hardcore floquet bloch scattering problem help

[yefj]

Hello i have the following floquet bloch hardcore problem i want to solve as shown bellow.
Is there some manual or a book or an article i could use to help me with the math of this hardcore scattering problem?
Thanks.

 

[PlanarMetamaterials]

This is essentially a standard boundary condition problem with the added complexity of a periodic condition along one axis.

Check out this great resource from EMPossible: https://empossible.net/wp-content/uploads/2020/04/Lecture-The-Plane-Wave-Spectrum.pdf

 

[yefj]

Hello planarmetamaterials, thank you very much for the manual.
I am trying to tackle the problem as following:
1.i have a boundary condition as following,

2.my incident wave is as following:

3.the tangential incident is E_inc*sin(theta) the normal components is E_inc*cos(theta)
4.we can use the boundary condition to get the tangential H magnetic fiels
5.finding the fourier seriec of the periodic impedance Z_s(y )

i understand that the floquet bloch is is also periodic.
so i think i should link the two periodic expressions?
what is the next step?
In the lecture you posted there is no link between floquet and impedance.
if i am correct regarding my assumption.
could you please help me withe expression for the next step?
thanks.

 

[yefj]

Hello, is there some manual aboutscattering from a surface with Z surface impedance ?
Thanks

 

[PlanarMetamaterials]

In the lecture you posted there is no link between floquet and impedance.

It's not just the fields that are periodic, the impedance is periodic too. This means you can also express the impedance as a Fourier series, as suggested in part (ii). From slide 7 of the linked lecture, you could then express Zs = sum_inf(Z(m)*exp(-j*2*pi*m*y/A) (where A is the period). Each of the impedances Z(m) should then correspond to the surface impedance seen by a particular diffraction order m.

what is the next step?

I think just answering the questions in the order provided would be best.

Hello, is there some manual aboutscattering from a surface with Z surface impedance ?

A diffraction grating is an example of such a periodic surface, you might be able to find some useful texts by searching these.

Good luck!

 

[yefj]

Hello, I have defined the Maxwell equations shown bellow, then we have
K_inc=k*sin(theta)y^+cos(theta)z^
K_ret=k*sin(theta)y^-cos(theta)z^
from the maxwell equations i got the Hy Hz Ex
then i got Js and we want to develop the currents from the H discontinuety.
then i need to go back to maxwell equation to find the scattered fields.

given J how do i find the E,H from maxwell?
Thanks.