Download EE 420 HW#3

EE 420 HW#3
1. A plane electromagnetic wave is incident (perpendicular incidence) from glass onto
air, calculate:
a) the critical angle c .
b) the reflection and transmission coefficients for i  30o .
c) the reflection and transmission coefficients for i  50o .
d) the magnitude and phase of the reflection coefficients in parts (b) and (c).
2. A plane electromagnetic wave is incident (parallel incidence) from glass onto air,
calculate:
a) the critical angle.
b) the reflection coefficient for i  50o .
c) the magnitude and phase of the reflection coefficient in parts (b).
d) the brewester angle.
3. Show that the Brewster angle  B is always less than the critical angle c for any two
dielectric with refractive indices n1 and n2 .
4. A perpendicularly polarized plane electromagnetic wave is incident from glass onto
air at i  50o as shown in the figure below. The incident electric field intensity vector is
given by:
Ei  a y Eioe j (t k0n1 cosi xk0n1sini z )
Where k0  free space phase constant.
air (n2  1.00)
x
t
Et
z
i
Ei
r
Er
glass (n1  1.50)
Given that Eio  1.00 [V/m] and f  5 1014 [Hz] :
a) Write an expression for the reflected electric field.
b) Write an expression for the transmitted electric field.
c) Write an expression for the total electric field in glass ( x  0 ).
d) Plot the amplitude of the total electric field in glass ( x  0 ) and in air ( x  0 ).
[A single plot showing the amplitude of the total electric field versus x is required. This
plot should show an evanescent wave for x  0 and a standing wave pattern for x  0 ].
5. With reference to the previous problem, answer the following questions:
a) What range of  i causes an evanescent wave to exist in air?
b) For what range of  i there is no evanescent wave in air?
c) What range of  i causes a standing wave to exist in glass?
6. A plane EM wave is incident from glass ( x  0 ) onto air ( x  0 ) at i  60o , which is
higher than the critical angle. The free space wavelength of the EM wave is   1.55  m .
The electric field amplitude of the resulting evanescent field in air is given by:
E  10e x V / m (valid for x  0 )
Calculate:
a)  in Np /  m (Neper per micrometer).
b) The electric field amplitude at the glass/air interface.
c) The electric field amplitude in air at a distance of 1  m from the glass/air interface.
d) Repeat part c) when the distance is increased to 10  m .