Compare Photon Properties: Spontaneous vs. Stimulated Emission

The fundamental difference is that spontaneous emission is a random, isolated event, whereas stimulated emission is a non-random, externally triggered event.

Spontaneous Emission

(The process in LEDs, light bulbs, and stars)

• Trigger: A random, probabilistic event. An excited atom decays on its own timescale.
• Phase: The emitted photon’s phase is completely random and independent of other photons.
• Direction: The photon is emitted in a random direction (isotropically, over $4\pi$ steradians).
• Frequency: Centered on the transition $\nu =\frac{E_2-E_1}{h}$, but subject to broadening (e.g., Doppler broadening), resulting in a range of frequencies.
• Resulting Light: Incoherent — a mixture of phases, directions, and (to a lesser extent) frequencies.

Stimulated Emission

(The process in lasers and optical amplifiers)

• Trigger: An incoming photon of the correct frequency interacts with an excited atom.
• Phase: The emitted photon’s phase is identical to that of the stimulating photon.
• Direction: The emitted photon’s propagation direction is identical to that of the stimulating photon.
• Frequency: The emitted photon’s frequency is identical to that of the stimulating photon.
  • Resulting Light: Coherent — photons in phase, traveling in the same direction, at the same frequency.