Rayleigh range (z₀) is defined as the distance from the beam waist until the beam area is doubled (see figure 7.8).

Figure 7.8: Rayleigh Range.

At the distance of Rayleigh Range the radius of the beam W(z) is  times the radius of the beam at the beam waist W₀:

 n = The index of refraction of the medium that the beam pass through.

Knowing z₀, and the beam radius at z₀ (W₀), it is easy to calculate the beam diameter at any point z:

In the last mathematical calculation the Taylor series expansion was used:

Thus, at large distance (z) from the beam waist, the beam radius can be approximated as a linear function of z.