A laser emits a cylindrical beam of light at wavelength of 630 nm. The radius of

Question

A laser emits a cylindrical beam of light at wavelength of 630 nm. The radius of the beam is 1 mm and the power is 1.2 times 10^-3 W. The beam is linearly polarized along the x-axis and traveling in the positive z-direction. a) Determine the irradiance of the beam. b) Determine the amplitude of the electric field in the electromagnetic wave emitted by the laser. c) Determine the frequency of this electromagnetic wave. d) Assuming E(0, 0) = 0, Write the vector function for the electric field of electromagnetic wave.

Explanation / Answer

part a:

irradiance=power/area

=1.2*10^(-3)/(pi*radius^2)

=1.2*10^(-3)/(pi*0.001^2)=381.97 W/m^2

part b:

power per unit area=0.5*epsilon*E^2*c

where epsilon=electrical permitivity of free space

E=amplitude of electric field

c=speed of light

then E=sqrt(2*381.97/(8.85*10^(-12)*3*10^8))=536.41 N/C

part c:

frequency=speed/wavelength=3*10^8/(630*10^(-9))=4.762*10^14 Hz

part d:

E=Em*sin(w*t-k*x)

where Em=amplitude of electric field=536.41 N/C

w=angular frequency=2*pi*frequency=2*pi*4.762*10^14=2.9921*10^15 rad/s

k=wave number=2*pi/wavelength

=2*pi/(630*10^(-9))=9.9733*10^6

hence electric field vector=536.41*sin(2.9921*10^15*t-9.9733*10^6*x)

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