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2D geometry but illuminated from below
Posted 4 mars 2013, 15:43 UTC−5 RF & Microwave Engineering, Geometry, Modeling Tools & Definitions, Parameters, Variables, & Functions Version 4.3, Version 5.0 9 Replies
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Hi,
I want to create a 2D geometry but illuminate it from below, or out of plane, with a plane wave. Whenever I try and set the Background Field as exp(-i*emw.k0*z) (in x direction) I get errors as it fails to evaluate the variable z.
Any help is greatly appreciated!
Daniel
I want to create a 2D geometry but illuminate it from below, or out of plane, with a plane wave. Whenever I try and set the Background Field as exp(-i*emw.k0*z) (in x direction) I get errors as it fails to evaluate the variable z.
Any help is greatly appreciated!
Daniel
9 Replies Last Post 25 janv. 2017, 11:19 UTC−5
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Posted:
1 decade ago
Daniel,
If 2D geometry is illuminated from below, then wavevector is k={0,k0,0}, meaning that wave is propagating along y-axis.
For plane wave, electric and magnetic fields are normal to the propagation direction. Hence, you have two choices: electric field can be x-polarized or z-polarized.
For x-polarization, background electric field is defined as E={exp(-j*emw.k0*y,0,0)}.
For z-polarization, background electric field is defined as E={0,0,exp(-j*emw.k0*y,0,0)},
as illustrated in the attached plot.
Regards,
Sergei
If 2D geometry is illuminated from below, then wavevector is k={0,k0,0}, meaning that wave is propagating along y-axis.
For plane wave, electric and magnetic fields are normal to the propagation direction. Hence, you have two choices: electric field can be x-polarized or z-polarized.
For x-polarization, background electric field is defined as E={exp(-j*emw.k0*y,0,0)}.
For z-polarization, background electric field is defined as E={0,0,exp(-j*emw.k0*y,0,0)},
as illustrated in the attached plot.
Regards,
Sergei
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Posted:
1 decade ago
Thanks, Sergei. I see--whatever geometry I make is extended to infinity in the z-direction.
Maybe you can help with another question I have, and I've uploaded my file. I've been trying to make a 2-D axisymmetric geometry which will represent a thin metal disk illuminated by a plane wave. Somehow my PML is messed up and I feel like I'm doing the polarization incorrectly. What I want is a linearly polarized wave, but it doesn't let me put any phi dependence in the plane wave form. I feel like I could be overanalyzing--and I should just make it r-polarized and that'll do it.
I model this geometry in 3D so I'm trying to get my 2D results to match up with the 3D ones so I can save some computing time =)
Thanks again for your help!
Daniel
Maybe you can help with another question I have, and I've uploaded my file. I've been trying to make a 2-D axisymmetric geometry which will represent a thin metal disk illuminated by a plane wave. Somehow my PML is messed up and I feel like I'm doing the polarization incorrectly. What I want is a linearly polarized wave, but it doesn't let me put any phi dependence in the plane wave form. I feel like I could be overanalyzing--and I should just make it r-polarized and that'll do it.
I model this geometry in 3D so I'm trying to get my 2D results to match up with the 3D ones so I can save some computing time =)
Thanks again for your help!
Daniel
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Posted:
1 decade ago
Daniel,
Problem is not PML – your setup for PML is correct. Problem is how to express analytically plane wave in cylindrical coordinates – not sure if it’s possible in a straightforward way.
If your concern is computational resources in 3D, then you can use Transition Boundary Condition to replace thin disk by circular surface. This boundary condition allows specify all electrical properties and thickness of the disk and capture field discontinuity accross disk thickness. This approach might be computationally very effective to solve your problem in 3D (plus two symmetry planes).
Regards,
Sergei
Problem is not PML – your setup for PML is correct. Problem is how to express analytically plane wave in cylindrical coordinates – not sure if it’s possible in a straightforward way.
If your concern is computational resources in 3D, then you can use Transition Boundary Condition to replace thin disk by circular surface. This boundary condition allows specify all electrical properties and thickness of the disk and capture field discontinuity accross disk thickness. This approach might be computationally very effective to solve your problem in 3D (plus two symmetry planes).
Regards,
Sergei
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Posted:
1 decade ago
Sergei,
First, thank you. Your help has been perfect.
I got the transition boundary condition to work (thanks again). Now I'm trying to simulate a transition boundary condition with a hole in the middle. The structure will radiate (PML needed?) but I want the thin material to appear infinite (Infinite element domain?). Just making the transition boundary big doesn't work--it either needs to be HUGE or I need to somehow 'trick' COMSOL into thinking it's infinite. Ideas?
