Lattice absorption

The conductive properties of many materials that are suitable for use as optical substrates can provide a good indication of the expected spectral performance, as the systematic tendencies in the electrical properties tend to parallel the optical behaviour. Insulator materials show some regions of transparency, either in the near or far-infrared, whilst good electrical and thermal conductors exhibit a continuous background of electronic absorption over the whole infrared region.

All of the resonant absorption processes involved in an infrared material can be explained by the same common principal. At particular frequencies the incident radiation is allowed to propagate through the crystal lattice producing the observed transparency, other frequencies however, are forbidden when the incident radiation is at resonance with any of the properties of the lattice material, and as such are transferred as thermal energy, exciting the atoms or electrons. The resonant vibrational absorption characteristics created by the lattice are highly complex, consisting of several types of fundamental vibrations. In order that a mode of vibration can absorb, a mechanism for coupling the vibrational motion to the electromagnetic radiation must exist.

Transfer of electromagnetic radiation from the incident medium to the material is in the form of a couple, where the lattice vibration produces an oscillating dipole moment which can be driven by the oscillating electric field (E) of the radiation. In order for the total transfer of energy to be complete, the following three conditions must be satisfied;

  1. the conservation of energy is maintained,
  2. the conservation of momentum is maintained, and
  3. a coupling mechanism between the material and the incident medium is present.

The conservation of momentum is governed by the relationship between de Broglie's particle/wave duality, from the photon and phonon momenta, where the photon momentum is P = h/λ. The phonon momentum in the crystal is given by P = h/a, where α is the lattice constant for the unit cell. When λ=a, the conservation of momentum is preserved between the incident photon and thermal phonon, resulting in complete absorption of the incident radiation by the lattice. However, the photon has a low momentum when compared to the momentum of a phonon, therefore two or more photons are required to satisfy the conservation of momentum and produce total absorption.

The coupling mechanism between the incident photon and the lattice phonon is produced by a change of state in the electric dipole moment (M) of the crystal. A dipole moment arises when two equal and opposite charges are situated a very short distance apart, and is the product of either of the charges with the distance between them. Thus energy absorbed from the radiation will be converted into vibrational motion of the atoms. In simple gas molecules this gives rise to a characteristic spectral absorption band, as the many molecules form a large number of coupled dipole moments.

In more complex lattice structures, in order for a mode of vibration to absorb any incident radiation, the basic mechanism for coupling must be present. Three different coupled absorption mechanisms exist;

  1. Reststrahl absorption, this only occurs in ionic crystals and is caused by the creation of single phonons in the lattice.
  2. Multi-phonon absorption which occurs when two or more phonons simultaneously interact and produce an electric moment with which the incident radiation may couple.
  3. Defect induced one phonon absorption, which in a pure crystal is where the creation of a single phonon is not accompanied by a transitional change of state in dipole moment that can act as a couple, but is induced by the existence of a crystal defect or impurity to aid the coupling mechanism.

Infrared material absorption theory

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