Plane Waves in Nonconducting Media

The dielectric tensor describes the linear response of a material to an electric field. In many experiments, and particularly in optical rheometry, anisotropy in is the object of measurement. This anisotropy is manifested as birefringence and dichroism, two quantities that will be discussed in detail in Chapter 2. The nonlinear terms are responsible for such effects as second harmonic generation, electro-optic activity, and frequency tripling. These phenomena occur when certain criteria are met in the material properties, and at high values of field strength. 

The solutions to the Maxwell field equations that are most often used in the applications discussed in this book are referred to as plane waves of monochromatic light. These are derived from the Maxwell curl equations. In a system free of charges and currents, these are 

For an isotropic medium without optical rotation, use of the constitutive relations (1.4) yields 

Using the general vector identity, VxVxE = V(V E)-V2E, and that V E = 0 in a space free of charge, the following wave equation results  

A plane wave is defined as a field propagating in a single direction (taken to be z in this example), and that is uniform in the perpendicular plane. In this case, there are no gradients in x and y, and equation (1.9) becomes, 

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