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⟩…
Einstein A+B coefficients (1917)
Einstein 1917: A21 spontaneous + B12/B21 stimulated absorption/emission rates; thermal-equilibrium ratio A21/B21 = 8 pi h nu^3 / c^3;…
Population inversion (3-level scheme)
Maiman 1960 ruby laser; 3-level scheme: pump |1> -> |3>, fast decay |3> -> |2>, lasing |2> -> |1>; condition N2 > N1 for net stimulated…
Optical cavity (Fabry-Perot resonator)
Fabry-Perot 1899 resonator: m lambda = 2 n L (longitudinal modes); finesse F = pi sqrt(R) / (1-R); cavity Q = omega tau_photon; basis of…
Mode locking (ultrashort pulses)
Hargrove-Fork-Pollack 1964 mode-locking: phase-coherent superposition of N longitudinal modes -> pulse train Delta_t = T_rt / N; sub-fs…
Gas-discharge lasers (He-Ne, CO2)
Javan-Bennett-Herriott 1960 He-Ne 632.8 nm; Patel 1964 CO2 10.6 um (industrial cutting / surgery); collisional-energy-transfer pumping in…
Semiconductor laser diode
Hall-Holonyak-Nathan 1962 GaAs diode; Alferov-Kroemer 1970 double-heterostructure (Nobel 2000); modern InGaAsP / InGaN diodes power telecom…
Ruby laser (Maiman 1960)
T Maiman 1960 first ruby-laser pulsed; modern flash-pumped Nd:YAG + Cr:Al2O3 + diode-pumped solid-state lasers.
Townes maser (1958)
C Townes 1958 (Nobel 1964) ammonia maser + Schawlow-Townes 1958 laser-paper; foundational stimulated-emission devices.
Schawlow-Townes linewidth (1958)
Schawlow-Townes 1958 quantum-limit Δν=πhν(Δν_c)²/P; modern sub-Hz cavity-stabilized lasers Hänsch+Hall (Nobel 2005).
Mode-locking (Hargrove 1964)
L Hargrove 1964 active-mode-locking + DiDomenico 1964 + Hellwarth 1962 Q-switching; foundation of fs/ps pulsed lasers.
OPO (Giordmaine-Miller 1965)
J Giordmaine-R Miller 1965 first OPO in LiNbO3; modern PPLN + KTP + tunable mid-IR + sub-fs comb generation.
CPA (Strickland-Mourou 1985)
D Strickland-G Mourou 1985 (Nobel 2018) chirped-pulse-amplification; modern PW peak-power + relativistic optics + LWFA driver.