1. What is the Gaussian Beam Equation?

The Gaussian beam equation describes the distribution of light intensity in a laser beam as it propagates. It's fundamental in optics for modeling laser beams that have a Gaussian intensity profile across their wavefront.

2. How Does the Calculator Work?

The calculator uses the Gaussian beam intensity equation:

Where:

• \( I(r,z) \) — Intensity at radial distance r and axial distance z (W/m²)
• \( I_0 \) — Peak intensity at beam center (W/m²)
• \( w_0 \) — Beam waist radius (minimum beam radius) (m)
• \( w(z) \) — Beam radius at axial distance z (m)
• \( r \) — Radial distance from beam axis (m)

Explanation: The equation shows how intensity decreases both radially (due to the exponential term) and axially (due to beam expansion).

3. Importance of Beam Intensity Calculation

Details: Understanding beam intensity distribution is crucial for laser applications including material processing, optical communications, and medical lasers.

4. Using the Calculator

Tips: Enter all values in meters except intensity (W/m²). Beam waist (w₀) is the minimum beam radius, typically at the focus.

5. Frequently Asked Questions (FAQ)

Q1: What is the beam waist (w₀)?
A: The minimum radius of the beam where it is most concentrated, typically at the focal point of a focusing lens.

Q2: How does w(z) relate to w₀?
A: The beam radius w(z) grows with distance z from the waist according to: \( w(z) = w_0 \sqrt{1 + (z/z_R)^2} \), where z_R is the Rayleigh range.

Q3: What is the Rayleigh range?
A: The distance over which the beam remains relatively collimated: \( z_R = \pi w_0^2 / \lambda \), where λ is the wavelength.

Q4: When is the Gaussian beam model not valid?
A: For highly aberrated beams, non-Gaussian profiles, or when diffraction effects dominate.

Q5: How does intensity vary along the beam axis (r=0)?
A: On axis, intensity decreases as \( I(0,z) = I_0 (w_0/w(z))^2 \), showing the inverse square relationship with beam radius.