# Ratio between spontaneous/stimulated emission

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• greypilgrim
In summary, the ratio between spontaneous and stimulated emission in thermodynamic equilibrium is determined by the Einstein coefficients and is dependent on frequency. In the case of lasers, where the population of energy levels is inverted, there is typically a higher amount of stimulated emission. This is especially true for forbidden transitions. The argument for the difficulty of building Röntgen or gamma lasers based on the incoherent noise increasing with higher frequencies is flawed, as this calculation only applies to the thermal case and lasers operate outside of equilibrium. However, the Einstein A coefficient still plays a role in this argument.
greypilgrim
Hi.

In thermodynamic equilibrium, the ratio between spontaneous and stimulated emission is
$$\frac{A_{21}\cdot N_2}{B_{21}\cdot N_2\cdot u(f)}=e^{\frac{hf}{k_B T}}-1$$
where ##A_{21}## and ##B_{21}## are Einstein coefficients. This means, that there's always much more spontaneous than stimulated emission, and it's getting worse for higher frequencies.

What can be said about this ratio for lasers, i.e. if the population of energy levels is inverted (no thermal equilibrium)? Obviously this depends on the type of laser, I'm just asking about a qualitative statement: Is there still more spontaneous emission, more or less the same or far more stimulated emission? My guess would be the latter, but I'm not sure.

I also saw above calculation as an argument for the difficulty of building Röntgen or gamma lasers, saying that incoherent noise increases for higher ##f##. However this seems flawed to me since it's based on the assumption of thermodynamic equilibrium (by using ##u(f)##), and laser systems operate outside this equilibrium.

greypilgrim said:
What can be said about this ratio for lasers, i.e. if the population of energy levels is inverted (no thermal equilibrium)? Obviously this depends on the type of laser, I'm just asking about a qualitative statement: Is there still more spontaneous emission, more or less the same or far more stimulated emission? My guess would be the latter, but I'm not sure.
You don't need a laser. Any sufficiently intense source of radiation can lead to a predominance of stimulated emission, giving Rabi oscillations. This is especially true for forbidden transitions, where the rate of spontaneous emission is very low to start with.

greypilgrim said:
I also saw above calculation as an argument for the difficulty of building Röntgen or gamma lasers, saying that incoherent noise increases for higher ##f##. However this seems flawed to me since it's based on the assumption of thermodynamic equilibrium (by using ##u(f)##), and laser systems operate outside this equilibrium.
I would agree with you that the above equation only applies to the thermal case, and lasing is definitely an out-of-equilibrium process. But the Einstein A coefficient is proportional to ##f^3##, so the argument is valid, but not on the grounds of that equation.

## 1. What is the ratio between spontaneous and stimulated emission?

The ratio between spontaneous and stimulated emission is a measure of the relative strengths of these two processes in a particular system. It is typically represented as the ratio of the rate of stimulated emission to the rate of spontaneous emission.

## 2. How does the ratio between spontaneous and stimulated emission affect laser performance?

The ratio between spontaneous and stimulated emission plays a crucial role in determining the performance of a laser. A high ratio of stimulated to spontaneous emission leads to a more efficient laser with a higher output power and better beam quality.

## 3. Can the ratio between spontaneous and stimulated emission be controlled?

Yes, the ratio between spontaneous and stimulated emission can be controlled by adjusting the properties of the lasing medium, such as its temperature, density, and chemical composition. This allows for fine-tuning of the laser's performance.

## 4. What is the significance of the ratio between spontaneous and stimulated emission in quantum mechanics?

In quantum mechanics, the ratio between spontaneous and stimulated emission is an important concept that helps to explain the behavior of atoms and molecules. It is a key factor in understanding how light interacts with matter and is essential for the development of laser technology.

## 5. Are there any real-world applications of the ratio between spontaneous and stimulated emission?

Yes, the ratio between spontaneous and stimulated emission has numerous real-world applications, with the most notable being in the field of laser technology. It is also relevant in telecommunications, medical devices, and various scientific research areas, such as spectroscopy and quantum optics.

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