Gaussian Spot Size Calculator

Gaussian Beam Spot Size Equation:

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

Gaussian Spot Size w(z):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Gaussian Spot Size Equation?

The Gaussian beam spot size equation describes how the beam diameter of a laser or other Gaussian beam expands as it propagates through space. It is fundamental in optics and laser physics for understanding beam behavior.

2. How Does the Calculator Work?

The calculator uses the Gaussian beam propagation equation:

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

Where:

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

Explanation: The equation shows how the beam expands hyperbolically as it moves away from the beam waist, with the Rayleigh range determining the rate of expansion.

3. Importance of Gaussian Beam Calculation

Details: Accurate calculation of Gaussian beam propagation is crucial for laser system design, optical alignment, focusing applications, and understanding beam quality in various optical systems.

4. Using the Calculator

Tips: Enter beam waist in mm, distance from waist 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 Rayleigh range (z_R)?
A: The Rayleigh range is the distance from the beam waist where the beam area doubles. It's calculated as \( z_R = \frac{\pi w_0^2}{\lambda} \), where λ is the wavelength.

Q2: How does beam quality affect the calculation?
A: This equation assumes perfect Gaussian beam (M²=1). For real beams with M²>1, multiply the result by M to get the actual spot size.

Q3: What are typical values for beam parameters?
A: Beam waist typically ranges from microns to millimeters, Rayleigh range from millimeters to meters, depending on wavelength and focusing optics.

Q4: When is this equation most accurate?
A: The equation is most accurate for fundamental TEM₀₀ mode Gaussian beams propagating through homogeneous media without aberrations.

Q5: How does this relate to beam divergence?
A: The far-field divergence angle θ is related to the beam parameters by \( \theta = \frac{\lambda}{\pi w_0} \), where λ is the wavelength.