# Phonon Dispersion Relation: Reflection of Photons Explained

• Goodver
So, in summary, the dispersion relation curve for phonon shows that the optical branch is not zero at k = 0, meaning that a solid can be transparent for all photon wavelengths except for the wavelength corresponding to the energy of an optical phonon at k = 0. This allows for the absorption or reflection of photons, with about 90% being reflected. This is due to the strong interaction between the optical phonons and electromagnetic waves, as the phonons act as large electrical dipole oscillators. It is not clear how photons can be reflected, as it would require a change in the direction of the k vector to the opposite direction. It is possible that incident photons convert to optical phonons, which then convert back to optical photons
Goodver
in the dispersion relation curve for phonon, optical branch is not zero at k = 0. Thus generally speaking solid might be transparent for all photon wavelengths except the wavelength which corresponds to the energy of an optical phonon at k = 0. Thus photons can be absorbed or reflected. It says that about 90 percents of photons are reflected. Why?

Also, It is not clear for me how photon can be reflected? It requires to change the direction of the k vector, to opposite direction. Or is it that incident photon converts to optical phonon, which then converts to optical photon in opposite direction statistically?

I am on a master level.
Thank you.

The momentum of infrared photons is negligible. The optical phonons near the center of the Brillouin zone are like large electrical dipole oscillators, which gives a very strong interaction with the electromagnetic waves.

Goodver

## 1. What is a phonon dispersion relation?

A phonon dispersion relation is a mathematical representation of the relationship between the energy and momentum of a phonon, which is a quantized vibrational mode in a crystal lattice. It describes how the energy of a phonon changes as its momentum changes.

## 2. How does the phonon dispersion relation relate to the reflection of photons?

The phonon dispersion relation is directly related to the reflection of photons in a crystal lattice. When a photon is incident on a crystal, it can interact with the lattice and create phonons. The phonon dispersion relation determines how these phonons will behave, including how they will reflect or interact with the incident photon.

## 3. What factors affect the phonon dispersion relation?

The phonon dispersion relation is affected by various factors such as the crystal structure, the strength of the bonds between atoms in the lattice, and the mass of the atoms. The type and number of atoms in the lattice also play a role in determining the phonon dispersion relation.

## 4. Can the phonon dispersion relation be experimentally measured?

Yes, the phonon dispersion relation can be experimentally measured through techniques such as inelastic neutron scattering or Raman spectroscopy. These methods allow scientists to directly observe the energy-momentum relationship of phonons in a crystal lattice.

## 5. How does the phonon dispersion relation impact material properties?

The phonon dispersion relation is closely linked to various material properties such as thermal conductivity, electrical conductivity, and mechanical properties. By understanding the phonon dispersion relation, scientists can gain insights into how these properties will behave in different materials, which is crucial for designing new materials with desired characteristics.

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