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Atomic Transition Processes for Lasers

Compare photon absorption, spontaneous emission and stimulated emission, then connect metastable states and pumping to laser gain.

  • A-Level Laser Physics extension
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Learning objectives

  • Explain excitation, spontaneous emission and stimulated emission.

1. Energy-level condition

For two stationary states with energies E₁ and E₂, a resonant photon has

hf = E₂-E₁,

where h is the Planck constant and f is photon frequency. The atom can exchange only the permitted energy difference in this simplified model.

Absorption, spontaneous emission and stimulated emissionThree energy-level sketches compare upward absorption, random spontaneous emission and matched-photon stimulated emission.AbsorptionE₂E₁Spontaneous emissionE₂E₁Stimulated emissionE₂E₁h f = E₂ − E₁random phase and directiontwo matched photons leaveEnergy levels and photon paths are schematic.
Scroll diagram horizontally to read all labels.
Absorption raises an atom when the photon energy matches the level separation. Spontaneous emission has random timing and direction; stimulated emission produces a second photon matched to the incident photon.

2. Absorption

In stimulated absorption, a particle in the lower state absorbs a matching photon and moves to the upper state. The photon is removed from the radiation field.

Electron-impact pumping is different: a colliding electron may transfer the required excitation energy and carry away any remaining kinetic energy. The incoming electron therefore need not have exactly the transition energy.

3. Spontaneous emission

An excited state can decay without an incident photon. The emitted photon has the transition energy, but its emission time, phase, polarisation and direction are not locked to photons from other atoms. Light dominated by independent spontaneous events is therefore incoherent.

4. Stimulated emission

An incident photon of the transition frequency can induce an excited particle to decay. The emitted photon matches the stimulating photon in frequency, phase, direction and polarisation. One photon has become two matched photons, so this process can amplify an optical field.

The atom supplies the emitted photon energy by losing internal energy; the incident photon is not split in half.

5. Metastable states and pumping

A metastable state is an excited state with an unusually long lifetime. It helps particles accumulate instead of decaying immediately. A pump transfers energy into the medium by electrical discharge, light, current injection or another suitable mechanism.

Neither a metastable state nor pumping alone is sufficient. The populations and losses must allow stimulated emission to dominate.

5A. Common mistakes

  • Saying spontaneous emission produces photons with zero energy variation but random frequency. The transition fixes the photon energy within the level linewidth; randomness concerns timing, phase, direction and polarisation.
  • Saying the stimulated photon replaces the incident photon. Both leave the event.
  • Treating every excited population as an inversion. Inversion compares the upper and lower populations of the chosen laser transition.
  • Assuming a brighter source is automatically coherent.

6. Worked Examples

Modelled example 1

Finding the photon wavelength

Core

Problem

An atomic transition has energy separation 3.20 × 10⁻¹⁹ J. Find the emitted wavelength using h = 6.63 × 10⁻³⁴ J s and c = 3.00 × 10⁸ m s⁻¹.
Study the worked solution

  1. Relate photon energy and frequency

    Method

    Δ E = hf.

    Reason

    The emitted photon carries the atomic transition energy in this model.

    Working

    f = Δ E/h

  2. Replace frequency with wavelength

    Method

    λ = hc/Δ E.

    Reason

    Use c = fλ and eliminate f.

    Working

    λ = c/f = hc/Δ E

  3. Calculate

    Method

    λ = 6.22 × 10⁻⁷ m = 622 nm.

    Reason

    Substitution gives a wavelength in the visible range.

    Working

    λ = ((6.63 × 10⁻³⁴)(3.00 × 10⁸))/(3.20 × 10⁻¹⁹) = 6.22 × 10⁻⁷ m

Next: Population Inversion and Optical Feedback