http://pdfserve.informaworld.com/669949_770849120_727073531.pdf
In this one, I recommend page 117, a section entitled "Crystal Structure and Phase Transitions". There's a diagram and a description in the couple of pages following that describe the crystal structure in some detail. Also at this link:
http://books.google.com/books?id=tc...&hl=en&sa=X&oi=book_result&resnum=2&ct=result, scroll up a little for another view or two of the crystal structure.
Yeah, it's complicated. When you get down to it, it is orthorhombic, which mean the most basic unit that contains all symmetry of the crystal is a rectangular prism (a box, where all sides have different lengths, but all corners are still right angles).
No one really knows for sure what gives the crystal it's non-linearity. One of those links suggests that the potassium atom rides in a channel, and can move farther back and forth in that 1 dimension along the channel with relatively little force. It can't move as far side to side, but along the channel it can move farther. Sounds good to me, so I'll assume that's the mechanism.
What causes frequency doubling specifically? Very complicated. But here's the idea:
Think of an atom, sitting in one place on a lattice. It vibrates some with thermal energy, temperature, but basically just sits there bonded to it's nearest neighbors. You have a positively charged nucleus, and a negative cloud of electrons around it. When bonded, that electrons could distorts, and the electrons stick a little closer tot he bonds, but still fly around everywhere. The electrons are also REALLY fast, they can move to either side extremely fast, but the nucleus, being bigger, moves more slowly.
Now, apply an electric field, just a normal non-changing electric field. The electrons and nucleus have opposite charges, and will therefore move in opposite directions. The electrons will shift to one side, according to the direction of the field, and the nucleus will shift to the other. Neither will de-localize, the atom will stay bonded in place, but the nucleus and electrons will shift to opposite sides of that atom's "slot" in response to the applied electric field. In doing so, the atom has become a dipole, and become polarized (since the charges are separated). The atom has created it's OWN electric field in response to the applied electric field, and the resultant electric field is opposite of the applied electric field (not that it really matters here).
Now, as a photon passes an atom, what an atom sees is an oscillating electric field, going positive to negative to positive, in a sinusoid. Under normal conditions, with normal linear materials, the atom's polarization responds to the sinusoidal electric field linearly, so it oscillates back and forth itself at the same frequency as the sinusoidal electric field, so it oscillates at the same frequency as the photon passing it, and all is good.
But with non-linear materials and when there is a HUGE amount of light coming through, funny things can happen: The atom can start oscillating at a frequency other than the frequency of the passing photon: It can start oscillating at a different harmonic of the passing wave. Instead of going up once and down once for each wavelength of the wave that passes, the atom will go up twice and down twice for each wavelength that passes it. So this atom oscillating at a new frequency, twice the frequency of the light causing it to oscillate, emits it's own light with its own frequency. As long as the incident and resultant waves stay in phase, and all the oscillating atoms oscillate like the first one we talked about, the farther the wave goes, the more of it gets converted to the new wave. Since the index of refraction is different for different wavelengths, the waves move different speeds though, so they don't stay directly in phase and there are losses, and there is a point where more length actually starts being a detriment. How does the atom's resulting polarization field oscillate at a different frequency? It just finds it's own harmonic frequency as a result of the passing wave, at the 2nd harmonic of the passing wave (if could also be at other harmonics, but in this case, it's the 2nd). Not sure of all the details, but I imagine it has to do with how fast and how far the nucleus can shift with the field relative to the electrons, how the bonding allows the atoms to move, etc.
Kind of. Does this make any sense? If those people in the article above were right, and if I understand correctly, when the IR light is oriented correctly, the potassium atom and it's electrons in the channel will run back and forth in the channel since it is more loosely bonded in that direction, and it will oscillate in the channel at the 2nd harmonic frequency of the IR light instead of at the same frequency as the IR light. Since the channel only runs in 1 dimension, that is way the KTP orientation is crucial to achieve green light: the IR waves have to move the atom in that direction to get it to oscillate at the 2nd harmonic.
Make sense? Also, both those resources and some others have more descriptions.
If those people are wrong and it's not the K that makes the nonlinearity, I've seen another resource saying it's due to "chains of TiO6 octahedra linked at 2 corners by alternating long and short Ti-O bonds". Either way, it is an an atom bonded in a specific way that allows it to oscillate at
other harmonics of the passing wave, besides the main harmonic.
