A dielectric slab waveguide with parameters mud element ofd

A dielectric slab waveguide with parameters mu_d, element of_d is made with a PEC layer attached to the bottom surface of the slab. What are the boundary conditions in this scenario What modes propagate, and what modes do not propagate in this scenario What are the cutoff frequencies of the propagating modes in this case

Solution

dielectric slab waveguide is made with a PEC layer

the parameters are also mentioned i.e,permitivityetc

going further

the boundary conditions

first boundary is that that the tangential component of the electric field is continuous across a boundary.

E₁(r_b)=E₂(r_b)

r_b is any point on the boundary

The second dielectric boundary condition is that the normal vector component of the electric flux density is continuous across the dielectric boundary

D₁(r_b)=D₂(r_b)

degenerate and dominant modes can propogate

f_c=C/2a