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EM waves: multiple planar interfaces (PEC-backed lossy dielectric)

  1. Dec 14, 2012 #1
    1. The problem statement, all variables and given/known data
    Our prof has told us we can get help from wherever/whoever we want as long as it isn't classmates. This is a take-home test. The relevant question:

    You have a three-layer dielectric.

    | Layer 1 | Layer 2 | Layer 3 |

    Layers 1 and 3 are semi-infinite.

    Layer 1 is air (εr = 1, μr = 1), σ = 0.
    Layer 2 is a lossy dielectric, εr = 2, μr = 1, σ = 0.01S/m. Its length is 1m.
    Layer 3 is a perfect electric conductor (PEC).

    The freespace wavelength of an incident EM wave is 1m.

    Find the power reflection coefficient R's numerical value for an incident angle of 0°, 40°, and 80°, and plot R for 0<θ<90.



    2. Relevant equations
    Maxwell's equations, boundary conditions, and matrix methods for solving multiple dielectric interfaces. I've posted some, the rest I can link to or post them on request: they're quite lengthy (probably about 20-30 pages).


    3. The attempt at a solution

    I've tried to find a closed form for the transfer matrix between the lossy dielectric and the PEC, but it always comes up singular. I'm not sure how to procede. As the σ = ∞ for the PEC, the wavenumber is also infinite, and so I can't reasonably find a closed form for the matrices. I have done a numerical solution that literally measures reflections (and attentuation causes it to quickly drop off anyway), but I'm wondering if I was beating my head against the desk for nothing.

    If someone could explain what a PEC does in this case (does it absorb all the energy? Does it completely reflect it?) it would be really helpful, information on that seems scant too.

    I can, again, post my attempt if you wish, but it's about 300-400 lines of matlab code. If in the end the answer is just "there is no closed form for the matrix" then I guess that'll be that.

    Thanks and if there are any additional questions please don't hesitate. You guys are the best, that's why I keep coming back.
     

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