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Gaussian Beam

U (r) = A_{0} \frac{W_{0}}{W (z)} \exp [- \frac{ρ^{2}}{W^{2} (z)}] \exp [- jkz - jk \frac{ρ^{2}}{2 R (z)} + j ζ (z)]

W (z) = W_{0} {[1 + {(\frac{z}{z_{0}})}^{2}]}^{1 / 2}

R (z) = z [1 + {(\frac{z}{z_{0}})}^{2}]

ζ (z) = \tan^{- 1} \frac{z}{z_{0}}

W_{0} = {(\frac{λ z_{0}}{π})}^{1 / 2}

θ_{0} = \frac{2}{π} \frac{λ}{2 W_{0}}

2 z_{0} = \frac{2 π W_{0}^{2}}{λ}

Waist radius

W'_{0} = {MW}_{0}

Waist location

(z' - f) = M^{2} (z - f)

Depth of focus

2 z'_{0} = M^{2} (2 z_{0})

Divergence

2 θ'_{0} = \frac{2 θ_{0}}{M}

Magnification

M = \frac{M_{r}}{(1 + r^{2})^{1 / 2}}

r = \frac{z_{0}}{z - f}

M_{r} = | \frac{f}{z - f} |