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Lecture 11- Maxwell part 3

# Lecture 11- Maxwell part 3 - Lecture Lecture11 :PlaneWave...

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Lecture 11 Maxwell’s Equations Part 3: Plane Wave model and reflection from Oblique incidence at boundaries Hayt CH 12 1 McGill ECSE 352, Fall 2011, D. Davis

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Oblique Incidence It is often the case that the plane wave is travelling in a direction that is not parallel to one of the coordinate axis one of the coordinate axis. In this case the wave propagation is described as a function of the sum of vector components. T ill hi d l ill l k h To illustrate this model we will look to the following example. McGill ECSE 352, Fall 2011, D. Davis 2
Oblique Incidence Given a plane wave propagating within a medium along a path: ܴ ൌݔݏ݅݊ ߠ ݅ ܽ ݔ ൅ ݖܿ݋ݏ ߠ ݅ ܽ ݖ With a magnetic field polarized in the y di i ݔݏ݅݊ direction. Write an expression for the electric field (a vector phasor field). McGill ECSE 352, Fall 2011, D. Davis 3

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Oblique Incidence We can use either inspection or Maxwell’s We can use either inspection or Maxwell s Equations directly to obtain the electric field. From inspection we can note that the electric field polarization is perpendicular to both the magnetic field polarization and the direction of propagation. Thi ld i di h This would indicate that: ܧ ൈ ܪ ൌ ܵ ҧ McGill ECSE 352, Fall 2011, D. Davis 4
Oblique Incidence The electric field polarization direction must satisfy the relationship: ܣ ܽ ൅ ܣ ܽ ൅ ܣ ܽ ൈ ܽ ൌ ݏ݅݊ ߠ ܽ ൅ ܿ݋ݏ ߠ ܽ In this case we can immediately determine h h f h l i fi ld i ܣ 1 ܽ ݔ ൅ ܣ 2 ܽ ݕ ൅ ܣ 3 ܽ ݖ ݕ ݅ ݔ ݅ ݖ that the y component of the electric field is zero. From the cross product: ܣ 1 ൌ ܿ݋ݏ ߠ ݅ , ܣ 3 ൌ െݏ݅݊ ߠ ݅ McGill ECSE 352, Fall 2011, D. Davis 5

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Oblique Incidence This will allow us to write the electric field as: h i f h fi ld i di l ܧ ൌ ܧ ݋ ܿ݋ݏ ߠ ݅ ܽ ݔ െ ݏ݅݊ ߠ ݅ ܽ ݖ ݁ െߛ ݔݏ݅݊ ߠ ݅ ൅ݖܿ݋ݏ ߠ ݅ ݁ ݆߱ݐ
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