Laser: CW-oscillation in a 3-level laser

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In summary, the conversation discusses the expression for steady-state population-inversion in a three-level laser and the contradiction it poses with the gain at CW-oscillation. It also mentions the phenomenon of gain clamping or upper population clamping when increasing the pumping power after laser oscillation sets in. This can lead to relaxation oscillations according to the fluctuation-dissipation theorem.
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Niles
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Hi

At continuous-wave oscillation the gain is equal to the threshold gain, i.e. g = gthreshold. Now in my book, I have the following expression for the steady-state population-inversion for a three-level laser

N2, steady state - N1, steady state = (P-Γ12)/(P+Γ12)NT

where NT=N1, steady state+N2, steady state, P is the pump rate and Γ12 is the rate at which level 2 decays into level 1. Now my question is: If at CW-oscillation g=gt, then why is it that we can change N2, steady state - N1, steady state (and thereby the gain) in a three-level laser at steady-state? Isn't this a contradiction?
 
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What happens if you increase the pumping power further after laser oscillation sets in, is called gain clamping or upper population clamping. Any atoms you pump into the upper level will be almost immediately converted into laser light as fast as you pump them up (well - on statistical average, of course not necessarily the same atoms you just pumped up). Therefore the decay rate will also momentarily increase. If you do not increase the pump power constantly but just add short pulses of high pump power, you might also see the population numbers and the intracavity photon number undergo relaxation oscillations according to the fluctuation-dissipation theorem.
 
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Thank you for your question. The expression you have provided for the steady-state population inversion in a three-level laser is correct. However, it is important to note that this expression assumes that the system is in thermal equilibrium and that the pump rate (P) and decay rate (Γ12) are constant. In a real laser system, these conditions may not always be met.

At continuous-wave oscillation, the gain is equal to the threshold gain, as you have stated. This means that the laser is operating at its maximum efficiency, and the population inversion is at its steady-state value. However, if the pump rate or decay rate changes, the population inversion will also change, and the gain will no longer be equal to the threshold gain. This does not necessarily contradict the fact that the laser is operating at continuous-wave oscillation, as the conditions for steady-state population inversion may no longer be met.

In a real laser system, the pump rate and decay rate can be controlled by adjusting the input power or the laser cavity parameters. This allows for the gain to be changed and for the laser to operate at different levels of efficiency. Therefore, it is possible to change the population inversion and gain in a three-level laser at steady-state without contradicting the fact that it is operating at continuous-wave oscillation.

I hope this explanation helps clarify any confusion. Please let me know if you have any further questions.
 

1. How does a 3-level laser achieve CW-oscillation?

A 3-level laser achieves CW-oscillation by having three energy levels within its active medium. The lower two levels are populated by a constant energy source, such as a pump laser, while the upper level is depopulated by spontaneous emission. This creates a population inversion, where there are more particles in the upper level than the lower levels. When a photon passes through the active medium, it stimulates the emission of more photons through stimulated emission, thus creating the continuous wave of light.

2. What is the difference between CW-oscillation and pulsed operation in a 3-level laser?

CW-oscillation refers to a continuous wave of light being produced by a 3-level laser, while pulsed operation involves the emission of light in short bursts. This is achieved by manipulating the energy source or the active medium in a way that allows for population inversion to occur only briefly. Pulsed operation can be advantageous for certain applications, such as in laser cutting or welding, where high intensity is needed for short periods of time.

3. Can a 3-level laser operate without a population inversion?

No, a population inversion is necessary for a 3-level laser to operate. Without a population inversion, there would be no stimulated emission, and thus no amplification of light. This is why a constant energy source, such as a pump laser, is needed to maintain the population inversion in a 3-level laser.

4. What factors affect the CW-oscillation in a 3-level laser?

Several factors can affect the CW-oscillation in a 3-level laser, including the energy source, the active medium, and the cavity design. The energy source must provide enough energy to maintain the population inversion, while the active medium must have the proper energy level structure for stimulated emission to occur. The cavity design also plays a role in ensuring that the photons are reflected back and forth through the active medium to create continuous amplification.

5. What are some practical applications of CW-oscillation in a 3-level laser?

CW-oscillation in a 3-level laser is used in a variety of applications, including telecommunications, laser printing, and medical procedures. Its continuous wave of light allows for precise and stable output, making it useful for tasks such as data transmission, printing high-resolution images, and performing delicate surgeries. CW-oscillation is also used in scientific research, such as in spectroscopy and laser cooling experiments.

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