Calculator Input
Formula Used
This calculator multiplies pulse duration by frequency bandwidth to estimate the time-bandwidth product. It then compares the result with the selected transform-limited constant. Larger values often indicate chirp, dispersion, filtering, or measurement definitions that do not match the chosen reference constant.
How to Use This Calculator
- Select the pulse shape or choose a custom transform-limit constant.
- Enter the pulse width and choose its unit.
- Select either frequency bandwidth or wavelength bandwidth input.
- Enter the spectral width. Add the center wavelength if needed.
- Optionally add percentage uncertainties for both measurements.
- Press Calculate to display the result above the form.
- Review the ratio, transform-limited estimates, and assessment message.
- Download the result summary as CSV or PDF if required.
Example Data Table
| Case | Pulse Shape | Pulse Width | Bandwidth | TBP | Interpretation |
|---|---|---|---|---|---|
| 1 | Gaussian | 100 fs | 4.41 THz | 0.441 | Very close to the Gaussian transform limit. |
| 2 | Sech² | 200 fs | 1.58 THz | 0.316 | Nearly transform-limited for a Sech² pulse. |
| 3 | Gaussian | 2 ps | 0.40 THz | 0.800 | Above the limit, suggesting chirp or dispersion. |
Frequently Asked Questions
1. What is the time-bandwidth product?
The time-bandwidth product is the product of pulse duration and spectral bandwidth. It measures how tightly a pulse is localized in both time and frequency. Smaller values indicate a pulse closer to its transform limit for the chosen shape definition.
2. Why does pulse shape matter?
Different pulse shapes have different transform-limited constants. A Gaussian pulse uses about 0.441, while a Sech² pulse uses about 0.315 when intensity FWHM values are used. Choosing the correct shape avoids misleading interpretations.
3. What does a larger-than-limit result mean?
A result above the reference limit usually means the pulse is not transform-limited. Chirp, dispersion, spectral filtering, or measurement mismatch can broaden time or frequency content and increase the time-bandwidth product.
4. Can I use wavelength bandwidth instead of frequency bandwidth?
Yes. The calculator converts wavelength bandwidth to frequency bandwidth with Δν ≈ cΔλ/λ₀². This works best for relatively narrow bandwidths around a known center wavelength and is widely used for quick pulse analysis.
5. Why might my result fall below the transform limit?
That usually indicates inconsistent definitions, incorrect units, conversion assumptions, or experimental uncertainty. For example, mixing field-width and intensity-width values can make the result appear smaller than the accepted transform-limited reference.
6. What is the Gaussian chirp estimate?
For Gaussian pulses, this calculator estimates a simple chirp parameter from the measured ratio above the transform limit. It is a practical indicator, not a full pulse-retrieval result, so detailed diagnostics may still require advanced characterization methods.
7. Do the uncertainty fields change the main result?
The central time-bandwidth product stays the same. The uncertainty inputs estimate a reasonable spread around that value using standard fractional uncertainty propagation, helping you judge whether the result is clearly above the transform limit.
8. When should I use a custom transform-limit constant?
Use a custom constant when your experiment relies on a pulse shape or width definition not covered by the preset options. This keeps comparisons aligned with your measurement method, simulation setup, or published reference model.