What Conditions Produce Population Inversion In a Gain Medium?

A population inversion is a non-equilibrium state in a material (the “gain medium”) where there are more atoms in a higher-energy excited state than in a lower-energy state. This is the fundamental requirement for light amplification (lasing).

Under normal thermal equilibrium, the population of states is governed by the Boltzmann distribution, which implies lower energy levels are more populated. To achieve an inversion ( $N_2>N_1$), energy must be actively supplied to the system, a process called pumping.

Key Conditions:

1. A Strong Pumping Source

You must supply energy at a rate faster than the atoms can decay. This energy can be in the form of:

• Optical Pumping: Using high-intensity light (e.g., a flash lamp or another laser).
• Electrical Pumping: Using an electrical discharge (e.g., in gas lasers like He–Ne) or current injection (in semiconductor diode lasers).
• Chemical Pumping: Using the energy released from a chemical reaction.

2. A “Metastable” Upper State

A simple two-level system is very difficult to invert because the pumping (absorption) and stimulated emission rates are nearly equal. The key is to use a multi-level system that includes a metastable state.

A metastable state is an excited state with an unusually long lifetime (a low $A_{21}$coefficient). Atoms pumped to this state do not decay quickly, allowing them to “pile up” and build a large population.

3. A Multi-Level Energy Structure

Because of the issues with two-level systems, practical lasers use three- or four-level systems:

• Three-Level System: (e.g., Ruby laser)
  1. Pump: Atoms are pumped from the ground state (1) to a high-energy “pump band” (3).
  2. Decay: Atoms rapidly decay (non-radiatively) to the metastable upper laser level (2).
  3. Inversion: Population builds in state 2. Lasing occurs between state 2 and the ground state 1.
  4. Challenge: This requires immense pumping power because you must move more than half the entire population of atoms out of the ground state to achieve $N_2>N_1$.
• Four-Level System: (e.g., Nd:YAG, He–Ne lasers)
  1. Pump: Atoms are pumped from the ground state (0) to a pump band (3).
  2. Decay: Atoms rapidly decay to the metastable upper laser level (2).
  3. Lasing: Lasing occurs between state 2 and a lower laser level 1.
  4. Key Advantage: This lower level (1) is also designed to be short-lived, so it decays rapidly to the ground state (0).
  5. Result: The population of the lower laser level ( $N_1$) is always kept near zero. This makes it extremely easy to achieve a population inversion ( $N_2>N_1\approx 0$), making four-level lasers much more efficient.