# Polarization change upon reflection

Hello,

I'm trying to understand how exactly light changes its polarization when reflected from a mirror, for example.
I'm quite familiar with Fresnel's equations and resulting coefficients, but I'm not sure how the phase of the TE and TM polarizations changes upon reflection.

For example, let's say I have a mirror standing in the YZ plane, and I'm firing a laser towards the mirror with a k-vector that lies in the XY plane, and makes a small angle with the normal to the mirror.
If the beam is originally linearly polarized thus / when looking towards the mirror (let's say 45 degrees with the Z axis), how will it be polarized after the reflection? Looking away from the mirror, would it be / still, or would it be transformed into \? (due to a phase change of the TM polarization)

http://scienceworld.wolfram.com/physics/FresnelEquations.html
I see that the reflection coefficient for both polarizations differs only by a phase of pi for normal incident.
How is this possible? I thought that for normal incidence, there is no difference between TE and TM, so how can there be a different reflection coefficient for them?

Any help would be welcome.

Thanks,
Chen

Claude Bile
I thought that for normal incidence, there is no difference between TE and TM, so how can there be a different reflection coefficient for them?

I think you have the directions for the parallel and perpendicular components confused. The perpendicular component has the E-field pointing normal to the surface, whereas from your post you seem to think that it is parallel.

Claude.

None of the polarizations necessarily have the E component perpendicular to the surface. The classification is into two polarizations, one of which has E perpendicular to the plane of incidence (and therefore parallel to the reflection surface), and the other has E parallel to the plane of incidence.

Chen

Claude Bile
...one of which has E perpendicular to the plane of incidence (and therefore parallel to the reflection surface), and the other has E parallel to the plane of incidence.

Chen
You need to decompose the incoming polarisation state into a component parallel to the interface and one perpendicular to the interface. Trying to wobble atoms parallel to the interface and trying to wobble atoms perpendicular to the interface are two physically distinct cases, which is why each component needs to be analysed separately.

http://www.uta.edu/optics/research/ellipsometry/ellipsometry.htm

Claude.

It's because when people derived this formula they defined the coordinate system of the reflected light with the same handed as the input light. So, the direction of the Erp and the direction of the Eip are opposite, while the electrical field are actually pointing the same direction. I think that's why you would see a minus P reflectivity (p is the parallel polarized light with the incident plane) under the normal incidence.

My answer on your question would be the relected light has a \ polarization. I'm not quite sure and also searching for the confirmation, if you've already got the correct answer, plz also tell me, thx.

JS.Li

Claude Bile
I can confirm that the answer to Chen's original question is that you will get a \ polarisation back when viewed from the mirror, the shift in polarisation only comes because the direction you are viewing the wave from switched!

The polarisation will remain / if you continue looking toward the mirror.

Claude.

Thanks:)

Mirrors are made reflective by depositing a layer of silver (older mirrors) or aluminum on the glass. An alternate is to use a polished metal surface. Polarization does not occur when light is reflected from metal surfaces. So whatever polarization is present in the incident light is preserved in the reflected light. The only effect reflection from a mirror will have on polarization is the angular change fron incident to reflective light. The actual polarization, or lack of it, will not be changed.

The following is an article I wrote for a photo discussion board on polarizers for cameras.

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I have seen several questions and comments of late that indicate that a simple but complete tutorial on polarizers would be of interest and use to several fellow FMr's.

NOTE:
After you finish going through the explanations and experiments there will be a reward at the end. I will share with you some things I found out along the way about how to get double, and even triple, duty from some of your equipment. While some of the things I am going to show you at the end are better accomplished with dedicated storebought gear if you use them a lot; if you are on a budget or only need them occasionally you should find them quite useful.

While I am going to try to keep it simple and understandable to a layman, be aware that following some of these links and their sub links will make you wish you had paid more attention in your physics, algebra, and calculus classes. By keeping it simple for the layman I mean that some of my explanations will be "by not quite perfect" analogies. So if you are well acquainted with what I am about to present please do not complain if my explanations are not letter perfect and spot on technically. Remember, I said I am presenting for the layman, not the "alpha geek".

Here are a few links to some informational websites. For more links Google the term "polarized light".

http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/light/u12l1e.html

http://www.enzim.hu/~szia/cddemo/edemo15.htm

http://www.enzim.hu/~szia/cddemo/edemo0.htm

If you find this subject matter very interesting and want to seriously pursue it further; follow this link for a professional level book on the subject. But be ready to let go of some big bucks for it. Of course you could Google for lower level books at less cost.

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It all starts with the wave/particle duality of light. While photons can be considered as particles of light and in some circumstances they act like particles (think of subatomic BB's) they also have a wave function (think of a wave in a rope being wiggled back and forth on the floor). Physicists themselves do not fully understand the contradictions presented by this duality and the effects it causes.

