Learning Forum

[gufranskhan]

Hello,

I am simulating a multilayer dielectric grating and facing some issues related to bloch boundary conditions,

Kx value of the bloch boundary condition is fixed for the incident light theta and remains same for the complete simulation

The issue is when light is incident on a grating at an angle, after transmission it gets split into 2 orders i.e. 0th order and 1st order,  the 0th order is getting propagated correctly in multilayer structures wheres the angle of 1st order is different for the kx value (automatically set from angle of incidence) and is not getting propogated correctly in the multilayer structures.

Does the bloch boundary has this limitation?

[Guilin Sun]

 

 

Bloch Boundary condition is the general periodic boundary condition to ensure the angled plane wave is excited correctly:

https://optics.ansys.com/hc/en-us/articles/360034382714-Bloch-boundary-conditions-in-FDTD-and-MODE

If you check the theory for bloch modes, you will notice that the envelope is periodic however the wave has extra phase term, which is shown in the above link at the boundary only. eg

and E(x) is spatially periodic as the normal periodic function when incident angle is zero.

The commonly known “periodic boundary condition” is the special case of Bloch boundary condition.

 

 

[gufranskhan]

Thank you for the reply

So that means the bloch BC cannot propagate two orders at different angles in multilayer structures, which are generated through the diffraction from the grating.

[Guilin Sun]

 

Dear Prof. Gufran,

I did not say so. The Bloch BC is to ensure the angled excitation correctly, and so does all other “modes” excited. It should be correct when higher order diffraction appears.

 

For whatever the mode, E(x), adding a phase change at the boundary will guarantee its correctness. This is my understanding. Please correct me if I am wrong.

 

[gufranskhan]

I mean to say that the kx is defined for only the incidence angle of the light and upon diffraction the light which is going in the +1order has a different angle so how does the bloch boundary match the phase of +1 order light in multilayer structures.

[Guilin Sun]

You are right that the correction is for the incident angle. The rest is included in E(x), regardless the incident angle.