1. What is the Gaussian Beam Waist Equation?

The Gaussian beam waist equation calculates the focused spot size (w₀') of a laser beam after passing through a lens, based on the wavelength (λ), focal length (f), and initial beam waist (w₀). This is fundamental in laser optics and photonics applications.

2. How Does the Calculator Work?

The calculator uses the Gaussian beam waist equation:

Where:

• \( w_0' \) — Focused beam waist (m)
• \( \lambda \) — Wavelength of the laser (m)
• \( f \) — Focal length of the lens (m)
• \( w_0 \) — Initial beam waist before focusing (m)

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

3. Importance of Beam Waist Calculation

Details: Accurate beam waist calculation is crucial for laser applications like microscopy, optical trapping, laser cutting, and fiber coupling where precise control of the focal spot is required.

4. Using the Calculator

Tips: Enter wavelength in meters (e.g., 532nm = 532e-9), focal length in meters, and initial waist in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is beam waist in Gaussian optics?
A: The beam waist is the point along the propagation direction where the beam has the minimum radius.

Q2: How does wavelength affect the focused spot?
A: Longer wavelengths produce larger focused spots, which is why UV lasers can achieve smaller spots than IR lasers.

Q3: What's the relationship between initial waist and focused waist?
A: A larger initial waist will produce a smaller focused waist, assuming other parameters remain constant.

Q4: Is this calculation valid for all laser types?
A: This applies specifically to TEM00 Gaussian beams. Higher-order modes will have different beam profiles.

Q5: What practical factors might affect the actual spot size?
A: Lens aberrations, beam quality (M² factor), alignment errors, and diffraction effects can all impact the actual spot size.