A continuous-wave (cw) argon-ion laser beam has an average power of 92.0 W and a

Question

A continuous-wave (cw) argon-ion laser beam has an average power of 92.0 W and a beam diameter of 6 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.
=3.25*10^6 W/m^2


Compare this with the average intensity of sunlight at Earth's surface (1400 W/m2).
Ilaser/Isun= 2320

(b) Find the (magnitude of the) root-mean-square electric field in the laser beam.
= 35000 V/m

(c) Find the (magnitude of the) average value of the Poynting vector over time.
=3.25*10^6 W/m^2

(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.)

I NEED THE ANSWER FOR THIS PART, HOW TO GET THIS EQUATION:
S(x,t)= 6.51e+06sin^2(1.22e+07 * x -3.66e+15 * t) W/m^2
S(x,t)= KINDLY SHOW ME HOW TO CALCULATE THE ABOVE VALUES.

(e) Calculate the (magnitude of the) root-mean-square value of the magnetic field in the laser beam.

=.000117 T

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

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.