Find the solution to the given simultaneous equations by matrix inversion method.

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Chapter A.2, Problem 4PP

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Find the solution to the given simultaneous equations by matrix inversion method.

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A plane wave propagating in the +z direction in medium 1 is normally incident to medium 2 located at the z=0 plane as below. Both mediums are general, characterized by ( ε i, Mi, Ơi ). tot = [ ει μη σ] [ε, μη σε ] Ex Ex tot E₁₂ (z) = Ee Ex z=0 From conservation of energy: P₁AV'(z=0) + Piav'(z=0) = P2av²(z=0). Using the above show for lossless media that: ( 1 - ||²) = (1/M2 )|T|² .

A plane wave propagating in the +z direction in medium 1 is normally incident to medium 2 located at the z=0 plane as below. Both mediums are general, characterized by ( ε i, Hi, σ¡ ). [ ει μη σ] Ex [ ει μη ση ] Ex tot E₁₂ (z) = E'₁e¹² -122 E(z) = Ee+ E₁₁₁² E₁x z=0 1. Specify the electric field reflection coefficient г and transmission coefficient T: E ΓΔ E E TA EL 2. Show that T=1+г. Can the transmitted electric field amplitude in region 2 be LARGER than the incident electric field amplitude? 3. Determine expressions for P₁AV'(z), PIAV'(z) and P2AV'(z) (note the sign for the reflected power direction should be (-z).