Solving the nonlinear diffusion model of the ion exchange process using finite element method

Mohamed M. Badr; Mohamed A. Swillam

doi:10.1117/12.2251468

22 February 2017 Solving the nonlinear diffusion model of the ion exchange process using finite element method

Mohamed M. Badr, Mohamed A. Swillam

Proceedings Volume 10098, Physics and Simulation of Optoelectronic Devices XXV; 100981X (2017) https://doi.org/10.1117/12.2251468
Event: SPIE OPTO, 2017, San Francisco, California, United States

Abstract

Due to its low cost and simplicity, ion exchange is considered one of the most commonly used processes to produce glass waveguides nowadays. This fabrication technology is based on the substitution of some ions already present in the glass with other ions having different sizes and polarizabilities. A careful study of the resultant refractive index profile is crucial in the impact on the waveguide characteristics. In this paper, we introduce, for the first time, a novel solution of the nonlinear diffusion equation that model this process using finite element method (FEM) approach. The ion exchange can be modelled as a nonlinear diffusion equation, as the exchanged ions Ka+ diffuse into their new sites where the original ions were existing. Numerical instabilities are encountered when solving for the exchanged ions with similar diffusion coefficients as in the case of Ka+/Na+, which is used in fabricating integrated optical devices with refractive index differences compatible with those of the optical fibers. Different novel FEM techniques are proposed in solving the problem in 1D space. The stability and accuracy of the different methods outperforms the current numerical methods and provide a good tool for highly nonlinear diffusion problem.

Citation Download Citation

Mohamed M. Badr and Mohamed A. Swillam "Solving the nonlinear diffusion model of the ion exchange process using finite element method", Proc. SPIE 10098, Physics and Simulation of Optoelectronic Devices XXV, 100981X (22 February 2017); https://doi.org/10.1117/12.2251468

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available