These two waves may be linearly circularly or

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These two waves may be linearly, circularly, or elliptically polarized. For example, a circularly polarized wave can be decomposed into two linearly polarized waves with polarizations at right angles. This construction is sometimes how circularly polarized waves are generated. All antennas transmit and receive signals with a specific polarization. Waves with polarizations orthogonal to the antenna’s are invisible to them. Efficient communication and radar links require matched polarizations. 44
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x y E H x’ y’ α/2 Figure 2.11: Elliptically polarized TEM wave. Reflection/scattering can affect the polarization of a signal, as can propagation in certain interesting materials (crystals, plasmas). Signals reflected off a surface at or near to the Brewster angle will retain only one linear polarization, for example. In space plasmas and birefringent crystals, waves spontaneously decompose into orthogonal polarizations (called the X and O modes) which then propagate differently. Polarimetry involves monitoring the polarization of a signal scattered from the ground to detect surface prop- erties. As depicted in Figure 2.12, the sense of rotation of circularly polarized waves reverses upon reflection. It can reverse multiple times upon scattering from rough surfaces. Revealing imagery can be constructed by monitoring the fraction of the power in one circular polarization of a scattered wave. RC LC RC LC RC Figure 2.12: Illustration of polarization changes occurring upon reflection or scattering. The generic expression for an elliptically polarized wave is arguably difficult to visualize. However, its meaning can be clarified with a couple of revealing variable transformations that make use of some of the principles stated above. The first of these involves decomposing the wave into left- and right-circularly polarized components, i.e. ( E 1 ˆ x + E 2 e ˆ y ) = E l x + j ˆ y ) + E r x j ˆ y ) where we take E 1 and E 2 to be real constants. A little algebra quickly reveals that E r = 1 2 bracketleftbig E 1 + jE 2 e bracketrightbig E l = 1 2 bracketleftbig E 1 jE 2 e bracketrightbig 45
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Now, the complex amplitudes E r and E l can always be expressed as real amplitudes E R and E L modifying a complex phase term involving symmetric and antisymmetric phase angles φ and α , i.e. E r = E R e jα/ 2+ jφ/ 2 E l = E L e jα/ 2+ jφ/ 2 We leave it as an exercise to solve for the new constants. In terms of them, the total electric field becomes E = E L e jα/ 2 x + j ˆ y ) e j ( ωt kz + φ/ 2) + E R e jα/ 2 x j ˆ y ) e j ( ωt kz + φ/ 2) Define the total phase angle to be φ = ωt kz + φ/ 2 . Then, after taking the real part of the electric field, we find ( E ( z,t )) = cos φ x cos α 2 + ˆ y sin α 2 ) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright ˆ x ( E L + E R ) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright E + sin φ y cos α 2 ˆ x sin α 2 ) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright ˆ y ( E L E R ) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright E = braceleftBig ( E + ˆ x + jE ˆ y ) e
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  • Spring '13
  • HYSELL
  • The Land, power density, Solid angle

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