Question

The nearly parallel beam of a laser with wavelength λ = 10μm and output power of P = 10 W has a beam diameter of d = 3 cm. It is focused by a lens with f = 20 cm. a) How large is the beam waist w0 in the focal plane? b) The intensity distribution in this plane is I(r) = I0 × exp[−(r/w0) 2] . What is the value of I0? c) Assume that 10% of the laser power can be used for evaporating material from a steel sheet with thickness t = 1 mm placed in the focal plane. How long will it take for the laser beam to produce a hole through the steel sheet, if the evaporation heat is 6 × 106 J/Kg

Answer 1

a] Beam waist in the focal plane can be determined using Rayleigh's diffraction limit criteria.

this is the beam waist in the focal plane.

b] The intensity at this point is:

c] Power used up for evaporation = 10% of 10 W = 1 W

Radius of the hole =

thickness of the hole = 1 mm = 1 x 10^-3 m

so, volume of the hole =

density of steel = 8050 kg/m³

therefore, mass of the steel evaporated = density x volume = 1.67295 x 10^-7 kg

Energy required = mass x evaporation heat = 1.67295 x 10^-7 x 6 x 10⁶ = 1.00377 J

time = Energy / Power = 1.00377/1 = 1.00377s

this is how long it will take for the laser beam to produce the hole.