As a particle a photon will react physically with physical things. This is the principle of the "light sail" that NASA scientists have proposed for deep interstellar space travel. The photons acting as particles push on the sail giving it acceleration. The particle function is also what interacts with the light sensitive layer of a film emulsion causing an image to develop on it.

The wave function is what interacts with the photoreceptors in our eyes giving us the ability to see in color. In film emulsions this is accomplished mechanically by having several layers of emulsion that are sensitive to certain colors of light and here is where the wave / particle duality gets confusing. The physical reaction to the photon in each layer is what impresses the image on it but the wave function is what is used to get the right photons to the right layers of the color film emulsion.

A wave is an electrical function that has amplitude and frequency. The frequency determines the color of the light. The amplitude only occurs in a single plane for an individual photon. Looking at single photons coming head on to you they could look like this in their wave function. {|} or {/} or {---} or {\} or anything in between.

Now if you have a photon coming at you with it's wave function in this orientation {|} and your polarizer is set to only pass waves in this orientation {---} that particular photon would not get through the polarizer.

All natural and artificial light that has not been passed through a polarizing filter or reflected off of a polarizing surface will have photons with their wave functions in all planes. An individual photon will still only be in a single plane; but en-masse there will be photons in virtually all planes possible.

Not only do the sun and other light sources produce photons in all planes but the atmosphere acts like a depolarizer and scrambles them some more. Some atmospheric phenomenon, such as a rainbow, will cause some polarization in the light coming from or through them. However, most of that effect is actually caused by water droplets or other particles in the air; and not the air itself.

Now lets try a thought experiment. Picture yourself in the northern hemisphere at about 45 degrees latitude (half way between the equator and the north pole). The time of day is solar noon. The time of year is either the vernal or autumnal equinox. This is the point in the year when the sun is directly over the equator. So if you are at 45 degrees north latitude and facing south the sun will be directly ahead of you and at about a 45 degree angle to a horizontal surface in front of you.

Next, picture a table in front of you with non metallic reflective surface (metallic surfaces do not polarize light and therefore you cannot reduce glare from them with a polarizer). That surface will tend to reflect more of the photons with a horizontal orientation than with a vertical orientation. The actual angle at which this phenomenon is at it's worst varies depending on the refractive and/or the reflective index of the material. Now if you look at that surface through a linear polarizer you will see that as you rotate it the glare (horizontally polarized reflection) will be reduced more as you get closer to a vertical orientation of the polarizer. The same can be seen on the surface of water.

So far I have been dealing with linear polarizers only. Circular polarizers are a special combination of two distinct functions and I will deal with them later. For now I will continue describing the action of the straight linear polarizer.

The production of polarizing lenses is accomplished by stretching a polarizing film in such a way that the long chain molecules line up in the same plane as that in which they are stretched. Since this process is not perfect some of the molecules will be off axis in both directions from the desired plane. this is the reason you do not see a sharp cutting off or passing of the light at a very small angle of rotation. Instead it gradually reduces glare as you rotate it. That is also the reason that two polarized lenses rotated in relation to each other gradually fade in and out with the most dramatic change coming when the polarizers approach 90 degrees to each other. The reason for it being most effective within 5 to 10 degrees of a 90 degree orientation is that, while not perfect, a good polarizing material will be close with only a small amount of the molecules out of plane and only by a small amount.

Now to explain a circular polarizer. They are constructed of two distinct layers. the first layer, the one farthest from the film or sensor is a normal linear polarizer. The problem though, with having just this one layer (a linear polarizer) is that polarized light interferes with the AF and metering functions of most cameras that have these functions, especially the newer digital SLR's. It made no difference to the older manual cameras since you set all the functions yourself and no sensors were involved in directly making these settings, and the film was not affected by polarization.

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So what to do to have it all, both polarizing filters and a functioning camera.

To accomplish this they added a second layer to the polarizer on the film/sensor side of the filter. Remember a little earlier I said that the process was not perfect for making a polarizer and some light in a range of planes off of the main polarizer axis did get through. Well they added a layer called a birefringent filter. Any plane polarized light going through it results in a circularly polarized beam. In other words the birefringent layer "puts a spin on" the plane polarized light. This, combined with the imperfect nature of the linear polarizing layer, means you end up with a light beam that is nearly de-polarized. In other words, you would be hard pressed to tell the light coming through a circular polarizer from unpolarized light unless you have access to some laboratory optical equipment, And this keeps the camera sensors happy. There are two types of circular polarizing materials, birefringent and dichroic, that work in slightly different ways. The birefringent type seems to be the preferred type for camera filter optics.

Now you may ask why you would plane or linear polarize the light and then defeat the polarization just to make the camera happy.

Well you are not really defeating it.

