Classical optics representation of the quantum mechanical translation operator via ABCD matrices

TL;DR

This paper extends the classical ABCD matrix formalism in optics to arbitrary beam trajectories and establishes a direct correspondence with the quantum mechanical translation operator, bridging classical and quantum descriptions.

Contribution

It introduces a generalized ABCD matrix formalism for arbitrary beam trajectories and links it to quantum translation operators, providing a novel theoretical connection.

Findings

Extended ABCD formalism for arbitrary trajectories

Established correspondence with quantum translation operator

Bridged classical optics and quantum mechanics

Abstract

The ABCD matrix formalism describing paraxial propagation of optical beams across linear systems is generalized to arbitrary beam trajectories. As a by-product of this study, a one-to-one correspondence between the extended ABCD matrix formalism presented here and the quantum mechanical translation operator is established.