# Einstein Coefficients - Laser Beams

• Ivor Denham
In summary, the conversation discusses a two level laser system with no degeneracy and a constant sum of N1 and N2. The goal is to show that B12 equals B21. The equations for the rate of change of N1 and N2 are given, and the attempt at a solution involves manipulating these equations and using the fact that the sum of N1 and N2 is constant. However, the attempt at a solution reaches a point where it is unclear how to proceed and the speaker asks for guidance.
Ivor Denham

## Homework Statement

Assume a two level laser system with no degeneracy (g1 = g2 = 1).
If [tex]N_2 + N1 = \text{constant}[\tex], show that [tex]B12 = B21[\tex].

## Homework Equations

[tex]\frac{\partial N_1}{\partial t}=-B_{12}\rho(v_{21}N_1[\tex]
[tex]\frac{\partial N_2}{\partial t}=-B_{21}\rho(v_{21}N_2[\tex]

## The Attempt at a Solution

I think there might be something up with the signs in the relevant equation, a convention I am not observing.

[tex]N_1+N_2=c[\tex]
[tex]\frac{\partial N_1}{\partial t}+\frac{\partial N_2}{\partial t}=\frac{\partial c}{\partial t}[\tex]
[tex]\frac{\partial N_1}{\partial t}+\frac{\partial N_2}{\partial t}=0[\tex]
[tex]-B_{12}\rho(v_{21}N_1+-B_{21}\rho(v_{21}N_2=0[\tex]
[tex]-B_{12}N_1+-B_{21}N_2=0[\tex]

From here I am stuck, where have I gone wrong?
[/B]

Also could someone tell me how to fix the latex?

## 1. What is the significance of Einstein coefficients in relation to laser beams?

Einstein coefficients are important in understanding the behavior of laser beams. They describe how atoms interact with light, specifically how they absorb and emit photons. This is crucial for understanding how laser beams are created and how they function.

## 2. What are the three types of Einstein coefficients?

The three types of Einstein coefficients are the absorption coefficient, the stimulated emission coefficient, and the spontaneous emission coefficient. These coefficients describe the probability of an atom absorbing, emitting, or spontaneously emitting a photon.

## 3. How do these coefficients affect the intensity of a laser beam?

The absorption and stimulated emission coefficients determine the rate at which photons are produced in a laser. The spontaneous emission coefficient affects the overall intensity of the laser beam as it determines the number of photons emitted without any external stimulation.

## 4. Can Einstein coefficients be used to predict the behavior of laser beams?

Yes, Einstein coefficients can be used to predict the behavior of laser beams. They provide a mathematical description of how atoms interact with light, which allows scientists to understand and manipulate the properties of laser beams.

## 5. How are Einstein coefficients related to the gain medium in a laser?

The gain medium in a laser is composed of atoms that can absorb and emit photons. The absorption and stimulated emission coefficients describe how these atoms interact with light, which ultimately determines the gain of the laser. The higher the gain, the more powerful the laser beam.

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