Given a 1 W TEM₀₀ laser beam with λ₀ = 514.5 nm from an argon ion laser with a minimum spot size w₀ = 2 mm located at z = 0:
(a) How far does this beam propagate until w(z) = 1 cm?
(b) At z = 1 cm, what is the radius of curvature of the phase front?
(c) What is the electric field amplitude at r = z = 0?