Focused Gaussian Beam Waist Calculator

Focused Waist Equation:

\[ w_f = \frac{\lambda f}{\pi w_0} \]

Focused Waist (w_f):

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1. What is the Focused Gaussian Beam Waist?

The focused Gaussian beam waist (w_f) describes the minimum radius of a laser beam at its focal point after passing through a lens. It's a fundamental parameter in laser optics that determines the smallest achievable spot size.

2. How Does the Calculator Work?

The calculator uses the focused waist equation:

\[ w_f = \frac{\lambda f}{\pi w_0} \]

Where:

\( w_f \) — Focused beam waist radius (m)
\( \lambda \) — Wavelength of the laser (m)
\( f \) — Focal length of the lens (m)
\( w_0 \) — Initial beam waist radius before the lens (m)
\( \pi \) — Mathematical constant Pi (~3.14159)

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 size.

3. Importance of Focused Waist Calculation

Details: Calculating the focused waist is crucial for applications like laser microscopy, optical trapping, laser material processing, and any application requiring precise control of laser spot size.

4. Using the Calculator

Tips: Enter wavelength in meters (e.g., 532 nm = 5.32e-7 m), focal length in meters, and initial beam waist in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What factors affect the focused spot size?
A: The focused spot size depends on the laser wavelength, lens focal length, and the beam diameter incident on the lens.

Q2: How can I achieve the smallest possible spot size?
A: Use shorter wavelength light, a shorter focal length lens, and expand the beam before the focusing lens to maximize w₀.

Q3: What's the difference between beam waist and beam diameter?
A: The beam waist is the radius at the narrowest point, while diameter is twice the radius (2w₀).

Q4: Does this equation work for all laser types?
A: This equation is specifically for fundamental mode (TEM₀₀) Gaussian beams. Multimode beams will have different characteristics.

Q5: What's the Rayleigh range of the focused beam?
A: The Rayleigh range (z_R) can be calculated as πw_f²/λ, which describes the depth of focus.