Exactly unitary discrete representations of the metaplectic transform for linear-time algorithms

• DOI: 10.1364/josaa.417412
• Publication Date: 2021-03-26T15:30:06Z
• Authors: N. A. Lopez; I. Y. Dodin
• Keywords: 0103 physical sciences; FOS: Physical sciences; Mathematical Physics (math-ph); 01 natural sciences; Mathematical Physics; Physics - Optics; Optics (physics.optics)

The metaplectic transform (MT), a generalization of the Fourier sometimes called linear canonical transform, is tool used ubiquitously in modern optics, for example, when calculating transformations light beams paraxial optical systems. MT also an essential ingredient geometrical-optics modeling caustics that we recently proposed. In particular, this application relies on near-identity (NIMT); however, NIMT approximation so far not exactly unitary and leads to numerical instability. Here, develop discrete unitary, approximate it obtain can be computed time. We prove converges iterated, thereby allowing compute MTs are necessarily near-identity. then demonstrate new algorithms with series examples.