Interaction of Gaussian Beams with Optics

[barefeet]

Homework Statement

In a youtube video() it is explained how gaussian beams propagate through an optical lens. Using the complex parameter q $\frac{1}{q} = \frac{1}{R} - \frac{j\lambda}{\pi n w^2}$ (with R the radius of curvature), one can use the ABCD matrix to calculate the effect of an optical system. Then it is explained how one can calculate the minimum waist $w_0$ and at which position z this minimum waist occurs. But at 3.12 the position z for the minimum waist is given as:
$$z = \frac{Re[\frac{1}{q}]}{|\frac{1}{q}|^2}$$

What I don't understand is that $Re[\frac{1}{q}] = \frac{1}{R}$ but the radius of curvature at $w_0$ is supposed to be infinite so z is always zero.

 

[blue_leaf77]

At the very first minute of the video, $q_{out}$ was defined to be the $q$ parameter just after system B, not at the waist.