1. What is the Gaussian Beam Focusing Equation?

The Gaussian Beam Focusing Equation calculates the new beam waist (w₀') after a Gaussian laser beam passes through a focusing lens. It's fundamental in laser optics for determining beam characteristics after optical elements.

2. How Does the Calculator Work?

The calculator uses the Gaussian beam focusing equation:

Where:

• \( w_0' \) — Focused beam waist (m)
• \( M^2 \) — Beam quality factor (dimensionless)
• \( \lambda \) — Wavelength (m)
• \( f \) — Focal length of lens (m)
• \( w_0 \) — Initial beam waist before lens (m)

Explanation: The equation shows how the focused spot size depends on the beam quality, wavelength, lens focal length, and initial beam size.

3. Importance of Beam Waist Calculation

Details: Calculating the focused beam waist is crucial for laser applications like material processing, microscopy, and optical trapping, where spot size determines resolution and intensity.

4. Using the Calculator

Tips: Enter all values in meters. Typical values: M² (1 for ideal Gaussian, 1.1-2 for good lasers), wavelength (e.g., 532nm = 532e-9m), focal length (e.g., 50mm = 0.05m), initial waist (1-5mm = 0.001-0.005m).

5. Frequently Asked Questions (FAQ)

Q1: What is M² factor?
A: M² measures how close a beam is to an ideal Gaussian beam (M²=1). Higher values indicate poorer beam quality.

Q2: Why does wavelength affect spot size?
A: Longer wavelengths diffract more, resulting in larger focused spots for the same optical system.

Q3: How does focal length affect the result?
A: Shorter focal lengths produce smaller focused spots, but with greater divergence after the focus.

Q4: What's the smallest possible spot size?
A: The diffraction-limited spot size is approximately λ/2, but real beams are larger due to M² > 1 and finite input beam size.

Q5: Does this work for non-Gaussian beams?
A: The equation works best for Gaussian-like beams. Highly irregular beams require more complex analysis.