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Energy Dynamics in Dispersive and Non-Dispersive Dielectrics: A Comprehensive Review

This review explores energy behavior in dispersive and non-dispersive dielectrics, discussing the internal energy difference of bodies under electromagnetic fields while maintaining constant entropy and density. We analyze how dispersive media dissipate energy and the implications of energy inflow necessary for sustaining electromagnetic energy. The treatment includes both monochromatic and non-monochromatic fields, emphasizing the importance of real expressions in non-linear functions, the behavior of permittivity, and time-integrated net dissipation. This examination is vital for understanding thermal dynamics and energy conservation in advanced materials.

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Energy Dynamics in Dispersive and Non-Dispersive Dielectrics: A Comprehensive Review

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  1. Field energy in a dispersive medium Section 80

  2. Review energy in non-dispersive dielectrics U = internal energy difference for body with and without fields, holding entropy and density constant.

  3. Dispersive media dissipate energy • Mean evolved heat density per unit time Q = <-divS>t • Electromagnetic energy U is not constant. • Net inflow of energy is needed to sustain it.

  4. Assume monochromatic fieldsE = E0e-iwt dU = (E.dD +H.dB)/4p dU/dt = Need to use real expressions in non-linear functions

  5. Result is a constant dU/dt= -divS= <-divS>t =Q

  6. Dissipation of field energy per unit time is given bye” and m”

  7. e” and m” are positive • Second law of thermodynamics dQ = TdS > 0

  8. Which is true? • Real and imaginary parts of permittivity are always positive. • Real part of permittivity can be negative, but the imaginary part is always positive. • Both parts of the permittivity can be positive or negative.

  9. Non-monochromatic fields • Monochromatic fields are a fiction because their durations are finite. • Instead of dissipation per unit time, consider time-integrated net dissipation. • Amplitude of nearly monochromatic (e.g. laser) varies slowly.

  10. Any time dependent field can be written as a sum of monochromatic fields

  11. Electric part of net dissipation is a triple integral

  12. Perform integral over w’. The delta function makes w’ -> -w

  13. Transparency ranges • e” and m” are never zero except at w = 0. • However, they may be very small e”<<|e’| • Then, neglect absorption, reintroduce internal energy concept.

  14. Purely monochromatic fields do not accumulate U

  15. Amplitude varies slowly

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