Mathematically model beam propagation of Gaussian beam using simple geometric parameters. Calculator uses first order approximations and assumes TEM_{00} 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, *Z _{R}* (mm):

Rayleigh Half Diameter, ω_{R}(b/2): **-- **

Half Angle Divergence, *θ* (mrad): **-- **

$$ z_R = \frac{\pi \omega_0 ^2}{\lambda} $$

$$ \omega \! \left( z \right) = \omega_0 \sqrt{1 + \left( \frac{z}{z_R} \right) ^2} $$

$$ \omega_R \! \left( \tfrac{b}{2} \right) = \sqrt{2} \, \omega_0 $$

$$ z_R = \frac{b}{2} $$

$$ R \! \left( z \right) = z \left[ 1 + \left( \frac{z_R}{z} \right)^2 \right] $$

$$ \theta = \frac{\lambda}{\pi \, \omega_0} $$

λ |
Wavelength |

z_{R} |
Rayleigh Range |

z |
Axial Distance |

ω(z) |
Half Beam Diameter |

ω_{0} |
Beam Waist |

b |
Confocal Parameter |

Ζ_{R} |
Rayleigh Half Diameter |

R(z) |
Radius of Curvature |

θ |
Half Angle Divergence |