3.3 Photons from an industrial CO2 laser CO2 lasers are used in metal cutting. T

Question

3.3 Photons from an industrial CO2 laser CO2 lasers are used in metal cutting. The laser beam output has a wavelength of 10.6 um. The laser generates repetitive pulses of radiation in which the radiation is on for a time ton and off for a time toff and the pulses are repeated at a repetition rate of fHz. The duty cycle for this operation is defined as ton/(ton + loff). A typical CO2 laser used in metal cutting has an average power of 1 kW and a duty cycle of 60%. The repetition frequency is 1 kHz. The beam diameter is 10 mm. What is the photon energy? What is the photon flux density as photons per cm2? What is the electric field in the radiation? Typical bulk concentration nbulk of atoms in a metal is of the order of 1025 cm-3 (for example in Al. nbulk = 6.0× 1022 cm-3). The surface concentration nsurface of atoms is on the order of nbulk(See Chapter I.) What is the rate at which each surface meal atom is bombarded by photons? What is the time between two consecutive photons bombarding a given atom? What is your conclusion? 2/3

Explanation / Answer

given power of laser P = 1 kW = 1000 W
that means the power output of laser is 1000 J for 1 s
but out of this , due to 60 percent duty cycle, the laser is switched on for just 0.6 s
so Power of laser while its switched on = 1000/0.6 = 1666.67 W
wavelength, lambda = 10.6 micro m
energy of each photon, E = hc/lambda

so photon energy = E = 1.8764*10^-20 J

photon flux density = n
n*E = P/A
A = pi*d^2/4
d =- bean diameter = 10 *10^-3 m
so, n = 4*1666.67/pi*(10^-2)^2 *E = 1.13*10^27 photons per second per m^2

Electric field of the radiation = E
now intensity, S of beam = P/A = 1666.67*4/pi*(10^-2)^2 = 21220701.52 W/m^2
but S = Em^2/2*c*muo
and 4*pi*muo = 10^-7
S = Em^2*4*pi/2*c*10^-7
hence Em = 10065.8524 V/m

bulk atom concentration = 10^23 /cm^3 = 10^17 / m^3
surface atom concentration = (10^17)^2/3 = 2.1544*10^11 atoms/m^2
so, rate at which each atom is bombarded = 1.13*10^27 / 2.1544*10^11 = 5.244*10^15 photons per s

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