Dielectric materials as well as semiconductors exhibit some range of optical wavelengths where they are more or less transparent, i.e., exhibit low absorption. The long-wavelength limit of that transparency range, called the infrared absorption edge, is determined by the onset of strong multiphonon absorption: absorption processes where multiple phonons are created in conjunction with the absorption of a single photon. For even longer wavelengths, single-phonon absorption becomes possible, where one phonon per absorbed photon is generated.
In classical models, the same processes can be understood as resulting from overtones of anharmonic oscillators. Note that one usually does not have a single isolated absorption line in the infrared and its corresponding overtone absorption lines, but rather a more complex ensemble of broad absorption lines which effectively form a continuum.
Multiphonon absorption is most relevant for ionic crystals and glasses, where neighbored ions with opposite electrical charges can perform vibrations against each other. Such vibrations, related to optical phonons, exhibit substantially higher frequencies than vibrations related to acoustical phonons, where neighbored atomic constituents vibrate approximately in phase. Still, such optical phonon frequencies are typically rather low compared with optical frequencies, except in the mid infrared. However, multiple such phonons combined can have an energy which equals the energy of one photon. Processes creating multiple phonons from a single photon involve complex coupling processes based on the anharmonicity of phonon modes and in some cases also electrical nonlinearities. They can lead to substantial absorption tails in spectral regions where one would otherwise have low absorption. The contributed absorption decays exponentially towards shorter optical wavelengths, as increasingly higher-order processes are required in that spectral region. Note that although multiphonon absorption is usually rather weak compared with single-phonon absorption, it can still easily be strong enough e.g. to prohibit the use of a material in a certain spectral region. The onset of that absorption is sometimes called the multi-phonon absorption edge, although that absorption rises quite continuously, so that one does not have a well-defined edge.
Multiphonon absorption must not be confused with multiphoton absorption, which is an entirely different process. Also not strongly related are multi-phonon transitions, where multiple phonons are emitted in conjunction with the relaxation of a dopant ion.
Example: Silica Fibers
As an example, consider fused silica (amorphous SiO2), which is the basis of silica fibers. The infrared absorption edge of silica is at approximately 2 μm; the propagation losses already rise substantially at wavelength longer than 1.7 μm (see Figure 1).
The observed infrared absorption edge is related to the stretching mode of Si–O bonds, which has a wavenumber of ≈1100 cm−1. Single-phonon absorption would thus require an optical wavelength of roughly 9 μm. Due to multi-phonon processes, significant absorption begins already for wavelengths below 2 μm. Although that absorption is still very weak compared to the absorption in the mid-infrared, it is strong enough e.g. to prohibit the use of silica fibers for long-distance signal transmission at 1.8 μm and beyond.
Depending on the used fiber fabrication process, the silica glass can be somewhat contaminated with water, which leads to hydroxyl (OH) groups. The fundamental resonance of the OH groups corresponds to wavelengths of ≈2.75 μm, and the second overtone at ≈1.38 μm falls into the intrinsic low-loss window of silica, forming an absorption peak, which can be detrimental for optical fiber communications in the 1.5-μm spectral region. The third harmonic is related to a peak at ≈0.95 μm, which can be relevant in other applications. These “OH overtone absorption peaks” constitute extrinsic losses, which can be minimized by resorting to fabrication techniques which lead to a minimum hydroxyl content of the material.
Low-phonon Energy Materials for Infrared Optics
The intrinsic multi-phonon absorption related to the Si–O bond limits the applicability of silica fibers for infrared optics. Therefore, one may resort to chalcogenide fibers, for example, which are made from heavier constituents, leading to lower vibration frequencies and therefore correspondingly longer infrared absorption edges. The articles on mid-infrared fibers and infrared optics give more details.
|L. L. Boyer et al., “Multiphonon absorption in ionic crystals”, Phys. Rev. B 11 (4), 1665 (1975); https://doi.org/10.1103/PhysRevB.11.1665
|C. R. Elliott and G. R. Newns, “Near infrared absorption spectroscopy of silica: OH overtones”, Appl. Spectroscopy 25 (3), 378 (1971)“,”https://www.osapublishing.org/as/abstract.cfm?uri=as-25-3-378
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