1. What is the Gaussian Beam Equation?

The Gaussian beam equation describes how a laser beam propagates in space, showing how the beam radius changes with distance from the beam waist. It's fundamental in light machinery and optical systems design.

2. How Does the Calculator Work?

The calculator uses the Gaussian beam equation:

Where:

• \( w(z) \) — Beam radius at distance z (m)
• \( w_0 \) — Beam waist radius (m)
• \( z \) — Distance from beam waist (m)
• \( z_R \) — Rayleigh range (m)

Explanation: The equation shows how the beam radius expands as it propagates away from the beam waist, with the Rayleigh range determining the rate of expansion.

3. Importance of Beam Radius Calculation

Details: Accurate beam radius calculation is crucial for optical system design, laser machining, alignment procedures, and determining beam characteristics at different distances.

4. Using the Calculator

Tips: Enter beam waist in meters, distance in meters, and Rayleigh range in meters. All values must be positive (except distance which can be zero).

5. Frequently Asked Questions (FAQ)

Q1: What is the Rayleigh range?
A: The Rayleigh range (z_R) is the distance over which the beam radius expands by √2 from its minimum value at the beam waist.

Q2: What are typical values for w₀ in light machinery?
A: Typical values range from micrometers (laser diodes) to millimeters (expanded beams), depending on the application.

Q3: How does this relate to beam divergence?
A: The far-field divergence angle θ can be calculated as θ ≈ λ/(πw₀), where λ is the wavelength.

Q4: What happens at z = z_R?
A: At z = z_R, the beam radius is w = √2 × w₀, and the beam area is doubled compared to the waist.

Q5: Can this be used for non-Gaussian beams?
A: This equation is specifically for fundamental Gaussian beams. Higher-order modes or non-Gaussian beams require different equations.