Question

11.34 1 Given a general elliptically polarized wave as per Eq. (93): (a) Show, using methods similar to those of Example 11.7, that a linearly polarized wave results when superimposing the given field and a phase- shifted field of the form: where ? is a constant. (b) Find ? in terms of ? such that the resultant wave is linearly polarized along x.

Answer 1

a) Adding the two fields gives E^-_s, total = [E_x0 (1 + e^i delta) a^-_x + E_y 0 (e^j phi + e^- i phi e^j delta) a^- y] e^- j beta z = E_x 0 e^i delta/2 (e^- i delta/2 + e^i delta/2) a^-_x + E_y 0 e^i delta /2 (e^- i delta/2 e^j phi + e^- i phi e^j delta/2) a^-_y] e^- j beta z This simplifies to E^-_s, tot = z (F_x 0 cos (delta/2) a^-_x + E_y 0 cos (phi - delta/2) a^- y] e^i delta/2 e^- j beta z which is linearly polarized b) By inspecting the part a result, we achieve a zero y component when 2 phi - delta = pi (or odd multiplies of pi)