# Gaussian Beams Calculator

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Axial Distance, $z \left[ \text{mm} \right]$:
Beam Waist, $\omega_0 \left[ \text{mm} \right]$:
Wavelength, $\lambda [ \large{\unicode[computer modern]{x03BC}} \text{m} ]$:

Half Beam Diameter, $\omega \! \left( z \right) \left[ \text{mm} \right]$: --

Radius of Curvature, $R \! \left( z \right) \left[ \text{mm} \right]$: --

Rayleigh Range, $Z_R \left[ \text{mm} \right]$: --

Rayleigh Half Diameter, $\omega_R \left[ \text{mm} \right]$: --

Half Angle Divergence, $\theta \left[ \text{mrad} \right]$: --

 $$z_R = \frac{\pi \omega_0 ^2}{\lambda}$$ $$\omega \! \left( z \right) = \omega_0 \sqrt{1 + \left( \frac{z}{z_R} \right) ^2}$$ $$Z_R = \frac{b}{2}$$ $$\omega_R = \omega \! \left( Z_R \right) = \sqrt{2} \cdot \omega_0$$ $$R \! \left( z \right) = z \left[ 1 + \left( \frac{z_R}{z} \right)^2 \right]$$ $$\theta = \frac{\lambda}{\pi \, \omega_0}$$
 $$\lambda$$ Wavelength $$Z_R$$ Rayleigh Range $$z$$ Axial Distance $$\omega \! \left( z \right)$$ Half Beam Diameter $$\omega_0$$ Beam Waist
 $$b$$ Confocal Parameter $$\omega_R$$ Rayleigh Half Diameter $$R \! \left( z \right)$$ Radius of Curvature $$\theta$$ Half Angle Divergence

## Description

Mathematically model beam propagation of Gaussian beam using simple geometric parameters. Calculator uses first-order approximations and assumes TEM00 mode to determine beam spot size in free space applications. Please note that results will vary based on beam quality and application conditions.

## Related Resources and Products

Application Note
Application Note