Abstract

We derive a diffraction integral to describe the paraxial propagation of an optical beam in a graded index medium with the permittivity linearly varying with the transverse coordinate. This integral transformation is irreducible to the familiar $ABCD$ transformation. The form of the integral transformation suggests that, unlike a straight path in a homogeneous space, any paraxial optical beam will travel on a parabola bent toward the denser medium. By way of illustration, an explicit expression for the complex amplitude of a Hermite–Gaussian beam in the linear index medium is derived.

© 2014 Optical Society of America

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