Caustic

Summary

A caustic is the envelope of a family of rays, the curve or surface where nearby rays focus. In symplectic terms, project a Lagrangian submanifold of a cotangent bundle to the base. The caustic is the set of critical values of this projection, that is, the image of the Lagrangian singularities. Caustics appear in optics as the bright curves of focused light. They also appear in the asymptotics of oscillatory integrals and of short-wave solutions of wave equations. Their generic local shapes, such as folds and cusps, are given by Arnold's classification of Lagrangian singularities.