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

2. 2 How light interacts with matter atoms and molecules are polarized by applied fields induced polarization modifies field propagation: refractive index; absorption

3. 3 Lorentz theory of atomic polarization bound or massive nuclei electrons confined in harmonic potential restoring force proportional to displacement Newtonian dynamics dissipation of motion through frictional force

4. 4 Lorentz theory of atomic polarization complex dielectric constant real part: refractive index imaginary part: (absorption) freq 0 1  =0.050

5. 5 Lorentz theory of atomic polarization freq 0 1  =0.050 complex dielectric constant real part: refractive index imaginary part: absorption  =0.075  =0.100  =0.125  =0.150  =0.175  =0.200  =0.225  =0.250  =0.275  =0.300  =0.325  =0.350  =0.375  =0.400  =0.425  =0.450  =0.475  =0.500

6. 6 Lorentz theory of atomic polarization freq 0 1 complex dielectric constant real part: refractive index imaginary part: absorption  =0.200 ‘stop band’ from to : strong attenuation even for small 

7. 7 Lorentz theory of atomic polarization freq 0 1  =0.050 complex dielectric constant real part: refractive index imaginary part: absorption  =0.075  =0.100  =0.125  =0.150  =0.175  =0.200  =0.225  =0.250  =0.275  =0.300  =0.325  =0.350  =0.375  =0.400  =0.425  =0.450  =0.475  =0.500 ‘stop band’ from to : strong attenuation even for small 

8. 8 Causality and the dispersion relations causality: effect follows cause time E   E E causality:  must obey

9. 9 the Kramers-Krönig dispersion relations causality: effect follows cause Kramers-Krönig relations relate the real and imaginary parts of  (  ) if, then

10. 10 Implication for all dielectrics evaluate  1 as  → 0 if  1 ≠ 1, there must be frequencies at which  1 ≠ 0 (absorption) dielectrics cannot be transparent at all wavelengths

11. 11 Application to a single sharp absorption suppose a single absorption at  =  0 freq 0 1 Kramers-Krönig then gives

12. 12 Quantum description of atomic polarization full time-dependent eigenfunctions therefore spatial part of eigenfunctions given by and any state of the two-level atom may hence be written energy 0

13. 13 Quantum description of atomic polarization full time-dependent eigenfunctions therefore spatial part of eigenfunctions given by and any state of the two-level atom may hence be written write time-dependent Schrödinger equation for two-level atom insert energy of interaction with oscillating electric field reduce to coupled equations for a(t) and b(t)

14. 14 Quantum description of atomic polarization full time-dependent eigenfunctions therefore spatial part of eigenfunctions given by and any state of the two-level atom may hence be written write time-dependent Schrödinger equation for two-level atom insert energy of interaction with oscillating electric field reduce to coupled equations for a(t) and b(t)

15. 15 Quantum description of atomic polarization x/a 0 electron density depends upon relative phase of superposition components

16. 16 Atomic polarization response of massive electrons to applied electric field resonant frequency due to confining potential of electrons in atom electron displacement leads to atomic polarization frequency-dependent amplitude and phase lag of response related by causality Newtonian and quantum mechanical models give same result freq 0 1  =0.050  =0.075  =0.100  =0.125  =0.150  =0.175  =0.200  =0.225  =0.250  =0.275  =0.300  =0.325  =0.350  =0.375  =0.400  =0.425  =0.450  =0.475  =0.500