Notes 8 Spring 2005

Notes 8 Spring 2005 - Notes 8 Spring 2005 Wave Propagation...

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Notes 8 Spring 2005 Wave Propagation in Dielectric Media Dielectrics (insulators) differ from conductors in that they have few (if any) free charges available for conduction. They do, however, have fixed, or bound, charges that influence the field within the material. Imagine the electron clouds surrounding the atoms that constitute the medium as an EM wave passes through. The electric field component of the wave pulls the electrons one direction and the positive nucleus the other direction thereby establishing an electric dipole that is aligned with the field 1 . This polarization process results in a slight phase difference between the D -field and the E - field. Since the permittivity is the quantity relating these two fields, this phase difference is mathematically accommodated by writing the permittivity as a complex number, . ε ′ ε′ = ε j Additionally, we note that in the process of repeatedly forming these dipoles (and flipping reluctant permanent dipoles) energy is dissipated as heat in the medium. The ultimate source of this energy, of course, is the EM wave itself and so the EM wave loses energy as it propagates through and we say that the wave is attenuated via this process or a polarization loss occurs. Finally we note that if is zero then the implication is that (the permittivity is a real number) and no attenuation occurs due to this process. ε′ ε′ = ε Another, separate, loss mechanism for the EM wave is the conductivity , , of the medium. A non- zero conductivity gives rise to conduction currents in the presence of the electric field component of the EM wave resulting in energy loss from the subsequent heat produced by these currents. σ The range of value for conductivity is extreme as we move from the best insulators to semi-conducting materials and then to the best conductors. In siemens per meter ( ) m S the conductivity, σ , ranges from for fused quartz,10 for poor plastic insulators, roughly unity for semiconductors to almost for metallic conductors at room temperature. These values cover a range of 25 orders of magnitude! HUGE! 17 10 8 10 7 The polarization loss mechanism and the conductivity loss mechanism may or may not both be present in any given material and it is often not well known how much each contributes to the total loss. Usually this is an empirically derived value. We will derive an effective conductivity to represent the overall loss which will allow us to quantify the relative contributions of these mechanisms when they are known. ( eff σ ) We recall Maxwell’s second equation, Ampere’s law and include all appropriate terms now that we are no longer in free space: () ( ) E j E E j j E E j E J J H d c r r r r r r r r r r ε′ ω + ε ′ ω + σ = ε ′ ε′ ω + σ = ωε + σ = + = × 1 1 What we are describing here is a non-polar material. Some dielectric atoms/molecules have permanent dipoles even in the
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Notes 8 Spring 2005 - Notes 8 Spring 2005 Wave Propagation...

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