1. Consider the dielectric slab waveguide shown in the figure below. Upper cladding 2 = 1.5 m m = 2.9 Core a=1 m n = 3.4 Lower n = 2.9 cladding (a) Find the number of the modes supported by this waveguide. (b) Calculate the effective indices and phase velocities of the TE modes. (c) Write expressions for the E, component of the TE modes. Give the numerical values of the constants involved for each mode. (d) (e) Plot E, for the TE modes at z = 0 as a function of x. Consider the fundamental mode, which is the lowest order TE mode. Calculate its phase velocity and plot E, for this mode at 20 = 1.3 m and 2 = 1.6 m. Comment on the result.