Abstract
In this work, we have studied the propagation dynamics of a secant soliton travelling through six types of Fibonacci and parabolic-Fibonacci-ordered multilayers. Although the propagation of solitons in different mediums such as graded-index inhomogeneous media is considered, their propagation in the fractal geometries has not yet been addressed. In this way, we utilise a fractional nonlinear Schrödinger equation formalism. Then, a numerical split-step Fourier method is employed to solve the resulting equation. Besides, we used a wave expansion method to calculate the band structure of the system by solving the stationary Schrödinger equation at different wavenumbers, because the refraction index that governs the beam divergence can be described using the band structure curvature. Our motivation is to engineer the band structure curvature that is an important parameter in obtaining the desired waveguiding properties.
Similar content being viewed by others
References
J S Russell, Report on waves, Report of the 14th Meeting of the British Association for the Advancement of Science, York, 311 (1844)
D J Korteweg and G de Vries, Phil. Mag. 39, 422 (1895)
N J Zabusky and M D Kruskal, Phys. Rev. Lett. 15, 240 (1965)
Z Y Yang, L C Zhao, T Zhang, Y H Li and R H Yue, Opt. Commun. 283, 3768 (2010)
J R He and L Yi, Opt. Commun. 320, 129 (2014)
G Wang, K Yang, H Gu, F Guan and A H Kara, Nucl. Phys. B 953, 114956 (2020)
G Wang, Appl. Math. Lett. 113, 106768 (2021)
G Wang and A H Kara, Phys. Lett. A 383, 728 (2019)
G Wang and A H Kara, Nonlin. Dyn. 81,753 (2015)
G Wang, Y Liu, Y Wu and X Su, Fractals 28, 2050044 (2020)
G Wang, Nonlin. Dyn. 104, 1595 (2021)
A Neirameh, Comput. Math. Math. Phys. 56, 1336 (2016)
A Neirameh, Pramana- J. Phys. 85, 739 (2015)
L Turgeman, S Carmi and E Barkai, Phys. Rev. Lett. 103, 190201 (2009)
N Bouzid, M Merad and D Baleanu, Few-Body Syst. 57, 265 (2016)
H Buluta, T A Sulaimana, H M Baskonusd, H Rezazadeh, M Eslami and M Mirzazadeh, Optik – Int. J. Light Electron Opt. 172, 20 (2018)
L Esquivel and E I Kaikina, Nonlinearity 29, 2082 (2016)
B H Wang, P H Lu, C Q Dai and Y X Chen, Results Phys. 17, 103036 (2020)
M N Alam and X Li, Phys. Scr. 95, 045224 (2020)
R Herrmann, Phys. Lett. A 372, 5515 (2008)
R Ahmad El-Nabulsi, Few-Body Syst. 61, 25 (2020)
S T R Rizvi, K Ali, S Bashir, M Younis, R Ashraf and M O Ahmad, Superlatt. Microstruct. 107, 234 (2017)
N Laskin, Phys. Lett. A 268, 298 (2000)
X Y Jiang, Eur. Phys. J. Special Topics 193, 61 (2011)
M Al-Raeei and M Sayem El-Daher, Phys. Lett. A 383, 125831 (2019)
E K Lenzi, H V Ribeiro, M A F dos Santos, R Rossato and R S Mendes, J. Math. Phys. 54, 082107 (2013)
Y Luchko, J. Math. Phys. 54, 012111 (2013)
X Yao and X Liu, Photon. Res. 6, 875 (2018)
Y Meng, R Ning, K Ma, Z Jiao and Y Liu, Opt. Commun. 440, 68 (2019)
M Al-Raeei and M Sayem El-Daher, AIP Adv. 10, 035305 (2020)
M Moustapha Fall, F Mahmoudi and E Valdinoci, Nonlinearity 28, 1937 (2015)
E Capelas de Oliveira and J Vaz Jr, J. Phys. A 44, 185303 (2011)
