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Scattered field problems with oblique incident plane waves
Posted Apr 9, 2011, 2:13 p.m. EDT RF & Microwave Engineering Version 4.1, Version 4.4 11 Replies
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Hi
I need to simulate a square array of nanoparticles placed on top of a substrate and illuminated by a non normally impinging plane wave. The problem should be solved in a straightforward way in comsol 4.1 using the scattered field formulation. One just has to implement the Fresnel formula for reflection and refraction in order to specify the proper background field in absence of particle. All seems to work without the particle for any angle of incidence (If I check the scattered field this is correctly 0 everywhere). However if I now put in the particle I find out that the scattered field is correctly absorbed by the PML only in case of normal incidence.. Otherways I always find Fabry-Perot resonances within the air domain that indicate that the PMLs do not correcty absorb the scattered field.
Comsol support answered me in this way:
"The problem with the scattered field formulation is that it only works for
cases where the scatterer is entirely enclosed within a homogeneous medium.
It cannot directly be used to model situations where you have a an
interface between two infinite half spaces with different material
properties. Further, tuning a PML so that it will absorb a wide range of
angles of incidence well is not trivial so you need anyway to know
precisely what diffraction orders you excite."
Did anyone face this problem? Does anyone have suggestions?
The last comsol bug fix (march 2011) suggested to use ports and full field formulation instead of the scattered field formulation. Following the "plasmonic wire grating" example, one should define a port in order to correctly absorb each diffracted wave. However if this technique works fine in case of 2d models, it is to be noted that in case of 3d models one has to define a huge number of ports. Morever for each port one should specify the correct polarization for each diffracted wave and this is not always simple to know a priori (especially in case of grating placed on a substrate)..
Summarizing, is there a simple way to simulate square arrays of particles placed on a substrate with non normal illumination (in comsol 4.1)?
Any suggestions will be highly appreciated
Thanks
Pierfrancesco Zilio
I need to simulate a square array of nanoparticles placed on top of a substrate and illuminated by a non normally impinging plane wave. The problem should be solved in a straightforward way in comsol 4.1 using the scattered field formulation. One just has to implement the Fresnel formula for reflection and refraction in order to specify the proper background field in absence of particle. All seems to work without the particle for any angle of incidence (If I check the scattered field this is correctly 0 everywhere). However if I now put in the particle I find out that the scattered field is correctly absorbed by the PML only in case of normal incidence.. Otherways I always find Fabry-Perot resonances within the air domain that indicate that the PMLs do not correcty absorb the scattered field.
Comsol support answered me in this way:
"The problem with the scattered field formulation is that it only works for
cases where the scatterer is entirely enclosed within a homogeneous medium.
It cannot directly be used to model situations where you have a an
interface between two infinite half spaces with different material
properties. Further, tuning a PML so that it will absorb a wide range of
angles of incidence well is not trivial so you need anyway to know
precisely what diffraction orders you excite."
Did anyone face this problem? Does anyone have suggestions?
The last comsol bug fix (march 2011) suggested to use ports and full field formulation instead of the scattered field formulation. Following the "plasmonic wire grating" example, one should define a port in order to correctly absorb each diffracted wave. However if this technique works fine in case of 2d models, it is to be noted that in case of 3d models one has to define a huge number of ports. Morever for each port one should specify the correct polarization for each diffracted wave and this is not always simple to know a priori (especially in case of grating placed on a substrate)..
Summarizing, is there a simple way to simulate square arrays of particles placed on a substrate with non normal illumination (in comsol 4.1)?
Any suggestions will be highly appreciated
Thanks
Pierfrancesco Zilio
11 Replies Last Post Jan 22, 2016, 1:31 p.m. EST
Hello Pierfrancesco Zilio
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Posted:
1 decade ago
Hi
I'm facing with the same problem as you. Yes there is a way to solve this problem by using assembly. See the example in www.comsol.com/showroom/gallery/6141/, but the problem is that the model example is in COMSOL version 3.5, not v4.1. I was trying to realize this in v4.1 but not succeeded.
