Laser Beam Diameter Calculator

Gaussian Beam Diameter Equation:

\[ w(z) = w_0 \times \sqrt{1 + \left(\frac{z}{z_R}\right)^2} \]

Beam Diameter w(z):

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1. What is the Gaussian Beam Diameter Equation?

The Gaussian beam equation describes how a laser beam propagates through space. It calculates the beam diameter at any distance z from the beam waist, accounting for the natural divergence of laser beams due to diffraction.

2. How Does the Calculator Work?

The calculator uses the Gaussian beam equation:

\[ w(z) = w_0 \times \sqrt{1 + \left(\frac{z}{z_R}\right)^2} \]

Where:

\( w(z) \) — Beam diameter at distance z (mm)
\( w_0 \) — Beam waist radius (minimum beam size) (mm)
\( z \) — Distance from the beam waist (mm)
\( z_R \) — Rayleigh range (characteristic distance) (mm)

Explanation: The equation shows how a laser beam expands as it propagates away from its focus point (beam waist), with the Rayleigh range determining how quickly the beam diverges.

3. Importance of Beam Diameter Calculation

Details: Accurate beam diameter calculation is crucial for laser system design, optical alignment, material processing applications, and determining power density at different distances from the laser source.

4. Using the Calculator

Tips: Enter beam waist in mm, distance in mm, and Rayleigh range in mm. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the beam waist (w₀)?
A: The beam waist is the minimum radius of the laser beam, typically at the focus point of the laser system.

Q2: How is Rayleigh range (zR) calculated?
A: Rayleigh range can be calculated as \( z_R = \frac{\pi w_0^2}{\lambda} \), where λ is the laser wavelength.

Q3: What is the divergence angle of a Gaussian beam?
A: The far-field divergence angle is \( \theta = \frac{\lambda}{\pi w_0} \), where λ is the wavelength.

Q4: Does this equation work for all laser types?
A: This equation specifically describes fundamental Gaussian (TEM₀₀) beams. Higher-order modes have different propagation characteristics.

Q5: How does beam diameter affect power density?
A: Power density decreases with the square of beam diameter, making accurate diameter calculation critical for applications requiring specific energy densities.