Maxwell’s equations in a medium CGS Comparing Units MKS Maxwell’s equations in a medium where r and J refer to “free” charge and currents. The electric field E, the displacement field D and the polarization P are related by For typical optical materials and at non-too-high-field strengths, the polarization goes linearly with the electric susceptibility of the material, ce . e = 1 in vacuum e r = 1 in vacuum

Comparing Units, continued MKS CGS Comparing Units, continued MKS The magnetic induction H, the magnetic field B and the magnetization, M, are related by For typical optical materials and at typical optical frequencies, the magnetization is negligible, so we can write: Except for at boundaries between different materials, in optical problems there is no free charge or free current, so finally we can write our “optical Maxwell’s Equations as shown:: In vacuum, in a plane E&M wave there is a relation between peak electric field and peak magnetic field: When |Ep|=1 statvolt/cm, |Bp|= 1 Gauss When |Ep|=1 volt/meter, |Bp|= 1/c = 3.33x10-9 Tesla

Comparing Units, continued CGS MKS conversion cm second gm erg esu statvolt statvolt/cm Gauss esu-cm/cc l length t time m mass U energy q charge V Elec. potential E electric field B magnetic field P polarization meter second kilogram Joule Coulomb Volt erg/joule = 10-7 esu/Coulomb = 3.33 x 10-9 statvolt/volt = 300 statvolt/cm / volt/m = 3x108 Gauss/Tesla = 10-4