# Discussion Forum

Note: This discussion is about an older version of the COMSOL Multiphysics® software. The information provided may be out of date.

## 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

31 Replies Last Post Jul 8, 2017, 3:57 PM EDT
Posted: 5 years ago

Posted: 5 years ago
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.

Posted: 5 years ago
www.rp-photonics.com/optical_intensity.html

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

Posted: 5 years ago
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

Posted: 5 years ago
I use the formula which Yevgeniy Davletshin mentioned before to calculate the scatter crossection.

Posted: 5 years ago
Can you write the exact expression you use to do the integral, as you write it in COMSOL? Thank you

Posted: 5 years ago
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?

Posted: 5 years ago
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.

Posted: 5 years ago
Look how Comsol defined different eq. and define your own based on the COmsol syntax.

Posted: 5 years ago

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.

Posted: 5 years ago
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.

Posted: 5 years ago

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]

Posted: 5 years ago
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.

Posted: 5 years ago
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,

Posted: 5 years ago

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

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.

Best regards
Wu

Posted: 5 years ago
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.

Posted: 5 years ago
Delete mesh sequence and try default meshing

Posted: 5 years ago

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.

Posted: 5 years ago

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!

Posted: 5 years ago
Update Comsol 4.3a library there is a new model Scatterer on substrate.

Posted: 5 years ago
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

Posted: 5 years ago
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)))

Posted: 5 years ago
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

Posted: 5 years ago
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

Posted: 4 years ago

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

Posted: 4 years ago

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

Posted: 2 years ago

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)))

Hello Yevgeniy,

I recently read your article "Modeling the optical properties of a single gold nanorod for use in biomedical applications" and I found it very helpful. So thank you very much. But I have a question concerning about the model. Since I am only trying to model gold nanorods in homogeneous environment, I used the "Scatterer on Substrate" (www.comsol.com/model/scatterer-on-substrate-14443) as an starting point. I believe this model solves the total field first and then introduce the scatterer. I managed to model gold nanosphere with the help of this model. The SPR position and amplitude showed up just fine. However, when I only changed the geometry to gold nanorod, the numbers are totally off. I checked the polarization and I have already aligned the rod with the polarization direction. So I am really struggling to understand what went wrong in my model. Hopefully you can offer me some insights on this. Thank you very much in advance!

Posted: 12 months ago
Hi Jeremy,

Would you happen to still have a copy of the nanosphere on a substrate simulation model?
Mind if I take a look?

Posted: 12 months ago
Hello Grace,

There seem to be a couple of out-of-date links in some of these older comments in this thread.
The discussion here seems to be related to these two application examples:

www.comsol.com/model/scatterer-on-a-substrate-14699

www.comsol.com/model/optical-scattering-by-gold-nanospheres-14697

Best Regards,

Posted: 3 months ago
Hi

I want simulate gold nano-sphere (also nano-particle in general with other shapes) on a substrate of glass or silicon. I already simulated gold and silver nano-sphere with homogeneous surrounding but for the substrate case I failed to simulate using COMSOL 5.1. I found an example 'scatterer on substrate' but in the case of nano-sphere I cant follow that model. Also in that model, perfectly matched layers are as a block. I want to know, how spherical perfectly matched layers can be modeled using that 'scatterer on substrate' project and how to simulate nano-spheres on a substrate using COMSOL.

Posted: 2 months ago
#Arpan - For a scatterer on a substrate i would suggest using a rectangular simulation domain rather than a spherical one. You should then add PMLs on top/bottom (where the excitation wave enters/exists). The sides should be first order SBC or PML depending on the size of your simulation domain and the amount of light scattered by the scatterer. Finally, rather than the full-field formulation, you should use the scattering-field formulation with the background field evaluated analytically from the Fresnel reflection formulas (for a bare substrate it's simple enough to do by hand).