For the dielectric slab waveguide given below: x n1 d/2 12 -d/2- n1 n(x) = {m \x\ d/2 and starting with Maxwell's equations in the form of: and a trial solution of: VXH = VXE = -iwH Z E(x,t) = Em(x)ei(wt-z). a. (4 pts) Using the appropriate boundary conditions and assuming TE modes, find the general solution to Em(x) for each layer and determine the range of possible values for which a guided mode may be supported (this should be a range, and not an exact solution). b. (2 pts) For both TE and TM modes, list the respective field components (Ex, Ey, Ez, Hx, Hy, Hz) that must be continuous at the interfaces (x = +d/2). c. (1 pts) What is (are) the primary parameter(s) that govern the number of modes supported by the waveguide? d. (1 pts) Qualitatively plot the first four TE modes and identify symmetric (even) and anti-symmetric (odd)modes e. (2 pts) Qualitatively plot and describe how the mode distribution changes if the slab is asymmetric as shown below with n < n3 < n.