A symmetric planar waveguide has a waveguiding layer with thickness = 3 μm and index n2 = 1.5. The waveguide is excited with a He-Ne laser (λ0 = 0.6328 μm). Assume that the surrounding medium is air...

A symmetric planar waveguide has a waveguiding layer with thickness =

3 μm and index n2 = 1.5. The waveguide is excited with a He-Ne laser

(λ0 = 0.6328 μm).

Assume that the surrounding medium is air (i.e., n1 = n3 = 1)

(a) How many TE modes can the waveguide support?

(b) Suppose that instead of the surrounding medium being air it is dielectric

so that n1 = n3 = 1.48, how many TE modes can now propagate?

(c) In the case of the waveguide of part (b), how thin can the waveguiding

layer be made and still allow the lowest order mode to propagate?