- #1
Phrak
- 4,267
- 6
A laser cavity consists of a couple mirrors, a bunch of metastable molecules and some radiation. What's the partition of energy between molecules and radiation at equilibrium?
Cthugha said:That depends on a lot of stuff.
I suppose you want to take the fraction of molecules, which are in some excited state, into account for calculating the amount of energy you assign to the molecules.
Still there are a lot of parameters: Are you operating near, at, above or far above threshold? How high is the Q factor (how good are the mirrors). On what order is the beta factor. How many modes of the radiation field do you need to take into account? How many molecules are there inside the laser? Do you have a three level laser or a four level laser? Is there mode competition?
And so on and so on...
The easiest way might be to formulate laser rate equations for the laser design you are interested in and to solve them using mathematica or some other program for scientific computing.
Phrak said:So in the simplest cases, at least, the relationship is quite different than I had thought, where the ratio of excited state molecules vs. ground state molecules is the interesting number, and is independent of the radiation intensity.
Cthugha said:The population inversion is usually not independent of the radiation intensity. But I suppose in the case of many emitters, fast pumping and a not too high Q factor, you will always end up in a steady state regime, where relaxation oscillations will always guide you back to this steady state for a wide range of the distortions of the photon number inside the laser cavity.
Phrak said:hmm. Perhaps I scanned the relevant portion of the Wiki article too quickly.
For a two state system they give the equation
[tex]\frac{N_2}{N_1} = exp \left( \frac{-(E_2-E_1)}{kT} \right)[/tex]
where no dependence on the radiation is contained.
Cthugha said:Well, as usual the temperature becomes important if the thermal energy corresponding to that temperature becomes comparable to the difference between the energy levels.
Phrak said:I'm not sure what you mean by that. Isn't there plenty of radiation at the difference frequency in the beam itself?
Cthugha said:Well, yes of course. I thought you are still referring to the equation you posted above as that equation is usually just taken to show that there is no inversion in equilibrium independent of how high the temperature is. As soon as you have steady state lasing emission, the rolle of temperature is usually not that crucial anymore.
The role temperature plays in lasers depends strongly on the lasers. For example you might change the band gap of the gain medium in semiconductor lasers so that you move the main emission frequency out of resonance with the laser cavity. However the influence of temperature depends very strongly on the kind of laser you look at.
Phrak said:That's a very practicle point of veiw. From what I've been reading, the temperature would only have a significant effect, at perhaps 10K to 20K degrees, for a beam in the visible spectrum.
Phrak said:From a less practical point of veiw, there are two questions I find interesting about lasers. Why is there stimulated emission, and how did Einstein predict it?
Phrak said:And how does temperature play a role in the partition of energy between bosons and fermions?
Energy partition in a laser cavity refers to the distribution of energy between molecules and radiation within the cavity. This is important for understanding the efficiency and performance of a laser.
Molecules and radiation interact through a process called stimulated emission, where molecules are stimulated by radiation to release photons of the same frequency. This creates a chain reaction that results in the amplification of the radiation within the cavity.
Understanding energy partition is crucial for optimizing the performance of a laser. By knowing how much energy is distributed between molecules and radiation, scientists can adjust the conditions within the cavity to achieve the desired output.
The energy partition in a laser cavity is influenced by several factors, including the type of molecules used, the temperature and pressure within the cavity, and the intensity and frequency of the radiation.
The energy partition in a laser cavity can be measured by analyzing the output of the laser, which includes the intensity and frequency of the radiation. Additionally, specialized equipment such as infrared spectrometers can be used to directly measure the energy levels of the molecules within the cavity.