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Setting up Hexagonal Lattice BC

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For those interested and knowledgeable,

I am trying to model an infinite array of 3D particles in a hexagonal lattice that will be illuminated by a source perpendicular to the plane. How would I set up the periodic (floquet?) boundary conditions on a (triangular cross-sectioned?) bounding box to mimic the infinite extent of the array? If it matters any to this model, I am interested in a close-packed hexagonal array (particles' edges touch).

As an abstraction, one could imagine the particles located at the vertices of the triangles in the picture linked here: en.wikipedia.org/wiki/File:Tile_3,6.svg

Cheers,
JDS

7 Replies Last Post Apr 10, 2012, 2:15 p.m. EDT

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Posted: 1 decade ago Apr 9, 2012, 5:28 p.m. EDT
There is a way to define orthorhombic unit cell for 3D hexagon lattice. The unit cell will have two identical atoms (or particles in your case). Then using floquet BC is straight-forward. Here is a good starting point: en.wikipedia.org/wiki/Bravais_lattice
There is a way to define orthorhombic unit cell for 3D hexagon lattice. The unit cell will have two identical atoms (or particles in your case). Then using floquet BC is straight-forward. Here is a good starting point: http://en.wikipedia.org/wiki/Bravais_lattice

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Posted: 1 decade ago Apr 9, 2012, 7:59 p.m. EDT
I understand how the unit cell tessellates to fill space, and for the sake of simplicity - i think this would be a simpler in modeling, correct me if i'm mistaken - i have modeled a non-primitive hexagonal unit cell similar to

www.doitpoms.ac.uk/tlplib/crystallography3/unit_cell.php

with square boundaries.


what i am not sure of is how to input the floquet conditions on the 4(?) sides of the unit cell in comsol. if you could advise on that matter it would be greatly appreciated.
I understand how the unit cell tessellates to fill space, and for the sake of simplicity - i think this would be a simpler in modeling, correct me if i'm mistaken - i have modeled a non-primitive hexagonal unit cell similar to http://www.doitpoms.ac.uk/tlplib/crystallography3/unit_cell.php with square boundaries. what i am not sure of is how to input the floquet conditions on the 4(?) sides of the unit cell in comsol. if you could advise on that matter it would be greatly appreciated.

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Posted: 1 decade ago Apr 9, 2012, 8:17 p.m. EDT
you put 2 floquet conditions for each pair of opposing boundaries. When defining your unit cell, make sure your boundaries are either along y or x direction. This makes it easier to define kx and ky vectors. Plasmonic wire grating explains implementation of floquets in detail
you put 2 floquet conditions for each pair of opposing boundaries. When defining your unit cell, make sure your boundaries are either along y or x direction. This makes it easier to define kx and ky vectors. Plasmonic wire grating explains implementation of floquets in detail

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Posted: 1 decade ago Apr 9, 2012, 8:41 p.m. EDT
hi alexander, thanks for bearing with me.

i have read through the documentation, but what i am not clear on is using ports, and why they are not used in the rf library model for a periodic boundary condition.

that is, i am not sure what ports are, and thus how to modify the appropriate inputs for a 3D model.

hi alexander, thanks for bearing with me. i have read through the documentation, but what i am not clear on is using ports, and why they are not used in the rf library model for a periodic boundary condition. that is, i am not sure what ports are, and thus how to modify the appropriate inputs for a 3D model.

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Posted: 1 decade ago Apr 9, 2012, 9:29 p.m. EDT
port are used to specify input excitation. For launching plane waves, scattering boundary conditions may be used as well (as in periodic BC example). Port are discussed in different waveguide tutorials.
port are used to specify input excitation. For launching plane waves, scattering boundary conditions may be used as well (as in periodic BC example). Port are discussed in different waveguide tutorials.

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Posted: 1 decade ago Apr 10, 2012, 2:15 p.m. EDT
Since I am using a plane illumination, i have set up scattering boundary conditions to bypass the difficulty of using ports, however, I am still having trouble setting up the floquet conditions correctly.

My unit rectangular cell is aligned along the x-y axes, and the illumination is in-plane (the z-direction) and polarized in the Y-direction. I define he paired X-Z and paired Y-Z sthingurfaces as having floquet periodicity uch that k_f only has a Y-component (kf_y = emw.k0). Is that correct?

When I solve my model I get a notice that the matrix is nonsymmetric, which is not the usual case for EM simulations, so I think there is someincorrectly defined.



Since I am using a plane illumination, i have set up scattering boundary conditions to bypass the difficulty of using ports, however, I am still having trouble setting up the floquet conditions correctly. My unit rectangular cell is aligned along the x-y axes, and the illumination is in-plane (the z-direction) and polarized in the Y-direction. I define he paired X-Z and paired Y-Z sthingurfaces as having floquet periodicity uch that k_f only has a Y-component (kf_y = emw.k0). Is that correct? When I solve my model I get a notice that the matrix is nonsymmetric, which is not the usual case for EM simulations, so I think there is someincorrectly defined.

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Posted: 1 decade ago Apr 10, 2012, 2:15 p.m. EDT
Since I am using a plane illumination, i have set up scattering boundary conditions to bypass the difficulty of using ports, however, I am still having trouble setting up the floquet conditions correctly.

My unit rectangular cell is aligned along the x-y axes, and the illumination is in-plane (the z-direction) and polarized in the Y-direction. I define he paired X-Z and paired Y-Z sthingurfaces as having floquet periodicity uch that k_f only has a Y-component (kf_y = emw.k0). Is that correct?

When I solve my model I get a notice that the matrix is nonsymmetric, which is not the usual case for EM simulations, so I think there is someincorrectly defined.



Since I am using a plane illumination, i have set up scattering boundary conditions to bypass the difficulty of using ports, however, I am still having trouble setting up the floquet conditions correctly. My unit rectangular cell is aligned along the x-y axes, and the illumination is in-plane (the z-direction) and polarized in the Y-direction. I define he paired X-Z and paired Y-Z sthingurfaces as having floquet periodicity uch that k_f only has a Y-component (kf_y = emw.k0). Is that correct? When I solve my model I get a notice that the matrix is nonsymmetric, which is not the usual case for EM simulations, so I think there is someincorrectly defined.

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