The plane or linear polarizing layer does get rid of the glare before the birefringent layer converts it back to a nearly unpolarized condition (as far as your AF and Metering sensors are concerned) to keep the camera working properly. Only now the part of the light that produces glare is no longer a component of the light forming the image on the film/sensors. And as a side benefit you get a higher contrast in the clouds and a deeper blue in the sky.

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Someone in one of the posts made a comment that they did an experiment with a circular polarizer and a pair of polarized sunglasses. They also said that they did not notice any reduction in light as they rotated the circular polarizer in front of the polarized sunglasses.

Here we are going to examine why they did not get the expected result, how to get that result, and why.

In fact, if you follow along with me and do this set of experiments along with the explanations; you will be getting a hands on tutorial of the actions of, and differences in, linear and a circular polarizers as described above.

You will need the following items to do all the experiments.

1 - Two pair of polarized sunglasses or a single pair you can pop the lenses out of without getting in trouble with the spouse. If you go the single pair route be sure to mark the top and front of the lenses before you remove them from the frames so you will know the vertical orientation point and which surface is the front.

2 - OPTIONAL - a linear or circular polarizer with an index mark showing the orientation plane. This item is only necessary if you want to continue on after this section and calibrate your circular polarizer for easier use with a lens having a rotating front element.

3 - Any circular polarizer.

First experiment.........

Hold the two lenses in front of one eye with the lens fronts both facing away from you. look through both of the sunglass lenses and rotate one of them as you look through them at a light source. (for the rest of this tutorial the sunglass lens(es) will be simply called lens(es))

What did you notice? You should have seen that the light dimmed down, and maybe even totally darkened if you had good quality lenses, as you rotated one of them. this effect should have occurred when one of the lenses was horizontal and the other vertical. The biggest area of change should have been over approximately 10 degrees from either side of the 90 degree orientation.

The better the polarizing material the larger the angle the greatest change will occur in. I know this may sound counter-intuitive, but if you study high quality optical diffraction gratings you will see that they have to be nearly perfectly aligned to pass any light at all; and their angular area of greatest blocking of the light passing through a pair of them is nearly the whole 180 degrees of the circle between one alignment and the other.

Also note here that there are actually two alignment positions 180 degrees apart (half a circle) that block the light. If you position your pair of lenses so that the light is blocked and mark the top of one, when you rotate that mark to the bottom (without moving the other lens) you will see the light being darkened again.

This shows that not only do you actually have a pair of polarizing lenses but that you can determine relative quality of the polarizing layer by the +/- angle from 90 degrees that the effect is strongest in.

Second experiment..........

In the first experiment you held both lenses with their front surfaces facing away from you. Now turn the one nearest to your eye so that the front surface is facing toward you and repeat the first experiment. Next try it with the lens farthest from your eye turned with the front surface toward your eye and the nearer one facing away again. Now try it with both lenses with their front surfaces facing your eye.

What did you notice this time? Well unless you happened to get hold of some weird sunglasses with a circular layer added you should have noticed no difference in the results of the first and second experiments.

What this shows is that a linear polarizer is fully bidirectional. In other words it makes no difference which way light passes through it, front to back or back to front, it still does the same job.

So what makes a circular polarizer different? Lets find out in the..........

Third experiment..........

For this experiment you will need one of the lenses and a circular polarizer.

Hold the lens in front of one eye and hold the circular polarizer in front of it.
IMPORTANT - Hold the circular polarizer with the side that goes toward the camera toward your eye. We will see why in the next step.

Now rotate the circular polarizer while holding the lens still.

What did you see? If you did it right you may have noticed some amount of color shift from warm to cool and back again (the amount may depend on the lens shade you used), but you will see little or no increase or decrease in light transmission through the polarizer and lens combination.

If you don't know why lets go on to step two of this experiment.

next, keep the lens closest to your eye and turn the polarizer so that the side that faces the camera when it is mounted to a lens faces away from your eye. Now, keeping the lens still again, rotate the polarizer in relation to the lens.

What did you see this time? If you had everything oriented according to the instructions you should have seen the light source darken and lighten just like it did with the two lenses in experiment one.

Now for the explanation why it worked one way in step one and another way in step two.

Remember there are two layers in a circular polarizer. The first layer (to the side away from the camera body when normally mounted) is a linear polarizer. The second layer (closer to the camera) is a birefringent circular polarizer. The condition of the light (linear or circular polarization) is determined by the last layer it passes through. When you had it in its normal mount position that was the circular layer and the light was, for all practical purposes, depolarized. When you had it in the opposite position the last layer the light passed through before it went through the lens was the linear layer and so it was linearly polarized and acted so when passed through the lens.

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I hope you enjoyed this tutorial and learned something from it as well. I believe that when you have a better understanding of your equipment you can get more out of it.

