Coherent stimulated-emission light sources — gain media, optical cavities, threshold conditions, Q-switching, mode-locking, Gaussian beam propagation. Distinct from optics-as-classical-EM and from quantum-optics-as-Fock-space; this tree is…
laser-physics
Population inversion
Non-equilibrium condition N_2 > N_1 between an upper and lower level of a quantum system. Required for net stimulated emission (gain) at…
Einstein A and B coefficients
Per-atom transition rates between two levels: A_{21} (spontaneous emission), B_{12} ρ(ν) (absorption), B_{21} ρ(ν) (stimulated emission),…
Stimulated emission
An incident photon induces an excited atom to emit a second photon identical in frequency, phase, polarization, and direction. Coherent…
Optical cavity (Fabry–Pérot)
Resonator formed by two (typically partially-reflecting) mirrors separated by L. Supports longitudinal modes ν_q = q c/(2L) and transverse…
Gain medium
Material providing optical gain via population inversion — Nd:YAG crystal, He-Ne gas, semiconductor heterostructure, dye solution.…
Laser threshold condition
Round-trip gain equals round-trip loss: 2g L = −ln(R_1 R_2) + 2αL, where R_i are mirror reflectivities and α is distributed loss. Pumping…
Rate equations (laser)
Coupled ODEs for upper-level population N and intra-cavity photon number n: dN/dt = R_p − N/τ − cσnN; dn/dt = cσnN − n/τ_c. Predict turn-on…
Q-switching
Cavity loss is held high (low Q) while the gain medium is pumped well past the static threshold; suddenly switching Q high releases the…
Mode locking
Phasing N longitudinal cavity modes coherently produces a pulse train of duration ~1/(NΔν), down to femtoseconds in Ti:sapphire. Active…
Gaussian beam (TEM_{00})
Lowest-order paraxial-wave solution: w(z) = w_0√(1+(z/z_R)²) with Rayleigh range z_R = πw_0²/λ; phase has Gouy term ψ(z) = arctan(z/z_R).…
Laser coherence (temporal & spatial)
Temporal: coherence time τ_c ≈ 1/Δν, length ℓ_c = c τ_c (cm to km depending on linewidth). Spatial: high transverse coherence yields…
Four-level laser system
Pumping populates a short-lived state |3⟩ that decays rapidly to upper laser level |2⟩; lasing transition |2⟩→|1⟩ is fast, |1⟩→|0⟩…