Discussion Forum

I'm guessing that by "Radially Polarized" you meant what is more-commonly called "Circularly Polarized" light. If so, the following thread on this forum may be helpful to you:
www.comsol.com/community/forums/general/thread/2948

No radially polarized light is different from circular polarized light.

For better i am giving you wikipedia reference "en.wikipedia.org/wiki/Radial_polarization"

Oh, OK, I see what you mean. Unlike planar, circular, or elliptical polarization, what some people are evidently calling "radial" polarization is not a localized point-like property. I.e., planar, circular, or elliptical polarization can exist at a point in space, while radial polarization only has meaning as a geometric distribution or array of polarization vectors. And I think that realization holds the key to defining your field here. You need to specify a vector field of radially oriented vectors (each of which has simple linear polarization). Of course, this must have a hole on the symmetry axis (which is also how it looks in Wikipedia). As an RF guy, I can tell you that such a distribution looks a lot like the transverse component of E in a circular waveguide TM_01 mode, so you might start with that. Or, write your own distribution function for the x & y components of E, as functions of (x,y).

Thanks Robert

Could you please help me out in the analytical expression of Radially polarized light which propagates in z direction ?

If you'd like to model it as the same as (or similar to) a circular TM01 mode, consider using the field expressions you'll find on pages 34-35 of:
cas.web.cern.ch/cas/Bilbao-2011/Lectures/Gerigk1.pdf
among others.

Hello Robert

Do you know how to write the polarization expression in spherical/ Cylinder coordinate in comsol rather than cartesian coordinate ?

For example :- E (r,theta) = E0*sqrt(r^2)*exp(-r^2)*cos(theta)
E (r,theta) = E0*sqrt(r^2)*exp(-r^2)*cos(theta)

I want to write this expression in comsol, these are the polarization in cylindrical coordinate.

Hmm. Are you asking about the trigonometry? Suppose you are working in the (x,y) plane and have an expression in terms of polar coordinates (r,theta)

Replace r by sqrt(x^2+y^2)
Replace theta by atan2(y,x)

Finally, bear in mind that there should not be any functional dependence on angle in an axisymmetric mode.

No i am not asking about trigonometry.

I know the relation between x,y and r,theta.

My question is that when we define the polarization in comsol for example if we define the circular polarization in comsol we usually write Ex = E0 exp(-ik*z); Ey = i*E0exp(-ik*z)

But when i am trying to write Ex = E0*r*exp(-r^2) sin(theta)
and Ey = E0*r*exp(-r^2) cos(theta) lets suppose for constant value of "r", then here my Ex and Ey becomes the function of "theta". Obviously for considerig radially/ azimuthally polarized light i have to consider "theta" from [0,2*pi].

I don't know how to do this here.

Hmm. I'm still not sure what the difficulty is here. Like I said, just replace r and theta exactly as I indicated. To be explicit, I'll even use your own expressions (for which I take neither credit nor blame), to make this as clear as possible:

YOUR expression: E0*r*exp(-r^2)*cos(theta)
REPLACEMENT expression: E0*sqrt(x^2+y^2)*exp(-(x^2+y^2))*cos(atan2(y,x))

YOUR expression: E0*r*exp(-r^2)*sin(theta)
REPLACEMENT expression: E0*sqrt(x^2+y^2)*exp(-(x^2+y^2))*sin(atan2(y,x))

Does that help? If not, sorry. Perhaps someone else at this forum will understand your question better and can provide you with a more helpful response. Good luck.

Hello Robert

I am posting my .mph file and the reference paper that result i want to reproduce (just for fun !)

Basically in my model I am trying to excited the plasmons first by simple linear polarization and then by radial polarization.
Initially I am stuck at the very first step i am not be able to match the result for linear polarization. Fig 2 in the reference paper.

Could yo just go through my model and point out my mistake ?

Sorry, but I am unable to devote lengthy times to analyzing your model and related technical papers. (I only participate in this forum in my spare time.) If you have a current Comsol support contract, then I encourage you to ask Comsol support personnel directly for assistance in the configuration of your model.

Hello Robert

Well I am looking for a way in which I want to deal with focusing of gaussian beam.

Actually what I want is to model, in which a gaussian beam propagates in air and after interact with lens gets focussed at focal plane. Then I can analyze the electric field at focal plane by using cut plane option.

But I am really confused how to model the focusing. In case of scattering through nanosphere it was easy, i have to just create the nanosphere and assign it material and choose the scattering mode and give the bacground field and rest is done by comsol. But I am confused how to model say Gaussian beam which propagated and then after interacts with lens focus on focal plane.


Robert if you have any idea suggest me.

A "Gaussian beam" may be circularly-symmetric in its power-density profile, but it will not exhibit what you called "radial polarization." As I noted above, what the literature calls "radial polarization" is not a genuine polarization, but rather a spatial distribution (a "mode," if you prefer) of electromagnetic fields, which in general requires some kind of wave-guiding structure to support. A free-space Gaussian beam cannot be a "radial polarization" mode, since: (1) the former is a TEM wave, while the latter is a TM wave, and (2) the former has its peak electric field in the center, while the latter has a null in the electric field at the center.

If you were previously interested in "radial polarization," but you are now interested in Gaussian beams, then I suggest you post your new question separately from this thread, and give it a new title.

Hello

I am also confused about setting the radial polarized beam in Comsol. Do you know it now? If so, can you give me a help?

If you can write down an expression of the radially polarized light, it would be straightforward to implement the field in COMSOL.

--
Pu, ZHANG
DTU Fotonik