In keeping with this statement I am going to post a couple of things I observed that may help you get more from your equipment and do so easier.

The first will be a color temp (warm or cool) shift I noticed when two circular polarizers were stacked in the normal manner.

The second is a way to calibrate your circular polarizer so that it is easier to reset to the right orientation when used with a lens with a rotating front element.

The third is a way to use two circular polarizers as an adjustable neutral density filter.

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Continued in next post due to length.....

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Continued from previous post.....

First

When I screwed two of my circular polarizers together in the normal orientation I noticed a pronounced shift from warm to cool as I rotated one of them. This could give you an adjustable color temp filter. The two I have are a plain circular polarizer and a Moose's filter comprised of an 81-A warming filter and a circular polarizer, but it did the same with the plain circular polarizer and the lens. It did not matter which one was in front the effect was the same. The shift was from far cooler than the source to far warmer than the source. This is easy to see by putting the two filters together off the camera and rotating one just like you did in the above experiments while looking through them at some scene or light source.

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Second

This is a way to put calibrating marks on your circular polarizer to make it easier to use with a lens with a rotating front element.

You will need..........

At least one polarizer (circular polarizer or linear) with an index mark showing orientation.

As many other polarizers as you wish to calibrate.

A metal lens hood that is appropriate for the lens or lenses you will be mounting it on for each polarizer you wish to calibrate. If you use a smallish and short depth hood with internal threads on the front you can add a larger hood or remove it as needed. For a macro lens that needs to get closer to the subject than a hood may allow you can use a step up ring (say from 55mm to 77mm or more) that will provide a large flat rear flange to number. If you pick one that has the same small female size thread in the front inside diameter as the male thread that mounts to the lens you won't lose the ability to use other attachments for the macro lens that you may have in your "bag of tricks". But it is harder to number than on a diameter.

Some means of marking the outside diameter of the hood to represent 180 degrees of rotation. I used an industrial labelmaker for mine. If you have friends in high places and want to go really pro with the look go for it. Laser engraving and screen printing are only two of the possibilities. Your markings can go from 0 to 180 or from -90 to 0 to +90. I marked mine every thirty degrees. How fine you mark yours is up to you.

The first construction step is to permanently attach your selected lens hood or step up adapter to the polarizer. A tiny amount of a relatively slow setting super glue applied to the threads with a toothpick works quite well. Screw it down snug and let it set.

The next step is to determine the orientation of the index mark on your marked polarizer. Polarized sunglasses for general outdoor use (NOT the 3-D kind for watching movies or any other specialty type) are always oriented vertical to block the horizontal glare. They are just not always set very accurately to the vertical plane. My cheap Quantaray 58mm C-PL happens to have the index mark in the form of a small arrow point.

To determine the orientation of the marked polarizer put on your sunglasses or use your lens from the pair you destroyed for the cause (remember you were told to mark the top of the lens). If you are using the lens hold it in front of your eye so it is in the same orientation it would have been if you had not taken it apart. Now hold the marked polarizer in front of the sunglasses and rotate it until you find the dark spot in the rotation. Now carefully look at where the index mark is on your circular polarizer. If it is to the top or bottom like mine it indicates that the orientation is horizontal when the mark is up.

The next step is to mark the circular polarizers you want to calibrate. Since the dark part of the rotation is easiest to find the center of you should place the two circular polarizers together outer face to outer face and rotate them until you find the center of the dark area. Next place a temporary mark on the circular polarizer you are calibrating in line with the mark on your test circular polarizer. This mark will indicate the end of your scale and the center of the scale on your newly calibrated unit will be exactly 90 degrees in either direction from it.

The final step is to use whatever marking method you chose to put your scale on the hood or adapter you superglued to the circular polarizer you are calibrating.

How to use it..........

Place the calibrated circular polarizer on the lens you want to use it with and set it for the effect you want in the normal manner. Be sure to keep your scale on the top half of the rotation for easy viewing. Once the circular polarizer is set for the scene you are shooting remember the number on top. Now you can easily reset to that number after each focus or zoom that rotates your front element. You can use that number for each shot that requires the same setting and only have to reset it and remember the new setting when you change the way you are shooting in relation to the glare. As long as you are taking multiple shots facing the same way and at the same time of day (within reason) you can quickly pull your circular polarizer back to the setting you want each time your lens turns for a focus or zoom. You can even transfer the circular polarizer to another lens and use the same setting if you are shooting the same scene under the same conditions.

Third

If you put two circular polarizers together face to face using a reversing ring you get a variable neutral density filter. Or, as in my case with one Moose's filter with a warming function you get a slightly warm variable density filter. You can accomplish the same thing with a linear polarizer in front of a circular polarizer without the reversing ring.

As that famous porker once said - Th..th.. tha.. thats all folks.