Optimum waist of localized basis functions in truncated series employed in some optical applications

The waist parameter is a particularly important factor for functional expansion in terms of localized orthogonal basis functions. We present a systematic approach to evaluate an asymptotic trend for the optimum waist parameter in truncated orthogonal localized bases satisfying several general conditions. This asymptotic behavior is fully introduced and verified for Hermite-Gauss and Laguerre-Gauss bases. As a special case of importance, a good estimate for the optimum waist in projection of discontinuous profiles on localized basis functions is proposed. The importance and application of the proposed estimation is demonstrated via several optical applications.