Laser Pulse Calculator
Essential calculations for ultrafast laser labs: time-bandwidth product, peak power from average power, and pulse broadening through dispersive media.
Time-Bandwidth Product
Time-bandwidth product. Δt · Δν ≥ TBP. Gaussian: 0.4413, sech²: 0.3148, Lorentzian: 0.2206. Δν = c Δλ/λ².
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Peak Power
Peak power. E = Pavg/frep, Ppeak = k E/Δt. k: Gaussian 0.94, sech² 0.88, rect 1.0.
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GDD Pulse Broadening
GDD broadening (Gaussian). Δtout = Δtin √(1 + (4 ln2 · GDD/Δtin²)²). GDD = GVD × L × passes.
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Gaussian Beam
Gaussian beam. zR = πw0²/(M²λ), w(z) = w0√(1+(z/zR)²), θ = M²λ/(πw0).
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Focus & Fluence
Focus. w0 ≈ M² λ f/(π win). I = Ppeak/(πw0²). F = E/(πw0²).
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Chirp & Compressor
Chirp compensation. GDD = ±Δtin √((Δtactual/ΔtTL)²−1)/(4 ln2). L = |GDD|/GVD. Sign of GDD tells you if pulse has positive or negative chirp.
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Nonlinear Conversion
SHG. ω + ω → 2ω. λout = λ/2.
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Spectral Brightness
Spectral brightness. B = P/(Δλ · A · Ω). For Gaussian beam: A·Ω = M4λ², so B = P/(M4λ²Δλ). Defaults from Elu et al., Nature Photon. (2021).
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Beam Modes
LGℓ,p. Modes with orbital angular momentum ℓℏ per photon and p radial nodes. Donut profile for ℓ≠0.