2. A periodic lens waveguide comprises concatenated unit cells, each comprising a pair of lenses. Light is confined in the periodic structure without dissipation. An example of a periodic lens waveguide is illustrated below. Planes Plane s + 1 The unit cell matrix of a periodic lens waveguide can be represented as a unimodular ABCD matrix that satisfy A D - BC = 1. Solve the following eigenvalue problem: (a) Show that the eigenvalues 1 of the equation are 1 = et with 0 given by 0 = cos-1 ( A+ D (5 pt ) (b) Show that the eigenvectors are (c) A matrix M can be found such that the ray matrix is diagonalized, Show that M can be written M = |610 3- A e- 18 -4/ 15 04) (d) Find the inverse matrix M-1. (5 pt) (e) Show that A B-M M- 1 (5 PD)