light line in photonic crystal slab

[minaesm]

I have problem understanding light line properties in photonic crystal slabs. When we talk about photonic crystal we should also calculate light line but when we consider light line it means that above the light line there are continuos modes (radiative modes) . having radiative modes means that we have out of plane diffraction and out of plane diffraction is because of Kz component . So it is out of plane not in plane. but in every where we calcute in plane not out of plane without considering Kz. I can't understand this . Can anyone help me plz. I 've read some dissertations and papers and book but I could'nt get it.

 

[tmalc]

considering that light propagating in the slab structure using the wave equation.

in the clad n0: (w*n0/c)^2=k0^2+kz^2, where k0 is the in plane vector, kz is the out of plane vector,
if k0>w*n0/c, kz is imaginary, and the z-vector is decay.
so it require that with the same w, k0 should choose a value bigger than w*n0/c.

 

[minaesm]

Thanks.
So the entering light should be out of plane to have kz ? I mean that is the entering light important to be inplane or out of plane ? Or even if the light once enter the crystal inplane with kz=0 it will have a nonzero kz because of index guiding? :?:

 

[tmalc]

I think it is expect that the light enter would have idea kz=0. however the launched light source is a spot. it will have different incident angles. only those angles satisfy the TIR condition would propagate along the waveguide.
for idea 2D PC, we don't consider kz, because the Ez or Hz is invariance along z-direction.

 

[minaesm]

So as I get , the light once entering in the slab with an angle with respect to the periodicity plane and while propagating in the slab have kz ≠0 ?!