Greens Function Solutions of the Wave Equations

This result demonstrates the tendency of an optically active material to rotate the electric vector as it propagates through the sample. Materials possessing this property are normally composed of molecules having chiral symmetry. This effect leads to circular birefringence and circular dichroism, two optical properties that are frequently used in the characterization of biomaterials. 

We seek here general solutions to Maxwell s equations and begin with equation (1.8) which resulted by combining the Maxwell curl equations, 

Equation (1.33) has been written in a form that motivates the use of a Green s function solution. The term on the righthand side represents the action of the dielectric properties of the material and formally renders this equation inhomogeneous. The Green s function, G (x, x ), is the solution to the following inhomogeneous equation, 

Once this tensor function is determined, the solution to equation (1.34) is the following convolution over the Green s function, 

A simple version of the Green s function can be found if V E = 0 everywhere in space. Under these circumstances, V G = 0, and equation (1.34) reduces to 

---