Rotate only H-Pol Component of Light beam by 90 degrees

[Swamp Thing]

Is there a single optical component that will do the following? Do nothing to the horizontally polarized input, but rotate the vertically polarized input by 90 degrees, so that both beams finally emerge with the same polarization?

I am looking for a single element that will replace the following arrangement.

Edit : Wait, what about the second PBS? It will transmit the H ray downwards ! So basically, I need something that will do properly what the figure actually tries to do, but fails.

 

[blue_leaf77]

Do you need the two beam to be spatially separated? Or do you actually want to make them coincide, i.e. they superpose?

 

[Swamp Thing]

I need them to be coincident, so that the detector will collect the photons from both paths together. (I have showed them as thin blue and red lines for clarity. In reality, they well be wide, circular, overlapping beams).

So as they are already overlapping at the input, you can't rotate one of the polarizations until you have first split them in the PBS. So it's "Split, rotate, merge".

 

[blue_leaf77]

In the upper branch of the beam, is there some kind of delay stage?
If not, I don't see the point of splitting the beam just to rotate one component if in the end what you want is a horizontally polarized beam. You can, for example, place the HWP directly in front of the incident beam (assuming it's linearly polarized) to rotate to the horizontal polarization.

 

[Swamp Thing]

But then the HWP will also rotate the horizontal beam (maybe not 90 degrees, but by some phase) ?? I would prefer the horizontal not to rotate ( or if it does, then the rotation on the vertical input should be slightly different, so that they end up aligned at the output. For example, horizontal rotates clockwise by 10 degrees, vertical rotates clockwise by 100 degrees. That would be OK. Possible?

 

[Andy Resnick]

Is there a single optical component that will do the following? Do nothing to the horizontally polarized input, but rotate the vertically polarized input by 90 degrees, so that both beams finally emerge with the same polarization?

Your thought experiment violates thermodynamics (conservation of etendue, in this case) and thus is not possible.

 

[blue_leaf77]

But then the HWP will also rotate the horizontal beam (maybe not 90 degrees, but by some phase) ?? I would prefer the horizontal not to rotate ( or if it does, then the rotation on the vertical input should be slightly different, so that they end up aligned at the output. For example, horizontal rotates clockwise by 10 degrees, vertical rotates clockwise by 100 degrees. That would be OK. Possible?

Let me summarize your idea, so what you want is
input: Linearly polarized beam at some angle from the vertical axis (superposition of blue and red beams)
output: Linearly polarized with horizontal polarization
Isn't this just a matter of rotating the polarization direction which can be accomplished by a single half-wave plate?

 

[Swamp Thing]

Isn't this just a matter of rotating the polarization direction which can be accomplished by a single half-wave plate?

I'm not sure about how the hwp would affect the horizontally polarized input. If the "H" passes right through and comes out still "H", then I'm happy. But if the "H" also gets rotated then it ends up as "V" and then my output would be "V+H". But what I would like to see is "H+H". Or at least, "Z + Z" where the Z could be anything.

 

[blue_leaf77]

You are apparently still fixated on the H + V resolution of your beam. Remember that EM field is a vector, given two field components they will superpose to form a single field vector and you can forget about the component fields completely as this is arbitrary. In your picture, you can simply draw the incident beam as composed of only one beam having polarization at some angle with respect to the vertical axis (since the H and V components superpose to form a single vector) and forget about the H and V components.
This way you get a single incident beam and if you place a HWP in its path, the polarization will rotate and again no need to consider what it does on the H and V components.

 

[Swamp Thing]

Remember that EM field is a vector, given two field components they will superpose to form a single field vector and you can forget about the component fields completely as this is arbitrary.

Thanks, I'm beginning to understand (I think).

In the upper branch of the beam, is there some kind of delay stage?

Yes, there would actually be a delay or phase shift in that branch.

So thanks again. Now I just need to sit down in a quiet corner and have a little think.

 

[Swamp Thing]

OK, so I've had my little think and I'm back with another question.
I'd just like to confirm this --- if the input to the polarizer is a superposition state composed of $+45^{\circ}$ and $-45^{\circ}$ (looking like X ) and the polarizer is vertical like this: I ... then all the light will go through? And this applies to all kinds of states i.e. thermal, coherent and Fock?

And thanks again for your patience responding to my earlier questions!

 

[Khashishi]

Try running it in reverse, and there are problems. In reverse, the component wouldn't know whether it needs to change H polarized light into H or V polarized light. So the component would have to include non-reciprocal optical effects, if it were possible at all.