Discussion Forum

Could the "expression" in the "plot" be written as "ewfd.Ex+i*ewfd.Ey"?

If you enter a complex expression, then it's the real part that is plotted. What kind of plot are you trying to create?

Thanks Gunnar,

As you say, I entered a complex expression of incident electric field of circular polarization, which is expressed as E0x=1, E0y=i, E0z=0 in COMSOL, and the polarization state of transmitted electric field is same. I am trying to plot this transmitted electric field with circular polarization state, but I can only find the "expression", such as "ewfd.Ex", "ewfd.Ey" or "ewfd.normE" in COMSOL. Could you do me a favor?

you mean I plotted the real part of electric field of E0x=1, E0y=i, E0z=0?

you mean I plotted the real part of electric field of E0x=1, E0y=i, E0z=0?

Yes, I think so.

Thanks Gunnar,

If I use the options like "ewfd.Ex" and "ewfd.Ey" in COMSOL, that means I plot the X or Y component of electric filed. Now I want plot total electric filed of circular polarized light, what should I do?

That depends on what aspect of circularly polarized light you want to capture.

The electric field components (in 3D to be general), ewfd.Ex, ewfd.Ey, ewfd.Ez are complex numbers and when plotting any of those as for example color or , more naturally, all as an arrow plot, what you see is the real part.

To see how the electric field varies in time (as a function of phase) you can choose to animate the arrow plot (add an animation->player under the export node, point it to the desired plot group and use "dynamic data extension" for sequence type). The animation will then show the expected rotating arrows provided that you have excited the model so that the polarization is circular, e.g. by using crossed dipoles that are 90 degrees out of phase.

If you choose to instead plot the electric field norm: "ewfd.normE", that is defined equivalently to

sqrt(abs(ewfd.Ex)^2+abs(ewfd.Ey)^2+abs(ewfd.Ez)^2)

which is the complex vector norm. This will not change when animating the solution.

If you are after the real, instantaneous vector norm, you can instead manually type in the plot expression

sqrt(real(ewfd.Ex)^2+real(ewfd.Ey)^2+real(ewfd.Ez)^2)

For circularly polarized light, this will be constant when animating (as described above) as the length of the E vector is independent of phase. For linearly polarized light, you will see oscillations.

If you just want to compare the relative phase of quantities, you will get the phase angle (in radians) by using the "arg" operator. Eg, plotting:

arg(ewfd.Ex)-arg(ewfd.Ey)

will display the phase difference (in radians) between the x and y components of E. For circularly polarized light, that should be close to +/-pi/2 - and abs(ewfd.Ex) should be close to abs(ewfd.Ey) as otherwise you have elliptically polarized light.

Best regards,

--
Magnus

Thanks Magnus,

Thank you for your detailed solution, now I understand the implication of "ewfd.Ex" with your help.
"ewfd.Ex" plots the real part of X component of electric filed, and it contains phase information, however "abs(ewfd.Ex)" only contains the amplitude of X component of electric filed.

Now, I am trying to simulate the transmitted electric field of a grating, which is similar to a sample of "plasmonic_wire_grating.mph" in COMSOL. The transmitted electric field contains several diffraction orders, but I want to analysis the transmitted electric field of one diffraction order, what should I do to separate them?

Thanks again
--
Ze Tao

Hi,

Well, there is only one electric field solution so when plotting in an arbitrary point one cannot easily filter out a single diffraction order. However, the ports do the filtering for you so the S-parameters from the periodic ports will tell you what the intensity of each of the diffraction orders is (compared to the incident wave). The propagation directions are given by the port mode wave vectors. With that information (amplitude and direction of propagation) a diffraction order is fully specified, right?

--
Magnus

Hi,

Well, there is only one electric field solution so when plotting in an arbitrary point one cannot easily filter out a single diffraction order. However, the ports do the filtering for you so the S-parameters from the periodic ports will tell you what the intensity of each of the diffraction orders is (compared to the incident wave). The propagation directions are given by the port mode wave vectors. With that information (amplitude and direction of propagation) a diffraction order is fully specified, right?

