A continuous-wave (cw) argon-ion laser beam has an average power of 25.0 W and a

Question

A continuous-wave (cw) argon-ion laser beam has an average power of 25.0 W and a beam diameter of 7 mm. Assume that the intensity of the beam is the same throughout the cross section of the beam (which is not true, as the actual distribution of intensity is a Gaussian function).
(a) Calculate the intensity of the laser beam.
Compare this with the average intensity of sunlight at Earth's surface (1400 W/m2).
Ilaser/ Isun =
(b) Find the (magnitude of the) root-mean-square electric field in the laser beam.
(c) Find the (magnitude of the) average value of the Poynting vector over time.

(d) If the wavelength of the laser beam is 514.5 nm in vacuum, write an expression for the (magnitude of the) instantaneous Poynting vector, where the instantaneous Poynting vector is zero at t = 0 and x = 0. (Use the following as necessary: x and t.)
S(x,t) = W/m^2
(e) Calculate the (magnitude of the) root-mean-square value of the magnetic field in the laser beam.

Explanation / Answer

a)
I = P/A = 25.0/(3.14*0.007*0.007) = 162485.376 W/m2

162485.376 > 1400 >>>> greater than the average intensity of sunlight at Earth's surface

b)

Erms = (2cI)/2 = (cI) = (3e8 * 4*3.14e-7 * 162485.376) = 7824.608 V/m

c)

Savr = I = 162485.376 W/m2

d)

k = 2/ = 2*3.14/(514.5e-9) = 12206025.267 m-1

Emax2 = 2*I**c = 2*162485.376*(4*3.14*10e-7)*(3e8) = 122448979.3536

S = E2/(c) = (Emax2)*(sin2(kx))/(c) = 324970.752*(sin2(12206025.267*x))

e)

B = E/c = 7824.608/(3e8) = 2608.2027 * 10^-8 T

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