Phys 225 Week 9 - 4 circular polarization

That was linear polarization, it has uses in your LCD screens and also your polarizing sunglasses Speaking of glasses, another polarizating state we often have to talk about is the circular polarization, it's actually the type of polarization of light that we use in 3D movies and in your 3D glasses we have circular polarizers and once you get through this, you can think about what we choose to use circular polarization instead of the simpler linear polarization circular polarization is a little hard to visualize so we will have to go through it a little slower. Please bear with me First of all, how does it look like? The good contributors to wikipedia has contributed this lovely GIF, as you can see as the EM propagates forward, it looks like that the electric field is spinning around in a circle in that plane that you see there, so in terms of describing it convention-wise this one we will be calling a left handed circularly polarized How's that? Because if you have the propagation direction out of the page, you see that this thing is spinning clockwise and that if you had your thumb in the direction of the propagation you get the finger curling in the right way, so this is what we call left circularly polarized technically we should state from the source, because some people do it the other way, but most people go this way the same case, we can have right circularly polarized by it going the other way so always point your thumb towards the propagation direction and see which way your fingers curl because the electric field of the circularly polarized light keeps moving, it's actually easier to understand it as the sum of two linearly polarized light, very special ones, in fact, that are equal in magnitude and they are perpendicular to each other and then after we see that, we have to understand the use of "retarders" we'll get into the in a second, so let's first deal with the simpliest case where you have your linearly polarized light adding up with another linearly polarized light, but that is perpendicular to it these are both E's, not your E and B here and if we look at it head-on what we would see is we have that and that going on, just for the sake of the argument we will call those both sides positive to see what's going on, let's draw out what each of the 2 components are doing at different points along the propagation path well, here we have it going up then at this point, we have it going down, up, down ... ... and this over here, we have it going to the right then left, then right, ... so what you have then is actually, as you work out the resultant, it's a linearly polarized light in 45° Now this isn't quite circular polarization yet, but if we combine the use of retarders this would eventually become circularly polarized light so it is important to talk about what a retarder does. We won't be so much concerned on how they are made but we are just going to focus on its effect we are going to draw this like a block for now it's usually a piece of crystal and what's special about them is that it's got a fast and a slow axis, so say it's got a slow axis along here and what that does is any EM wave that travels along that axis goes slower than travelling along the other axis so as a way to illustrate that we have this guy come through and nothing happens to this guy and it becomes along the slow axis, however, it somehow comes out slower, so instead of starting from this spot, it starts you can visualize it as starting back here and then it comes out as a result the two waves becomes offset, and depending on the thickness, it gets offset by different amounts so let's first look at the effects of a 1/2 wave retarder to look at its effect, we start with once again our normal wave like this, but it's easier to visualize it head-on, so this guy we have over here and it's over there so we have linearly polarized light in that direction, now 1/2 wave retarding it this guy doesn't change, so we can still draw the head on wave to look like this but if it's slowed down by 1/2 [a wavelength] what we have effectively done is we've flipped it around because, we'll draw it over here if we move this back by half a cycle 180°, we would get this wave instead, so instead of going up, it's going to go down being negative, and negative on the horizontal is like that, so using the 1/2 wave plate, we have changed the orientation of the linearly polarized light, instead of 45° to the right, it is now 45° to the left so that's the effect of a 1/2 wave retarder. If we go in between and do 90° or 1/4 wave retarder, that's when we get circularly polarized light, let's illustrate that too so for the 1/4 wave we can also draw a thing with a slow axis, 90°, 1/4 wave retarder. Initially we start again with for instance both of the components going positive at the same time giving us 45° that way but if one of them is now changed by a 1/4 wave, say this is a cos function we are starting with, we are going to get something like that now, of course, in 3D, it's kind of hard to draw and visualize, so let's just look at it head on for a series of points so the normal one is going to have a normal cos function, we'll pick points that are more or less like these and then, for the other one, it's a cos curve that's been shifted back 90°, so it kind of looks like that so it'll start out with zero but heading towards the negative it's often helpful to draw that in to know which 0 we are at and then it gets a little more negative and it gets really negative at that point and get shorter and starts to head towards the other way, so you can see where the [resultant] is going, the [resultant] is going here here, here... ... so you can see how the resultant is doing this circular motion and that's exactly what the circularly polarized light is composed of it's composed of 2 linearly polarized light that's 90° with respect to each other with the same magnitude but offset in time by this 90°, so in this case, this time we're getting the right circular and we can also get the left circular by instead of retarding the horizontal we can retard the vertical or we can advance the horizontal, either way to sum up, how you would create these circularly polarized light is to use a combination of a linear polarizer and a 1/4 wave retarder that's oriented in the correct direction with respect to the linear polarizer so the slow axis has to line up 45° from the actually linear polarizer because what that does is here we have randomly polarized light making two components and then because we're slowing this guy down, so let's work out the resulting light would be usually, it's important to start with a certain coordinate system so we can say positive and positive we draw the one case where we have the cosine curve like that and the other one, the other component, we considered separately It started out as a regular cosine curve but it got shifted back so it looks like that, so we know it's heading slightly negative. Negative is to the left in our case, so we have this and as time goes on, you know that the next one is going to look more like that so you know it's heading in the counterclockwise direction this is an important skill to have in order to workout how the circularly polarized light interact with others circular polarizers to see how we can get the effects that we want given that we have circular polarized light say, in this case, right circular, how is it going to interat with different polarizers that we have well if it's going through a linear polarizer as the actual electric field spins around, what's going to happen is it'll let through just that component along the axis of the linearly polarizer through but then the size of that component is going to change as it spins around so what you actually get is basically linearly polarized light but then the actual amplitude to get smaller and bigger now of course, this happens at 10^15 Hz which is the frequency of the light so you are not going to see it blinking that quickly, what you will see is that it'll get a little dimer, so that's not very exciting but what happens if we put another circular polarizer, another 1/4 wave retarder in front of that so here, we have this case, we know that for our right circular wave we have this guy going straight up and the other component is going there coming out of the 1/4 wave retarder, what do we have? we have the same thing, this one goes straight up, the other component, of course it was like this but it got shifted back even more by another 90° so you are actually at the most negative at that point so you end up flipping and you recollect your linear polarization but it's in the other direction which makes sense thinking back to our 1/2 wave retarder example doing 1/4 wave retarding and then another 1/4 wave retarding that's adding up to be 1/2 wave and so if your direction ends up perpendicular to the polarizer you will get nothing, you get 0% out and that's determined by the orientation of the polarizer with respect to the slow axes of the retarder conversely, for the same light if we orient the linear polarizer the other way, this still gives you that and you end up getting light coming through, funny enough though, if we have left polarized light in which case the situation start out like that as we pass it through our 90° retarder and through the same two linear polarizer you would get this doesn't get affected this, where we were at 0, going positive, so it looks like that retarded 90°, so that's the most positive so components like that this and nothing for the other one so maybe already you can start to see how we can use these as 3D glasses because if we send right circularly polarized light through both of these lens, this guy gets the light if w send left circular, it goes through the other one so as long as we can work out how the 1/4 wave retarder do to either components of the light, we can figure out if it becomes circularly polarized or linearly polarized and so we can figured out what the ultimate end results would be keeping in mind that, it's not so much now the orientation of the linear polarizer absolutely but it's related to how relative to the slow axis of the retarder the linear polarizer is oriented that would change circularly polarized light to linearly polarized light or vice versa