Mie scattering in 4.3

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João Azevedo

João Azevedo

January 7, 2013 1:44pm UTC

Mie scattering in 4.3

Hello,
I have already seen some discussion about mid scattering of a gold nanosphere. But I the discussions I have consulted, no one has yet implemented a mie scattering program in Comsol 4.2 or 4.3 that works as the one in 3.5. Has this problem been solved yet? Can anyone post the correct program here?
Thank you very much for the help

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Yevgeniy Davletshin

Yevgeniy Davletshin

January 7, 2013 5:33pm UTC in response to João Azevedo

Re: Mie scattering in 4.3

www.comsol.com/showroom/documentation/model/12415/

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João Azevedo

João Azevedo

January 9, 2013 4:57pm UTC in response to Yevgeniy Davletshin

Re: Mie scattering in 4.3

Ok, I have seen that script but the thing is, I can't plot the scattering vs. wavelength as in the script shown for 3.5. I mean, I think it should be possible but I do you do it? I want to plot the extintion vs. wavelength I can't seem to figure it out.
Thank you for your help in advance.

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Yevgeniy Davletshin

Yevgeniy Davletshin

January 9, 2013 5:10pm UTC in response to João Azevedo

Re: Mie scattering in 4.3

www.rp-photonics.com/optical_intensity.html

Define optical intensity and then use it for calculation of absorption and scattering or attenuation cross-sections.



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João Azevedo

João Azevedo

January 9, 2013 10:17pm UTC in response to Yevgeniy Davletshin

Re: Mie scattering in 4.3

Once again thank you for the quick reply. Let me be a little more precise about my problem. I used the exact same script as the model in COMSOL for scaterring and in the absorption we see a peak, as expected, around 500nm (see Fig.1). For the scattering plot, what I did was integrate over a surface the Far Field norm (emw.normEfar) and plot it against lambda. (see Fig2 for integration surface and Fig3 for scattering vs. lambda) and no peak is observed. This is unexpected and it represents my problem. So how can I calculate the scattering over a gold nanosphere and plot it vs. lambda?
Thank you very much for any help

Attachments:   Fig1.png   Fig2.png   Fig3.png  

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Richie Guo

Richie Guo

January 10, 2013 7:10am UTC in response to João Azevedo

Re: Mie scattering in 4.3

I use the formula which Yevgeniy Davletshin mentioned before to calculate the scatter crossection.

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João Azevedo

João Azevedo

January 10, 2013 2:07pm UTC in response to Richie Guo

Re: Mie scattering in 4.3

Can you write the exact expression you use to do the integral, as you write it in COMSOL? Thank you

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Nicola Basili

Nicola Basili

January 16, 2013 9:15am UTC in response to João Azevedo

Re: Mie scattering in 4.3

I am also interested in this topic. you have found a solution to graph the cross section of extinction vs. wavelength?
How do I write the formulas of COMSOL?

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João Azevedo

João Azevedo

January 16, 2013 10:12am UTC in response to Nicola Basili

Re: Mie scattering in 4.3

Honestly I do not know how. I have been surfing the web for an answer but so far no one has give me a good answer. They always direct me to a model already existing but I do not see a way to obtain a plot of scattering vs. wavelength. I tried to integrate the far field norm across a surface that includes the nanosphere but I do not see any resonance. If you have problems in integrating the far field I can help, but it won't solve your problem. Sorry for not giving you an answer you wanted.

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Yevgeniy Davletshin

Yevgeniy Davletshin

January 17, 2013 2:13pm UTC in response to João Azevedo

Re: Mie scattering in 4.3

Look how Comsol defined different eq. and define your own based on the COmsol syntax.

Attachments:   formulars.png  

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Yevgeniy Davletshin

Yevgeniy Davletshin

January 17, 2013 2:15pm UTC in response to João Azevedo

Re: Mie scattering in 4.3


Honestly I do not know how. I have been surfing the web for an answer but so far no one has give me a good answer. They always direct me to a model already existing but I do not see a way to obtain a plot of scattering vs. wavelength. I tried to integrate the far field norm across a surface that includes the nanosphere but I do not see any resonance. If you have problems in integrating the far field I can help, but it won't solve your problem. Sorry for not giving you an answer you wanted.


