Mathematical modelling of fiber optic cable with an electro-optical cladding by incommensurate fractional-order differential equations

Büşra Ersoy; Bahatdin  Daşbaşı; Ekin Aslan

doi:10.11121/ijocta.1369

Authors

Büşra Ersoy Department of Electrical and Electronics Engineering, Kayseri University, Turkey https://orcid.org/0000-0003-1383-3311
Bahatdin Daşbaşı Department of Engineering Basic Sciences, Kayseri University, Turkey https://orcid.org/0000-0001-8201-7495
Ekin Aslan Department of Electrical and Electronics Engineering, Kayseri University, Turkey https://orcid.org/0000-0003-0933-7796

DOI:

https://doi.org/10.11121/ijocta.1369

Keywords:

Electro-Optical Fiber, Fractional-Order Differential Equations (FODEs), Mathematical Model, Stability Analysis

Abstract

In this study, the mathematical model through incommensurate fractional-order differential equations in Caputo meaning are presented for time-dependent variables given as the numerical aperture, critical angle, and acceptance angle characteristics of a fiber optic cable with electro-optical cladding. The qualitative analysis including the existence and stability of the equilibrium points of the proposed model has been made according to the used parameters, and then, the results obtained from this analysis are supported through numerical simulations by giving the possible values that can be obtained from experimental studies to these parameters in the model. In this way, a stable equilibrium point of the system for the core refractive index, cladding refractive index and electrical voltage is obtained according to the threshold parameter. Thus, the general formulas for the critical angle, acceptance angle and numerical aperture have been obtained when this fixed point is stable.

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Author Biographies

Büşra Ersoy, Department of Electrical and Electronics Engineering, Kayseri University, Turkey

Büşra Ersoy was born on March 8, 1997, in Kayseri. She took English preparatory education for one year in the 2015-2016 academic year. Then she received a BS degree from the Electrical and Electronics Engineering Department of Erciyes University, Kayseri in 2020. In 2021, she started her Master's education in the Electronics Engineering Department at Kayseri University. She is currently working as a researcher assistant in the research project titled "Design, Fabrication, and Characterization of Meta-Lenses for Infrared and Visible Wavelengths" and has a Graduate Research Scholarship supported by the Scientific and Technological Research Council of Turkey (TUBITAK- ARDEB-121E518).

Bahatdin Daşbaşı, Department of Engineering Basic Sciences, Kayseri University, Turkey

Bahatdin Dasbas received a BS degree in Mathematics from Ankara University in 2002, the MS degree in the field of applied statistic in Mathematics department from the Nigde University in 2005 and a Ph.D. degree in the field of applied mathematics in mathematics department from the Erciyes University in 2016. He also has the title of Associate Professor in Mathematics since 2021. He is still working as an associate professor at the Department of Basic Engineering Sciences, Faculty of Engineering, Architecture and Design, Kayseri University. His current research interests include fractional order differential equations, mathematical modeling, stability analysis, and artificial neural networks.

Ekin Aslan, Department of Electrical and Electronics Engineering, Kayseri University, Turkey

Ekin Aslan received the BS degree in 2004 from the Electronics Engineering Department of Erciyes University, MS degree in 2011 from the Electrical and Electronics Engineering of Mustafa Kemal University, and PhD degree in 2017 from the Electrical and Electronics Engineering Department of Erciyes University. Dr. Aslan was a recipient of the Doctoral Research Fellowship from the Scientific and Technological Research Council of Turkey (TUBITAK) (2214-A). She worked as an Assistant Professor in the Departments of Electrical and Electronics Engineering at Nuh Naci Yazgan University and Hatay Mustafa Kemal University. She is currently working as an Associate Professor in the Electrical and Electronics Engineering Department of Kayseri University. Her research interests include integrated plasmonic systems for bio-detection, vibrational spectroscopy, plasmonic metamaterials, computational and experimental electromagnetics, and nanophotonic devices.

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