Analysis of laser beam quality degradation caused by quartic phase aberrations

Simple formulas are derived for the degradation in the beam-quality factor, M(2), of an arbitrary laser beam caused by quartic phase distortions such as those that might occur in a spherically aberrated optical component, a thermally aberrated laser output window, or a divergent beam emerging from a high-index dielectric medium as in a wide-stripe, unstable-resonator diode laser. A new formula for the defocus correction that is needed to collimate optimally a beam with quartic phase aberration is also derived. Analytical results and numerical examples are given for both radially aberrated and one-dimensionaltransversely aberrated cases, and a simple experimental measurement of the beam-quality degradation produced by a thin plano-convex lens is shown to be in good agreement with the theory.