Abstract

Gradient index materials (GRIN) are defined as those in which the refractive index (n) varies spatially. Lenses possessing both radial and axial gradients of n, because of their unique ability to correct Petzval field curvature and chromatic aberration, are not equivalent to anything in current lens design. We have developed bulk GRIN materials for IR applications based on Ge_xSi_1−x and Ge_xSi_1−xTe(IV–VI) semiconducting compounds. The Ge_xSi_1−x compound has an excellent transparency range, from 1.9 m to over 18 m, and shows no profound absorption peaks. By controlling the solidification parameters, both axial and radial profiles can be varied from linear to parabolic, a considerable departure from the simple law of normal freezing. The maximum gradients of the refractive index (n) in Ge_xSi_1−x for radial and axial profiles are equal to 0.2 cm⁻¹ and 0.1 cm⁻¹, respectively. Although having an inferior transparency characteristic, the Ge_xSi_1−xTe compound shows higher n: 0.3 cm⁻¹ and 0.2 cm⁻¹, respectively. Electrical resistivity () along with microhardness (H) measurements have also been performed. Both radial and axial variations of and H are in excellent agreement with optical tests. A model for the evaluation of the refractive index, resistivity, and microhardness is presented. Expressions interrelating n, and H are derived by using the energy-gap concept as an unified parameter. By measuring either resistivity or micro-hardness profiles, the refractive index gradient can be estimated. Assessments of the applicability and the limitations of the theory are given.

© 1990 Optical Society of America