For mie theory you need to use scattering in near field. Define eq. that I specified earlier.

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João Azevedo

João Azevedo

January 17, 2013 2:52pm UTC in response to Yevgeniy Davletshin

Re: Mie scattering in 4.3

Can you provide some assistance as on how to define those equations? The first part of both equations are constants, so no problem there. I know how to define an integral in volume and in surface. Now come the questions:

- How do I extract the real/imaginary part of a function?
- Do you use emw.Ex, emw.Ey, emw.Ez and emw.Mx, emw.My, emw.Mz for E and H?
- To define D do you use emw.Px, emw.Py, emw.Pz?
- How do you define sigma(w)? I assumed it was used sigma=0 for the gold.
- How do you define Escat and Hscat? I assumed it was the Efar but there is no Hfar in COMSOL...
- What is the surface you use to integrate the Escat and Hscat? How far away from the sphere?

Sorry for the insistence in the topic and for any stupid questions but I am really trying hard to get a good result in this simulation.

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Yevgeniy Davletshin

Yevgeniy Davletshin

January 17, 2013 10:37pm UTC in response to João Azevedo

Re: Mie scattering in 4.3


Can you provide some assistance as on how to define those equations? The first part of both equations are constants, so no problem there. I know how to define an integral in volume and in surface. Now come the questions:

- How do I extract the real/imaginary part of a function? [Type in the Help menu Mathematical functions]
- Do you use emw.Ex, emw.Ey, emw.Ez and emw.Mx, emw.My, emw.Mz for E and H? [Ey - is the full field, Eby - background field (incident), Erel - scattered field]
- To define D do you use emw.Px, emw.Py, emw.Pz? [emw.Dx = epsilon0_const*emw.Ey+emw.Py and is predifined already]
- How do you define sigma(w)? I assumed it was used sigma=0 for the gold.
[what sigma?]
- How do you define Escat and Hscat? [Escat =Erel] I assumed it was the Efar but there is no Hfar in COMSOL...
- What is the surface you use to integrate the Escat and Hscat? How far away from the sphere? [up to you]



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João Azevedo

João Azevedo

January 18, 2013 2:27pm UTC in response to Yevgeniy Davletshin

Re: Mie scattering in 4.3

First of all, thank you so much. I can now see a resonance peak at the right spot. However I have some final questions:

Scattering cross section:
- in the integral you wrote Re(Escat - H*scat): Do you mean norm(Re(Erelx-H*relx, Erely-H*rely, Erelz-H*relz)) ?

Absorption cross section:
- you wrote a sigma(omega) term. What is that and if it is the electric conductivity of air, where do you find the dependence of frequency? Is it not just 0?

Once again thank you for you patience and help.

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João Azevedo

João Azevedo

January 27, 2013 9:22pm UTC in response to Yevgeniy Davletshin

Re: Mie scattering in 4.3

Hello Yevgeniy,
I have received some emails asking me if I was already able to plot the absorption and scattering cross sections of a gold sphere, so I know that this is a topic of general interest. As I said in the last post I was already able to obtain a resonance peak of the scattering cross section. Nevertheless the values don't correspond to the Mie values obtained for the COMSOL 3.5 version. I send an attachment with my results and the expressions I used.

I only defined in Parameters: E_inc as 1[V/m] and introduced the expressions for the cross sections in Definitions - Variables.

You can see the expected and obtained results, together with the expressions I used. Can you please comment on these for the general community? We would all appreciate.

Best regards,

Attachments:   Results.pdf  

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YH Wu

YH Wu

January 28, 2013 10:23am UTC in response to Yevgeniy Davletshin

Re: Mie scattering in 4.3



Hello Yevgeniy,

i´ve download this model files for Optical Scattering off of a Gold Nanosphere. However when i computed it again without any modification, error showed up:

Failed to find a solution.
Singular matrix.

