# Optics: Anomalous Dispersion & Absorption Explained

• Niles
In summary, anomalous dispersion is when dn/dω<0, which leads to strong absorption due to the Kramers-Kronig relations and high dispersion. In optics, the index of refraction is found by equating n2 to the complex wavevector k, but this may be a mistake as n is unitless while k has units of inverse length. The formula k = n*omega/c still holds in this case.

#### Niles

Hi

I am reading about dispersion and index of refraction, and I have encountered the term "anomalous dispersion". This is where dn/dω<0, and where the absorption is strongest because of damping. Now, I can't seem to connect those two dots (and my book does not explain it nor Wiki): Why does dn/dω<0 imply strong absorption and vice versa?

Briefly- it's the Kramers-Kronig relations. Anamolous dispersion (and high dispersion generally) occurs in the same spectral region as absorption peaks.

Thanks.

I have another question related to optics, so I will ask it here rather than creating a new thread. When we solve Maxwells equations inside a conductor, we eventually get the Helmholtz equation, where the wavevector k is complex.

In order to find the index of refraction, my teacher told me that n2=k, where n is the complex index of refraction and k is the complex wavevector. Did he make an error? I really have to idea where that formula comes from.

Niles said:
In order to find the index of refraction, my teacher told me that n2=k, where n is the complex index of refraction and k is the complex wavevector. Did he make an error? I really have to idea where that formula comes from.

Sounds like a mistake to me--the quickest way to see this is to note that n is unitless while k has units of inverse length. If you're treating n as the complex index of refraction, and k as the complex wavevector, then the formula k = n*omega/c still holds.

Hi there,

Thank you for your question! Anomalous dispersion refers to a phenomenon where the index of refraction (n) decreases with increasing frequency (ω) of light. This is in contrast to normal dispersion, where n increases with ω. The term "anomalous" simply means that this behavior is unexpected or unusual.

Now, to understand why this leads to strong absorption, we need to look at the relationship between n and the imaginary part of the refractive index, which is related to the absorption coefficient. The imaginary part of the refractive index is given by the Kramers-Kronig relations, which show that it is proportional to the frequency derivative of the real part of the refractive index (dn/dω). When dn/dω is negative, the imaginary part of the refractive index becomes larger, leading to stronger absorption.

In other words, when light passes through a material with anomalous dispersion, the index of refraction decreases with increasing frequency, causing the light to slow down. This slowing down results in a longer interaction time between the light and the material, leading to stronger absorption.

I hope this helps to clarify the connection between anomalous dispersion and strong absorption. Let me know if you have any further questions.

## 1. What is anomalous dispersion?

Anomalous dispersion is a phenomenon in optics where the refractive index of a material decreases with increasing wavelength of light. This results in the light being split into different colors, causing a blurred or distorted image.

## 2. How does anomalous dispersion occur?

Anomalous dispersion occurs when the frequency of light approaches the frequency of an electronic transition in the material. This causes the electrons to oscillate at the same frequency as the light, resulting in a decrease in the refractive index.

## 3. What is the difference between normal and anomalous dispersion?

In normal dispersion, the refractive index increases with increasing wavelength, resulting in the light being bent towards the center of the prism. In anomalous dispersion, the refractive index decreases with increasing wavelength, causing the light to be bent away from the center.

## 4. How does absorption affect anomalous dispersion?

Absorption occurs when some of the light's energy is absorbed by the material, causing a decrease in the intensity of the light. In anomalous dispersion, absorption can further distort the image by causing some colors to be more strongly absorbed than others, resulting in uneven dispersion.

## 5. What are some real-world applications of anomalous dispersion?

Anomalous dispersion is used in various optical instruments, such as spectrometers and prism lenses, to analyze and separate different wavelengths of light. It is also a crucial factor in the design of optical fibers and telecommunications systems.