Propagation of Multimode Laser Beams – The M2 Factor

This chapter aims to extend earlier work by developing propagation equations for higher order modes and mixtures of modes, which are adequate in terms of accuracy and retains simple utility of fundamental Gaussian mode beam equations. A simple test of the generalized propagation equations has been to measure beam diameters at several distances in front of various lasers and to discover that by choosing suitable values for M2. The most economical design for such an optical system uses optical components of the smallest possible diameter consistent with allowing the entire beam to pass without significant aperture loss. A set of beam propagation equations are derived that permit beam diameter calculations to be made for beams made up of high–order modes or mixtures of modes. Experimental results confirm the continued utility of ray matrix methods for mathematical modeling of non–Gaussian beam propagation through optical systems. Finally, the design of optical systems for lasers having mixed and high–order modes is considered.