Transform Limited Pulse Calculator

Advanced Pulse Inputs

Pulse duration FWHM

Duration unit

Center wavelength

Wavelength unit

Pulse shape

Custom time bandwidth product

Measured bandwidth optional

Measured bandwidth unit

Pulse energy optional, nJ

Repetition rate optional, MHz

Project note optional

Formula Used

The main relation is:

Δν × Δt = K

Here, Δν is frequency bandwidth. Δt is pulse duration FWHM. K is the time bandwidth product for the selected pulse shape.

The calculator rearranges the formula as:

Δν = K / Δt

For wavelength spread, it uses the small bandwidth estimate:

Δλ ≈ λ² × Δν / c

Angular bandwidth is:

Δω = 2π × Δν

Photon energy spread is:

ΔE = h × Δν

How To Use This Calculator

Enter the pulse duration as a full width at half maximum value.
Select the correct time unit.
Enter the central wavelength of the optical pulse.
Choose the pulse shape that best matches your pulse model.
Use the custom factor when your lab method needs another value.
Add measured bandwidth to compare real output with the ideal value.
Add pulse energy and repetition rate for power estimates.
Press Calculate. The result appears above the form.
Use CSV or PDF export for reports and records.

Example Data Table

Pulse Shape	Duration	Center Wavelength	Transform Factor	Ideal Bandwidth	Wavelength Spread
Gaussian	100 fs	800 nm	0.441	4.410 THz	9.414 nm
Sech squared	80 fs	1550 nm	0.315	3.938 THz	31.548 nm
Rectangular	1 ps	1064 nm	0.886	0.886 THz	3.348 nm

Understanding Transform Limited Pulses

A transform limited pulse is the shortest pulse possible for a given optical spectrum. Its phase is flat across the usable bandwidth. Because of that, all frequency parts arrive in step. The calculator estimates this ideal relationship from pulse duration, center wavelength, and pulse shape.

Why Bandwidth Matters

Ultrafast lasers need enough bandwidth to support short pulses. A narrower spectrum cannot create an extremely brief pulse without extra shaping. A wider spectrum can support shorter time widths, but only when dispersion and chirp are controlled. This is why the time bandwidth product is useful. It connects the full width at half maximum pulse duration with the matching frequency bandwidth.

Pulse Shape Choice

Different pulse shapes have different transform factors. A Gaussian pulse uses about 0.441. A sech squared pulse uses about 0.315. A Lorentzian or rectangular estimate may suit special work, but those cases need care. The custom option lets you enter a measured or preferred factor for lab notes.

Using Wavelength Results

Frequency bandwidth is the direct transform limit. Wavelength bandwidth is an approximation that works best when the bandwidth is small compared with the center wavelength. The calculator uses the common small signal conversion. It also reports angular bandwidth and photon energy spread, which are helpful in optics reports.

Advanced Review

The measured bandwidth field lets you compare a real pulse against the ideal limit. If the measured time bandwidth product is much larger than the selected transform factor, chirp or dispersion may be present. The result should not replace a full autocorrelation or FROG measurement. It gives a fast planning value and a clear check before deeper analysis.

Practical Notes

Use consistent FWHM values. Do not mix rms width with FWHM width unless you convert first. Enter the central wavelength near the pulse carrier. Very broadband pulses, few cycle pulses, and strongly shaped spectra may need numerical Fourier analysis. For routine estimates, this calculator gives a clean starting point.

Checking Outputs

Review the result table before exporting. Small changes in duration can create large bandwidth changes. Save the CSV for spreadsheets. Save the document report for clients, lessons, or lab folders. Keep input assumptions with every exported value for later review.

FAQs

What is a transform limited pulse?

It is an ideal pulse with the shortest possible duration for its spectrum. Its spectral phase is flat, so no extra chirp stretches the pulse.

Which pulse shape should I choose?

Choose Gaussian for many laser estimates. Choose sech squared for soliton-like ultrafast pulses. Use custom when your experiment or reference gives another time bandwidth product.

Why does bandwidth increase when duration gets shorter?

Short pulses need more frequency content. The time bandwidth product links duration and bandwidth, so reducing duration requires a wider spectrum.

Is wavelength bandwidth exact?

It is an approximation. It works best when spectral width is small compared with the center wavelength. Very broad pulses may need numerical analysis.

What does measured to ideal ratio mean?

It compares your measured bandwidth with the transform limited estimate. A ratio near one suggests a near ideal pulse. Larger values may indicate chirp or dispersion.

Can I use rms pulse width?

This calculator expects FWHM duration. Convert rms width to FWHM before entering values, unless your custom factor was created for rms values.

What is the custom factor field?

It lets you enter your own time bandwidth product. This helps when using special pulse shapes, measured references, or course-specific values.

Does this calculator measure real chirp?

No. It estimates chirp risk from bandwidth comparison. Real chirp analysis needs phase-sensitive methods, autocorrelation, FROG, SPIDER, or similar diagnostics.