Measurement of fourth-order aberration in a lens-like medium

Abstract

Deformation of the spot of an off-axis Gaussian beam after passing through a lens-like glass fiber (SELFOC®) with the fourth-order aberration is investigated by using first-order perturbation theory and numerical calculation. A method for determining the coefficient of the fourth-order aberration is proposed. By this method, it is found that a SELFOC sample (0.5 mm in diameter and 150 mm in length) has a coefficient <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</tex> of about 1.1, if the dielectric constant in the meridional plane of the sample is expressed as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\epsilon(x) = \epsilon(0) (1 - g^{2}x^{2} + hg^{4}x^{4})</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</tex> is the distance from the axis of the medium and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</tex> is a positive constant.