# Absorption coefficient and Linear Optical Susceptibility

• PhysicsTruth
In summary, the absorption coefficient ##\alpha## is related to the complex part of the refractive index ##n^*=n+ik## and the linear optical susceptibility ##\chi## by a quadratic equation. To solve for ##\chi##, one can either assume a complex form and separate the real and imaginary parts, or solve for ##k## directly in terms of ##\chi##.
PhysicsTruth
Homework Statement
For a complex refractive index ##n^*=n+ik##, establish the relationship between the absorption coefficient and linear optical susceptibility. Take ##(n+ik)^2 = \epsilon = 1 + \chi##
Relevant Equations
##(n+ik)^2 = \epsilon = 1+ \chi##
##I=I_0 e^{-\alpha z}##
##\alpha = \frac{4\pi k}{\lambda}##
##\alpha## is considered to be the absorption coefficient for a beam of light of maximum intensity ##I_0##. It's related to the complex part of the refractive index as we have shown above. Now, I have a doubt. Should I solve for ##k## from the quadratic equation in terms of the linear optical susceptibility ##\chi## directly, or should I assume a complex form of ##\chi## and separate the real and imaginary terms and then proceed?

PhysicsTruth said:
Homework Statement:: For a complex refractive index ##n^*=n+ik##, establish the relationship between the absorption coefficient and linear optical susceptibility. Take ##(n+ik)^2 = \epsilon = 1 + \chi##
I've (extremely) limited knowledge of this topic. But, since no one else has answered yet, see if this helps...

First note that:
##(n+ik)^2 = \epsilon = 1 + \chi##
should be:
##(n+ik)^2 = \epsilon_r = 1 + \chi##

The equation tells you that susceptibility, ##\chi##, and relative permittivity, ##\epsilon_r##, are being treated as complex quantities.

PhysicsTruth said:
... or should I assume a complex form of ##\chi## and separate the real and imaginary terms and then proceed?
That sound like the way to go. It only requires simple algebra to express the real and imaginary parts of ##\chi## in terms of ##\alpha## (along with ##n## and ##\lambda##).

vanhees71 and PhysicsTruth
Yeah, I've done that thankfully. Thanks for the heads up!

vanhees71 and Steve4Physics

## 1. What is the absorption coefficient?

The absorption coefficient is a measure of how strongly a material absorbs light at a certain wavelength. It is represented by the symbol α and is typically expressed in units of inverse length (e.g. cm^-1).

## 2. How is the absorption coefficient related to the linear optical susceptibility?

The absorption coefficient is directly proportional to the square of the imaginary part of the linear optical susceptibility (χimag). This means that as the linear optical susceptibility increases, the absorption coefficient also increases.

## 3. What factors affect the absorption coefficient?

The absorption coefficient is affected by several factors, including the material's composition, structure, and electronic properties. It is also dependent on the wavelength of light being absorbed and the temperature of the material.

## 4. How is the absorption coefficient measured?

The absorption coefficient can be measured using various techniques, such as spectrophotometry or ellipsometry. These methods involve shining light of a known wavelength through the material and measuring the amount of light absorbed.

## 5. What is the significance of the absorption coefficient in materials science?

The absorption coefficient is an important parameter in materials science as it provides insight into a material's optical properties. It is used to understand how materials interact with light and can be used to design and engineer materials for specific applications, such as in solar cells or optical devices.

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