantum Electron. QE-21 (1985) 1538-1543. [Google Scholar]
  58. R.H. Enns, S.S. Rangnekar and A.E. Kaplan, Bistable-soliton pulse propagation: Stability aspects Phys. Rev. A 36 (1987) 1270. [Google Scholar]
  59. P.I. Khadzhi and L.V. Fedorov, Nonlinear surface waves for the simplest model of nonlinear medium, Phys. Tech. Lett. 61 (1991) 110–113. [Google Scholar]
  60. K.D. Lyakhomskaya and P.I. Hadji, Self-reflection effect in the simplest non-linear medium, Tech. Phys. 70 (2000) 86–90. [Google Scholar]
  61. G.E. Andrews, R. Askey, R. Roy, Special Functions. (Cambridge University Press, UK, 1999) 664. https://doi.org/10.1017/CBO9781107325937. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.