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Periodic FLOQUET boundary conditions: How to define the k-vector?

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In am simulating plane waves incident upon a stack of thin films (at oblique angle of incidence), each layer with different (real part of) refractive index, e.g. different k-vectors. Now the question is how i should define the k-vector to be used with a periodic FLOQUET boundary condition in COMSOL. I have come up with a few ideas:

1) Just use the k-vector associated with the upper layer, e.g. air.
kx | 0
ky | cos(theta_air)
kz | sin(theta_air)
2) Use a k-vector that is different in each layer.
kx | 0
ky | cos(theta_air)*(z =< z_air) + cos(theta_glass)*(z > z_air)*...
kz | sin(theta_air)*(z =< z_air) + sin(theta_glass)*(z > z_air)*...
3) Define multiple sets of periodic conditions, one for each layer. The first should be like in (1), the next should be
kx | 0
ky | cos(theta_glass)
kz | sin(theta_glass)

where i have assumed that the wave propagates in the z-direction with the electric field polarized in the x-direction and that the two first layers are "air" and "glass". I am aware that COMSOL can do the assignment of k-vectors automatically when periodic ports are used, but i would like to use scattered field formulation if possible, and in this case the k-vectors must be calculated manually AFAIK.

Any comments and/or good references on FLOQUET theory are much appreciated :)

1 Reply Last Post 17 nov. 2016, 06:01 UTC−5
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Hello Emil Eriksen

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Posted: 8 years ago 17 nov. 2016, 06:01 UTC−5
Emil,

I think if you have homogeneous mediums and the surfaces of your medums are perpendicular to periodic boundaries, there is no need to specify different types of Floquet, because only that component of the k-vector is importnant for Floquet periodicity, which is perpendicular to boundaries. This component is tangential to surfaces with different n and from Maxwell`s equations we know that this component is equal in each medium.


Regards,
Eugene
Emil, I think if you have homogeneous mediums and the surfaces of your medums are perpendicular to periodic boundaries, there is no need to specify different types of Floquet, because only that component of the k-vector is importnant for Floquet periodicity, which is perpendicular to boundaries. This component is tangential to surfaces with different n and from Maxwell`s equations we know that this component is equal in each medium. Regards, Eugene

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