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.Borek said:Lifetime of what? Rate constant of what? Concentration of what?
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 answerHAYAO said: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.
Chemmjr18 said: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
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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!HAYAO said: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.
Depending on at what fixed concentration you are talking about, yes.Chemmjr18 said: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!
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!HAYAO said: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.
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...HAYAO said:Wait, so are there size dependence of the material on the observed radioactive decay rate or not?
Chemmjr18 said:I do believe the there is a size dependence of the material on the observed radioactive decay
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.Borek said:You will need more than "I do believe" for this statement.
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.Borek said: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.
I meant "first-order decay lifetime" as the intrinsic lifetime of the radioactive decay.HAYAO said: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?
Chemmjr18 said:How are detection limits not related to our ability to measure?
It does decay at the same rate. If your sample is a factor 1000 larger then the overall activity will be a factor 1000 higher. How you measure that is irrelevant here.Chemmjr18 said: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?
The size of a crystal used for a laser does have an effect on its lifetime. Generally, larger crystals have longer lifetimes compared to smaller crystals. This is because larger crystals can absorb and dissipate heat more efficiently, which helps to prevent damage and prolong the laser's lifespan.
The efficiency of a laser is also affected by the size of the crystal used. A larger crystal has a larger surface area, allowing for more light to be absorbed and converted into laser light. This leads to a more efficient laser with a longer lifetime.
While crystal size does play a significant role in the lifetime of a laser, there are other factors that can also affect it. These include the quality and purity of the crystal, the type of laser pumping mechanism used, and the operating conditions of the laser.
There is no one optimal crystal size for all laser applications. The optimal size will depend on the specific needs and requirements of the laser system. In some cases, a larger crystal may be more beneficial, while in others, a smaller crystal may be more suitable.
While larger crystals generally have longer lifetimes, there is a limit to how large a crystal can be before it becomes less efficient. If the crystal is too large, it may have difficulty dissipating heat and can potentially lead to thermal damage and a shorter lifetime. Therefore, it is essential to find the right balance between crystal size and efficiency for optimal laser performance.