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Question about example- "Plasmonic wire grating"

Posted Jul 15, 2011, 12:38 p.m. EDT RF & Microwave Engineering Version 3.5a, Version 4.2a 14 Replies

Peijun Guo
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Dear all:
I have a question about the example "Plasmonic wire grating".
In this model, I saw that the Floquet boundary condition applied at the left and right boundary is that kF=kax (wave vector), which is equal to emw.k0*sin(alpha). However, we know that the wave vector depends on the wavelength, and wavelength depends on the refractive index of the medium. In that example, the lower sub-domain is a dielectric with refractive index of nb=1.2. So in the periodic boundary settings, why don't we set the kF=kax*nb for the lower sub-domain?
This question has bugged me for some time. I really appreciate for your idea!
14 Replies Last Post Apr 17, 2013, 8:28 a.m. EDT
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Pierfrancesco Zilio
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Posted: 1 decade ago Aug 28, 2011, 5:13 a.m. EDT
Because of Snell's law. In the lower half space you should set Kf = emw.k0*sin(alpha_transmitted)*nb. But this is just emw.k0*sin(alpha) because of Snell's law.

pierfrancesco
Because of Snell's law. In the lower half space you should set Kf = emw.k0*sin(alpha_transmitted)*nb. But this is just emw.k0*sin(alpha) because of Snell's law. pierfrancesco
Peijun Guo
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Posted: 1 decade ago Sep 12, 2011, 1:32 p.m. EDT
Thank you so much for your help, pierfrancesco.
However, what if I have a complex structure, for example, a nanorod, inside of the simulation box? This is more complicated than the case where I only have different layers/films of materials, and the k vector will be very hard (even impossible) to determine. Have you met the similar problems?
Thanks in advance!
Thank you so much for your help, pierfrancesco. However, what if I have a complex structure, for example, a nanorod, inside of the simulation box? This is more complicated than the case where I only have different layers/films of materials, and the k vector will be very hard (even impossible) to determine. Have you met the similar problems? Thanks in advance!
Pierfrancesco Zilio
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Posted: 1 decade ago Sep 12, 2011, 3:06 p.m. EDT
Hi Peijun,
yes I have met similar problems too. I mean, infinite periodic arrays of nanoobjects illuminated by plane waves.
Actually Floquet boundary condition is the exact boundary condition one should set when dealing with periodic systems illuminated by a non-normal plane wave.
You can easily see that the phase relation imposed by Floquet boundary condition to the field is actually a general property of the field of a periodic structure illuminated by a plane wave. So I usually set Floquet boundary conditions at the sides and everything works fine.
The "k-vector for Floquet periodicity" is just the parallel component of the incident wave wave vector.

Cheers

pierfrancesco
Hi Peijun, yes I have met similar problems too. I mean, infinite periodic arrays of nanoobjects illuminated by plane waves. Actually Floquet boundary condition is the exact boundary condition one should set when dealing with periodic systems illuminated by a non-normal plane wave. You can easily see that the phase relation imposed by Floquet boundary condition to the field is actually a general property of the field of a periodic structure illuminated by a plane wave. So I usually set Floquet boundary conditions at the sides and everything works fine. The "k-vector for Floquet periodicity" is just the parallel component of the incident wave wave vector. Cheers pierfrancesco
David Schäfer
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Posted: 1 decade ago Dec 21, 2011, 8:35 a.m. EST
Hi pierfrancesco,

Are you simulating in 2D or 3D? I tried to rebuild the "Plasmonic wire grating"-example in 3D, but the simulation does not converge when I set an incident angle other than 0.

Kind regards
David



Hi pierfrancesco, Are you simulating in 2D or 3D? I tried to rebuild the "Plasmonic wire grating"-example in 3D, but the simulation does not converge when I set an incident angle other than 0. Kind regards David
Alexander Kuznetsov
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Posted: 1 decade ago Dec 21, 2011, 8:26 p.m. EST
Probably you have a problem with boundary conditions. Here are BCs that will work:
plane (xz) - Perfect EC
plane (yz) - Floquet k = (k1x,0,0)
plane (xy) - Port BC E=(0,exp(-i*k1x*x),0) beta = abs(k1z)
k1x = k1*sin(alpha), k1z=-k1*cos(alpha)
That assumes (xz) to be plane of incidence and z-direction is orthogonal to the surface.
These set of BC work for S-polarization. For P-polarization replace PEC wth PMC and change Port BC accordingly.


Hi pierfrancesco,

Are you simulating in 2D or 3D? I tried to rebuild the "Plasmonic wire grating"-example in 3D, but the simulation does not converge when I set an incident angle other than 0.

