2. Optical interferometer. The Michelson interferometer shown below has the arms lengths of L - Ly NX for x = 0, where N is an integer and = 1064 nm is the laser wavelength, x is the position of one of the mirrors. Laser Ly Readout Lx In a) - c) assume monochromatic waves in the horizontal polarisation. In d) assume a realistic laser with coherence length lcoh. a) Find the power Pout at the readout port as a function of a given the input laser power Pin and sketch the result. M = b) Find , the smallest value of x when the optical gain dP/dx is maximum. c) Find how would the result in a) change if a half-wave plate was installed in the Y-arm of the interferometer with a Jones matrix = [0.83 0.56 0.56 -0.83 d) Find a condition on the coherence length of the laser for interference fringes to be visible at the readout port.