Have you solved your problem? could you please post it here if you've solved it in some simple way instead of using the way specified in the "plasmonic wire grating"? Thank you
Regards
Honghui
I'm facing with the same problem as you. Yes there is a way to solve this problem by using assembly. See the example in www.comsol.com/showroom/gallery/6141/, but the problem is that the model example is in COMSOL version 3.5, not v4.1. I was trying to realize this in v4.1 but not succeeded.
Have you solved your problem? could you please post it here if you've solved it in some simple way instead of using the way specified in the "plasmonic wire grating"? Thank you
Regards
Honghui
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Posted:
1 decade ago
I may be misunderstanding your problem, but if your array is infinite, you might want to try to applying Floquet type boundary conditions.
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Posted:
1 decade ago
It seems that in the new version of Comsol, 4.2.0.228, the problem does not appear any more. Probably it was a bug of previous versions of Comsol...
@Robert: the problem was that, despite we actually set Floquet boundary conditions, PMLs and proper background electric field, there was no way to obtain correct results in case of oblique incidence.
@Robert: the problem was that, despite we actually set Floquet boundary conditions, PMLs and proper background electric field, there was no way to obtain correct results in case of oblique incidence.
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Posted:
1 decade ago
As you said, if following the way in 'plasmonic wire grating', one has to set a lot of ports for reflection and transmission, which is not convenient especially for one who does not care intensity in each diffraction order.
how did tackle your problem? did you follow the 'plasmonic wire grating' to simulate 2D array of particle?
how did tackle your problem? did you follow the 'plasmonic wire grating' to simulate 2D array of particle?
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Posted:
1 decade ago
I set up a model using the scattered field formulation. Basically you draw a single period of your periodic model as in the 'plasmonic wire grating' example, placing a couple of PML above and below the grating and setting Floquet periodic boundary conditions at the two sides. Then you tell comsol to solve for the scattered field (Electromagnetic waves -> Settings -> "Solve for:" ). Then you have to specify the proper background electric field in the form that appears. If the grating (or array of nanoparticle) is embedded in vacuum then the background field is just the incident plane wave. If it is placed on a substrate you have to specify the field according to Fresnel laws (i.e. it is a superposition of incident, reflected and refracted fields). It works nicely, now also for non-normal incidence.
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Posted:
1 decade ago
Hi Pierfrancesco，
Thank you. yes you are right, we can use the way as you said when the background structure (the structure without particle) is consist of only two semi-infinite layer. But in some cases, e.g., the structure I have now is multilayer, which means between the two semi-infinite layers there are other layers too. In this case, it is not that easy to specify the incident field (back ground field).
In comsol 3.5, for this case we can use assembly to introduce a kind of a soft source to tackle the problem. but in comsol 4 and later versions, the way to introduce a soft source by assemble seems it is not implemented any more, instead they have the way specified in the 'plasmonic wire grating'.
and of course there is another way still using the scattered formula as you use, but instead to specify the background field analytically , one can use the comsol to calculate the background field numerically as the first step and then in the second step just follow the way you use. but this will take extra time for the first step.
Any way thanks a lot for sharing.
Thank you. yes you are right, we can use the way as you said when the background structure (the structure without particle) is consist of only two semi-infinite layer. But in some cases, e.g., the structure I have now is multilayer, which means between the two semi-infinite layers there are other layers too. In this case, it is not that easy to specify the incident field (back ground field).
In comsol 3.5, for this case we can use assembly to introduce a kind of a soft source to tackle the problem. but in comsol 4 and later versions, the way to introduce a soft source by assemble seems it is not implemented any more, instead they have the way specified in the 'plasmonic wire grating'.
and of course there is another way still using the scattered formula as you use, but instead to specify the background field analytically , one can use the comsol to calculate the background field numerically as the first step and then in the second step just follow the way you use. but this will take extra time for the first step.
Any way thanks a lot for sharing.
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Posted:
1 decade ago
Hi Pierfrancesco，
Thank you. yes you are right, we can use the way as you said when the background structure (the structure without particle) is consist of only two semi-infinite layer. But in some cases, e.g., the structure I have now is multilayer, which means between the two semi-infinite layers there are other layers too. In this case, it is not that easy to specify the incident field (back ground field).
