Worked examples (Lesson 1)

Example 1.1 — Photon needed. An atom has levels E₁ = 0 and E₂ = 1.96 eV. What photon is needed for excitation, and what are the properties of a photon released by stimulated emission? hν = 1.96 eV, λ = 1240/1.96 = 633 nm (red). The stimulated photon has the same 633 nm wavelength, travels in the same direction and in phase with the stimulating photon.

Example 1.2 — Amplification. One photon passes along a column of excited atoms. If every photon stimulates one new photon in each pass (doubling), how many photons after 10 passes? 2¹⁰ = 1024 photons, all coherent. After 20 passes: more than a million. This shows the idea of the "chain reaction" of stimulated emission (in a real laser, losses such as the mirror leak reduce the gain).