This problem concerns using the state variable method to

determine the EM fields that result when a plane wave, possessing arbitrary

polarization, is obliquely incident on a uniform bianisotropic layer located

between free space on the incident side and an infinite dielectric region on

the transmit side. The EM fields of the bianisotropic system are defined by the

relations of Ref. [6], namely, are lossy, in general, nonzero complex

constant dyadic quantities. Figure 4.10 shows the general layer system geometry

assuming that an arbitrarily polarized plane wave is obliquely incident on

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This problem concerns using the state variable method to

determine the EM fields that result when a plane wave, possessing arbitrary

polarization, is obliquely incident on a uniform bianisotropic layer located

between free space on the incident side and an infinite dielectric region on

the transmit side. The EM fields of the bianisotropic system are defined by the

relations of Ref. [6], namely, are lossy, in general, nonzero complex

constant dyadic quantities. Figure 4.10 shows the general layer system geometry

assuming that an arbitrarily polarized plane wave is obliquely incident on the

system and that characterize the Region 2 material

parameters of the system. The analysis of this problem is to be carried by

formulating state variable and associated matrix equations to solve Maxwells

equations and then using this formulation to solve a specific numerical

example. Complete the following parts to perform the just stated analysis.

(a) Assume that the oblique incident plane wave is given

mathematically by

Assume that the wave vector values kx and kz

are known and given, and that the incident plane waves polarization is

specified by known, given values of ExI = SxI

and EzI = SzI. From Maxwells equations and

the assumed known valuefind the other field components of the

incident plane wave. Find the form of the reflected and transmitted plane waves

that propagate in Regions 1 and 3, respectively.

(b) In Region 2, write out Maxwells curl equations

in dimensionless form lettingusing dimensionless dyadics defined by

(c) Let all EM field components in the Region 2 material

layer be proportional to the factor exp(since an incident plane wave possessing

this factor is incident on the layer, and phase matching must occur at the

interfaces of the slab). Substitute these EM field expressions into Maxwells

normalized equations, and find and write the resulting equations.

(d) From the resulting six equations of (c), simplify these

equations to a set of four equations involving only the transverse electric and

magnetic field components (i.e., -, -components)

by expressing the longitudinal electric and magnetic fields in terms of the

transverse electric and magnetic field components. Put the resulting four

equations in the state variable form

Why, possibly, is it useful to reduce the set of six

equations to a set of four equations involving only tangential field

components?

(e) Solve the state variable equation of (d) for the

eigenfunctions of Region 2 and express the general EM field solution of Region

2 in terms of these eigenfunctions.

(f) By matching EM boundary conditions, using the Regions 1,

2, and 3 solutions of (a) and (e), formulate the final matrix equation from

which all of the unknowns of the system may be determined.

(g) Using the formulation described in (a)(f), solve the

following numerical example assuming: in Region 1, _1 =

1.3 and _1 = 1.8, the incident plane wave has the amplitude SxI

= 1 (V/m), SzI = 0.9 (V/m), kx = sin(_I

) cos(I ), and kz

= sin(_I ) sin(I ), where _I

= 35°, I = 65°; in Region 3,

_3 = 1.9 and _3 = 2.7; in Region 2, we take the

layer thickness and we consider a complicated numerical

example where all material parameters of are taken to be nonzero and are given by

(h) Make sample plots of the EM fields in Regions 1, 2, and

3.

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