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ArcticMyst Security by Avery

The inner workings of a KTP crystal???

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How do Potassium Titanyle Phosphate crystals double the energy of photons?

It confuses me when i think about it in its simplest form =

a single 1.16ev (1064nm) photon enters the crystal.
a single 2.33ev (532nm) photon exits the crystal.

How did that photon change to a higher energy state??
Is the photon that exits still the same photon that entered?
Does the higher energy photon posses any net gain in power?
Or is there wasted energy in the process?

Thank you for helping me understand this.
 





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I just did a little research and realised that my simple way of looking at it is incorrect, The output photon is a combination of two input photons. so there is a gain in power if measuring individual photons but no gain in power if measuring the whole emission.

Still, how does a crystal combine two photons?? what atomic/photonic interactions are going on?
 
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Correct me if I'm wrong but I don't think non-linear crystals "change" the frequency of the photons persay, I think it just emits another wavelength of photons after being "excited" by the pump. Scratch that...

It actually occurs because the crystal creates a non-linear polarization wave from the pump wave that oscillates with twice the initial frequency and half the wavelength...
 
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digital_blue said:
Correct me if I'm wrong but I don't think non-linear crystals "change" the frequency of the photons persay, I think it just emits another wavelength of photons after being "excited" by the pump.

I don't mean to be rude but I would tend to believe that is incorrect just for one reason, if that were true then i would imagine you could just pump the KTP as the lasing medium.
 
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k-shell said:
I don't mean to be rude but I would tend to believe that is incorrect just for one reason, if that were true then i would imagine you could just pump the KTP as the lasing medium.

Read the edit ;)

That was my original understanding of the frequency doubling process.
 
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Does anyone know of a link that shows or explains the geometry of the crystalline structure?

and how critical is the entrance angle?
 
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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.  
 
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Sorry for the necro, but this is interesting, and I finally found what I had been looking for all this time. I was looking for a good way to visualize the KTP crystal structure, and finally found a good source for the data needed and a good way to visual it. It's complicated, but cool. So, if you're interesting in viewing the crystal structure of KTP, follow the instructions below. Also, if you're interested in ANY other crystal structure out there, the program I'm going to link will help you do just that, you just have to find the data for the structure you want to look at.

First, get a program called CrystalMaker: http://www.crystalmaker.com/ You can download the free demo version, it does very well. Download, and install it.

You can now play around with it. They give some sample structure, ways to view the model, and so on.

To build crystals, you need to know something called the space group (there are something like 230 space groups that encompass basically all solid crystal matter), and then where the atoms reside in that space group. Luckily, these things are tabulated by smart people in places like http://cst-www.nrl.navy.mil/lattice/index.html and http://rruff.geo.arizona.edu/AMS/amcsd.php.

For KTP, go to the second one, the one under arizona.edu. In the General Search box, the last box, type in KTP. In the search results, you see the first result is for our friend KTP. It gives the space group (Pna2_1), the lattice constants right in front of the space group, and the positions of all the atoms in the unit cell.

Iof you want, you can type all that into CrystalMaker under "New crystal", but instead, just click the little link "Download CIF Data" and save the file. Now, in CrystalMaker, under "File", go to "Import", and select CIF, then select the file you just saved from the website. This will bring up the KTP crystal structure, with atoms and bonds in place. You can now explore the entire structure of the KTP crystal in full 3-D, with many different rendering options.

Don't be afraid to play around with the program, it can be quite interesting. To see how the structure builds, go to "Range" right above the image, and where the values are 0 to 1 in all three directions, you can make the range 0 to 2 in all three directions, giving you 8 unit cells so you can see how the structure it put together, and how the symmetry work in the crystal.

Anyway, I had been looking for a download of the KTP crystal data, and finally found that database for the CIF data, and thought I would share. If you have any more questions on CrystalMaker or crystal structure in general, I can try to answer them.
 

Benm

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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.

It is all very complicated solid state phyisics really, but the main concept is that you have a material that has allowed energy states both at the pump energy level, and double that. Furthermore, the transition from the doubly excited state to the singly excited state must be difficult (forbidden) - otherwise no doubling would occur. Also, the transistion from the doubly excited state back to ground must not be a forbidden one, so this becomes the main pathway for foton emission.

There are paralels with how gas lasers work, but doing this in solids is not as easy.
 
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^Maybe I'm misunderstanding what you're saying, but that, to me, sounds like pumping. You're not pumping KTP when converting 1064 to 532, you're generating oscillations.

------------------------------------------

If I'm reading what you're saying correctly, then you're saying that you use the 1064nm light to promote electrons up in energy not just up one transition of EXACTLY the wavelength of the light, but to exactly twice the energy of the wavelength of light you're using, and then those electrons are falling back down in energy and releasing the 532nm photons.

That's not what's happening. That's optical pumping, and if that were the case, then you could use any wavelength of light that is shorter than 1064 to make it work. KTP uses a non-linear optical process involving oscillations and producing harmonics, not simple pumping of the crystal.

You're right, it is a very complicated physics problem, but I don't think you have described it. Maybe you're trying to say something that I'm not getting?
 




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