20 December 1996 Perturbative method to modelize ion-exchange processes: application to surface waveguides
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Proceedings Volume 2954, Fiber Integrated Optics; (1996) https://doi.org/10.1117/12.262449
Event: Advanced Imaging and Network Technologies, 1996, Berlin, Germany
Abstract
It is known that the ion-exchange process in glass is described by a non linear diffusion equation whose solutions represent the index profile of the waveguide formed. The diffusion equation depends on the relative mismatch of the incoming and original ion mobilities, characterized by the parameter (alpha) . If they are equal, the diffusion equation becomes linear, and its solutions are normally used as an approximation for non-linear processes. Nevertheless, empirical solutions often provide a better modelization, but they must be found in each particular case of diffusion. In this work, we develop a perturbative method for solving the non linear equation, thus approximated analytical solutions can be obtained up to intermediate (alpha) -values ((alpha) equals 0.5). We have applied it to a simple surface thermal waveguide. By another hand, a proper dependent variable change is performed in the diffusion equation, and then the perturbative method is applied. It provides a solution much more exact that can be used with great accuracy up to (alpha) equals 0.8, which is a situation where Gaussian functions are normally used as empirical solutions. The method can be applied to more complex situations as buried waveguides, field-assisted processes and so on.
© (1996) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Xesus Prieto, Jesus Linares, Carlos Montero, "Perturbative method to modelize ion-exchange processes: application to surface waveguides", Proc. SPIE 2954, Fiber Integrated Optics, (20 December 1996); doi: 10.1117/12.262449; https://doi.org/10.1117/12.262449
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