1. What is Gaussian Beam Propagation?

The Gaussian beam describes the propagation of electromagnetic radiation where the transverse electric field and intensity distributions are Gaussian functions. This calculator determines the beam diameter at a given propagation distance from the beam waist.

2. How Does the Calculator Work?

The calculator uses the Gaussian beam propagation equation:

Where:

• \( D \) — Beam diameter at distance z (meters)
• \( \lambda \) — Wavelength of the light (meters)
• \( z \) — Propagation distance from beam waist (meters)
• \( w_0 \) — Beam waist radius (meters)

Explanation: The equation accounts for both the natural divergence of the Gaussian beam (first term) and the initial beam waist (second term).

3. Importance of Beam Diameter Calculation

Details: Accurate beam diameter calculation is crucial for laser applications, optical system design, and understanding beam behavior in free space propagation.

4. Using the Calculator

Tips: Enter wavelength in meters, propagation distance in meters, and beam waist radius in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the beam waist?
A: The beam waist (w₀) is the point along the propagation axis where the beam has its minimum diameter.

Q2: How does wavelength affect beam divergence?
A: Shorter wavelengths result in less divergence, while longer wavelengths diverge more rapidly.

Q3: What is the Rayleigh range?
A: The Rayleigh range (z_R) is the distance from the beam waist where the beam area doubles, given by \( z_R = \pi w_0^2 / \lambda \).

Q4: When does the far-field approximation apply?
A: When z ≫ πw₀²/λ, the equation simplifies to D ≈ 2λz/(πw₀), showing linear divergence.

Q5: How does this relate to beam quality (M² factor)?
A: For non-ideal beams, multiply the divergence term by M² to account for beam quality.