Factoring in the metaplectic group and optics

Abstract

Abstract. The metaplectic group is generated by the Fourier transform and multiplications by functions of particular exponential type. Based on the use of the metaplectic representation and a factorization of symplectic matrices, in this paper a bound on the number of terms needed to factor an arbitrary metaplectic operator is derived. The approach is constructive and numerically stable, leading to a reliable factorization algorithm in practice. The problem is partially motivated by the task of constructing lens systems in diffractive optics.Mathematics subject classification (2010): 42B10, 78M25, 65F30.