I'm working on Electro-optic devices in Comsol 4.4.
Part of the solution are surface plots of the electric field. The shape of the field distribution is dictated by the specific eigenvalue problem; however, the actual values given by COMSOL are quite arbitrary. How then, does COMSOL determine what numbers to give in the solution for field components, power, etc.?
Is there any physical basis to perform normalization?
Does anybody know how to perform normalization to have proper values?
Thank you.
Hi Kamal,
actually it's quite easy to get the mode shape and there is no need to export the file in matlab, but since Comsol use arbitrary values for the amplitudes, those are not real field values. It is necessary to normalize them in order to perform further calculation i.e. overlap integral. I've been trying with different normalizations, i.e. total energy density, maximum value of the field but still not getting what I was expecting.
In comsol compute the integral of conj(u)*u over the domain, where u is the eigenfunction and conj is the complex conjugate, then divide your solution u by the value of the integral.
Edit: have you an eigenvalue problem or a generalized eigenvalue problem?
Hi Fabio,
I'm actually doing modal analysis ( that is an eigen value analysis) using Wave Optics module (or RF module). To make things more clear, I'm getting the right mode and mode shape but not real amplitudes. My final goal is to calculate the overlap integral between the E-field of my mode (Wave Optics) and an applied electric field (calculated using static AC/DC solver). I've been trying to normalize the amplitudes using the total energy density, and also the integral of normE (as you suggest) but I'm not getting what I'm expecting. It seem that there's a multiplication factor somewhere...
the normalization factor is related to the problem you are solving. I cannot understand what is your problem, could you write the equations and the quantity do you want to estimate?
What I'm trying to calculate is the overlap itegral as described in the paper attached.
I get same mode shape and effective refractive index but I'm not convinced of the results presented in Fig 1e
Possibly is a question of normalization but I'm not sure.
Ok Domenico, as far as I can understand you're solving two equations. One for the optical field (Eopt) and the other for the RF field (Emod). Since the integral Gamma it contains Eopt^2 at num/den you do not need to take care about Eopt. Therefore, the normalization problem (if) concerns with Emod. Just to be sure that comsol returns normalized eigenfunctions, here attached you find a mph file that compute a generalized eigenvalue problem in weak form, and as you can see from the 1d plot of var1=intop1(u^2), the eigenfunctions are normalized to 1 (within numerical error). So I guess is not a problem about normalization. You can change the coefficient for the laplacian and the 'lambda' in the weak form and check by yourself. Any other idea?
Dear Fabio,
firstly thank you for taking your time to reply. You are right about Eopt. I've actually seen that the values of Emod calculated by COMSOL are greater of what I can expect by analyzing the structure. The max Emod I can expect is given by the Voltage applied over the electrode gap, considering just air in between. So possibly as you suggested I've to work on this normalization. Thank you for the support. I'll let you know.
Hi Fabio,
just to let you know that the difference in my simulation compared to the paper, was actually due to the relative permittivity of thedielectric, since they don't tell and there is uncertainty in literature and it varies a lot with frequency.
Anyhow, thanks for the help.
Best Regards,
Domenico
An eigenvalue analysis gives you the eigenvalues and the eigenmodes, however the value of primary variables are arbitrary. To find the correct value of primary variables at a particular natural frequency, a "Frequency domain" analysis should be performed and the excitation frequency should be the natural frequency at which the values are desired.
Hope you find it useful.
Hi,
you can define a normalized variable using the answers. Lets say the position dependent answers of your PDE (e.g. Schrödinger equation ) are {u} a long with Eigenvalues. you can define u_normalized=u/sqrt(intop1(u^2)). In which "intop1" is an integral operator that you already added to the "Component"/"Definition".
good luck
- Badges
- Science topic