HW01'sol - PHY 506 Classical Electrodynamics II Spring 2011...

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1 C:\User\Teaching\505-506\S11\HW01'sol.doc PHY 506 Classical Electrodynamics II Spring 2011 Homework 1 with solutions Problem 1.1 (to be graded of 25 points). A monochromatic, plane EM wave is normally incident from free space on a uniform slab of a material with electric permittivity and magnetic permeability , with slab thickness d comparable with the wavelength. (i) Calculate the power transmission coefficient F , i.e. the fraction of the incident power, which is transmitted through the slab. (ii) Assuming that and are frequency-independent and positive, analyze in detail the frequency dependence of F . In particular, how does function F ( ) depend on the film thickness d and the wave impedance Z = ( / ) 1/2 of its material? Solutions : (i) Since the wave may be partly reflected from the second interface (see Fig. on the right), we should look for the solution in the form of five traveling waves: . for , , 0 for , , 0 for , ) ( 0 0 0 0 0 z d e T d z e R Te z e R e e E E d z ik ikz ikz z ik z ik t i The four unknown (complex) coefficients R , R 0 , T , and T 0 , participating in these expressions may be found by plugging them into four boundary conditions which express the continuity of the electric field
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HW01'sol - PHY 506 Classical Electrodynamics II Spring 2011...

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