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Gaussian Beams Calculator

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Axial Distance, z[mm]:
Beam Waist, ω0[mm]:
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] : --        

Gaussian Beam Calculator

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
Notes:
  • Please use the American standard for number formatting rather than the European standard (i.e. for "two and a half," enter "2.5" rather than "2,5").
  • Results greater than 1,000,000 are rounded to infinity.

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.

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