Abstract
The present paper reports the diffusion study of cylindrical GRIN rod with elliptical cross section, developed by ion exchange process. The diffusion equation takes the form of Mathieu equations when transform into elliptic coordinate system and the solutions are derived in terms of angular and radial Mathieu functions. Computations of eigenvalues and expansion coefficients as well as angular and radial Mathieu functions are made which shows good agreement with the existing results. Simpler expression for ionic concentration is derived using asymptotic formulae of the functions which are used for final computation of ionic concentration of diffusing cations in elliptic GRIN. The plot of change in concentration versus diffusion depth along different directions approximately correlates with the results obtained by an earlier experimental study.
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