Just for the sake of clarity, I want to illuminate by plane wave an infinite (or big enough that the modes don't couple) transition boundary condition with a hole in the middle. An array of these holes in the transition boundary condition is also acceptable, so I've looked at periodic boundary conditions as well, but I feel there has to be an easier way.
Thanks again!
Daniel
First, thank you. Your help has been perfect.
I got the transition boundary condition to work (thanks again). Now I'm trying to simulate a transition boundary condition with a hole in the middle. The structure will radiate (PML needed?) but I want the thin material to appear infinite (Infinite element domain?). Just making the transition boundary big doesn't work--it either needs to be HUGE or I need to somehow 'trick' COMSOL into thinking it's infinite. Ideas?
Just for the sake of clarity, I want to illuminate by plane wave an infinite (or big enough that the modes don't couple) transition boundary condition with a hole in the middle. An array of these holes in the transition boundary condition is also acceptable, so I've looked at periodic boundary conditions as well, but I feel there has to be an easier way.
Thanks again!
Daniel
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Posted:
1 decade ago
Daniel,
Problem of single inhomogeneity (hole in your case) in infinite substrate is much more difficult and tricky to setup as compared to the problem of the periodic array of inhomogeneities.
So, if the array of holes is acceptable for you, I would suggest to use periodic BCs at boundaries normal to the substrate and PMLs at boundaries parallel to the substrate.
Regards,
Sergei
Problem of single inhomogeneity (hole in your case) in infinite substrate is much more difficult and tricky to setup as compared to the problem of the periodic array of inhomogeneities.
So, if the array of holes is acceptable for you, I would suggest to use periodic BCs at boundaries normal to the substrate and PMLs at boundaries parallel to the substrate.
Regards,
Sergei
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Posted:
1 decade ago
Hi Sergei,
I'm having trouble understanding how to implement Floquet BCs and illumination at the same time. I want to illuminate a circle with a plane wave and use periodic BCs to simulate a 2D array of these circles.
--I have a circle in the xy plane and want to simulate a 2D array of them in xy. If my simulation volume is a cube, this suggests making all yz and xz boundaries with Floquet BCs...right?
--I want to illuminate the discs from below, say, a plane wave coming from -z and polarized in the x-direction. Is this the wave that must enter in the Floquet BCs? What does the Floquet ACTUALLY do? Does that specific wavevector on one plane periodically 'wrap around' to the corresponding plane?
--Also, what to do with the last two sides of the cube? You suggested PMLs, but the Floquet BC example model uses PEC for 2 boundaries and Scattering BC for 2 boundaries.
All these permutations are just flying around in my head and are becoming confusing. Thanks again!
Daniel
I'm having trouble understanding how to implement Floquet BCs and illumination at the same time. I want to illuminate a circle with a plane wave and use periodic BCs to simulate a 2D array of these circles.
--I have a circle in the xy plane and want to simulate a 2D array of them in xy. If my simulation volume is a cube, this suggests making all yz and xz boundaries with Floquet BCs...right?
--I want to illuminate the discs from below, say, a plane wave coming from -z and polarized in the x-direction. Is this the wave that must enter in the Floquet BCs? What does the Floquet ACTUALLY do? Does that specific wavevector on one plane periodically 'wrap around' to the corresponding plane?
--Also, what to do with the last two sides of the cube? You suggested PMLs, but the Floquet BC example model uses PEC for 2 boundaries and Scattering BC for 2 boundaries.
All these permutations are just flying around in my head and are becoming confusing. Thanks again!
Daniel
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Posted:
1 decade ago
Daniel,
1.”Floquet periodicity” means that field magnitude is the same but there is phase shift due to wave propagation in the direction normal to the boundary. Suppose that at boundary 1 field is E1. Then, field at the boundary 2 is equal E2=E1*exp(-j*kn*delta), where “kn” is wavector component NORMAL to the boundary, and “delta” is the distance between boundaries. Typically, this BC is used in case of oblique incident wave.
If wave propagates PARALLEL to the boundary (kn=0), the Floquet BC reduces to the condition E1=E2, which is called “Continuity” type of periodicity. Both above options are available at the Periodicity Settings section under Periodic Condition.
Note that, under certain special circumstances, Periodic Condition is equivalent to Perfect Electric Conductor (PEC) or Perfect Magnetic Conductor (PMC) boundary conditions. For example, if incident field is x-polarized, then you can impose PEC boundary condition at planes x=const. This would be equivalent “Continuity” type of periodicity.
