Home
Back
Bandwidth Formula:
| From: | To: |
The time-bandwidth product is a fundamental relationship in optics that connects the duration of a laser pulse to its spectral bandwidth. For transform-limited pulses, this product is a constant that depends on the pulse shape.
The calculator uses the bandwidth formula:
Where:
Explanation: The equation shows that shorter pulses inherently have broader spectral bandwidths, which is a manifestation of the Fourier transform relationship between time and frequency domains.
Details: Knowing the spectral bandwidth is crucial for applications like spectroscopy, optical communications, and ultrafast optics where pulse characteristics affect system performance.
Tips: Enter the time-bandwidth product (typically 0.44 for Gaussian pulses, 0.315 for sech² pulses) and pulse duration in seconds. Both values must be positive numbers.
Q1: What is a typical time-bandwidth product value?
A: For Gaussian pulses it's ~0.44, for hyperbolic secant (sech²) pulses it's ~0.315.
Q2: How does pulse shape affect the calculation?
A: Different pulse shapes have different time-bandwidth products, so the constant changes based on the pulse profile.
Q3: What units should I use for pulse duration?
A: The calculator expects seconds, but common laser pulses are often measured in picoseconds (10⁻¹²) or femtoseconds (10⁻¹⁵).
Q4: Does this apply to all laser pulses?
A: This applies to transform-limited pulses. Chirped pulses or those with phase modulation will have larger time-bandwidth products.
Q5: How is bandwidth related to wavelength spread?
A: The frequency bandwidth (Δν) can be converted to wavelength bandwidth (Δλ) using Δλ = (λ²/c)Δν, where λ is center wavelength and c is speed of light.