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# Gaussian Beams Calculator

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.

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): --

## Equations and Corresponding Legend

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