Kind regards
David


Probably you have a problem with boundary conditions. Here are BCs that will work: plane (xz) - Perfect EC plane (yz) - Floquet k = (k1x,0,0) plane (xy) - Port BC E=(0,exp(-i*k1x*x),0) beta = abs(k1z) k1x = k1*sin(alpha), k1z=-k1*cos(alpha) That assumes (xz) to be plane of incidence and z-direction is orthogonal to the surface. These set of BC work for S-polarization. For P-polarization replace PEC wth PMC and change Port BC accordingly. [QUOTE] Hi pierfrancesco, Are you simulating in 2D or 3D? I tried to rebuild the "Plasmonic wire grating"-example in 3D, but the simulation does not converge when I set an incident angle other than 0. Kind regards David [/QUOTE]
David Schäfer
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Posted: 1 decade ago Dec 22, 2011, 7:06 a.m. EST
Hi Alexander,

thanks for your reply. That were pretty much my settings, except for having xy as the plane of incidence to keep it consistent with the 2D example.

I created a minimal example for an incident wave with periodic conditions from scratch, and now it works... (more or less, because there are still angles where it does not converge). But I still couldn't figure out what the mistake was in the previous model, also I double- and triple-checked all settings.

Kind regards
David
Hi Alexander, thanks for your reply. That were pretty much my settings, except for having xy as the plane of incidence to keep it consistent with the 2D example. I created a minimal example for an incident wave with periodic conditions from scratch, and now it works... (more or less, because there are still angles where it does not converge). But I still couldn't figure out what the mistake was in the previous model, also I double- and triple-checked all settings. Kind regards David
Alexander Kuznetsov
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Posted: 1 decade ago Dec 22, 2011, 4:17 p.m. EST
David,

It should converge at any angle below 90 deg. Maybe your mesh is the problem. Make sure you have identical mesh on periodic boundaries.
David, It should converge at any angle below 90 deg. Maybe your mesh is the problem. Make sure you have identical mesh on periodic boundaries.
Tianxun Gong
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Posted: 1 decade ago May 2, 2012, 10:52 p.m. EDT
I build a model with what exactly Alexander's setting, but the model does not converge, i don't know where is wrong, do u have any idea? Thanks
I build a model with what exactly Alexander's setting, but the model does not converge, i don't know where is wrong, do u have any idea? Thanks
Vijay Ramakrishnan
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Posted: 1 decade ago Mar 24, 2013, 9:07 a.m. EDT
Hello All,
I am trying to remodel the device in the 'plasmonic wire grating' example. As a background reading I wanted to read in depth about this device. It would be of great help if anyone could mention which source (research paper or book) this modeled device is based on so that I can understand it in better detail. If there are online material regarding the device modeled in this example, I request you to share them.
Thanking you all,
Vijay.
Hello All, I am trying to remodel the device in the 'plasmonic wire grating' example. As a background reading I wanted to read in depth about this device. It would be of great help if anyone could mention which source (research paper or book) this modeled device is based on so that I can understand it in better detail. If there are online material regarding the device modeled in this example, I request you to share them. Thanking you all, Vijay.
David Schäfer
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Posted: 1 decade ago Mar 25, 2013, 5:48 a.m. EDT
Hello Vijay,

plasmonic wire gratings and particles can be used to enhance solar cells. An quick introduction to this can be found on Wikipedia: en.wikipedia.org/wiki/Plasmonic_solar_cell

Here you can find two papers about this topic:
onlinelibrary.wiley.com/doi/10.1002/adma.200900331/abstract (Pala et al.)
www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-26-21793 (Catchpole et al.)

Hope I understood your question right?

Kind regards
David
Hello Vijay, plasmonic wire gratings and particles can be used to enhance solar cells. An quick introduction to this can be found on Wikipedia: http://en.wikipedia.org/wiki/Plasmonic_solar_cell Here you can find two papers about this topic: http://onlinelibrary.wiley.com/doi/10.1002/adma.200900331/abstract (Pala et al.) http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-26-21793 (Catchpole et al.) Hope I understood your question right? Kind regards David
Vijay Ramakrishnan
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Posted: 1 decade ago Apr 17, 2013, 4:53 a.m. EDT
Hello David,
I found wiki page as well as the second paper you recommended very useful. I could not access the first paper. But both these resources concentrated mainly on use of nanoparticles in solar cells. I specifically want to know about the applications and uses of plasmonic wire gratings. Where are they used ? How do they work ?
Also please let mention any research paper on plasmonic wire grating specifically. I am trying to vary the study plasmonic wire gratings by varying their materials and the diameter of the wire.
Thanking you,
Vijay.
Hello David, I found wiki page as well as the second paper you recommended very useful. I could not access the first paper. But both these resources concentrated mainly on use of nanoparticles in solar cells. I specifically want to know about the applications and uses of plasmonic wire gratings. Where are they used ? How do they work ? Also please let mention any research paper on plasmonic wire grating specifically. I am trying to vary the study plasmonic wire gratings by varying their materials and the diameter of the wire. Thanking you, Vijay.
David Schäfer
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Posted: 1 decade ago Apr 17, 2013, 5:36 a.m. EDT
Hello Vijay,

