1. What is the Gaussian Beam Focus Equation?

The Gaussian Beam Focus equation calculates the beam waist at the focal point of a laser beam. It describes how a Gaussian beam propagates through an optical system and focuses to a point.

2. How Does the Calculator Work?

The calculator uses the Gaussian Beam Focus equation:

Where:

• \( w \) — Beam focus (m)
• \( \lambda \) — Wavelength (m)
• \( f \) — Focal length (m)
• \( w_0 \) — Initial beam waist (m)
• \( \pi \) — Pi constant (~3.14159)

Explanation: The equation shows that the focused beam waist is proportional to the wavelength and focal length, and inversely proportional to the initial beam waist.

3. Importance of Beam Focus Calculation

Details: Accurate beam focus calculation is crucial for laser applications like microscopy, optical trapping, laser cutting, and fiber coupling.

4. Using the Calculator

Tips: Enter all values in meters. The beam waist (w0) should be the 1/e² radius of the beam before focusing. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a Gaussian beam?
A: A Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity distributions are described by Gaussian functions.

Q2: What is the 1/e² radius?
A: It's the radius at which the beam intensity falls to 1/e² (~13.5%) of its peak axial value.

Q3: Does this equation work for all wavelengths?
A: Yes, as long as the beam maintains a Gaussian profile and the optics are properly designed for the wavelength.

Q4: What affects the minimum achievable spot size?
A: The diffraction limit is determined by the wavelength and numerical aperture of the focusing system.

Q5: How does this relate to M² factor?
A: For non-ideal beams (M² > 1), multiply the result by M² to get the actual focused spot size.