The LIGO experiment, which historically detected gravitationalwaves for the first time in September 2015, uses a pair of highlysensitive Michelson interferometers. These have arms that are 4.00km long and use powerful Nd:Yag lasers with 1064 nm wavelength. Thebeams traverse the arms both ways 280 times before recombining,which effectively lengthens the arm length to 1120 km. The devicesare tuned so that the beams destructively interfere when theyrecombine if no gravitational wave is present. (a) The beam has apower of 100 kW, concentrated into an area of a square centimeter.Calculate the amplitude of the electric field in the beam. (b) LIGOcan detect a gravitational wave that temporarily lengthens one armby the minuscule amount of 10-18 m! When this happens,the beams combine with a phase difference of π+δ. Estimate theshift δ in radians. Note that the phase difference accumulatesduring both traversals of each round trip. (c) Use Eq. (35.7)toestimate the sensitivity of the photodetector in terms of theminimal electric field strength needed to detect a gravitationalwave.
Eqn 35.7
Ep = 2E |cos (theta/2) |
explanation pleasssssee.
Thanks in advance!
