Rami Arieli: "The Laser Adventure"

Rami Arieli: "The Laser Adventure" Chapter 2.10 page 1

2.10 Amplification

We saw in the rate equation that:

Two processes decrease the population number of the excited level: Spontaneous emission and stimulated emission.
One process increases the population number of the excited state - absorption.

Since the same amount of energy (hn) is involved in every transition up or down, than the rate at which energy is absorbed in a unit volume of atoms is given by the transition rate times the unit of energy: dU_adt = Kn(t)[N₁(t)-N₂(t)]*hn

U_a

Question 2.6:

Compare this equation to the rate equation. What is the difference? explain why.

The incoming energy is:

U_signal(t) = n(t)*hn

The absorbed energy is taken out of the incoming signal, so the rate of loss of energy from the incoming signal is:

dU_signal(t)/dt = -K*n(t)*[N₁(t)-N₂(t)]*hn = -K*[N₁(t)-N₂(t)]* U_signal(t)

The same equation can be written for the photon density:

dn(t)/dt = -K* [N₁(t)-N₂(t)]*n(t)