Chapter 5, Problem 5.35P

For a general elliptical polarization represented by $\text{E}\left(z,t\right)=E_{xo}\cos \left(\text{ω}t-\beta z\right){\text{a}}_x+E_{yo}\cos \left(\text{ω}t-\beta z+\varphi \right){\text{a}}_y$, the axial ratio and tilt angle can be found from the following formulas (from K. R. Demarest, Engineering Electroinagnetics, Prentice-Hall, 1998, pp. 451–453):

$a=\left|E_{xo}\right|,b=\left|E_{yo}\right|$

MAJ = length of majority-axis

MIN = length of minority-axis

$MAJ=2\sqrt{\frac{1}{2}\left[a^2+b^2+\sqrt{a^4+b^4+2a^2{b}^2\cos 2\varphi }\right]}$

$MIN=2\sqrt{\frac{1}{2}\left[a^2+b^2-\sqrt{a^4+b^4+2a^2{b}^2\cos 2\varphi }\right]}$

$\text{axial ratio}=\frac{MAJ}{MIN}$

$\tau =\frac{1}{2}{\tan }^{-1}\left[\frac{2ab}{a^2-b^2}\cos \varphi \right]$

Compose a program that not only draws a polarization plot like MATLAB 5.3 but also calculates the axial ratio and tilt angle. Run the program for Drill 5.11.