Complex beam parameter q propagated with ABCD matrices: q0 = i*pi*w0^2/lambda at the waist, free space [[1,d],[0,1]], thin lens [[1,0],[-1/f,1]]. The radius comes from Im(1/q) = -lambda/(pi*w^2) and the focused waist sits where Re(q) = 0. Ideal TEM00 beam, M^2 = 1, paraxial, in vacuum or air (wavelength as given). Checked against the closed-form Siegman results in the site test suite. Pure mathematics - nothing is fetched and nothing is recalled.
Open this on MakerPortal ยท Free to reuse with attribution