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.