Referring to Problem 4.3 and the geometry described therein,

this problem concerns calculating the real time-averaged power,

where _ = 2_/T, T is the temporal period

and represent

the real, time varying EM fields of the system.

(a) Using the general eigensolutions of Problem 4.3, give a

general expression for the real time-averaged power that is transmitted in the direction.

(b) Using the formula of (a), numerically calculate SAV

for the numerical case used in your Problem 4.3e solution (this was the

lossless case) in the regions exterior to the multilayer system.

»

Referring to Problem 4.3 and the geometry described therein,

this problem concerns calculating the real time-averaged power,

where _ = 2_/T, T is the temporal period

and represent

the real, time varying EM fields of the system.

(a) Using the general eigensolutions of Problem 4.3, give a

general expression for the real time-averaged power that is transmitted in the direction.

(b) Using the formula of (a), numerically calculate SAV

for the numerical case used in your Problem 4.3e solution (this was the

lossless case) in the regions exterior to the multilayer system. Verify

numerically that the incident power equals the sum of the power reflected and

transmitted from the multilayer system, thus verifying that conservation of

power holds for the system.

Problem 4.3

A plane wave of peak amplitude E0 is

normally incident on a four-layer system located between free space on the

incident side and an infinite dielectric region on the transmit side.

(a) Using general layer thicknesses (i.e., s_,

= 1, 2, 3, 4) and material

parameters (i.e., relative permeability __ and permittivity, __,

= 1, 2, 3, 4), using the state

variable method, and using coordinate system of Figure 5.19, find the general

form of the EM fields in each region, expressed in terms of forward and

backward traveling plane waves of unknown amplitude.

(b) By matching EM boundary conditions at all material

interfaces, formulate matrix equations from which the EM fields in all regions

of the system may be found.

(c) Form a ladder matrix equation, which relates the EM

field amplitudes of the plane waves of (b) in the layer that is adjacent to the

transmit side (call this layer Region 4, assumed to have width s4)

to the EM field amplitudes of the plane waves in the layer that is adjacent to

the incident side (call this layer Region 1, assumed to have width s1).

(d) Using the ladder matrix found in (c), matching EM

boundary conditions, formulate a reduced matrix equation from which the EM

fields in all regions of the system may be found.

(e) Picking specific layer thicknesses (i.e., s_,

= 1, 2, 3, 4) and lossless

layer material parameters (i.e., relative permeability __

and permittivity, __, = 1, 2, 3, 4) of your choice, solve numerically

all equations formulated in (a)(d). Present and compare numerical results of

(b) and (d).

(f) Repeat (e) using lossy layer material parameters.

(g) Comment on the advantages and disadvantages of the

solutions as determined by the methods described in (b) and with the solution

described in (d) and (e).

»

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