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Laser Pulse Calculator

Essential calculations for ultrafast laser labs: time-bandwidth product, peak power from average power, and pulse broadening through dispersive media.

v1.0.0·Updated 2026-06-10
Model & Assumptions Stable
Model
Standard ultrafast-optics relations: time–bandwidth product (Δt·Δν ≥ TBP), peak power from average power and duty cycle, GDD-induced pulse broadening for transform-limited input pulses.
Assumptions
Transform-limited input pulses (Gaussian, sech², or Lorentzian). Second-order dispersion only (GDD); higher-order dispersion neglected. Linear propagation — no self-phase modulation or nonlinear effects.
Limitations
No higher-order dispersion (TOD, FOD). No chirped input pulses. Gaussian-beam calculator assumes TEM00 mode only.

Time-Bandwidth Product

Pulse shape
Input (edit either)

Time-bandwidth product. Δt · Δν ≥ TBP. Gaussian: 0.4413, sech²: 0.3148, Lorentzian: 0.2206. Δν = c Δλ/λ².

Results

Transform-limited Δt —
Frequency bandwidth Δν —
Optical cycles —
TBP (actual / minimum) —
Export

Peak Power

Pulse shape
Parameters

Peak power. E = Pavg/frep,   Ppeak = k E/Δt. k: Gaussian 0.94, sech² 0.88, rect 1.0.

Results

Pulse energy —
Peak power —
Duty cycle —
Peak / Average ratio —

GDD Pulse Broadening

Input pulse
Material

GDD broadening (Gaussian). Δtout = Δtin √(1 + (4 ln2 · GDD/Δtin²)²). GDD = GVD × L × passes.

Results

Total GDD —
Output Δt —
Broadening factor —

Gaussian Beam

Parameters
Beam quality factor. M^2 = 1 is a diffraction-limited Gaussian; larger values increase divergence and focused spot size.
Waist size (edit any)
Evaluate at distance

Gaussian beam. zR = πw0²/(M²λ),   w(z) = w0√(1+(z/zR)²),   θ = M²λ/(πw0).

Results

Rayleigh range zR —
Divergence θ (half-angle) —
Confocal parameter 2zR —
w(z) at selected z —

Focus & Fluence

Beam before lens
Focusing optic
Pulse

Focus. w0 ≈ M² λ f/(π win). I = Ppeak/(πw0²). F = E/(πw0²).

Results

Spot radius w0 —
Spot diameter 2w0 —
Peak intensity —
Fluence —
Rayleigh range zR —
Depth of focus 2zR —

Chirp & Compressor

Measured pulse
Transform limit
Compressor material

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.

Results

Chirp ratio Δt/ΔtTL —
GDD on the pulse —
Compensating GDD —
Material needed —

Nonlinear Conversion

Process
Input wavelengths

SHG. ω + ω → 2ω. λout = λ/2.

Results

Output wavelength —
Output energy —

Spectral Brightness

Source
Spectrum
Beam quality

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).

Results

Pulse energy —
Peak power —
Avg spectral density —
Peak spectral density —
Avg spectral brightness —
Peak spectral brightness —

Beam Modes

Mode family
LG indices
Beam

LGℓ,p. Modes with orbital angular momentum ℓℏ per photon and p radial nodes. Donut profile for ℓ≠0.

Intensity profile

Mode label —
OAM per photon —
Examples