A plane wave of E0 is obliquely incident

on a four-layersystem located between free space on the incident side and an

infinite dielectric region on the transmit side. Using the coordinate system of

Figure 5.19 (assuming the vertical direction in this figure to be the

x-direction), the incident plane wave is given by where _I

, _I are the relative permeability and permittivity,

respectively, of the incident region and _I is the

incident angle of the plane wave.

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

_ = 1, 2, 3, 4) and material parameters (i.e., relative

permeability

»

A plane wave of E0 is obliquely incident

on a four-layersystem located between free space on the incident side and an

infinite dielectric region on the transmit side. Using the coordinate system of

Figure 5.19 (assuming the vertical direction in this figure to be the

x-direction), the incident plane wave is given by where _I

, _I are the relative permeability and permittivity,

respectively, of the incident region and _I is the

incident angle of the plane wave.

(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), write Maxwells equations in component form in

any region for the problem under consideration.

(b) Put the resulting equations of (a) in state variable

form for the EM field components that are parallel to the interfaces of the

multilayer system and solve for the eigenfunctions associated with the state

variable equations.

(c) Using the eigenfunction solutions of (b), find the

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

backward, obliquely, traveling plane waves of unknown amplitude.

(d) Assuming that the transmit region has material

parameters _T, _T, 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.

(e) 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).

(f) Using the ladder matrix found in (e), matching EM

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

fields in all regions of the system may be found.

(g) 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)(f). Present numerical results of (d), (e), and (f).

(h) For your numerical example, verify that the conservation

of power holds in the system.

»

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