Adding and subtracting shouldn't be this hard

     We all know how to add and subtract numbers, even if some of us avoid doing so by becoming good friends with our calculators.  Performing addition and subtraction on numbers is one thing, but what about doing the same with light?  Specifically, can we add and subtract photons, light particles, from each other?  Does this seem possible?  Photons are essentially light particles.  Try taking two particles of matter, like a piece of your computer or even the air you are breathing, and combining them to make one particle.  Only nuclear reactions do this, and to tell the truth, how easy is it for us to mimic what the sun does?  Well we can combine two light particles together to make a single, different light particle.

     This post will give you an introduction to the concept and applications of nonlinear optics.  I have mentioned in a previous post how a nonlinear crystal can be used for frequency-doubling of light.  I will help to explain how this works as well as explain the other things that can be done using similar techniques.  But first, I have to explain what is nonlinear at all about the topic.

     In many aspects of physics, phenomena appear linear.  Things like gravity and springs and even atoms are modeled by physicists with linear models at first.  What does this mean?  Think of a rubber band.  We have all stretched one, shot one, twirled one, and broken many.  But rubber bands are fun for us because when we pull on them, they pull back.  In fact, if we stretch the rubber band, the rubber band pulls harder and harder back the farther we pull it.  Why is this?  It is because when the rubber band is pulled a little, some of the atoms in the rubber band resist being pulled apart.  Stretch the rubber band some more, and not only do those first atoms want to pull back, but even more are taking part in resisting the stretching.  The amount of pulling power the rubber band exerts is directly, or linearly, related to the distance we pull on the rubber band.  Thus, the rubber band's pulling power can be modeled with a linear equation.  We can plot this model as shown in the figure below (you may need to click on the figure to enlarge it):

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The diagram shows that at first, the rubber band's pulling force increases linearly (along the straight, blue, dotted line).  However, if the rubber band is stretched far enough, the rubber band actually pulls harder than expected.  We usually feel the rubber band pull back harder just before we snap it in half.  This is because the model for the rubber band is mostly linear with a nonlinear term that kicks in after the rubber band is stretched a lot.

     The nonlinear nature of the rubber band is similar to the nonlinear nature of atoms in crystals.  When dim light shines on the crystal, the atoms behave normally and the light just passes through.  But when very bright light hits the crystal, the atoms start to enter the nonlinear zone and strange things happen to the light.  Sometimes, two photons of light are absorbed by the atom and the atoms spits out a single, different color photon.  This is how frequency-doubling works.  But there are other variations.  Let's say a blue and red photon are near an atom.  The blue one gets absorbed, and the red one passes through.  However, the blue one that gets absorbed turns into two photons, one just like the red photon that passed straight through, and one that is a "difference" photon.  The "difference" photon is neither red nor blue, but is actually infrared, and it shoots off in some different direction.

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The details of these occurrences are complex, but the fact that these photons are essentially being added or subtracted from each other is pretty cool.  One source even takes the nonlinear effects to the extreme by generating photons that are essentially the addition of more than 300 of the input photons.  Their setup is a little different, but they are still generating x-rays from infrared/red light.  That is pretty amazing.