1. What is a Laser Pulse Width Bandwidth Calculator?

Definition: This calculator determines the minimum spectral bandwidth of a laser pulse based on its temporal width.

Purpose: It helps laser technicians, physicists, and engineers understand the fundamental relationship between pulse duration and spectral bandwidth.

2. How Does the Calculator Work?

The calculator uses the Fourier transform limit formula:

Where:

• \( \Delta f \) — Spectral bandwidth (Hz)
• \( \tau \) — Pulse width (seconds)
• 0.441 — Time-bandwidth product for Gaussian pulses

Explanation: This relationship shows that shorter pulses inherently require broader bandwidths, a fundamental principle in Fourier optics.

3. Importance of Pulse Width-Bandwidth Calculation

Details: Understanding this relationship is crucial for laser system design, spectroscopy, and applications requiring precise control of temporal and spectral properties.

4. Using the Calculator

Tips: Enter the pulse width in seconds (e.g., 1e-12 for 1 picosecond). The value must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the time-bandwidth product?
A: It's a constant that relates the minimum possible product of pulse duration and spectral bandwidth, typically 0.441 for Gaussian pulses.

Q2: Does this apply to all pulse shapes?
A: No, the constant varies (e.g., 0.315 for sech² pulses). This calculator assumes Gaussian pulse shapes.

Q3: What units should I use for pulse width?
A: The calculator uses seconds, but you can enter values in scientific notation (e.g., 1e-12 for picoseconds).

Q4: What if my laser exceeds this bandwidth?
A: Pulses can have broader bandwidths than calculated, but never narrower - this represents the Fourier-transform limit.

Q5: How does this relate to uncertainty principle?
A: This is essentially an optical manifestation of the Heisenberg uncertainty principle for photons.