D Zhang, Y Zhang, Z Zhang, N Ahmed, Y Zhang, F Li, M R Belic and M Xiao, Ann. Phys. (Berlin) 529, 1700149 (2017)
L Zeng and J Zeng, Opt. Lett. 44, 2661 (2019)
Y Zhan, X Liu, Milivoj, R Belić, W Zhong, Y Zhang and M Xiao, Phys. Rev. Lett. 115, 180403 (2015)
M Chen, S Zeng, D Lu, W Hu and Q Guo, Phys. Rev. E 98, 022211 (2018)
P Li and C Dai, Ann. Phys. (Berlin) 532, 2000048 (2020)
Z Wu, P Li, Y Zhang, H Guo and Y Gu, J. Opt. 21, 105602 (2019)
X Huang, Z Deng, X Fu, J. Opt. Soc. Am. B 34, 976, (2017)
L Zhang, C Li, H Zhong, C Xu, D Lei, Y Li and D Fan, Opt. Exp. 24, 14406 (2016)
Z Wu, Y Zhang, J Ru and Y Gu, Results Phys. 16, 103008 (2020)
K Zhan, Z Jiao, Y Jia and X Xu, IEEE Photon. J. 9, 6102508 (2017)
Y Zhang, R Wang, H Zong, J Zhang, M R Belic and Y Zhang, Opt. Exp. 25, 32402 (2017)
S I Muslih and D Baleanu, J. Vib. Control 13, 1209 (2007)
S Z Rida, H M El-Sherbiny and A A M Arafa, Phys. Lett. A 372, 553 (2008)
B Agheli and R Darzi, Opt. Quant. Electron. 49, 219 (2017)
G Z Wu, L J Yu and Y Y Wang, Optik – Int. J. Light Electron Opt. 207, 164405 (2020)
G Wang and T Xu, Laser Phys. 25, 055402 (2015)
G Zhang, C Huang and M Li, Eur. Phys. J. Plus 133, 155 (2018)
A Patra, Eur. Phys. J. Plus 133, 104 (2018)
E M E Zayed and A G Al-Nowehy, Opt. Quant. Electron. 50, 164 (2018)
A Neirameh, SeMA J. 73, 309 (2016)
A Patra, Math. Meth. Appl. Sci. 43, 10287 (2020)
A Patra, Progr. Fract. Differ. Appl. 5, 125 (2019)
Y Zhang, R Wang, H Zhong, J Zhang, M R Belić and Y Zhang, Sci. Rep. 7, 17872 (2017)
G P Agrawal, Nonlinear fiber optics (Academic Press, San Diego, 2001)
J W Cooley and J W Tukey, Math. Comput. 19, 297 (1965)
J A Fleck, J R Morris and M D Feit, Appl. Phys. 10, 129 (1976)
O V Sinkin, R Holzlohner, J Zweck and C R Menyuk, J. Lightwave Technol. 21, 61 (2003)
L Shu-Guang, X Guang-Long, Z Gui-Yao, H Ying, H Lan-Tian, H Ming-Lie, L Yan-Feng and W Qing-Yue, Chin. Phys. 15, 437 (2006)
M D Feit and J A Fleck, Appl. Opt. 17, 3990 (1978)
G P Agrawal, J. Appl. Phys. 56, 3100 (1984)
Y T Lin, T F Duda and A E Newhall, J. Comput. Acoustics 21, 1250018 (2013)
M Lax, G P Agrawal, M Belic, B J Coffey and W H Louisell, J. Opt. Soc. Am. A 2, 732 (1985)
M Amini, M Soleimani and M H Ehsani, Superlatt. Microstruct. 112, 680 (2017)
A Suryanto and E van Groesen, J. Nonlin. Opt. Phys. Mater. 10, 143 (2001)
F Garzia, C Sibilia and M Bertolotti, Opt. Commun. 139, 193 (1997)
R H Lipson and C Lu, Eur. J. Phys. 30, S33 (2009)
F Gaufillet and É Akmansoy, Opt. Mater. 47, 555 (2015)
M Charbonneau-Lefort, E Istrate, M Allard, J Poon and E H Sargent, Phys. Rev. B 65, 125318 (2002)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ghalandari, M., Tehrani, D.H.T. & Solaimani, M. Soliton propagation through three types of Fibonacci-ordered photonic multilayers in the fractional medium. Pramana - J Phys 96, 41 (2022). https://doi.org/10.1007/s12043-021-02289-5
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12043-021-02289-5
Keywords
- Fractional Schrödinger equation
- split-step Fourier method
- wave expansion method
- Fibonacci-ordered multilayers
- band structures