In comsol 3.5, for this case we can use assembly to introduce a kind of a soft source to tackle the problem. but in comsol 4 and later versions, the way to introduce a soft source by assemble seems it is not implemented any more, instead they have the way specified in the 'plasmonic wire grating'.
and of course there is another way still using the scattered formula as you use, but instead to specify the background field analytically , one can use the comsol to calculate the background field numerically as the first step and then in the second step just follow the way you use. but this will take extra time for the first step.
Any way thanks a lot for sharing.
Hello Honghui Shen,
Thank you so much for sharing the other way of using the scattered formula! Would you please tell more details about how to implement the numerical background field?
Actually, I am facing a similar problem. I am using comsol 3.5a to simulate light (532 nm, Nd:YAG laser) scattering from a waveguide with a square cross-section (1 micrometer times 1 micrometer). The waveguide is made of polymer (refractive index 1.58) and it is supported by a layer of the same polymer with the thickness of 0.3 micrometer. Beneath the polymer layer, there is SiO2 substrate (refractive index 1.45). The case is modeled in a 2D geometry.
The effect of the infinite multilayer-ed substrate on the background field should be taken into account. However, it is not straightforward to get the analytical expression (Fresnel formulation) of the background field in the presence of the polymer layer and the SiO2 substrate. On the other hand, it is either incorrect to simply put a plane wave onto the whole structure including the scatter and the supporting layers since the supporting layers are then limited in later size and it also causes scattering.
I tried the mode of RF Module/In-Plane TE Waves/Scattered TE waves. I followed a 2-step procedure. First, I calculated the background field with the infinite supporting layers (by setting periodic boundary conditions) but without the scatter. Second, I stored the solution (Solve Manager/Store Solution) of the first step and then used it as an initial value (Solve Manager/Initial Values/Stored Solution) for the second-step calculation. However, I found this method not so correct because the initial value is not regarded as the excitation field by Comsol so that this 2-step calculation just gives the same result as simply putting a plane excitation wave, exp(-j*k0_rfweh*y), onto the scatter and the supporting layers which also serve as scatters due to its limited lateral size.
Fortunately, I found your helpful comment in this discussion thread. Would you please give me some suggestions on how to set the numerical background field? Thank you so much!
Sincerely,
Jing Zhou
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Posted:
1 decade ago
Hi,
Thank you for your discussion about this problem.
I appreciate if you can explain a little bit more about background electric field.
I am going to calculate reflection off the interface between Air and Si. Both air and Si are semi-infinite. I am going to use PML (I know how to find it by port and full filed) and scattered field method.
As you said I put " Ex=0, Ey=0, Ez= E0*exp(-j*emw.k0*na*y)+rs*E0*exp(-j*emw.k0*na*y)+ts*E0*exp(-j*emw.k0*nb*y)" as my background field. Ez is the superposition of incident, reflected and transmitted fields. Direction of propagation is y and the incident field is normal to the interface of air-Si.
rs = (na-nb)/(na+nb) and ts= 2na/(na+nb) are respectively reflection and transmission coefficients in normal incident angle from Fresnel equation, where, na=1, nb=3.48.
I calculate reflected power and it gives me negative values and reflection is strange. It should be 0.3, but it is not.
Am I inserting background field in a wrong way?
Thanks,
Mohammad
Thank you for your discussion about this problem.
I appreciate if you can explain a little bit more about background electric field.
I am going to calculate reflection off the interface between Air and Si. Both air and Si are semi-infinite. I am going to use PML (I know how to find it by port and full filed) and scattered field method.
As you said I put " Ex=0, Ey=0, Ez= E0*exp(-j*emw.k0*na*y)+rs*E0*exp(-j*emw.k0*na*y)+ts*E0*exp(-j*emw.k0*nb*y)" as my background field. Ez is the superposition of incident, reflected and transmitted fields. Direction of propagation is y and the incident field is normal to the interface of air-Si.
rs = (na-nb)/(na+nb) and ts= 2na/(na+nb) are respectively reflection and transmission coefficients in normal incident angle from Fresnel equation, where, na=1, nb=3.48.
I calculate reflected power and it gives me negative values and reflection is strange. It should be 0.3, but it is not.
Am I inserting background field in a wrong way?
