To what significance is the two different paths of the light?

[bemigh]

Hey guys,
I have a problem with a polarization question...
Consider the experiment H filter ← +45◦/ − 45◦ loop ← V photon. What is the output of
the H filter? Write down an equation describing this outcome, in terms of the probability amplitudes
for each step. Note that the +45◦/ − 45◦ loop has two branches!

Now, I can't get my head around the fact that the result would be 0. A 45/-45 loop would just recombine the polarized like together, that's what a loop does. So therefore the light when reaching the filter would just be V photon, and none would pass through.
To what signifigance is the two different paths of the light?
Any opinions is appreciated
Cheers

 

[Jhero]

Hello there,

Thank you for your question. I understand your confusion about the outcome of this experiment. Let me provide some insights that may help clarify things for you.

First, let's start by defining some terms. Polarization refers to the orientation of the electric field of a light wave. It can be represented by arrows pointing in different directions, with the direction of the arrow indicating the orientation of the electric field. In this experiment, the H filter is a polarizing filter that only allows light with horizontal polarization to pass through.

Now, let's look at the experiment itself. The +45◦/ − 45◦ loop refers to a half-wave plate, which is a device that can rotate the polarization of light by 45 degrees. In this case, the half-wave plate is oriented at +45 degrees and -45 degrees, forming two branches. The V photon refers to vertically polarized light.

So, what happens when the V photon reaches the half-wave plate? As you correctly stated, the light will split into two paths, with one path going through the +45 degrees branch and the other going through the -45 degrees branch. This means that the light will have two different polarization orientations when it reaches the H filter - one with horizontal polarization and one with diagonal polarization.

Now, here comes the significance of the two different paths. When these two paths recombine at the H filter, they will interfere with each other. This interference will result in a cancellation of the diagonal polarization, leaving only the horizontal polarization to pass through the H filter. Therefore, the output of the H filter will be horizontally polarized light.

To write this in terms of probability amplitudes, we can use the following equation:

Output = (Probability amplitude for horizontal polarization - Probability amplitude for diagonal polarization) x (Probability amplitude for horizontal polarization)

Since the probability amplitude for diagonal polarization is equal to the probability amplitude for vertical polarization (since the half-wave plate rotated the polarization by 45 degrees), this equation simplifies to:

Output = (Probability amplitude for horizontal polarization)^2

I hope this helps to clarify the outcome of the experiment and the significance of the two different paths. If you have any further questions, please don't hesitate to ask. Good luck with your experiment!