Difference between two polarization directions

[Kruger]

Light can be x- or y-polarized. However, the polarization depends on the direction of the electric field (lets talk only of linear polarization). Now, what's the difference between x and y polarization? I mean why isn't there an intermediate polarization direction. One could rotate the electric field and yields a lot more polarization direction than only x- and y.

You know what I mean?

 

[Galileo]

There is no difference, ofcourse. It just depends on how you choose your coordinate axes. If you put your x-axis along the E-field it is polarized in the x-direction and if you choose your y-axis along the E-field it is polarized in the y-direction. If you're in a bad mood you may even choose your axes as to polarize the light in an arbitrary direction. Nature doesn't care one bit.

 

[Claude Bile]

Arbitrary polarisations can be expressed as a linear combination of two orthogonal polarisations. This is useful because we can analyse each polarisation component separately, then add them at the end to arrive at the total result.

Claude.

 

[Kruger]

Why can then certain materials only absorb light of a certain polarization if the direction of the polarization depends only on the manner one has chosen the x and y axis? (I mean the material does not care about my chose)?

 

[Galileo]

That depends on the structure of the material. In the case of linear polarizers they will stop linearly polarized light in one direction and let light that is polarized along an other direction through. These principal directions are generally perpendicular so naturally you choose your axes such that the coordinate axes coincide with those directions.

 

[pinestone]

Light can be rotated by an electromagnetic field. See http://www.teachspin.com/instruments/faraday/index.shtml

 

[pervect]

Light can be x- or y-polarized. However, the polarization depends on the direction of the electric field (lets talk only of linear polarization). Now, what's the difference between x and y polarization? I mean why isn't there an intermediate polarization direction. One could rotate the electric field and yields a lot more polarization direction than only x- and y.
You know what I mean?

This is a quantum-mechanical effect, due to the quantum mechanical nature of spin. Clasically, light can have an infinite number of degrees of polarization. However, a single photon, treated quantum mechanically, will be polarized either x or y. When you shine light through a calcite crystal, the quantum nature of polarization shows up - light follows one of two paths, not a continuum of paths.

This is very similar to the manner in which an electron (actually, to be really precise, a silver ion) in the Stern-Gerlach experiment is either polarized "up" or "down". The calcite crystal example is the optical analog of the Stern-gerlach experiment.

Maybe someone else can address the "why" question a little better (of course, ultimately, no why question has an answer, but sometimes useful things can be said about "why" questions in the context of a certain theory. This may be a more abstract answer than you really want, though.]

I can describe the math a bit, though.

A general state of spin can be represented by $\alpha$ |x-polarized> + $\beta$ |y-polarized>, where $\alpha$ and $\beta$ are complex number. Here |x> and |y> are vectors - together, these form a basis for the general represnetation of spin. This is why we say that spin must be |x> or |y>, because these two vectors span the vector space of possible spins.

So if you know what a vector space is, that has all the math you need to calculate how spin acts.

There are alternative vector bases for spin, for instance light can also be represented as a linear combination of left-circularly-polarized and right-circularly-polarized light.

 

[vanesch]

This is a quantum-mechanical effect

I'm not sure that it is necessary to resort to quantum effects to describe light polarization. The classical description (the direction of the E-field vector) should be sufficient to address the OP's question, no ?

 

[pervect]

I'm not sure that it is necessary to resort to quantum effects to describe light polarization. The classical description (the direction of the E-field vector) should be sufficient to address the OP's question, no ?

The OP asks

I mean why isn't there an intermediate polarization direction?

The way I look at it, the classical answer is that there are intermediate polarization directions - an infinite number of them. The idea that light has only two fundamental polarization states is a quantum-mechanical idea.

 

[Claude Bile]

This is a quantum-mechanical effect, due to the quantum mechanical nature of spin. Clasically, light can have an infinite number of degrees of polarization. However, a single photon, treated quantum mechanically, will be polarized either x or y. When you shine light through a calcite crystal, the quantum nature of polarization shows up - light follows one of two paths, not a continuum of paths.

The x and y-axis in the absence of an external reference are completely arbitrary. The dual paths in a calcite crystal are due to an external reference being imposed on the system via the crystal structure of the calcite.

I see no need to involve photon spin in this discussion whatsoever, the math you quote is simply expressing a vector as the linear sum of a predefined orthognal basis. You don't need to know anything about spin, you just need to understand basic linear algebra, if you understand the concept of an orthogonal basis, then understanding polarisation is a breeze.

Claude.