Question

A 160 MW laser pulse is focused with a lens to a diameter of 2.0 μm .

What is the laser beam's electric field amplitude at the focal point?

Answer 1

given

Power of the laser pulse is P = 160*10^6 W

diameter d = 2*10^-6 m , radius r = 1*10^-6 m

we know that , intensity is I = P/A

I = (160*10^6)/(pi*(1*10^-6)^2) W/m^2

I = 5.0929*10^19 W/m^2

now from the relation the intensity = U *c

where U is average energy , U = (1/2) (*E^2)

I = (c**E^2)/2

2I = (c**E^2)

E^2 = (2I/(c*))

E = sqrt((2I/(c*)))

substituting the values

E = sqrt((2*5.0929*10^19/(3*10^8*8.854*10^-12))) V/m

E = 195824572021.24472 V/m  

E = 195.82457*10^9 V/m