A uniform (z-invariant) evanescent coupler comprises 2 identical single-mode par

A uniform (z-invariant) evanescent coupler comprises 2 identical single-mode parallelcores that are embedded in an infinite cladding. The entrance ports for the two cores canbe excited separately with the respective fundamental mode. By considering thesymmetric and anti-symmetric super-modes of the coupler or otherwise determine themaximum and minimum power in each core along the length of the coupler for each ofthe following excitation situations at the beginning of the coupler:(i) The field amplitudes of the fundamental modes in the two cores are equal withzero relative phase between them;(ii) The field amplitudes of the fundamental modes in the two cores are equal butwith a relative phase difference of pi/2between them;(iii) The field amplitudes of the fundamental modes in the two cores are equal butwith a relative phase difference of pibetween them;(iv) Only the fundamental mode in one core is excited.