lecture 9

Lecture 9
Interaction of electromagnetic radiation (light) with matter.
Speed of Light in a Medium
Maxwell s equations for isotropic non-conducting media are identical to those for a vacuum, with the exception that ?_o and ?_o are replaced by their media values ? and ?, these provide a velocity of v=(??)^(-1/2). The terms ? and ? can be related to ?_o and ?_o by:
K=?/?_o (relative permittivity) … (52)
K_m=?/?_o (relative permeability) … (53)
Thus:
v=(??)^(-1/2)=?(K_m ?_o K?_o)?^(-1/2)=c?(K_m K)?^(-1/2) ……… (54)
and the index of refraction n is defined as:
n=c/v=?(K_m K)?^(1/2)
Most transparent media are nonmagnetic, yielding K_m=1. The index of refraction is therefore given by:
n=K^(1/2)=(?/?_o )^(1/2) …………. (55)
Maxwell’s equations in a medium
In applying Maxwell s equations to dielectric materials, we can write them in the following form using the fact that M and ? are both zero in such materials:
??E=-1/?_o ??P ………….. (56)
??H=0 ………….. (57)
?×H=?_o ?E/?t+?P/?t+J ………….. (58)
?×E=?-??_o ?H/?t ………….. (59)
Accordingly, a general wave equation can be derived from these equation to be in the form: (prove it)
?×(?×E)+1/c^2 (?^2 E)/(?t^2 )=-?_o (?^2 P)/(?t^2 )-?_o ?J/?t ……… (60)
The left-hand side of this equation is the familiar wave equation for a vacuum, as described in eq. (22). The two additional terms on the right-hand side are called source terms. The first source term involves polarization charges, relating to localized charge effects in dielectric (non-conducting) media; the second term involves conduction charges that are applicable to metallic materials. The first term, for dielectric media, can be used to explain many optical effects, including dispersion, absorption, double refraction, optical activity, and so forth. The second term, for metals, can explain the high absorption and large reflectivity of such materials.