1. Light and Matter Tim Freegarde School of Physics & Astronomy University of Southampton Classical electrodynamics

2. 2 Electromagnetic waves electrostatic force acts through vacuum net force due to oscillating dipole retardation due to finite speed of light, enhanced by inertia of any charged particles

3. 3 Maxwell’s equations Gauss no monopoles Faraday Ampère constitutive equations

4. 4 Constitutive equations constitutive equations conservation of charge

5. 5 Maxwell’s equations constitutive equations conservation of charge

6. 6 Electromagnetic wave equation constitutive equations conservation of charge use constitutive equations to reduce electric & magnetic fields to single functions differentiate equations to allow electric or magnetic field to be eliminated apply vector relations to produce wave equation

7. 7 Sinusoidal plane wave solutions

8. 8 Maxwell’s equations constitutive equations conservation of charge

9. 9 Electromagnetic wave equations constitutive equations conservation of charge use constitutive equations to reduce electric & magnetic fields to single functions differentiate equations to allow electric or magnetic field to be eliminated apply vector relations to produce wave equation

10. 10 Constitutive equations use constitutive equations to reduce electric & magnetic fields to single functions differentiate equations to allow electric or magnetic field to be eliminated apply vector relations to produce wave equation use constitutive equations to reduce electric & magnetic fields to single functions differentiate equations to allow electric or magnetic field to be eliminated apply vector relations to produce wave equation

11. 11 Electromagnetic waves in isotropic media atoms and molecules are polarized by applied fields induced polarizationalignment of permanent dipole moment polarization modifies field propagation: refractive index; absorption

12. 12 Constitutive equations governed by properties of the optical medium define polarization P and magnetization M vapours, dielectrics, plasmas, metals apply Newtonian mechanics to determine response of medium to applied field use result to write (complex) conductivity, dielectric constant etc. insert into constitutive equations and hence derive wave equation as usual magnetization usually too slow to have effect at optical frequencies assume (for now) D[E] to be linear and scalar

13. 13 Vapours and dielectrics bound or massive nuclei electrons confined in harmonic potential restoring force proportional to displacement Newtonian dynamics frequency dependence (dispersion)

14. 14 Metals and conductors free charges diffusion in response to applied field equilibrium velocity characterized by conductivity frequency dependence (dispersion) damped solutions (absorption) dissipation through resistive heating

15. 15 Plasmas and the ionosphere independent, free charges inertia in response to applied field Newtonian dynamics frequency dependence (dispersion)

16. 16 Electromagnetic energy density & flow constitutive equations conservation of charge

17. 17 Electromagnetic energy density & flow BBC Radio 4 long wave transmitter, Droitwich frequency:198 kHz = 1515 m power:400 kW MSF clock transmitter, Rugby frequency:60 kHz = 5000 m power:60 kW

18. 18 Constitutive equations governed by properties of the optical medium define polarization P and magnetization M vapours, dielectrics, plasmas, metals apply Newtonian mechanics to determine response of medium to applied field use result to write (complex) conductivity, dielectric constant etc. insert into constitutive equations and hence derive wave equation as usual magnetization usually too slow to have effect at optical frequencies assume (for now) D[E] to be linear and scalar

19. 19 Continuity conditions transverse waves on a guitar string x continuity of y continuity of … finite extension … finite acceleration conservation of energy conservation of momentum TT

20. 20 Continuity conditions electromagnetic fields conservation of energy conservation of momentum E // 2 1 1 2 parallel components perpendicular components

21. 21 Reflection at metal and dielectric interfaces electromagnetic fields conservation of energy conservation of momentum E // 2 1 1 2 parallel components perpendicular components combine forward and reflected waves to give total fields for each region apply continuity conditions for separate components hence derive fractional transmission and reflection

22. 22 Reflection at metal and dielectric interfaces combine forward and reflected waves to give total fields for each region apply continuity conditions for separate components hence derive fractional transmission and reflection

23. 23 Reflection at multiple dielectric interfaces combine forward and reflected waves to give total fields for each region apply continuity conditions for separate components hence derive fractional transmission and reflection

24. 24 Reflection at multiple dielectric interfaces

25. 25 Reflection at multiple dielectric interfaces