Tip:
Highlight text to annotate it
X
Next up we have polarization, now we won't be able to deal with all the nitty-gritty details
for polarization, but we will aim for the lower hanging fruit so we can explain
a couple of really useful devices, namely the liquid crystal display
and moving onto the 3D glasses that you see in theaters so much now
Polarization comes from the fact that our TEM wave propagates in 3D, let's quickly draw that out
you have your poynting vector going that way, which is the direction of propagation
then you have your
electric fields making this wave going in one direction
and from that we can totally define the direction of the magnetic field as well
and since the propagation direction and the direction of the electric field defines where the magnetic field goes
we normally just won't draw the magnetic field just to save us some trouble
from that, there is nothing stopping another wave at the same time
that has the electric field pointing in another direction though, because of superposition. This could be a little bit like that
or a little bit like that
so gets a little messy, so if we draw a plane here, we may see
we have some electric field going that way, some that way, some that way
so any which way that you have, and that is what we mean by polarization, it is the actual direction of the electric field
within this plane that's perpendicular to the direction of propagation
now as it is right now, this is what's called "randomly polarized"
or even "unpolarized"
because it is not very well defined, it is going everywhere
but this is a very common type of light, light that comes from most light bulb or sunlight, would be this
kind of light, it would be a mix of all different kinds of polarizations
however, there are these devices called polarizers that we can make certain states of polarization
which can then interact with other polarizers to give us some interesting behavior and ultimately
very useful device
and one of the easiest devices would be a linear polarizer
it makes linearly polarized light which is arguably the easiest special polarization state to understand
as far as the device goes, it can take a few forms
but one of the simplest form would be a bunch of parallel wires that absorb
all of a certain component of your electric field in a certain direction while letting the rest through
in terms of illustrating it, we think of it as a gatekeeper, so it is kind of like
the exit of a sewage tunnel with a bunch of bars in it
so when you start with
randomly polarized light like this
we are going to say that it lets things that are parallel to it passes through
you can visualize it like that
in reality, depending on the form that the polarizer itself is, it may work a little differently, but visualizing it
you can see that the linear polarizer has a certain axis and it lets
components of things that are parallel to it through
now how much of the power it lets through?
well, let's first quickly look at what happens if I have
a linear polarizer, let's draw this over here
bunch of lines
define the axis of the polarizer
and then I have an electric field amplitude
that's kind of like that, that's making an angle θ with it
well, what passes through?
the part that passes through is this component right here
the component that's parallel to the axis, therefore you can write
that the outgoing field amplitude is the cosθ of the incoming field amplitude
and if we are talking about intensity
we have to square both sides, because, once again, the intensity is directly proportional to the amplitude of the field squared
so this is going to be cos^2(θ)
of the incoming
so from that you can probably work out that you a cos^2 curve
which, over the entire 2π, would have 2 periods like this
and if you average out
basically taking the "root mean square"
you find that the area is going to be 50% of everything
so you are letting through 50%, so if this is 100% of the intensity
this will be 50% of the original intensity of the unpolarized light
and this here
we call Malus' law
which relates how much intensity you get through a certain polarizer with θ being the angle
between your polarized light and the axis of your polarizer
and now let's mix our now-polarized light with different polarizers to see how we can make this more useful
Problably the most obvious combination we would use would be
if we have a polarizer like this
and later on, we have a polarizer that is 90° from the original, what would happened is we have randomly polarized light
giving us 100% over here
and then it becomes linearly polarized with 50% intensity, and once it hits this one
because you hit a cos^2(90) term which is 0
so you nothing out
and so
you may be familar with if you have two of these linearly polarizing sheets
and you may put one in front of a window and put the other one in front of that, and you spin them around with respect to each other
you will see things go brighter and then dark and the bright again
and there are a number of youtube video that you can search for to see this effect, so I won't show you that directly here
now when you have 2 polarizers at 90° and let's no light through, we call that having "crossed polarizers"
However, if you put third polarizer in between
that's at say at 45°
something kind of strange happens
first off, you still get randomly polarized
lights here and then you still get the 50% here
but this one is 50% times cos^2 of 45° because it's only offset by 45 between
this polarizer and the last one
and so it gives you 25%, but now the exit
is off on a 45° angle, so it only makes 45° with the next one
again, you have
this becomes 12.5%
and so instead of getting zero as we have up here
adding an intermediate linear polarizer
twists it around and you get some power out
and that is actually the bases of your liquid crystal display, your LCD display
so surely you've seen LCDs either in the form of flat screen TV or laptop monitors
or your calculator, even earlier, and your phones and whatnot, so they are very prevalent
and polarizer is essentially how they work, now we are going to focus on the nematic type
of LCD which have these liquid crystal in them
the liquid crystal is nice and long so they act as linear polarizers and also they are charged
so what the LCD is usually comprised of is it has two layers:
one where the liquid crystal is forced to go this way
and the other one on the other side is forced to go 90° from that
now if there is nothing else going on, there is not charge built up
the crystals settles into an equilibrium and it likes to gradually makes this change from one side to the other
and if you have, let me draw this on this side here, if you start out with
this and then you gradually move towards 90° from here
each of these steps, now we are talking about 1000's of steps here because the crystals are so small
each of these step is angle is small, so the cosine term is roughly equal to 1
so you are not losing very much intensity, but you are achieving the fact that
you are switching the polarization
of your light from this way
to 90° from it, while keeping all your intensity
so that's this case, where we have no voltage and we have light, kind of backwards
but once you apply the voltage on this side here
it'll get dark
why is that? Because now all your crystals is lined up straight up so
they don't actually affect the field that is going through,so all you have
is these 2 things
which are crossed polarizers
with the 90° between them and so you get darkness
and that's fairly simply how a LCD work
based on linear polarizers