1. What is Gaussian Beam Propagation?

The Gaussian beam propagation describes how a laser beam spreads as it propagates through space. The beam radius R(z) describes how the beam size changes with distance z from the beam waist.

2. How Does the Calculator Work?

The calculator uses the Gaussian propagation equation:

Where:

• \( R(z) \) — Beam radius at distance z (meters)
• \( z \) — Distance from beam waist (meters)
• \( z_R \) — Rayleigh range (meters)

Explanation: The equation shows how the beam radius depends on the distance from the beam waist and the Rayleigh range, which characterizes the beam's divergence.

3. Importance of Beam Radius Calculation

Details: Understanding beam propagation is crucial for laser system design, optical alignment, and applications like laser cutting, medical lasers, and optical communications.

4. Using the Calculator

Tips: Enter the distance from beam waist (z) and Rayleigh range (z_R) in meters. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the Rayleigh range?
A: The Rayleigh range is the distance over which the beam area doubles from its minimum value at the beam waist.

Q2: What's the difference between beam radius and beam diameter?
A: The beam diameter is simply twice the beam radius (D = 2R).

Q3: How does wavelength affect beam propagation?
A: The Rayleigh range depends on wavelength - shorter wavelengths produce less divergent beams (larger z_R for given beam waist).

Q4: What is the beam waist?
A: The beam waist is the location where the beam has its minimum radius and wavefront is flat (plane wave).

Q5: What happens when z is much larger than z_R?
A: Far from the waist (z ≫ z_R), the beam diverges linearly with angle θ ≈ λ/(πw₀), where w₀ is the waist radius.