Reduced substrate-temperature effects

The transmittance of all optical substrate materials used in the far-infrared are strongly temperature dependent. When these materials are used at reduced cryogenic temperatures, the ambient room temperature data on the optical properties is frequently inadequate for obtaining an accurate predictive performance model.

In semiconductor materials, the most dominant absorption mechanism is caused by two-phonon absorption. As the temperature reduces, the two-phonon absorption bands become significantly weaker and narrower, increasing the transparency bandwidth of the material. The absorption in this region results from the combined effect of two inter-related mechanisms, (i) the electric moment (M) associated with the distributed charge density of the atomic bonding, to which the incident radiation couples, and (ii) anharmonic interactions distributed between the atomic charge density states of the crystal. As the phonon vibration modes are excited by interaction with the electric moment (M), they may also further dissipate energy through anharmonic interactions within the crystal, creating additional harmonics to that caused by the primary coupling absorption mechanism. As the temperature is reduced the lattice contracts and oscillations of the atoms about their equilibrium points reduces. This in turn reduces the size of the phonon vibration amplitudes and subsequently reduces the intensity of the absorption profile. The availability of information on the optical properties of infrared materials at reduced temperatures is limited, even non-existent, from most reference literature sources. Stierwalt et al measured the transmittance spectra of BaF₂, Sapphire, KRS-5, Irtran 2 (ZnS) and Quartz materials at 77 and 4K in the early 1980's using a Beckman IR-3 spectrophotometer.

Substrate optical theory

• Introduction
• Absorption and extinction coefficient theory
• Loss-free incoherent internal reflection
• Incoherent multiple internal reflection
• Reduced substrate-temperature effects
• Angle of incidence effects
• Total internal reflection
• Coherence of multiple internal reflections