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Does the size of a crystal used for a laser affect lifetime?

  1. Nov 3, 2017 #1
    I would imagine that it doesn't. I'm really sure how to rationalize this. If emission is a decay process, I don't think the rate constant would change with concentration, and likewise crystal size. Any spectroscopist out there?
     
  2. jcsd
  3. Nov 3, 2017 #2

    Borek

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    Lifetime of what? Rate constant of what? Concentration of what?
     
  4. Nov 3, 2017 #3
    The lifetime of the excited state of whatever the lasing material is I guess. For the rate constant (or decay constant) I mean the rate at which the excited state in lasing material decays to short-live, lesser excited state under it. For concentration I mean the amount of "things" in the lasing material undergoing some population inversion.
     
  5. Nov 3, 2017 #4

    jim mcnamara

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    Your question is really too general, as @Borek is trying to tell you.

    Yes, laser crystals can have an MTBF - mean time before failure. It is all over the map; the range is a few months to hundreds of years. MTBF is typically reported in hours of operation. I found one calculation that yielded an MTBF estimate greater than 5 million hours. Obviously you cannot directly test this since that MTBF is ~600 years.

    I'm pretty sure a technical link is not helpful for you, since your question does not seem to reflect understanding of the subject.

    But in simple terms, different laser types have different MTBF values. I do not know what "concentration" means, so I cannot answer other parts of your question.
    Someone else can surely give betters than I did.
     
  6. Nov 3, 2017 #5
    Hmmm. I see where you all are coming from. Perhaps it's due to my poor understanding/wording. Say that I have a neodymium doped yttrium aluminum Garnet (Nd:YAG) laser crystal rod. If i'm using this crystal in a laser, will the size of the crystal affect any characteristics of the laser itself. That is, will a laser containing a 4-by-7 mm Nd:YAG rod operate differently than a laser containing a 20-by-35 mm Nd:YAG rod?
     
  7. Nov 4, 2017 #6

    HAYAO

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    It's not impossible to believe that the optical property may change with a larger laser medium under operation because larger medium makes it harder to cool to the core. That means the temperature of the core is higher than the outer and it could cause expansion in the inside. And an expansion in the inside means the "optical" property of the medium is changed (refractive index is often temperature dependent, leading to a situation similar to thermal lensing) and the "photophysical" property of dopant (crystal field is changed) is also changed. This decreases the quantum efficiency. Furthermore, if the medium is too big then internal stress may cause fracture. This applies for most solid-state lasers.

    That being said, YAG has rather high thermal conductivity, rather low thermal expansion, with fairly large Young's modulus. I don't think a laser rod size of what you've just said really make much difference as long as the cooling system is doing its job.

    I'm not an expert in lasers.
     
  8. Nov 4, 2017 #7
    I thought it would only effect the quantum yield. How would any of these things impact the amount time it takes for a photon to be emitted from an long-lived excited state a short-lived lesser excited state? The lifetime is inversely proportional to the rate constant. I've heard of the rate constant being temperature dependent, but not dependent on sample size. Also, thanks for the response. This was a very insightful answer
    .
     
  9. Nov 4, 2017 #8

    HAYAO

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    I'll answer this along with the OP that mentions concentration:
    1) Concentration does affect the emission lifetimes (and the quantum yield).
    2) Size of the crystal does affect the emission lifetimes depending on the concentration.

    1) Is called "concentration quenching". For example, you mentioned Nd, which has multiple 4f-state levels. Energy transfer between multiple Nd(III) ions could doubly excite a Nd(III) ion, leading to an emission of higher energy (and not 1064 nm line used for lasing). This usually lead to shorter emission lifetimes. There could also be a "killer-site", which could be a impurity or defect site that completely quenches the energy once the energy is delivered to this site, but most laser medium is very pure.

    2) Is called "self-trapping". This is basically a reabsorption of a emitted photon by a different ion of the same type. Obviously, the larger the crystal, there are more dopant site that can absorb the photon. This causes the emission lifetimes to be come longer, and also decreases quantum yield.

    This paper is relevant for this discussion:
    F. Auzel, G. Baldacchini, L. Laversenne, G. Boulon, "Radiation trapping and self-quenching analysis in Yb3+, Er3+, and Ho3+ doped Y2O3", Opt. Mater. 2003, 24, 103-109.


