1. What is Beam Divergence?

Beam divergence is the angular measure of the increase in beam diameter with distance from the beam waist. It describes how much a laser beam spreads out as it propagates.

2. How Does the Calculator Work?

The calculator uses the beam divergence formula:

Where:

• \( \theta \) — Beam divergence (radians)
• \( \lambda \) — Wavelength of the laser (meters)
• \( w \) — Beam waist radius (meters)
• \( \pi \) — Mathematical constant Pi (~3.14159)

Explanation: The equation shows that divergence is directly proportional to wavelength and inversely proportional to beam waist size.

3. Importance of Beam Divergence Calculation

Details: Understanding beam divergence is crucial for laser applications where beam quality and focus are important, such as in laser cutting, optical communications, and scientific experiments.

4. Using the Calculator

Tips: Enter wavelength in meters (e.g., 532 nm = 532e-9 m) and beam waist in meters. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical beam divergence value?
A: For many lasers, divergence ranges from 0.1 to 10 milliradians, depending on wavelength and beam quality.

Q2: How does divergence affect laser applications?
A: Lower divergence means the beam stays focused over longer distances, which is critical for applications like free-space communication.

Q3: Can divergence be reduced?
A: Yes, by using beam expanders or improving beam quality (lower M² factor), but the fundamental limit is given by the formula.

Q4: What's the difference between half-angle and full-angle divergence?
A: This formula gives half-angle divergence. Full-angle divergence would be 2θ.

Q5: Does this formula work for all laser types?
A: This is the theoretical minimum divergence for a Gaussian beam. Real beams with higher-order modes will have greater divergence.