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Eigen-frequency analysis of metal grating

Posted Aug 9, 2012, 11:17 a.m. EDT RF & Microwave Engineering Version 4.2a, Version 4.3 15 Replies

Marvin Farrell
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Dear all,

For a metal grating (see attached Structure_Reference.jpg), now I would like to analysis the dispersion relationship of surface plasmon wave supported by a metal grating, which propagates along the surface of the grating.

I choose Eigen-frequency analysis method:

I set left-right boundary as periodic boundary condition with Floquet periodicity (the related setting as well as other boundary conditions see Structure. JPG);

Here giving an example, when alpha is set as 80 degree, then the related eigenfrequency of surface plasmon mode is analyzed, the corresponding field distributions are see attached (a.jpg and b.jpg).

From the distributions, we can see that they are indeed the surface plasmon wave supported by the structure.

Then the dispersion relationship can be obtained simply based on these eigenfrequency values.

Above is my thought about the model.

Is it reasonable? If not, anybody could give me some suggestions?

Million thanks!
15 Replies Last Post Feb 6, 2015, 6:30 a.m. EST
Alexander Kuznetsov
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Posted: 1 decade ago Aug 9, 2012, 2:51 p.m. EDT
I'd include PML on the bottom as well. Other than that, everything seems fine.
I'd include PML on the bottom as well. Other than that, everything seems fine.
Marvin Farrell
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Posted: 1 decade ago Aug 9, 2012, 5:23 p.m. EDT
Hi, Alexander,

Thanks for your reply.
Actually, when the dimension of PML changes, the eigenfrequency changes as well, it is unreasonable.
Hi, Alexander, Thanks for your reply. Actually, when the dimension of PML changes, the eigenfrequency changes as well, it is unreasonable.
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Aug 10, 2012, 3:26 a.m. EDT
Hi

perhaps you PML is not 100% then, reflecting back energy, or it's too close to the grating

--
Good luck
Ivar
Hi perhaps you PML is not 100% then, reflecting back energy, or it's too close to the grating -- Good luck Ivar
Marvin Farrell
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Posted: 1 decade ago Aug 10, 2012, 5:28 a.m. EDT
Hi, Ivar,

Yeah the reason is that PML is close to the structure.

Yet, maybe my thought is not right, the dispersion relationship of surface plasmon wave is wrong.

I am so stuck with this model i.e. how to get the dispersion curve of surface plasmon wave that propagates along the metal grating.

Regards!
Hi, Ivar, Yeah the reason is that PML is close to the structure. Yet, maybe my thought is not right, the dispersion relationship of surface plasmon wave is wrong. I am so stuck with this model i.e. how to get the dispersion curve of surface plasmon wave that propagates along the metal grating. Regards!
Alexander Kuznetsov
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Posted: 1 decade ago Aug 10, 2012, 1:16 p.m. EDT
You won't get dispersion curve with eigen solver. You might want to use frequency domain simulations instead.
You won't get dispersion curve with eigen solver. You might want to use frequency domain simulations instead.
Marvin Farrell
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Posted: 1 decade ago Aug 10, 2012, 3:38 p.m. EDT
Hi, Alexander,

Does it to do the frequency_incident angle sweep?

Regards!
Hi, Alexander, Does it to do the frequency_incident angle sweep? Regards!
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Aug 10, 2012, 4:15 p.m. EDT
Hi

isnt that "just" making a parametric sweep node (for the angle) in front of a frequency domain solver (with a range definition)

--
Good luck
Ivar
Hi isnt that "just" making a parametric sweep node (for the angle) in front of a frequency domain solver (with a range definition) -- Good luck Ivar
Alexander Kuznetsov
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Posted: 1 decade ago Aug 10, 2012, 5:23 p.m. EDT
No, it's different type of study + small changes to the model.
Eigen-solver finds eigen-frequencies of the system which does not depend on excitation.
For frequency domain studies excitation (input wave) is required so boundaries should be changed.
No, it's different type of study + small changes to the model. Eigen-solver finds eigen-frequencies of the system which does not depend on excitation. For frequency domain studies excitation (input wave) is required so boundaries should be changed.
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Aug 11, 2012, 3:13 a.m. EDT
Hi
another point that strikes me is that the field response is not periodic, but looks more antiperiodic w.r.t. left-right F boundaries, or have I missed a point ?

--
Good luck
Ivar
Hi another point that strikes me is that the field response is not periodic, but looks more antiperiodic w.r.t. left-right F boundaries, or have I missed a point ? -- Good luck Ivar
Chris Curwen
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Posted: 1 decade ago Dec 4, 2012, 4:44 p.m. EST
Marvin (or anyone else who may have ideas),

Can you explain in some detail how you set up that PML at the top? I'm performing a very similar simulation with a dielectric waveguide at the bottom rather than the SP waveguide and I can't figure out how to set up the PML. I've attached a screenshot that shows the upper portion of my air domain on top of the unit cell and the PML at the top. The magnetic field of one of the eigenfreq solutions is shown in the attached image. It appears as though the boundary between the PML and the air is just a PEC.

How did you define the boundaries? Is meshing important? Do you generally have to provide any inputs, or do you just add the domain, designate it PML and solve (it seems that's all they do in the tutorials)?

Any advice would be appreciated, thanks.

