Technical Reference

Complex Index of Refraction

In the material property database, TracePro represents the complex index of refraction by

nˆ = n + ik

where k is the extinction coefficient, and

λα k = ------ .

4π

Here λ is the wavelength and α is the absorption coefficient. In the TracePro Material Property Editor you can enter either α or k, and TracePro will calculate the other parameter.

Some textbooks define the complex index of refraction as

nˆ = n(1 + κ)

with κ denoted as the extinction coefficient or attenuation index, while still others use

nˆ = n – ik

or

nˆ = n(1 – iκ).

Calculating the Fresnel Coefficients, i.e. the relative flux of a reflected or transmitted wave and its polarization state at the interface of two media is a complicated procedure. However, for a wave at normal incidence on an interface between air and a medium with complex refractive index, the calculation of the reflectance is simpler (Born and Wolf, Fifth Edition, §13.2),

	ˆ		2 n2(1 + κ2) + 1 – 2n
R =	n – 1		=
	-----------			-----------------------------------------------	2		2
	ˆ
	n + 1			n		(1 + κ		) + 1 + 2n

where we have used κ = k/n.

It is important to be aware that k and κ depend on λ while α does not. When interpolating the material property data, n and α are interpolated, and k is calculated from α.

7.14	TracePro 5.0 User’s Manual