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emhw25 - Electromagnetic Theory II Problem Set 11 Due 11...

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Electromagnetic Theory II Problem Set 11 Due: 11 April 2011 43. The electric field of a plane wave e i · is perpendicular to the propagation direction k . The polarization vector is by definition a unit vector parallel to the electric field. We have found it useful to describe the fields with complex vectors whose real parts are the physical fields. In this description polarization vectors can be complex when they describe elliptic polarization, in which case we adopt the normalization * · = 1. Complex vectors belong to a three dimensional complex vector space, and it is convenient to pick an orthonormal basis. Let n = ˆ k be the unit vector parallel to k . Then choose e 3 = n , e 1 = , and e 2 = n × * . a) Show that the three e a are othonormal in the sense that e * a · e b = δ ab , and prove the completeness relation
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