Solve Physics Questions: Circular Polarization, Poynting Vector, Loss Tangent

[unstoppable]

2) A researcher claims that she can convert a circularly polarized plane wave in air into a linearly polarized one by simply reflecting it from a suitably chosen lossless nonmagnetic dieletric. Assume the dielectric she will use has refractive index n. Is this feat possible for normail incidence, as she claims? Calculate the reflected wave to justify your answer. If she is right, is there a mininum value of n for this to work? If she is wrong; briefly explain why, based on your calculation.



3) A source of unidirection plane waves operates within a medium with moderate conductivity sigma. Suppose we measure the complex electric field amplitudes at the source and at some distance z and find that E(z)/E(0)-0.3-j0.4.
(a) Calculate the loss tangent sigma/(omega*epsilon) of the medium. (Give a numerical value)

(b) What is the ratio of complex magnetic field amplitudes H(z)/H(0) for the same z?




equation for phase velocity: Vp=Vp(omega)=omega/k= c*omega/squarerootof(omega^2-omega^2) Note: The second omega^2 is the cuttoff frequency


equation for group velocity: Vg=Vg(omega)=c*squarerootof(omega^2-omega^2)/(omega)
Note: The second omega^2 is the cuttoff frequency.


c=the speed of light 3 X 10^8 m/s


Circular Polarization: E(0)=Eox=1/2Eo(x+jy) +1/2Eo=(x-jy)
Note: j=the imaginary complex number
E(z)=1/2*Eo(x+jy)*e^-j(ko+K)z+1/2*Eo(x-jy)*e^-j(ko-K)z

Poynting Vector: The Vector E X H is the Poynting Vector. It gives the power per unit area that flows at a point;


Loss Tangent:Theta/(omega*epsilon)

 

[BigJDubs]

= sigma/(omega*epsilon).Answer to Question 2: No, it is not possible for normal incidence as she claims. The reflected wave will be the same as the incident wave since the reflection coefficient for a lossless nonmagnetic dielectric with normal incidence is 1. There is no minimum value of n required for this to work since the reflection coefficient is independent of n.