Jones calculus is a technique used to describe polarized light, and the polarization transformations imposed by optical components, using vectors and matrices. Let us write the complex electric field of a plane EM wave propagating in the z-direction as a column vector: [Ex(z, t)] [Eore] E(z, t) = Ey(z,t) 0 = J Foyee(kx-wt) Here Eoz and Eoy are the real amplitudes of the x and y polarization components of the wave, O and dy describe the relative phase between the components, and the remaining symbols (k, w, t, z) have their usual meaning. The Jones vector corresponding to the EM wave is 0 Eoreid Eoyeidy Thus, the Jones vector represents the amplitude and phase of the electric field in the r and y directions. To simplify calculations, it is conventional to normalize the Jones vectors such that the first non-zero component is real and the sum of the absolute values squared of the components (which is proportional to intensity) is equal to unity, i.e., E+Ey Complete the following tasks. =