Light Polarization Reflected from Parabolic Mirror

[lvb884]

Let's say I have a linearly polarized laser beam, and I focus it to a small spot using a parabolic mirror. Does the light retain its polarization at the focal point? Why or why not? I understand that flat mirrors and concave/convex mirrors preserve linear polarization, and I would like to make sure that a parabolic mirror would also preserve polarization. Thanks!

 

[goodphy]

You can have imagination of how polarization evolves when it is propagating. When the light, for example linear polarization, just traverses the space with preserving their direction, polarization is also maintained, of course. When they bend, vector along to polarization is also bent with the angle mount. Remember: polarization is stick to k vector or wavenumber or propagation vector. Thus when propagation direction changes, the polarization also changes the same amount.

In addition, you can change S polarization to P polarization or vice versa by using periscope which optical elements are only flat mirrors.

 

[lvb884]

Thanks! I forgot to mention that I'm most interested in S vs. P polarization. So I'll adjust my scenario a bit...

Let's say I have a collimated and linearly polarized laser beam, and it reflects off of a parabolic mirror onto a flat absorbing surface. The plane of the absorbing surface is positioned at the focal point of the beam, where the k-vector of the beam is at an angle theta with respect to the normal vector of the surface. The surface is oriented parallel to the floor, and for simplicity we can call this orientation horizontal.

If the incident collimated beam is horizontally polarized, will I have pure S polarization at my absorbing surface? If the beam is vertically polarized, will I have pure P polarization at the surface? I'm assuming the answer is yes in both cases, but I want to make sure. Is there any reason why the rotation of the polarization with respect to the k-vector would not be maintained?

 

[goodphy]

I'm not sure my geometric understanding of your setup is right. From my view of point, collimated beam height is higher than flat absorbing surface and parabolic mirror is positioned such that beam is focused-reflected to down to surface from the height. You might know that if the surface is really at precise position of focal plane of mirror, at that position, beam is collimated. (without surface, the beam diverge as the beam continues to propagate from the focal plane.) Thus polarization is just the same to the original.

 

[lvb884]

Yes, in this case, the incident beam and the parabolic mirror are at the same height, and the flat surface is below (or above, whichever you prefer).

I do not understand how the beam would be considered collimated at the focal point. To me, this suggests that a setup like this can be used for imaging, but I believe parabolic mirrors distort the image quite a bit. I'm not concerned about whether the optical image is maintained but only polarization. How do you know that the polarization would be maintained after the light is reflected from a parabolic mirror?

 

[tech99]

Yes, in this case, the incident beam and the parabolic mirror are at the same height, and the flat surface is below (or above, whichever you prefer).

I do not understand how the beam would be considered collimated at the focal point. To me, this suggests that a setup like this can be used for imaging, but I believe parabolic mirrors distort the image quite a bit. I'm not concerned about whether the optical image is maintained but only polarization. How do you know that the polarization would be maintained after the light is reflected from a parabolic mirror?

Sorry I am not an expert on the maths described here, but I do know that if a linearly polarised source is placed at the focus of a parabolic mirror, the beam which emerges has "curved" polarization as we move away from the axis. It looks like the same effect as spherical aberration, and has been quite a problem in microwave communications in the past. However, on axis, everything is fine. I presume that a plane polarised incoming beam will produce a curved polarization pattern around the focus.

 

[lvb884]

Sorry I am not an expert on the maths described here, but I do know that if a linearly polarised source is placed at the focus of a parabolic mirror, the beam which emerges has "curved" polarization as we move away from the axis. It looks like the same effect as spherical aberration, and has been quite a problem in microwave communications in the past. However, on axis, everything is fine. I presume that a plane polarised incoming beam will produce a curved polarization pattern around the focus.

Thanks! So basically this means that if the alignment isn't perfect, there's a good chance that the polarization becomes distorted? Do you know where I can look to find more info about this curved polarization resulting from parabolic mirrors?

 

[tech99]

Thanks! So basically this means that if the alignment isn't perfect, there's a good chance that the polarization becomes distorted? Do you know where I can look to find more info about this curved polarization resulting from parabolic mirrors?

Although I mention this from the academic standpoint, if your f/D is very large the effect is small.Spherical aberration is small for large f/D.
The original work on this for microwaves was done by Condon; the following paper has lots of information and references in the context of microwave: http://scholarworks.csun.edu/bitstream/handle/10211.2/4180/DiFonzoDaniel1972.pdf?sequence=1. In the microwave case, it is usual to see additional sidelobes which are cross polarised, and these lie in the 45 degree planes.

 

[lvb884]

Thanks!

 

[blue_leaf77]

Consider this simplified configuration:

 

[lvb884]

Can you explain what you're showing here? My question was about parabolic mirrors, not symmetrical lenses.

 

[goodphy]

Yes, in this case, the incident beam and the parabolic mirror are at the same height, and the flat surface is below (or above, whichever you prefer).

I do not understand how the beam would be considered collimated at the focal point. To me, this suggests that a setup like this can be used for imaging, but I believe parabolic mirrors distort the image quite a bit. I'm not concerned about whether the optical image is maintained but only polarization. How do you know that the polarization would be maintained after the light is reflected from a parabolic mirror?

Okay. collimated beam at the focus is better seen via https://en.wikipedia.org/wiki/Gaussian_beam.

Please see the 4th figure of Gaussian focusing. You can see that at the very exact point of focus, all k vectors of the beam becomes parallel with each other. That's th collimated I mean.

 

[lvb884]

Okay. collimated beam at the focus is better seen via https://en.wikipedia.org/wiki/Gaussian_beam.

Please see the 4th figure of Gaussian focusing. You can see that at the very exact point of focus, all k vectors of the beam becomes parallel with each other. That's th collimated I mean.

Thanks for the clarification. But how do you know the beam is still Gaussian after it reflects from the parabolic mirror?

 

[goodphy]

Thanks for the clarification. But how do you know the beam is still Gaussian after it reflects from the parabolic mirror?

You can measure the beam profile in combination of objective lens (to magnify such a small spot to the size of many data-points). But as long as input beam is Gaussian and parabolic mirror is adjusted to get best focus, you can think Gaussian beam at the focus.

 

[blue_leaf77]

Can you explain what you're showing here? My question was about parabolic mirrors, not symmetrical lenses.

The action of mirrors and lenses are similar. My point showing that picture is that as long as the field strength coming from the bottom of the lens and that coming from the upper part of the lens (with arbitrary lens shape) are equal, the field vector in the focal point will be vertical.

 

[lvb884]

Ok, so I finally got to the bottom of the issue I was having, and it has more to do with basic reflection properties than parabolic mirrors. Anytime you reflect a beam at a 3D angle, the polarization will shift. I searched all over for answers to this, and a friend finally pointed me in the right direction. I decided to write a separate post about the topic: https://www.physicsforums.com/threads/reflected-light-at-3d-angle-shift-in-polarization.836848/