Field energy in a dispersive medium

1. Field energy in a dispersive medium Section 80

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

7. 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.

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

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

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

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

12. 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.

13. 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.

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

15. Electric part of net dissipation is a triple integral

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

18. 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.

19. Purely monochromatic fields do not accumulate U

24. Amplitude varies slowly