Calculate transform limited pulse width from spectral bandwidth. Switch units, shapes, and export results easily. Useful for ultrafast optics planning, teaching, validation, and testing.
Time bandwidth relation: Δt × Δν = K
Transform-limited pulse duration: Δt = K / Δν
Required frequency bandwidth: Δν = K / Δt
Wavelength to frequency conversion: Δν ≈ cΔλ / λ2
Equivalent wavelength bandwidth: Δλ ≈ Δνλ2 / c
Pulse shapes: Gaussian K = 0.441, Sech2 K = 0.315, Rectangular K = 0.886
Approximate optical cycles: cycles = ν0 × Δt
The wavelength conversion is most accurate when spectral bandwidth is small compared with the central wavelength.
| Central Wavelength | Bandwidth Input | Pulse Shape | Time Bandwidth Product | Estimated Pulse Duration |
|---|---|---|---|---|
| 800 nm | 10 nm | Gaussian | 0.441 | 94.145 fs |
| 1550 nm | 2 nm | Sech^2 | 0.315 | 1.262 ps |
| 1030 nm | 5 nm | Rectangular | 0.886 | 627.072 fs |
A transform limited pulse is the shortest pulse possible for a given spectrum. It has no extra chirp. It has no added phase distortion. This makes it a key concept in ultrafast optics, laser physics, spectroscopy, and photonics. When a pulse is transform limited, its temporal width and spectral width follow a fixed time bandwidth product. That product depends on pulse shape.
This transform limited pulse duration calculator helps estimate pulse width from measured bandwidth. It also works in reverse. You can enter pulse duration and find the required spectral bandwidth. That is useful during laser design, pulse compression, cavity tuning, optical diagnostics, and lab validation. The tool supports Gaussian, sech2, rectangular, and custom pulse models. It also converts wavelength bandwidth into frequency bandwidth automatically.
The main relation is Δt × Δν = K. Here, Δt is pulse duration, Δν is frequency bandwidth, and K is the time bandwidth product. A Gaussian pulse uses K = 0.441. A sech2 pulse uses K = 0.315. A rectangular pulse uses K = 0.886. When bandwidth is given in wavelength units, the calculator uses Δν ≈ cΔλ / λ2 for narrowband estimates. This links central wavelength, optical frequency, pulse cycles, and transform limited duration in one workflow.
You can use this calculator for femtosecond laser planning, pulse measurement checks, nonlinear optics setup work, dispersion analysis, and educational demonstrations. It is also useful for comparing laser sources at 800 nm, 1030 nm, 1064 nm, and 1550 nm. The result section highlights derived bandwidth, pulse duration, optical frequency, and approximate cycles per pulse. That makes technical decisions faster and clearer for research and engineering tasks.
Start with the pulse shape that best matches your source. Then choose accurate units for wavelength, bandwidth, or pulse duration. After calculation, review the transform limited value first. Next, compare it with your measured pulse width. If the measured value is longer, the pulse may contain chirp or dispersion. This comparison helps identify compression needs, optical losses, and system limits before deeper testing.
It also improves experiment planning and equipment selection in fast workflows.
It means the pulse is as short as its spectrum allows. No extra chirp or phase distortion is present. The pulse reaches the minimum duration predicted by the time bandwidth product.
Different pulse shapes have different time bandwidth products. A Gaussian pulse and a sech2 pulse with the same bandwidth will not have the same transform limited duration. Shape selection changes the result directly.
Use wavelength bandwidth when your optical spectrum analyzer reports bandwidth in nm, pm, or similar units. The calculator converts that width into frequency bandwidth before estimating pulse duration.
It works best for narrow spectra relative to the central wavelength. If the bandwidth becomes large, the simple conversion can lose accuracy. That is why the calculator shows a note for broad inputs.
Yes. Compare the transform limited result with your measured pulse width. A longer measured pulse often suggests chirp, dispersion, or incomplete compression in the optical system.
Femtoseconds are usually best for ultrafast laser work. Picoseconds are useful for longer pulses. The calculator accepts both and automatically reports results in readable units.
Optical cycles help you judge how short the pulse is relative to the carrier wave. Few-cycle behavior matters in ultrafast optics, nonlinear interaction studies, and pulse shaping analysis.
The downloads include the current calculation summary. That makes it easier to save design checks, share pulse estimates, document lab work, and compare different input conditions later.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.