Consider an Al2O3 slab waveguide with a core layer thickness of 3 m and nf-1.53. The refractive indices of the substrate and cladding layers are ns=1.40 and nc=1.2, respectively. The waveguide is operating at a wavelength of =1.5 m. (a) How many modes propagate in the waveguide both for TE and TM polarization? (b) Find the effective indices of the fundamental modes (TE and TMO) and list them (neff-?). (c) Calculate and plot the power confinement factor of the TM mode (if it is an allowed mode)? (d) Plot the electric field amplitude as a function of thickness for the TE mode.