Traveling wave refraction coefficients

When propagation of the electromagnetic wave is of interest, it is useful to express the dielectric constant (w) in terms of the complex refractive index N((o). The complex refractive index is defined as Af = n -i- ik where = e, so that ei — n — and 2 = Here, n is the refractive index and k is the extinction coefficient. The traveling wave solutions to Maxwell s equations for a lossy optical medium are of the form ... 

Ametani, A. 1973. Modified traveling-wave techniques to solve electrical transients on lumped and distributed constant circuits Refraction-coefficient method. Proc. lEE 120(2) 497-504. 

Attention must now be paid to the exponential factor, exp( 2nir (n iij)/A), in Equation 6.5, where (n it) is known as the complex refractive index of a substance. It can be seen that the effect of this factor upon the electromagnetic wave increases with the distance Irl that the light travels in that medium. In the general case of an anisotropic medium, n and are referred to as a specific set of axes, usually chosen to coincide with the optical axes of the medium. For example, the axes of maximum and minimum transmittance are selected for anisotropic absorption. The extinction f for an anisotropic medium is related to the extinction coefficient through Equation 6.9. 

The first exp-term represents the exponential decay of the wave amplitude with penetration into the (absorbing) medium, while the second exponential term describes the time and phase dependence of the electromagnetic wave, traveling with phase velocity v - c/n. The two quantities n and k are called the refractive index and extinction coefficient, respectively, and are commonly referred to as the optical constants. 

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