TL;DR
This paper explores the geometric and dynamical properties of ray optics in thin film systems, deriving new differential equations that reveal symplectic and Hamiltonian structures on mirror surfaces.
Contribution
It introduces a novel set of differential equations modeling ray optics in thin films, connecting geometric optics with symplectic and Hamiltonian frameworks.
Findings
Derivation of new differential equations for thin film optics
Identification of symplectic structure in the equations
Insights into Hamiltonian mechanics in optical systems
Abstract
We study ray optics in the context of double mirror systems, in the limit as the two mirrors approach one another (thin films). This leads to a novel set of differential equations on a mirror surface which have interesting structure as seen from the perspective of symplectic geometry and Hamiltonian mechanics.
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