Hamiltonian Optics in Euclidean Spaces
According to Hamilton (Hamilton 1828), a “system of rays” is a congruence of straight lines in the Euclidean three-space, orthogonal to a family of surfaces. This orthogonal integrability of the rays fails in the presence of a caustic. Moreover, a system of rays can be modified through the use of optical devices, as mirrors and lenses, or by passing through surfaces that delimit two media with different refraction index. In our approach, a system of rays without caustic is represented by a regular Lagrangian submanifold of the cotangent bundle of the Euclidean space, whereas all the optical devices are represented by symplectic relations. This chapter discusses some of the most important elementary examples.
KeywordsGenerate Family Euclidean Space Distance Function Parametric Equation Cotangent Bundle
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