1Prof. David Attwood / UC Berkeley EE213 & AST210 / Spring 2009 03_Maxwell_RefracIndx_2009.ppt

Charles-Augustin de

Coulomb

CarlFriedrichGauss

MichaelFaraday

André-MarieAmpère James Clerk

Maxwell

Heinrich Hertz

Maxwell’s Equations

Courtesy of Andrew Aquila (AS&T, UC Berkeley)

The Equations of Light

2Prof. David Attwood / UC Berkeley EE213 & AST210 / Spring 2009 03_Maxwell_RefracIndx_2009.ppt

The time derivative of the current density,∂J/∂t, drives electromagnetic waves~

3Prof. David Attwood / UC Berkeley EE213 & AST210 / Spring 2009 03_Maxwell_RefracIndx_2009.ppt

The wave equation in vacuum, with a density n ofbound electrons of resonant frequency ωs

4Prof. David Attwood / UC Berkeley EE213 & AST210 / Spring 2009 03_Maxwell_RefracIndx_2009.ppt

Special cases: Propagation in vacuum, no electrons

5Prof. David Attwood / UC Berkeley EE213 & AST210 / Spring 2009 03_Maxwell_RefracIndx_2009.ppt

Special cases: Propagation with many electrons,but all free

6Prof. David Attwood / UC Berkeley EE213 & AST210 / Spring 2009 03_Maxwell_RefracIndx_2009.ppt

Special case: Propagation in a material of naatoms/unit volume, each with many bound electrons

7Prof. David Attwood / UC Berkeley EE213 & AST210 / Spring 2009 03_Maxwell_RefracIndx_2009.ppt

Special case: Propagation in a materialwith ω2 >> ωs

2, for x-rays and EUV

8Prof. David Attwood / UC Berkeley EE213 & AST210 / Spring 2009 03_Maxwell_RefracIndx_2009.ppt

Quantum mechanical model of refractive index