The non-diffracting nature of truncated Hermite–Gaussian beams

Using the asymptotic formula of the Hermite polynomials for higher-orders n ≫ 1 , an elegant mathematical expression that makes Hermite–Gaussian beams and cosine beams equivalent is obtained. Two factors of merit, the similarity and the power content ratio, are used to quantify the degree of equivalence between the two beams. These results yield a new nondiffracting Hermite–Gaussian beam in one dimension (1D) and that is easily extended to 2D.