7.4.12. Stimulated Emission

Table of Contents

Core Idea

Stimulated emission is the process in which an incoming photon causes an excited atom to emit a second photon. The emitted photon is not random. It matches the incoming photon in frequency, direction, phase, and polarization. This makes stimulated emission the key physical process behind laser light.

An atom has discrete energy levels. If an atom is in a higher energy state $E_2$ and a photon with the right energy passes by, the atom can be forced to drop to a lower energy state $E_1$. The energy difference appears as a photon:

$$
E_2 - E_1 = hf
$$

where $h$ is Planck's constant and $f$ is the photon frequency.

In spontaneous emission, the atom emits on its own. In stimulated emission, the emission happens because a suitable photon interacts with the excited atom.

For stimulated emission to occur, the incoming photon must have energy equal to the energy gap between the two atomic states:
$$
hf = E_2 - E_1
$$
The emitted photon is coherent with the stimulating photon, meaning both waves stay in step.

How the Process Works

Imagine an atom already in an excited state. This means one of its electrons has been raised to a higher allowed energy level. If a photon of the correct energy arrives, it can trigger the atom to return to a lower level. During this transition, the atom emits a photon.

The remarkable feature is that the new photon is an exact copy of the incoming one in its main wave properties. After the interaction, there are now two photons traveling together.

This is very different from ordinary glowing objects, where light is usually emitted spontaneously in many directions and with random phase relationships.

Rendering scientific sketch…

Stimulated emission from an excited atom

Comparison with Other Emission Processes

To understand stimulated emission clearly, it helps to compare it with absorption and spontaneous emission.

In absorption, an atom in a lower state takes in a photon and moves to a higher state. In spontaneous emission, an excited atom drops to a lower state on its own and emits a photon randomly. In stimulated emission, an excited atom is induced by an incoming photon to emit a second matching photon.

Process	Initial atomic state	Role of photon	Final result
Absorption	Lower energy state	Photon is absorbed	Atom moves to higher state
Spontaneous emission	Higher energy state	No incoming trigger needed	Atom emits one photon randomly
Stimulated emission	Higher energy state	Incoming photon triggers emission	Atom emits a second matching photon

Stimulated emission increases the number of photons in a light beam without changing their frequency, provided the photons match the atomic transition.

Why It Matters

Because the emitted photon matches the incoming one, stimulated emission can amplify light. If many atoms are in excited states, one photon can stimulate emission from one atom, then the two photons can stimulate more atoms, and so on. This chain effect produces a strong, organized beam of light.

This is why stimulated emission is central to laser operation. The word LASER stands for Light Amplification by Stimulated Emission of Radiation.

The special properties of laser light, such as high intensity, narrow frequency range, and strong coherence, come from this process.

Conditions for Strong Stimulated Emission

Stimulated emission only becomes dominant if many atoms are already in excited states. In ordinary matter at thermal equilibrium, most atoms are in lower energy states, so absorption is usually more likely than stimulated emission.

For light amplification, the number of atoms in the upper state must exceed the number in the lower state for the relevant transition. This is called population inversion. The detailed creation of population inversion belongs to laser operation, but the idea is important here because stimulated emission needs a large supply of excited atoms.

If there are too few excited atoms, the incoming light is more likely to be absorbed than amplified.

A medium can amplify light by stimulated emission only when excited atoms are sufficiently abundant. In practice, this requires population inversion.

Coherence and Photon Copying

The emitted photon in stimulated emission is often described as a clone of the incident photon. This does not mean it comes from nowhere without energy cost. The atom supplies the energy by moving from the excited state to the lower state.

The copied properties are what make stimulated emission so useful. The emitted and stimulating photons have the same

Property	Match in stimulated emission
Frequency	Same
Direction	Same
Phase	Same
Polarization	Same

Because the waves remain in step, the light is coherent. Coherence is one of the defining features of laser beams.

Energy View

The atom loses energy when it undergoes stimulated emission. That lost atomic energy becomes the energy of the emitted photon.

If the transition is from $E_2$ to $E_1$, then

$$
\Delta E = E_2 - E_1 = hf
$$

The incoming photon does not lose its own energy in the ideal picture. Instead, it triggers the release of another photon with the same energy. After the process, there are two photons, each with energy $hf$.

So total photon energy after the event is $2hf$, but one of those photons came from the incoming beam and the other came from the atom's stored excitation energy.

Simple Picture of Amplification

Suppose one photon enters a material containing many excited atoms. It stimulates one atom to emit, giving two photons. Those two photons may stimulate two more excited atoms, producing four photons. Under the right conditions, the number of photons can grow rapidly.

Rendering scientific sketch…

Simple amplification by stimulated emission

This drawing is only a simplified idea. Real laser media involve many atoms, repeated reflections, and carefully controlled conditions.

Relation to Atomic Transitions

Stimulated emission depends on the existence of discrete atomic energy levels. Only certain transitions are allowed, so only certain photon energies can trigger the process. This is why atoms and materials emit or amplify only specific wavelengths unless many transitions are involved.

The exact structure of energy levels belongs to atomic spectra and laser physics, but for stimulated emission the essential point is simple. The photon must match an allowed energy difference.

Summary

Stimulated emission occurs when an excited atom is triggered by an incoming photon to emit a second photon. The two photons have the same energy and travel together with the same direction and phase. This makes stimulated emission the foundation of light amplification and laser action.

Essential facts about stimulated emission:
$$
E_2 - E_1 = hf
$$
An excited atom plus a matching incoming photon can produce two matching photons.
The emitted photon has the same frequency, direction, phase, and polarization as the incoming photon.
Stimulated emission is the physical basis of laser amplification.

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