1. What is the Gaussian Beam Diameter?

The Gaussian beam diameter (D) is the diameter of a laser beam where the intensity falls to 1/e² of its peak value. It's twice the beam waist (w₀), which is the smallest radius of the beam.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( D \) — Beam diameter (m)
• \( w_0 \) — Beam waist radius (m)

Explanation: The beam diameter is simply twice the beam waist radius, as the waist is defined at the point of minimum beam radius.

3. Importance of Beam Diameter Calculation

Details: Knowing the beam diameter is crucial for optical system design, laser safety calculations, and determining beam propagation characteristics.

4. Using the Calculator

Tips: Enter the beam waist radius in meters. The value must be positive (w₀ > 0).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between beam diameter and beam waist?
A: The beam waist (w₀) is the minimum radius of the beam, while the diameter (D) is twice the waist (2w₀) at the waist location.

Q2: Does this formula work for all positions along the beam?
A: No, this calculates the diameter only at the beam waist. For other positions, you need the full Gaussian beam propagation equations.

Q3: What are typical values for w₀ in laser systems?
A: Common values range from micrometers (fiber optics) to millimeters (laser pointers) to centimeters (industrial lasers).

Q4: How does beam diameter relate to divergence?
A: Smaller waist diameters generally lead to greater beam divergence according to the diffraction limit.

Q5: Is this the same as 1/e² diameter?
A: Yes, this calculates the diameter where intensity falls to 1/e² (about 13.5%) of the peak intensity.