--
Magnus

Thanks Magnus,

I am very sorry for the late reply to you. Yes, you are right, with the S-parameters (reflectivity and transmittance) and propagation direction, a diffraction order is determined definitely. However I want to plot the distribution of electric field for one diffraction order at the direction of period and propagation, can you give me some suggestion?

Thank you again!
best regards!
--
Ze Tao

COMSOL allows you to plot any expression so given that you have extracted the mode field, "E0" , and wave vector, "( kx , ky , kz )", of the diffraction order you wish to plot, you can always plot an expression like:

E0*exp(-i*(kx*x+ky*y+kz*z))

Applying suitable selections on the data sets and/or filter subfeatures on the plotted entities, would allow you to make it appear only in certain domains.

That said, I realize this is not entirely straightforward and requires extracting fields and making some manual definitions. For a future version, we might consider creating global field definitions of the diffraction orders in a uniform homogeneous medium (supposedly the medium of the port). That would be fairly easy. When plotting such a field it would appear over the entire geometry, or according to your manual selections/filters, and it would behave as propagating in one single homogeneous medium (that of the port defining the mode). Would that be of use to you?

Best regards,
--
Magnus

Thanks Magnus,

Your detailed answer will be great of use to me. According to your suggestion, I'll try to plot the diffractive field with "E0*exp(-i*(kx*x+ky*y+kz*z))". In addition, looking forward to the realization of "global field definitions of the diffraction orders".

Thanks again.
best regards.

Hi Ze Tao,
Would you mind sending this model to me for reference? I want to learn how the animation function of COMSOL to observe the development of polarization. Did you set a "boundary mode analysis" model for this ?

Many thanks!
Yuanhang Zhang

Hi,

The problem I analysed is time-independent, so I used "frequency domain" to calculate my model and I did not plot the dynamic graph.

I did not set "boundary mode analysis".

sorry.

Ze Tao

Hi, Magnus,

I have one question when I am trying to calculate the transmittance for my structure with Right-handed circularly polarized (RCP) incidence. For the RCP incidence, I want to know the components of Left-handed circularly polarized (LCP) light and linearly polarized light in transmission mode.

So for the incident port, port 1, I set Ex=1, Ey=i, Ez=0; for the output, port 2, I set Ex=1, Ey=-i, Ez=0;
for another output, port3, I set Ex=1, Ey=0, Ez=0; and port 2 and port 3 share the same boundary.
Then I calculate S21 and S31 as components of LCP and linear polarization in transmittance.

Do you think this is a correct method? I am wondering if the two ports can share one boundary?
I find I get different S21 before and after adding port 3, but I don't know why. Could you help me out? Thanks in advance.

Best
Tianjing

Dear Tianjing,

Yes, the general idea with the port feature is that you can add several ports to the same boundary. As long as each port is set up for a separate port eigenmode it should work fine. For example the circular waveguide operating below the cutoff frequency for anything but the TE11 mode would require two port features on each circular port boundary. The two port features could have orthogonal "linear" (within quotes as that mode has bending E-lines that do not rotate) polarizations or the RCP and LCP (rotating) TE11 modes respectively.

If the simulated structure has the power of rotating the polarization (in reflection and/or transmission) , one obviously need to have enough port features to span the possible "mode space", that is for the circular waveguide example either the two orthogonal "linear" TE11 modes or the two rotating TE11 modes (RCP and LCP). If you go from having an incomplete set of port modes (ports) and add more relevant modes (ports), the S-parameters may change. Adding a passive (not excited) port mode that does not propagate should not change the results (and give zero transmission/reflection for that mode).

For the periodic port, we are helping you with the bookkeeping and setting up of the necessary orthogonal modes aka diffraction orders as in that case you can have a rather large number of propagating/reflected modes at a given frequency.

Best regards,
Magnus

Hi, Magnus,

Thanks for your quick and comprehensive answer. I really appreciate your help.

Now I understand, I need to have a complete set of port modes, considering my structure has the power of rotating the polarization. And I cannot set linear polarization and LCP at the same boundary. The two port modes should have orthogonal linear polarizations or LCP and RCP.

I will try with your suggestions. Thanks again.


Best
Tianjing