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光子学·激光
12
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激光粒子数反转:三能级 vs 四能级
Laser population inversion: 3-level vs 4-level
3能级vs4能级 · 阈值抽运 · ΔN=N2−N1 · 能级图
Why a 4-level laser reaches threshold more easily — ΔN = N₂ − N₁ vs pump
光学增益饱和
Optical gain saturation
g(I)=g0/(1+I/Is) · I=Is时g=g0/2 · 稳态钳位
g(I) = g₀ / (1 + I/I_s) — saturated gain and steady-state clamping
时间相干性:相干时间与相干长度
Temporal coherence: coherence time & length
Lc=c/Δν=λ²/Δλ · HeNe 20cm · 二极管0.21mm
τ_c = 1/Δν, L_c = c·τ_c = c/Δν = λ²/Δλ — linewidth sets coherence
激光谐振腔纵模
Laser cavity longitudinal modes
νq=q·c/2nL · FSR=c/2nL · 增益带宽内模数
Cavity length sets the mode spacing (free spectral range); the gain bandwidth sets how many modes oscillate
高斯光束传播
Gaussian beam propagation
束腰w0 · zR=πw0²/λ · w(z)=w0√(1+(z/zR)²)
Beam waist w₀, Rayleigh range z_R, the w(z) spot-size hyperbola, and wavefront curvature R(z)
激光束发散角与光束质量 M²
Laser beam divergence & M² beam quality
θ=λ/πw0 · M²光束质量 · 束腰↔发散折衷
Far-field half-angle θ = λ/(πw₀); real beam θ = M²·λ/(πw₀); the smaller the waist, the larger the divergence
调 Q 激光(巨脉冲)
Q-switched laser (giant pulse)
低Q储能→高Q放巨脉冲 · P峰=E/τ · 纳秒MW级
Hold the cavity Q low to store energy, then switch Q high to dump it as a nanosecond giant pulse
锁模激光(超短脉冲列)
Mode-locked laser (ultrashort pulse train)
N纵模同相→超短脉冲 · τ≈1/Δν · 间隔2L/c
Lock the phases of N longitudinal modes and the output turns from noisy CW into a periodic train of ultrashort pulses
二次谐波(倍频)与相位匹配
Second-harmonic generation & phase matching
χ⁽²⁾ ω→2ω · 相位匹配Δk=0 · η∝sinc²(ΔkL/2)
Doubling ω to 2ω in a χ⁽²⁾ crystal: 1064 nm infrared → 532 nm green, efficiency set by phase matching Δk = 0
半导体激光二极管(L-I 曲线)
Semiconductor laser diode (L-I curve)
λ=hc/Eg · 阈值电流Ith · L-I:P=η(I−Ith) · 斜率效率
Emission wavelength set by the bandgap; optical power rises linearly with drive current above threshold
发光二极管(带隙决定颜色)
Light-emitting diode (bandgap sets colour)
λ=1240/Eg nm · 带隙定色 GaN蓝/GaP绿/GaAsP红 · 谱宽~1.8kT
Photon energy hν ≈ Eg, peak wavelength λ = 1240 / Eg(eV) nm; linewidth ≈ 1.8kT
光电二极管响应度(R = ηλ/1240)
Photodiode responsivity (R = ηλ/1240)
R=ηλ/1240 A/W · 量子效率η · 截止λc=1240/Eg
Photocurrent per watt of optical power; responsivity drops to zero beyond the cutoff