Abstracts

The incorporation of gradient-index (GRIN) materialinto optical systems offers novel and practical solutions to lensdesign problems. However, widespread use of gradient-index opticshas been limited by poor correlation between gradient-index designsand the refractive index profiles produced by ion exchange betweenglass and molten salt. Previously, a design-for-manufacture modelwas introduced that connected the design and fabrication processesthrough use of diffusion modeling linked with lens design software.This project extends the design-for-manufacture model into atime-varying boundary condition (TVBC) diffusion model. TVBCincorporates the time-dependent phenomenon of melt poisoning andintroduces a new index profile control method, multiple-stepdiffusion.
The ions displaced from the glassduring the ion exchange fabrication process can reduce the totalchange in refractive index (An). Chemical equilibrium is used tomodel this melt poisoning process. Equilibrium experiments areperformed in a titania silicate glass and chemically analyzed. Theequilibrium model is fit to ion concentration data that is used tocalculate ion exchange boundary conditions.
The boundary conditions are changed purposelyto control the refractive index profile in multiple-step TVBCdiffusion. The glass sample is alternated between ion exchange witha molten salt bath and annealing. The time of each diffusion stepcan be used to exert control on the index profile. The TVBCcomputer model is experimentally verified and incorporated into thedesign-for-manufacture subroutine that runs in lens designsoftware. The TVBC design-for-manufacture model is useful forfabrication-based tolerance analysis of gradient-index lenses andfor the design of manufactureable GRIN lenses. Several opticalelements are designed and fabricated using multiple-step diffusion,verifying the accuracy of the model. The strength of multiple-stepdiffusion process lies in its versatility. An axicon, imaging lens,and curved radial lens, all with different index profilerequirements, are designed out of a single glasscomposition.