2. Back to your problem. You case of x-polarized incident wave propagating in the z-direction is:
k={0,0,kz}, E={exp(-j*kz*z,0,0)}, H={0,exp(-j*kz*z),0}.
Boundary conditions are as following.
At boundaries x=const: PEC or Continuity type of periodicity.
At boundaries y=const: PMC, since magnetic field is normal to these boundaries.
At boundaries z-const you have two choices: use PML layers if Scattered Field formulation is used, or use Port boundary conditions if Full Field formulation is used (with excitation field E={exp(-j*kz*z,0,0)} and propagation constant beta=kz)
Attached is field distribution obtained using Scattered Filed formulation for periodic array slits in 2D case.
Regards,
Sergei
1.”Floquet periodicity” means that field magnitude is the same but there is phase shift due to wave propagation in the direction normal to the boundary. Suppose that at boundary 1 field is E1. Then, field at the boundary 2 is equal E2=E1*exp(-j*kn*delta), where “kn” is wavector component NORMAL to the boundary, and “delta” is the distance between boundaries. Typically, this BC is used in case of oblique incident wave.
If wave propagates PARALLEL to the boundary (kn=0), the Floquet BC reduces to the condition E1=E2, which is called “Continuity” type of periodicity. Both above options are available at the Periodicity Settings section under Periodic Condition.
Note that, under certain special circumstances, Periodic Condition is equivalent to Perfect Electric Conductor (PEC) or Perfect Magnetic Conductor (PMC) boundary conditions. For example, if incident field is x-polarized, then you can impose PEC boundary condition at planes x=const. This would be equivalent “Continuity” type of periodicity.
2. Back to your problem. You case of x-polarized incident wave propagating in the z-direction is:
k={0,0,kz}, E={exp(-j*kz*z,0,0)}, H={0,exp(-j*kz*z),0}.
Boundary conditions are as following.
At boundaries x=const: PEC or Continuity type of periodicity.
At boundaries y=const: PMC, since magnetic field is normal to these boundaries.
At boundaries z-const you have two choices: use PML layers if Scattered Field formulation is used, or use Port boundary conditions if Full Field formulation is used (with excitation field E={exp(-j*kz*z,0,0)} and propagation constant beta=kz)
Attached is field distribution obtained using Scattered Filed formulation for periodic array slits in 2D case.
Regards,
Sergei
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Posted:
10 years ago
Hey Sergei
I have couple of question regarding the model that you were explaining. If i want to calculated the scattering cross section and Extinction cross section through array of circular disc which is placed on glass substrate. What should i do ??
I have couple of question regarding the model that you were explaining. If i want to calculated the scattering cross section and Extinction cross section through array of circular disc which is placed on glass substrate. What should i do ??
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Posted:
8 years ago
Daniel,
1.”Floquet periodicity” means that field magnitude is the same but there is phase shift due to wave propagation in the direction normal to the boundary. Suppose that at boundary 1 field is E1. Then, field at the boundary 2 is equal E2=E1*exp(-j*kn*delta), where “kn” is wavector component NORMAL to the boundary, and “delta” is the distance between boundaries. Typically, this BC is used in case of oblique incident wave.
If wave propagates PARALLEL to the boundary (kn=0), the Floquet BC reduces to the condition E1=E2, which is called “Continuity” type of periodicity. Both above options are available at the Periodicity Settings section under Periodic Condition.
Note that, under certain special circumstances, Periodic Condition is equivalent to Perfect Electric Conductor (PEC) or Perfect Magnetic Conductor (PMC) boundary conditions. For example, if incident field is x-polarized, then you can impose PEC boundary condition at planes x=const. This would be equivalent “Continuity” type of periodicity.
2. Back to your problem. You case of x-polarized incident wave propagating in the z-direction is:
k={0,0,kz}, E={exp(-j*kz*z,0,0)}, H={0,exp(-j*kz*z),0}.
Boundary conditions are as following.
At boundaries x=const: PEC or Continuity type of periodicity.
At boundaries y=const: PMC, since magnetic field is normal to these boundaries.
At boundaries z-const you have two choices: use PML layers if Scattered Field formulation is used, or use Port boundary conditions if Full Field formulation is used (with excitation field E={exp(-j*kz*z,0,0)} and propagation constant beta=kz)
Attached is field distribution obtained using Scattered Filed formulation for periodic array slits in 2D case.
Regards,
Sergei
Hi Sergei,
so if I want to excite SPP on the surface of the air and matellic interface, and it is not periodic, what should the model be. since I find the transition BC is not applicable any more. and the PML and scattering BC are not so good any more. any idea?