An electromagnetic wave originates form a source far from the x=0 plane . It has an electric field given by EI(r,t) = ∑+

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An electromagnetic wave originates form a source far from thex=0 plane . It has an electric field given by
EI(r,t) = ∑+ { E0 rect(t/T) exp[i (ki . ṝ - 2πv0t)]} +c.c.
Where the unit vector, ∑+ is given by : ∑+= [ sin (π/12) x – cos (π/12) z] And “+c.c” adds the complexconjugate of the first term to make E1 a real valuedfunction. The function rect(x) is 1 for |x|≤ ½ and zero otherwise.This wave is incident on an interface located in the x-z plane atthe plane x = 0, with n1 = 1.0002 (i.e. air) andμ1 = μ0 for x <0 and n2(v) andμ2 = μ0 for x>0. There is neither asurface charge distribution (ρs = 0) nor a surfacecurrent (Js = 0) on this interface. The frequencydependences of n2 is known, but not given here and youdo not need to determine it for this problem. Find the complexelectric field spectrum ONLY (ER(v)) and its polarization directionin reflection using the parameters given in this problem.
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