G. Beadie

We use first-order optical principles to examine the ability of gradient index (GRIN) lenses to correct chromatic aberrations. We consider radial GRIN lenses with flat surfaces, with a flat diffractive surface, and with curved surfaces. We model the GRIN material system as a locally varying, subwavelength blend of three materials. In this model, we demonstrate that the color-correcting properties of each lens type can be expressed solely in terms of the dispersion properties of the base materials. We find, at this level of approximation, that the material condition for a two-material GRIN achromat with curved surfaces is identical to that for a homogeneous doublet achromat comprised of the same two materials. For the more general case of three-material, ternary GRIN elements, we use the theory to develop a figure-of-merit-based optimization approach. This allows us to identify promising material combinations without first fabricating a GRIN element. The optimization approach can be applied to alternate GRIN geometries and arbitrary glass catalogs. We use our model to search a large, commercial glass catalog to identify the best achromatic glass combinations for the three different GRIN lenses described above. Significant numerical effort was required to identify which glass combinations performed best. Ternary glass combinations are necessary to achieve good achromatic performance for flat geometries. Diffraction combined with a graded-index enables improved color correction for the same optical power or nearly a factor of two increase in power for the same level of color correction. Glass pairs that perform well as an achromatic doublet also perform well chromatically when blended in a GRIN singlet.

We analyze a new method for determining the out-of-plane coefficient of thermal expansion for thin films of transparent materials. The method is based on the measurement of interference peaks recorded in transmission spectra as a function of sample temperature. The locations of interference peaks depend on the optical path. We show how a consideration of Lorentz-Lorenz equation, in addition to the transmission peak equation, can separate the different contributions of index and physical pathlength to the optical path. The analysis is generalized to include the effects of uniaxial material properties (such as anisotropic linear thermal expansion and birefringence). By applying this method of analysis to recent data, we demonstrate the importance of including the effect of the thermo-optic coefficient in interpreting observed data.

Transmission spectroscopy and a small number of refractometer index measurements are combined to provide refractive index measurements of transparent samples ~50 um thick at hundreds of wavelengths with absolute accuracies −4. Key to the technique is the use of independent index measurements to circumvent the need for an independent thickness measurement of the sample. The method was demonstrated on glass samples where fits to Cauchy curves had RMS accuracies −5 from 415 to 1610 nm. Issues that must be addressed to reach this level of accuracy are discussed.

Gradient refractive index (GRIN) materials are attractive candidates for improved optical design, especially in compact systems. For GRIN lenses cut from spherically symmetric GRIN material, we derive an analogue of the “lens maker’s” equation. Using this equation, we predict and demonstrate via ray tracing that an achromatic singlet lens can be designed, where the chromatic properties of the GRIN counterbalance those of the lens shape. Modeling the lens with realistic materials and realistic fabrication geometries, we predict we can make an achromatic singlet with a 19 mm focal length using a matrix of known polymers.