Question

1. Consider the following problems concerning the electromagnetic wave propagation in three regions. The incident wave $E(x) = E_0e^{ikx}$ (here $E_0$ is a constant) is from the left in region I and strikes on the interface. Establish the 1-D wave equation for the electromagnetic waves in the three regions and the relevant boundary conditions. $\epsilon_0, \mu_0$ $\epsilon_1, \mu_0$ $\epsilon_2, \mu_0$ Region I Region II Region III $E(x) = E_0e^{ikx}$ Incident wave 0 L x 2. Obtain solutions to the above wave equations for E and then H in the three regions. 3. Obtain expressions for (a) instantaneous Poynting vectors of individual waves (incident, reflected, transmitted etc.) in the three regions; and (b) time averaged Poynting vectors of individual waves in the three regions. 4. Obtain the expressions for the reflectivity and transmitivity at interface between regions I and II, and those at the interface between regions II and III. 5. Obtain expression for absorptivity in region II.

          1. Consider the following problems concerning the electromagnetic wave propagation in three regions.
The incident wave $E(x) = E_0e^{ikx}$ (here $E_0$ is a constant) is from the left in region I and strikes on the
interface. Establish the 1-D wave equation for the electromagnetic waves in the three regions and the
relevant boundary conditions.
$\epsilon_0, \mu_0$
$\epsilon_1, \mu_0$
$\epsilon_2, \mu_0$
Region I
Region II
Region III
$E(x) = E_0e^{ikx}$
Incident wave
0
L
x
2. Obtain solutions to the above wave equations for E and then H in the three regions.
3. Obtain expressions for (a) instantaneous Poynting vectors of individual waves (incident, reflected,
transmitted etc.) in the three regions; and (b) time averaged Poynting vectors of individual waves in the
three regions.
4. Obtain the expressions for the reflectivity and transmitivity at interface between regions I and II, and
those at the interface between regions II and III.
5. Obtain expression for absorptivity in region II.

1. Consider the following problems concerning the electromagnetic wave propagation in three regions.
The incident wave E(x) = E0e^ikx (here E0 is a constant) is from the left in region I and strikes on the
interface. Establish the 1-D wave equation for the electromagnetic waves in the three regions and the
relevant boundary conditions.
ϵ0, μ0
ϵ1, μ0
ϵ2, μ0
Region I
Region II
Region III
E(x) = E0e^ikx
Incident wave
0
L
x
2. Obtain solutions to the above wave equations for E and then H in the three regions.
3. Obtain expressions for (a) instantaneous Poynting vectors of individual waves (incident, reflected,
transmitted etc.) in the three regions; and (b) time averaged Poynting vectors of individual waves in the
three regions.
4. Obtain the expressions for the reflectivity and transmitivity at interface between regions I and II, and
those at the interface between regions II and III.
5. Obtain expression for absorptivity in region II.

Added by Jonathan B.

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