# Gaussian Beams Calculator

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Axial Distance, z (mm):
Beam Waist, ω0 (mm):
Wavelength, λ (μm):

Half Beam Diameter, ω(z) (mm): --

Radius of Curvature, R(z) (mm): --

Rayleigh Range, ZR (mm): --

Rayleigh Half Diameter, ωR(b/2): --

Half Angle Divergence, θ (mrad): --

 $$z_R = \frac{\pi \omega_0 ^2}{\lambda}$$
 $$\omega \! \left( z \right) = \omega_0 \sqrt{1 + \left( \frac{z}{z_R} \right) ^2}$$
 $$z_R = \frac{b}{2}$$
 $$R \! \left( z \right) = z \left[ 1 + \left( \frac{z_R}{z} \right)^2 \right]$$
 $$\theta = \frac{\lambda}{\pi \, \omega_0}$$
 λ Wavelength zR Rayleigh Range z Axial Distance ω(z) Half Beam Diameter ω0 Beam Waist
 b Confocal Parameter ωR(b/2) Rayleigh Half Diameter R(z) Radius of Curvature θ 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