Complex refractive index ↩

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shorthands: {}
aliases: [Extinction coefficient]
created: 2021-10-25 20:11:13
modified: 2022-01-10 04:13:03

Complex refractive index is used to describe the opacity of an optical medium.

Where the real part is the refractive index and it indicates the phase velocity of light in the medium. The imaginary part however is the extinction coefficient and indicates the amount of attenuation when the electromagnetic wave propagates through the material.

Attenuation of planar waves

Let us take a look at the case of planar waves propagating through a medium with complex refractive index along the axis. In this case the wave number is1:

This can be inserted into the plane wave expression this way:

Based on the last line, gives an exponential decay of the electromagnetic wave. Since the intensity of the wave is the proportional to the square of the amplitude of the wave, the intensity decays according to:

From this the attenuation coefficient is defined like this:

And the penetration depth:

  1. Where is the wavelength in vacuum.
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