Discussion Forum

Caveats: First, I'm pretty sure there is more than one way to address this problem. Second, what I suggest may not necessarily be the best way, but it is almost guaranteed to work. OK, so here's my suggestion, which leverages superposition.
1. Create the full model, including the dipole source, dielectric body, material specifications, mesh, etc. Make sure your outermost/distant (absorbing/scattering) computational boundaries are far enough away from where all the important physics is (i.e., so that those boundaries do not perturb the model too much.) 2. Solve for the fields everywhere. Store the result. (There are various ways to do this, whether within the Comsol framework or, if worse comes to worst, you can always export various slices or cuts to a disk file, of the values of fields in various locations of interest to you.) 3. Now for the slightly clever part: Change the material properties of the subject dielectric body to match those of free space. Do NOT change the geometry or mesh (do not remesh!) This effectively removes the dielectric from the problem without perturbing the discretization or organization of the field data in any way.
4. Solve for the total field everywhere, again. You may wish (or need) to store this data set too. 5. Now, to find the "induced field acting on the dipole" that you mentioned in your question, subtract the second set of stored fields (the dipole in free space case) from the first (the dipole near dielectric body). Depending on how you implement this process, you can either accomplish the required subtraction of the fields entirely within the Comsol environment or by working with exported data. I hope that helps. {Note: Prior to Comsol's introduction of the "scattered wave" formalism in the RF module, the above process was a useful way to look at scattered fields in planewave-incident-on-a-target models. But (of course) if you are working with planewaves, using the included scattered wave formalism is preferable. But the question here has a dipole illumination, so we return to basics. And, to anyone who wants to check how well my suggested approach above works, I encourage you to compare it with what you get (for a planewave incident problem of your choice) using Comsol's wave scattering formalism.}

Caveats: First, I'm pretty sure there is more than one way to address this problem. Second, what I suggest may not necessarily be the best way, but it is almost guaranteed to work. OK, so here's my suggestion, which leverages superposition.
1. Create the full model, including the dipole source, dielectric body, material specifications, mesh, etc. Make sure your outermost/distant (absorbing/scattering) computational boundaries are far enough away from where all the important physics is (i.e., so that those boundaries do not perturb the model too much.) 2. Solve for the fields everywhere. Store the result. (There are various ways to do this, whether within the Comsol framework or, if worse comes to worst, you can always export various slices or cuts to a disk file, of the values of fields in various locations of interest to you.) 3. Now for the slightly clever part: Change the material properties of the subject dielectric body to match those of free space. Do NOT change the geometry or mesh (do not remesh!) This effectively removes the dielectric from the problem without perturbing the discretization or organization of the field data in any way.
4. Solve for the total field everywhere, again. You may wish (or need) to store this data set too. 5. Now, to find the "induced field acting on the dipole" that you mentioned in your question, subtract the second set of stored fields (the dipole in free space case) from the first (the dipole near dielectric body). Depending on how you implement this process, you can either accomplish the required subtraction of the fields entirely within the Comsol environment or by working with exported data. I hope that helps. {Note: Prior to Comsol's introduction of the "scattered wave" formalism in the RF module, the above process was a useful way to look at scattered fields in planewave-incident-on-a-target models. But (of course) if you are working with planewaves, using the included scattered wave formalism is preferable. But the question here has a dipole illumination, so we return to basics. And, to anyone who wants to check how well my suggested approach above works, I encourage you to compare it with what you get (for a planewave incident problem of your choice) using Comsol's wave scattering formalism.}

Hi Robert, thank you for the suggestion. I actually have tried this approach but didn't get sensible results. I suspect that's due to the fact that the field at the dipole position is divergent in theory. Numerically I'm not sure how it's handled in COMSOL but it might cause issue when using this approach.

Do you know other way where you can calculate the indiced field from quantities such as polarization density?

Hi Tom,

check the constitutive relations in es. You may consider to first calculate the complete model with the dipole and then use the displacement in the dielectric in a second model without the dipole.

Cheers Edgar

Hi Tom,

check the constitutive relations in es. You may consider to first calculate the complete model with the dipole and then use the displacement in the dielectric in a second model without the dipole.

Cheers Edgar

Hi Edgar,

Thank you for the sugguestion. Could you please ellaborate a little more? How does that relate to the induced electric field at the dipole position?

The induced field should result from the polarization or displacement in the dielectric, no?

I've attached an example. No intermediate file storage necessary. Two solutions found, just like I said. Then subtract one from the other. See the animations in the export section, to observe animations of the wave scattering (from the dielectric) of the Ey component or Hz component (pick one of the two to enable). You can easily see how to look at other field differences, such as between the Ex components. You might want to use a larger computational region to avoid errors arising from the boundaries.