Understand pulse duration limits with practical TBP calculations. Compare Gaussian and sech shapes instantly today. Use conversions, judge chirp, and share results easily online.
The time-bandwidth product is a dimensionless measure defined as: TBP = delta-t times delta-f where delta-t is pulse duration and delta-f is spectral bandwidth.
For transform-limited pulses, the minimum TBP depends on pulse shape and the width definition. Common FWHM transform-limit constants include Gaussian 0.441 and Sech squared 0.315.
When bandwidth is entered as a wavelength width, the calculator uses the small-bandwidth approximation: delta-f is about c times delta-lambda divided by lambda-0 squared, valid near the center wavelength.
| Pulse shape | Definition | Duration | Transform-limited bandwidth | TBPmin |
|---|---|---|---|---|
| Gaussian | FWHM | 100 fs | 4.41 THz | 0.441 |
| Sech squared | FWHM | 100 fs | 3.15 THz | 0.315 |
| Gaussian | FWHM | 250 fs | 1.764 THz | 0.441 |
These examples assume transform-limited pulses, so bandwidth equals TBPmin divided by duration.
The time bandwidth product (TBP) links how short a pulse can be to how broad its spectrum must become. In ultrafast optics, shorter pulses demand wider bandwidth, so TBP provides a quick consistency check between temporal and spectral measurements.
A transform-limited pulse has the smallest possible TBP for a chosen pulse shape and width definition. For common full-width at half-maximum (FWHM) definitions, Gaussian pulses use TBPmin = 0.441, while sech-squared pulses use TBPmin = 0.315. Values above TBPmin usually indicate chirp from dispersion or nonlinear phase.
This calculator reports a chirp factor, defined as TBP divided by TBPmin. A factor near 1 suggests near transform-limited behavior, while larger values point to time broadening, spectral broadening, or both. The quality label helps you quickly classify pulses as slight, moderate, or strongly chirped.
When bandwidth is entered as a frequency width, the relationship is direct: TBP = Δt × Δf. The tool supports femtoseconds through seconds and hertz through terahertz, which is useful for femtosecond lasers, mode-locked oscillators, and picosecond fiber systems.
Spectrometers often provide bandwidth in wavelength. For narrow relative bandwidths, the calculator estimates the equivalent frequency bandwidth using Δf ≈ c·Δλ / λ0², where c is the speed of light and λ0 is the center wavelength. This approximation works best when Δλ is small compared with λ0.
A 100 fs Gaussian pulse that is transform-limited needs about 4.41 THz of bandwidth. If the measured bandwidth is only 2 THz, the shortest transform-limited duration would be about 220.5 fs, indicating the 100 fs claim is inconsistent unless the bandwidth estimate is incomplete.
TBP is widely used to diagnose dispersion compensation, compressor alignment, and fiber delivery effects. After a pulse propagates through glass, gratings, or fiber, TBP typically increases. Comparing your computed TBP against TBPmin helps decide whether further compression is likely to succeed.
Exporting to CSV supports quick logging in spreadsheets, while PDF export produces a compact summary for lab notebooks. Record the pulse shape, definition, and units alongside TBP so results remain comparable across different experiments and instruments.
TBP summarizes the tradeoff between pulse duration and spectral width. It helps you check whether measurements are physically consistent and whether the pulse is close to the transform limit.
The minimum depends on pulse shape and how width is defined. Gaussian and sech-squared pulses have different spectra, and FWHM and RMS definitions scale the widths differently.
Use wavelength bandwidth when your instrument reports Δλ directly, such as an optical spectrum analyzer. The calculator converts it to an equivalent Δf using the center wavelength.
It is an approximation that works best for small relative bandwidths. For very broad spectra, the frequency mapping becomes nonlinear, and a full spectral transform is more accurate.
A chirp factor of 2 means TBP is twice the transform-limit constant for your chosen shape and definition. The pulse is broadened by dispersion, nonlinear phase, or measurement conditions.
In ideal physics, no. If you obtain TBP below TBPmin, it usually indicates mismatched definitions, incorrect units, insufficient spectral resolution, or a bandwidth measurement that missed spectral wings.
Use the definition that matches your measurement method. Many autocorrelators and datasheets report FWHM, while statistical analyses and some simulations use RMS widths for convenience.
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.