Beam Divergence of a laser beam is an angular measure of the increase in the beam diameter or the radius with the distance from the beam waist, from where the beam diverges. 

It is found that practically the laser beam cannot focus on a point, instead, there is a small beam thickness at the focal point. This smallest distance up to which a laser beam can converge is known as the beam waist (w₀). It is basically the focal point of a laser beam.

Beam diameter is calculated in terms of beam diameters at two different points far from the rayleigh range and the distance between these points.

Let D_f and D_i be the beam diameters at two different points away from the rayleigh range and let l be the distance between them. Then beam divergence (θ) is given by, 

If a collimated beam is focused using a lens with a focal length f, then the diameter D_m of the beam at a point far from the rayleigh range is related to the beam divergence θ as,

Rayleigh range (Z_R) is the distance from the beam waist where the beam radius has increased √2 times its initial value. This is the point at which the area of cross-section is doubled.

where 𝛌 is the wavelength of the laser beam.

Parallel (Horizontal) beam divergence is the angular measure of the increase in the beam diameter along the optic axis, i.e. along the Z-axis as in the figure.

Perpendicular (Vertical) beam divergence is the angular measure of the increase in the beam diameter along the axis perpendicular to the optic axis, i.e. along the Y-axis as in the figure.