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Dispersion of the permittivity

Dispersion of the permittivity. Section 77. An EM field that varies in time, varies in space too, due to finite propagation speed. Frequencies close to polarization resonances, but where the macroscopic description of the fields still applies, must exist.

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Dispersion of the permittivity

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  1. Dispersion of the permittivity Section 77

  2. An EM field that varies in time, varies in space too, due to finite propagation speed.

  3. Frequencies close to polarization resonances, but where the macroscopic description of the fields still applies, must exist.

  4. The derivation of divP = -<r>r is independent of the time dependence of the field. • Interpretation of P is the same.

  5. Rapidly varying fields are usually weak (except for laser fields in non-linear optics) D = D(E) is usually linear in E.

  6. A field with arbitrary time dependence can be decomposed into Fourier components • Because equations are linear, we can treat each monochromatic term in the expansion independently • Each has time dependence e-iwt

  7. For wth Fourier component A frequency dependent material property

  8. Dispersion relation, generally complex

  9. Well below resonances in the material, the dispersion effects are small.

  10. Static case: Limit w -> 0

  11. Conductors are a special case

  12. Expansion of e(w) begins with i/w term for metals • First term is imaginary, odd function of w • Next term is a real constant • This term is unimportant if effects of spatial variations (skin effect) are more important than effects of time variations.

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