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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 |
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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