For mesh-case 0 there are 2559 void equations (empty rows in matrix) for the variable mod1.E10.
at coordinates: (-3.55412e-007,3.20064e-008,3.4014e-008), (-3.75157e-007,3.37845e-008,3.59036e-008), (-3.57706e-007,1.60032e-008,1.7007e-008), (-3.77578e-007,1.68923e-008,1.79518e-008), (-3.52579e-007,5.79241e-008,3.4014e-008), ...
For mesh-case 0 there are 859 void equations (empty rows in matrix) for the variable mod1.E20.
at coordinates: (-3.54874e-007,4.19209e-008,1.7007e-008), (-3.74589e-007,4.42498e-008,1.79518e-008), (-3.4612e-007,8.05201e-008,4.01212e-008), (-3.65349e-007,8.49934e-008,4.23502e-008), (-3.94304e-007,4.65788e-008,1.88966e-008), ...
For mesh-case 0 there are 862 void equations (empty rows in matrix) for the variable mod1.E21.
at coordinates: (-3.54874e-007,4.19209e-008,1.7007e-008), (-3.74589e-007,4.42498e-008,1.79518e-008), (-3.4612e-007,8.05201e-008,4.01212e-008), (-3.65349e-007,8.49934e-008,4.23502e-008), (-3.94304e-007,4.65788e-008,1.88966e-008), ...
and similarly for the degrees of freedom (empty columns in matrix).
Returned solution is not converged.

have you got any idear about this error, thanks very much!
Best regards
Wu

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Yevgeniy Davletshin

Yevgeniy Davletshin

January 30, 2013 4:03pm UTC in response to João Azevedo

Re: Mie scattering in 4.3

Abs cross-section is just (emw.Qrh/I0) ( so replace it with const*int_L(emw.Qrh)) if you are using something other than Air then you need to scale it by refractive index.

For scattering I defined it a little bit different than Comsol in attached file below, so follow Comsol documentation to be safe.
Sorry I didn't realized that Comsol deleted 3.5 documentation.

in 3.5 scE = relE in 4.2


For scaling background E field, use E0*exp(-j*emw.k0*n_inc*z) or E0*exp(-j*emw.k*z) that should give you same results.




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Yevgeniy Davletshin

Yevgeniy Davletshin

January 30, 2013 4:04pm UTC in response to YH Wu

Re: Mie scattering in 4.3

Delete mesh sequence and try default meshing

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João Azevedo

João Azevedo

February 5, 2013 3:59pm UTC in response to Yevgeniy Davletshin

Re: Mie scattering in 4.3


Abs cross-section is just (emw.Qrh/I0) ( so replace it with const*int_L(emw.Qrh)) if you are using something other than Air then you need to scale it by refractive index.


It is true. Thank you. The problem with absorption is solved.


For scattering I defined it a little bit different than Comsol in attached file below, so follow Comsol documentation to be safe.
Sorry I didn't realized that Comsol deleted 3.5 documentation.

in 3.5 scE = relE in 4.2


I have been surfing the web and there are many forums with people trying to implement the 3.5 documentation with no success, so I am looking for alternatives. Have I defined correctly the expression for scattering according to your definition? Do you obtain similar results to those in 3.5? Can you provide the expression as written in COMSOL?


For scaling background E field, use E0*exp(-j*emw.k0*n_inc*z) or E0*exp(-j*emw.k*z) that should give you same results.


Can you please explain this sentence? What exactly should I do?

I know that it is not your job to teach this but we are so close to a final solution for absorption and scattering cross sections in COMSOL 4.2 that it would be a shame not to clarify this. Thank you in advance.

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YH Wu

YH Wu

February 6, 2013 9:10am UTC in response to Yevgeniy Davletshin

Re: Mie scattering in 4.3


Delete mesh sequence and try default meshing


Thank you for your help! I have tried the Mesh settings as "Physics-controlled mesh" with "Finer" Element size, but it Plot a different curve. Does the Mesh setting have such a big influence on the final results? Thanks again!