Chris
Marvin (or anyone else who may have ideas), Can you explain in some detail how you set up that PML at the top? I'm performing a very similar simulation with a dielectric waveguide at the bottom rather than the SP waveguide and I can't figure out how to set up the PML. I've attached a screenshot that shows the upper portion of my air domain on top of the unit cell and the PML at the top. The magnetic field of one of the eigenfreq solutions is shown in the attached image. It appears as though the boundary between the PML and the air is just a PEC. How did you define the boundaries? Is meshing important? Do you generally have to provide any inputs, or do you just add the domain, designate it PML and solve (it seems that's all they do in the tutorials)? Any advice would be appreciated, thanks. Chris

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Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Dec 5, 2012, 1:38 a.m. EST
Hi

in the last version 4.3a you define the infinite or PML's under the Model Definition node
Ideally the INF region should be meshed with quad/prisms in layers, I would adopt that for MPL's too, but in any case have > 5 elements across

In older versions the INF and PML were defined under the physics, do not forget to define the shape (cartesian spherical cylindrical), and for INF at least define the origin somewhere in the middle of your model, or easier centre your model at (0,0,0)

--
Good luck
Ivar
Hi in the last version 4.3a you define the infinite or PML's under the Model Definition node Ideally the INF region should be meshed with quad/prisms in layers, I would adopt that for MPL's too, but in any case have > 5 elements across In older versions the INF and PML were defined under the physics, do not forget to define the shape (cartesian spherical cylindrical), and for INF at least define the origin somewhere in the middle of your model, or easier centre your model at (0,0,0) -- Good luck Ivar
Ann Liu
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Posted: 1 decade ago May 2, 2013, 7:43 a.m. EDT
Hello,

May I know if I have to put an excitation source at one side of the periodic boundary for this case?
I am also trying to find the dispersion curve of a grating by using eigenfrequency solver.

Thank you.
Liu



Dear all,

For a metal grating (see attached Structure_Reference.jpg), now I would like to analysis the dispersion relationship of surface plasmon wave supported by a metal grating, which propagates along the surface of the grating.

I choose Eigen-frequency analysis method:

I set left-right boundary as periodic boundary condition with Floquet periodicity (the related setting as well as other boundary conditions see Structure. JPG);

Here giving an example, when alpha is set as 80 degree, then the related eigenfrequency of surface plasmon mode is analyzed, the corresponding field distributions are see attached (a.jpg and b.jpg).

From the distributions, we can see that they are indeed the surface plasmon wave supported by the structure.

Then the dispersion relationship can be obtained simply based on these eigenfrequency values.

Above is my thought about the model.

Is it reasonable? If not, anybody could give me some suggestions?

Million thanks!


Hello, May I know if I have to put an excitation source at one side of the periodic boundary for this case? I am also trying to find the dispersion curve of a grating by using eigenfrequency solver. Thank you. Liu [QUOTE] Dear all, For a metal grating (see attached Structure_Reference.jpg), now I would like to analysis the dispersion relationship of surface plasmon wave supported by a metal grating, which propagates along the surface of the grating. I choose Eigen-frequency analysis method: I set left-right boundary as periodic boundary condition with Floquet periodicity (the related setting as well as other boundary conditions see Structure. JPG); Here giving an example, when alpha is set as 80 degree, then the related eigenfrequency of surface plasmon mode is analyzed, the corresponding field distributions are see attached (a.jpg and b.jpg). From the distributions, we can see that they are indeed the surface plasmon wave supported by the structure. Then the dispersion relationship can be obtained simply based on these eigenfrequency values. Above is my thought about the model. Is it reasonable? If not, anybody could give me some suggestions? Million thanks! [/QUOTE]
Lin Chen
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Posted: 1 decade ago Oct 8, 2013, 6:34 a.m. EDT
Hi Million：
Currently I am also working on calculating the dispersion of periodical metallic gratings based on comsol. But I don't know how to use eigenfrequency solver? Can you show me how to use it or send me a copy of your desighed one for metallic grating based on comsol. Thank you very much.
Hi Million： Currently I am also working on calculating the dispersion of periodical metallic gratings based on comsol. But I don't know how to use eigenfrequency solver? Can you show me how to use it or send me a copy of your desighed one for metallic grating based on comsol. Thank you very much.
Ngoc Nguyen
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Posted: 1 decade ago Nov 5, 2013, 5:39 p.m. EST

Hi Million：
Currently I am also working on calculating the dispersion of periodical metallic gratings based on comsol. But I don't know how to use eigenfrequency solver? Can you show me how to use it or send me a copy of your desighed one for metallic grating based on comsol. Thank you very much.

Hi,
You might want to take a look at this video to calculate the dispersion curve based on eigensolver
www.youtube.com/watch?v=HMgdXMNigCA
[QUOTE] Hi Million： Currently I am also working on calculating the dispersion of periodical metallic gratings based on comsol. But I don't know how to use eigenfrequency solver? Can you show me how to use it or send me a copy of your desighed one for metallic grating based on comsol. Thank you very much. [/QUOTE] Hi, You might want to take a look at this video to calculate the dispersion curve based on eigensolver http://www.youtube.com/watch?v=HMgdXMNigCA
Pan Deng
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Posted: 9 years ago Feb 6, 2015, 6:30 a.m. EST
Did you try to smooth the corner of the grating? For example, using a grating of sine shape. I can reproduce your result. But when I use a sine shape grating, the field near the Floquet boundary show much fluctuations. Do you know what's wrong with my model? Thanks
Did you try to smooth the corner of the grating? For example, using a grating of sine shape. I can reproduce your result. But when I use a sine shape grating, the field near the Floquet boundary show much fluctuations. Do you know what's wrong with my model? Thanks

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