But both these resources concentrated mainly on use of nanoparticles in solar cells.

The Pala paper is about rectangular wire gratings, as you can see from the abstract-picture.

I specifically want to know about the applications and uses of plasmonic wire gratings. Where are they used ? How do they work?

The idea of using plasmonic wire gratings and plasmonic nanoparticles in photovoltaics is basically the same. For example the plasmon resonances are used to couple in more radiation power into the cell by "bypassing" the (partially) reflecting air-substrate-interface. Also light scattering at the wires/particles can be used to achieve light trapping (enhancing the path length of photons in the absorbtion layer).

More papers here:
www.opticsinfobase.org/josaa/abstract.cfm?uri=josaa-19-1-101 (Moreno et al., Cylindrical wires)
www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-26-21793 (Catchpole et al., Particles)
apl.aip.org/resource/1/applab/v93/i19/p191113_s1 (Catchpole et al., Particles)

Kind regards
David
Hello Vijay, [quote]But both these resources concentrated mainly on use of nanoparticles in solar cells.[/quote] The Pala paper is about rectangular wire gratings, as you can see from the abstract-picture. [quote]I specifically want to know about the applications and uses of plasmonic wire gratings. Where are they used ? How do they work? [/quote] The idea of using plasmonic wire gratings and plasmonic nanoparticles in photovoltaics is basically the same. For example the plasmon resonances are used to couple in more radiation power into the cell by "bypassing" the (partially) reflecting air-substrate-interface. Also light scattering at the wires/particles can be used to achieve light trapping (enhancing the path length of photons in the absorbtion layer). More papers here: http://www.opticsinfobase.org/josaa/abstract.cfm?uri=josaa-19-1-101 (Moreno et al., Cylindrical wires) http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-26-21793 (Catchpole et al., Particles) http://apl.aip.org/resource/1/applab/v93/i19/p191113_s1 (Catchpole et al., Particles) Kind regards David
Vijay Ramakrishnan
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Posted: 1 decade ago Apr 17, 2013, 6:53 a.m. EDT
Hello David,

I thank you for clarifying that plasmonic wire grating is used for the same purpose as nanoparticles in photovoltaics.

I have 2 other queries:

1. Are there any other applications of plasmonic wire gratings other than photovoltaics ?

2. I want to know from where the model specifications and values of parameters for the device modeled in the 'plasmonic wire grating' example are taken.
Are the specification taken from any paper or already fabricated device ?

Thanking you,
Vijay.
Hello David, I thank you for clarifying that plasmonic wire grating is used for the same purpose as nanoparticles in photovoltaics. I have 2 other queries: 1. Are there any other applications of plasmonic wire gratings other than photovoltaics ? 2. I want to know from where the model specifications and values of parameters for the device modeled in the 'plasmonic wire grating' example are taken. Are the specification taken from any paper or already fabricated device ? Thanking you, Vijay.
Vijay Ramakrishnan
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Posted: 1 decade ago Apr 17, 2013, 8:28 a.m. EDT
Hello David,

I thank you for clarifying that plasmonic wire grating is used for the same purpose as nanoparticles in photovoltaics.

I have 2 other queries:

1. Are there any other applications of plasmonic wire gratings other than photovoltaics ?

2. I want to know from where the model specifications and values of parameters for the device modeled in the 'plasmonic wire grating' example are taken.
Are the specification taken from any paper or already fabricated device ?

Thanking you,
Vijay.
Hello David, I thank you for clarifying that plasmonic wire grating is used for the same purpose as nanoparticles in photovoltaics. I have 2 other queries: 1. Are there any other applications of plasmonic wire gratings other than photovoltaics ? 2. I want to know from where the model specifications and values of parameters for the device modeled in the 'plasmonic wire grating' example are taken. Are the specification taken from any paper or already fabricated device ? Thanking you, Vijay.

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