Thanks,
Mohammad
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Posted:
1 decade ago
I either tried Ex=0, Ey=0, Ez= E0*exp(-j*emw.k0*na*y)+rs*E0*exp(j*emw.k0*na*y)+ts*E0*exp(-j*emw.k0*nb*y)
and Ex=0, Ey=0, Ez= E0*exp(-j*emw.k*y)+rs*E0*exp(j*emw.k*y)+ts*E0*exp(-j*emw.k*y)
but I can not get right reflection.
For reflected power calculation I define a surface in incident side and integrate emw.Poavy over that surface.
Then I subtract it from incident power (integral of ((1/2)*(E0)^2/Z0 over the same surface). Finally I divide reflected power over incident power to find reflection.
I appreciate if somebody answer help me to figure out this problem.
Thanks,
Mohammad
and Ex=0, Ey=0, Ez= E0*exp(-j*emw.k*y)+rs*E0*exp(j*emw.k*y)+ts*E0*exp(-j*emw.k*y)
but I can not get right reflection.
For reflected power calculation I define a surface in incident side and integrate emw.Poavy over that surface.
Then I subtract it from incident power (integral of ((1/2)*(E0)^2/Z0 over the same surface). Finally I divide reflected power over incident power to find reflection.
I appreciate if somebody answer help me to figure out this problem.
Thanks,
Mohammad
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Posted:
9 years ago
Mohammad, you write that you define
Ex=0, Ey=0, Ez= E0*exp(-j*emw.k0*na*y)+rs*E0*exp(j*emw.k0*na*y)+ts*E0*exp(-j*emw.k0*nb*y)
so the field is given by the superposition of incident field, reflected field and transmitted field. However, the incident and reflected field should only apply to the incident region whereas on the other side of the interval, only the transmitted field applies. So, to my understanding, one needs to define the background field as a piecewise function of y.
Does anybody know, how to implement such a piecewise background field?
Ex=0, Ey=0, Ez= E0*exp(-j*emw.k0*na*y)+rs*E0*exp(j*emw.k0*na*y)+ts*E0*exp(-j*emw.k0*nb*y)
so the field is given by the superposition of incident field, reflected field and transmitted field. However, the incident and reflected field should only apply to the incident region whereas on the other side of the interval, only the transmitted field applies. So, to my understanding, one needs to define the background field as a piecewise function of y.
Does anybody know, how to implement such a piecewise background field?
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Posted:
9 years ago
Hello All,
This thread is being closed down for further comments as it is primarily discussing some limitations of an older version of COMSOL (version 4.1) that have been fixed for quite some time. We do encourage all of our users to upgrade to the latest version of the software, currently version 5.2.
With regards to the technical questions raised in this thread, we first suggest that all of the following material be reviewed:
www.comsol.com/model/frequency-selective-surface-periodic-complementary-split-ring-resonator-15711
www.comsol.com/model/plasmonic-wire-grating-10032
www.comsol.com/model/fresnel-equations-12407
www.comsol.com/model/modeling-of-pyramidal-absorbers-for-an-anechoic-chamber-12129
www.comsol.com/model/hexagonal-grating-rf-22341
www.comsol.com/model/scatterer-on-a-substrate-14699
www.comsol.com/blogs/modeling-electromagnetic-waves-periodic-structures/
This material addresses the questions which are raised in this thread. If there are related questions, please feel free to open a new thread. This thread will remain visible, but closed for further comments.
Best Regards,
This thread is being closed down for further comments as it is primarily discussing some limitations of an older version of COMSOL (version 4.1) that have been fixed for quite some time. We do encourage all of our users to upgrade to the latest version of the software, currently version 5.2.
With regards to the technical questions raised in this thread, we first suggest that all of the following material be reviewed:
www.comsol.com/model/frequency-selective-surface-periodic-complementary-split-ring-resonator-15711
www.comsol.com/model/plasmonic-wire-grating-10032
www.comsol.com/model/fresnel-equations-12407
www.comsol.com/model/modeling-of-pyramidal-absorbers-for-an-anechoic-chamber-12129
www.comsol.com/model/hexagonal-grating-rf-22341
www.comsol.com/model/scatterer-on-a-substrate-14699
www.comsol.com/blogs/modeling-electromagnetic-waves-periodic-structures/
This material addresses the questions which are raised in this thread. If there are related questions, please feel free to open a new thread. This thread will remain visible, but closed for further comments.
Best Regards,