    Most of the laser medium are optimized in terms of dopant concentration for a particular size of crystal so that they can afford the maximum quantum efficiency possible for a given laser setup.

    EDIT: Both the effects explained above is probably a small deviation in a high-purity solids like laser medium.
     
    Last edited: Nov 4, 2017
  10. Nov 4, 2017 #9
    Thanks! Especially for the article. I can't read it right now since I'm not on campus but I'll make sure to. Just to make sure I'm understanding your answer: If the concentration of dopant remains exactly the same in the crystal, and we just increase the size the crystal, we can expect emission lifetimes to be longer? For some reason I was thinking about it from the perspective of radioactive decay. If you had 50g of some 1 wt% radioactive substance, why wouldn't it decay at the same rate as 50 kg of the same 1 wt% substance? Apples and oranges I guess! Again, thanks!
     
  11. Nov 4, 2017 #10

    HAYAO

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    Depending on at what fixed concentration you are talking about, yes.

    I don't really know about radioactive decay. I didn't know that they don't decay at the same rate.
     
  12. Nov 4, 2017 #11
    Half-lives are constant, but different for different species, of course (It may not be exactly independent of temperature though). The half-life is inversely proportional to the rate constant. Thus, the rate constant is constant. I just assumed the since they were they were both first-order decay, the rate constant for something like fluorescence or phosphorescence would also be constant. I also thought that since they were both first-order decay, changing the sample size would only affect how easy it is to detect decay. Similar to how having a lot of radioactive nuclei could produce a better detection signal. One too many assumptions I guess!
     
  13. Nov 4, 2017 #12

    HAYAO

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    Wait, so are there size dependence of the material on the observed radioactive decay rate or not?
     
  14. Nov 4, 2017 #13
    Don't quote me on this, but yes, I do believe the there is a size dependence of the material on the observed radioactive decay. Isn't there a size dependence on anything we use quantitative analysis on? I believe this is called the lower limit of quantitation. But just because we can't detect it doesn't mean it's not there...
     
  15. Nov 4, 2017 #14

    Borek

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    You will need more than "I do believe" for this statement.
     
  16. Nov 4, 2017 #15
    Ok. There are limits to how much of something we can detect. The detection limit is "the concentration of analyte that gives a signal equal to three times the standard deviation of signal from a blank". If the analyte (in this case whatever is decaying) isn't producing a significant enough signal or the method of analysis isn't sensitive enough, is it unreasonable to suggest that a larger sample size is necessary to get a better signal (or better instruments). Thus, there is some correlation to the amount of material being analyzed and the response we observe. A good example of this are reporting limits for consumables.
     
  17. Nov 5, 2017 #16

    Borek

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    This is a strawman.

    Yes, there are detection limits, but they are not related to our capability of measuring the radioactive decay. First - we are perfectly capable of observing decay of single atoms. Second - radioactive decay is known to have first order kinetics, this is in no way related to the sample size.
     
  18. Nov 5, 2017 #17
    No, it's not. You're just perceiving as a strawman. If it's a misunderstanding, then it's a misunderstanding and call it that. How are detection limits not related to our ability to measure? (this is a genuine question) I said the sample size would impact what we observe--but right after that I said it didn't mean it's not there. Never did I say it would impact what was actually happening. Read my previous post. If you did you would had also seen that I already said that first-order decay was independent of sample size. This is exactly why I was so confused about phosphorescence being dependent on sample size.
     
    Last edited: Nov 5, 2017
  19. Nov 5, 2017 #18

    HAYAO

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    I'm a bit confused here Chemmjr18, did you mean "first-order decay" lifetime as intrinsic lifetime of the radioactive decay? Or did you mean single-exponential decay?
     
  20. Nov 5, 2017 #19
    I meant "first-order decay lifetime" as the intrinsic lifetime of the radioactive decay.
     
  21. Nov 7, 2017 #20

    Borek

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    They are, but that's not the problem here. We know enough about the decay and its mechanism to not need measurements of the amount of products. It is much easier to measure activity, and we can do it with extremely high precision - in some cases we are capable of detecting almost every single decay. We are counting events, not measuring a signal proportional to the concentration.
     
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