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On an Airy function of two variables
Nonlinear Analysis: Theory, Methods & Applications, 2003The author discusses the Pearcey integral \(\int_C \exp( -t^4/4 + x t^2/2 + yt ) \, dt\) with \(C\) going from \(\infty\exp(2\pi i j/4)\) to \(\infty\exp(2\pi i k/4)\); in particular asymptotic expansions as \(y\to\infty\), uniformly in \(x\) as long as \(x=O(y^{2/3})\), or, for a more explicit asymptotic, \(x=O(1)\).
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Wigner distribution function of an Airy beam
Journal of the Optical Society of America A: Optics and Image Science, and Vision, 2011We study the Wigner distribution function (WDF) of an Airy beam. The analytical expression of the WDF of an Airy beam is obtained. Numerical and graphical results of the WDF of an Airy beam provide an intuitive picture to explain the intriguing features of an Airy beam, such as weak diffraction, curved propagation, and self-healing. Our results confirm
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