Unravelling interrelations between chemical composition and refractive index dispersion of infrared-transmitting chalcogenide glasses

Abstract

A facile procedure for compositional screening of chalcogenide glass (CG) is proposed to manage its infrared transmission edge (ωc) as well as refractive index dispersion (ν) in the long-wavelength infrared (LWIR) range. Both ωc and ν of CG turn out to be interpretable simply in connection with its chemical composition based on a postulation that CG behaves as a single average harmonic oscillator (SAHO). In this SAHO model, ωc is expressed as a function of molar mass and average bond energy, both of which are easily accessible for a given CG composition. Two prototypical CG-forming systems in Ge-Sb-Se and Ge-Sb-S compositions exemplify the empirical compositional dependence of ωc, which further plays a decisive role in determining ν. Following the present approach, a set of highly dispersive CG compositions in the Ge-Sb-S system is newly unveiled together with low-dispersion Ge-Sb-Se glasses. It is then experimentally demonstrated that a doublet lens configuration consisting of convex and concave lenses with low and high ν values, respectively, is able to reduce the optical aberrations. This finding presents an opportunity that ν can be envisaged just based on the compositional ratio of CG, thus facilitating completion of the LWIR Abbe diagram.

Compositional screening of chalcogenide glass for use as molded lens: an exemplary case of ternary Ge-Sb-Se glass

“…Here, A 0 and B 2 are numerical constants, and λ 2 denotes position of the fundamental infrared absorption that can be replaced with another parameter incorporating ω c in the framework of SAHO model [49]: As presented in Figure 13, the experimentally measured ν 10 values coincide reasonably well with the calculated ν 10 values for selenide, sulfide and sulfur-selenide glasses. The results described above imply that refractive index itself and its dispersion over wavelength together with infrared transmission edge can be predicted as a function of ChG composition at least qualitatively or quantitatively for some compositional systems.…”

“…Knowledge on compositional dependences of ν as well as infrared transmission cutoff wavelength is essential in engineering ChG compositions for use as molded lenses. In an effort to unravel correlations between chemical composition of ChGs and their refractive index dispersion as well as infrared transmission edge, we have carried out a systematic investigation [49]: As shown in Figure 11 (a), the infrared-side transmission edge is altered upon compositional change. This observation can be elucidated based on a postulation that ChG behaves as a single average harmonic oscillator (SAHO) in manifesting its infrared transmission edge via multiphonon absorption.…”

“…Specifically, R 2 = 0.93 is obtained from the least-squares fit to a straight line. It is worth mentioning that the SAHO model is already validated even when ChG compositions are expanded to ternary or quaternary selenide glasses (R 2 ¼ 0.84) and sulfide glasses (R 2 ¼ 0.83) [49]. Figure 12 presents n values measured at infrared wavelengths up to 12 μm for the best compositions in ternary Ge-Sb-Se system (see Figure 6 again) along with some representative quaternary Ge-Ga-Sb-S glasses [66]: The higher refractive index of selenide glasses can be understood in connection with atomic polarizabilities of Se (3.77 � 10 −24 cm 3 ) and S (2.90 × 10 −24 cm 3 ) [64].…”

“…This implies that their refractive index dispersion in wavelengths longer than the inflection point is mostly governed by the absorption due to vibrational excitations. As a result, a two-term Sellmeier equation turns out to be valid to describe refractive index dispersion in the LWIR range, which neglects the contributions of the UV-side absorption edge raised by bandgap transition [49]. The two-term Sellmeier equation can be expressed as a function of wavelength ðλ) as follows;…”

“…Figure 12. Measured refractive indexes of some representative ternary Ge-Sb-Se and quaternary Ge-Ga-Sb-S glasses, where the dotted lines are simply connecting the adjacent data points [49]. Note that the arrows indicate the inflection points of selenide and sulfide glasses at ~6 μm and ~5 μm, respectively.…”