Modified Airy function method for the analysis of tunneling problems in optical waveguides and quantum-well structures

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Abstract
A simple method for the analysis of tunneling through an arbitrary one-dimensional potential barrier, based on the modified Airy function approach, is presented. Truncated step-linear, step-exponential, parabolic, and quartic potential barriers are considered. The results are compared with those obtained by the conventional WKBJ, modified WKBJ, and matrix methods. The effect of the truncation level on the tunneling coefficient is investigated. The tunneling coefficient is sensitive to the truncation level. For the step-linear potential, the tunneling coefficient is a monotonically decreasing function of the truncation level, while for the parabolic potential, it oscillates before saturating to a constant value.

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