Meet Sara. She is a physics researcher working on ultrafast laser experiments. Her goal is to control how laser pulses broaden as they travel through optical components. But there’s a problem.
Sara is staring at numbers for refractive index, phase, angular frequency, group velocity dispersion, and fiber length. She feels completely overwhelmed. She keeps asking: “How can I calculate the group delay dispersion of my system without manually solving complex derivatives?”
If you’ve ever felt like Sara, you’re in the right place.
Introducing the Solution: The Group Delay Dispersion Calculator
Feeling stuck, Sara needed a way to cut through the confusion and get a clear answer. What she needed was a tool designed for exactly this moment.
That’s where our Group Delay Dispersion Calculator comes in. It’s a simple tool designed to give you accurate GDD values without the headache of advanced math.
Putting It to the Test
Let’s walk through how Sara uses the calculator.
First, she inputs the Group Velocity Dispersion (β₂) value, which is 20 ps²/km.
Next, for the length of the fiber (L), she enters 2 km.
Finally, she sets the unit conversion to femtoseconds squared.
Sara takes a breath and clicks “Calculate.”
Understanding the Results
The calculator instantly shows the answer: 40 ps², which equals 40,000,000 fs².
For Sara, this isn’t just a number. It’s a clear path forward. It means that her laser pulse will accumulate a GDD of 40 ps² as it passes through the fiber, giving her direct insight into how much temporal broadening will occur. The overwhelming equations are replaced with clarity.
Beyond the Calculator
Now that you have your number, just like Sara, what should you do next?
- Use this result to adjust your laser system’s dispersion compensation strategy.
- Compare different fibers or optical materials by changing β₂ and length to test scenarios.
- Consult your lab supervisor or optical engineer to fine-tune ultrafast laser performance.
Your Turn
Feeling inspired by Sara’s story? It’s your turn to go from confused to confident. Scroll back up and use the Group Delay Dispersion Calculator to find your numbers.
Quick Reference Table
| β₂ (ps²/km) | Fiber Length (km) | GDD (ps²) | GDD (fs²) |
|---|---|---|---|
| 10 | 1 | 10 | 10,000,000 |
| 20 | 2 | 40 | 40,000,000 |
| 15 | 0.5 | 7.5 | 7,500,000 |
| 30 | 3 | 90 | 90,000,000 |
| 50 | 0.2 | 10 | 10,000,000 |
Quick Reference
The Formula Behind the Tool
- Group Delay (GD):
GD(ω) = dΦ(ω) / dω - Group Delay Dispersion (GDD):
GDD(ω) = d²Φ(ω) / dω²
or
GDD(ω) = d(GD(ω)) / dω - From GVD Parameter (β₂):
GDD = β₂ × L - From Refractive Index Curve:
β₂ = -(λ³ / (2πc²)) × (d²n / dλ²)
Variable Definitions
Φ(ω) = Optical phase (radians)
ω = Angular frequency (rad/s)
GD = Group Delay (s)
GDD = Group Delay Dispersion (s²)
β₂ = Group Velocity Dispersion (s²/m or ps²/km)
L = Fiber or medium length (m or km)
λ = Wavelength (m)
c = Speed of light in vacuum (m/s)
n = Refractive index of medium
Frequently Asked Questions
GVD (β₂) is a material property per unit length, while GDD is the accumulated dispersion over a certain length.
Because it determines how much an ultrafast laser pulse will stretch or compress while traveling through optical components.
Typically ps² (picoseconds squared) or fs² (femtoseconds squared). 1 ps² = 1,000,000 fs².