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Yevgeniy Davletshin

Yevgeniy Davletshin

February 15, 2013 6:27pm UTC in response to YH Wu

Re: Mie scattering in 4.3

Update Comsol 4.3a library there is a new model Scatterer on substrate.

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Hassanain Al-Taiy

Hassanain Al-Taiy

March 13, 2013 9:59am UTC in response to Yevgeniy Davletshin

Re: Mie scattering in 4.3

Dear All


i hope that you are well, thanksssssssss allot for these information, i want to simulate the brillouin scattering in a silicon nano-wave guide surrounding by air, the idea is the interaction between the optical field withe the acoustic wave inside the silicon wave guide i.e the interaction between the pump wave with Stoke wave, please if you have any suggestions, should i use PDE or PMl or other thinks to simulate the scattering.


Best Regards

Attachments:   Waveguide.jpg  

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Yevgeniy Davletshin

Yevgeniy Davletshin

March 13, 2013 3:40pm UTC in response to Hassanain Al-Taiy

Re: Mie scattering in 4.3

The only question is:
How will you define optical properties of your waveguide?
If you for example, you are solving Acoustic-structure interaction in time-domain and obtaining time-dependent density variations, then you can couple it to stationary RF model where optical properties of your waveguide is density dependent (analytical function n(ast.rho(time)))

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Hassanain Al-Taiy

Hassanain Al-Taiy

March 14, 2013 9:54am UTC in response to Yevgeniy Davletshin

Re: Mie scattering in 4.3

Dear Davletshin


thanksssssssss allot for your reply, i will attach to you my model, in simple words it is the interaction between the optical field (photons) and the acoustic field (phonons), so light (pump photons) will be scattered by the phonons (stoke), this is called brillouin scattering but how can i model this, i can not find it until now, i just get the optical mods but not the acoustic modes.


Best Regards

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Hassanain Al-Taiy

Hassanain Al-Taiy

March 14, 2013 11:51am UTC in response to Yevgeniy Davletshin

Re: Mie scattering in 4.3

Dear Davletshin


you told me to couple the acoustic mode with the stationary Rf model, how can i do the coupling, do you mean that i should use a single stationary (study) for both RF and acoustic model, or i must change something in the (solve for) inside the study setting.



Best regards

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Hassanain Al-Taiy

Hassanain Al-Taiy

April 9, 2013 8:08am UTC in response to Yevgeniy Davletshin

Re: Mie scattering in 4.3


The only question is:
How will you define optical properties of your waveguide?
If you for example, you are solving Acoustic-structure interaction in time-domain and obtaining time-dependent density variations, then you can couple it to stationary RF model where optical properties of your waveguide is density dependent (analytical function n(ast.rho(time)))


Dear Davletshin

i tried to get the density fluctuation from the time dependent or frequency dependent studies but i get a fixed value for the density, i think i should get the fluctuation and then multiply by the refractive index (3.5) and then i put it as a diagonal refractive index in the wave equation of the RF, please if you have any idea ?


Best Regards

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Hassanain Al-Taiy

Hassanain Al-Taiy

April 9, 2013 8:28am UTC in response to Hassanain Al-Taiy

Re: Mie scattering in 4.3



The only question is:
How will you define optical properties of your waveguide?
If you for example, you are solving Acoustic-structure interaction in time-domain and obtaining time-dependent density variations, then you can couple it to stationary RF model where optical properties of your waveguide is density dependent (analytical function n(ast.rho(time)))


Dear Davletshin

i tried to get the density fluctuation from the time dependent or frequency dependent studies but i get a fixed value for the density, i think i should get the fluctuation and then multiply by the refractive index (3.5) and then i put it as a diagonal refractive index in the wave equation of the RF, please if you have any idea ?


Best Regards



Dear Davletshin


i attached to you the wave guide pic just to see it and may it helps you to think in way with me to solve the problem.


best regards

Attachments:   waveguide.jpg  

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