1. What is Laser Beam Divergence?

Beam divergence is the angular measure of the increase in beam diameter with distance from the optical aperture or beam waist. It's a key parameter in laser beam quality and propagation characteristics.

2. How Does the Calculator Work?

The calculator uses the fundamental beam divergence equation:

Where:

• \( \theta \) — Beam divergence angle (radians)
• \( \lambda \) — Laser wavelength (meters)
• \( w_0 \) — Beam waist radius (meters)

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

3. Importance of Beam Divergence

Details: Beam divergence affects laser spot size at target, intensity distribution, and the ability to focus the beam. Lower divergence means the beam stays collimated over longer distances.

4. Using the Calculator

Tips: Enter wavelength in meters (e.g., 532nm = 0.000000532), beam waist radius in meters, and optionally velocity for Doppler shift calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is typical beam divergence for lasers?
A: It varies widely from <0.1 mrad for high-quality lasers to several mrad for diode lasers.

Q2: How does velocity affect beam divergence?
A: Velocity itself doesn't affect divergence but can cause Doppler shift which changes effective wavelength.

Q3: What is M² factor and how does it relate?
A: M² (beam quality factor) multiplies the fundamental divergence. M²=1 for perfect Gaussian beam.

Q4: How to reduce beam divergence?
A: Use larger beam waist, shorter wavelength, or beam expanding optics.

Q5: Does this apply to all laser types?
A: This is for fundamental Gaussian modes. Higher-order modes have greater divergence.