Gaussian Beam Divergence Calculator

Gaussian Beam Divergence Formula:

\[ \theta = \frac{\lambda}{\pi w_0} \]

Beam Divergence (θ):

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1. What is Gaussian Beam Divergence?

Gaussian beam divergence describes the angular spread of a laser beam as it propagates through space. It is a fundamental parameter in laser optics that characterizes how quickly the beam expands away from its waist (minimum beam radius).

2. How Does the Calculator Work?

The calculator uses the Gaussian beam divergence formula:

\[ \theta = \frac{\lambda}{\pi w_0} \]

Where:

\( \theta \) — Beam divergence (radians)
\( \lambda \) — Wavelength of the laser light (meters)
\( w_0 \) — Beam waist radius (meters)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The divergence angle is inversely proportional to the beam waist - smaller waist results in larger divergence, and vice versa.

3. Importance of Beam Divergence Calculation

Details: Accurate beam divergence calculation is crucial for laser system design, optical communications, laser cutting applications, and determining the beam quality and focus characteristics of laser systems.

4. Using the Calculator

Tips: Enter wavelength in meters (e.g., 632.8e-9 for HeNe laser), beam waist radius in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between full and half-angle divergence?
A: This calculator gives the half-angle divergence (θ). Full divergence angle is 2θ.

Q2: How does wavelength affect beam divergence?
A: Shorter wavelengths result in smaller divergence angles, while longer wavelengths produce larger divergence for the same beam waist.

Q3: What are typical values for beam divergence?
A: Typical values range from 0.1-10 mrad for most laser systems, depending on the laser type and optical design.

Q4: Can this formula be used for non-Gaussian beams?
A: This formula is specifically for fundamental Gaussian beams. Multimode or non-Gaussian beams require different calculations.

Q5: How does beam quality factor (M²) affect divergence?
A: For real lasers with M² > 1, the actual divergence is M² times larger than the theoretical Gaussian beam divergence.