Theoretical considerations for anticipating of function analysis on a gradient index-lens fabrication through double ion-exchange process.

Based on precise and detailed theoretical examination of diffusion equation analysis, two-step Ag(+)-Na(+) and Na(+)-Ag(+) ion-exchange parameters were optimized in order to fabricate a gradient index (GRIN) lens in the BK7 glass rod. Using the diffusion equation, the impact of the concentration ratio of the exchanged ion during the first and second steps was examined in detail. Then, based on the calculated effective parameters such as concentration ratio and immersion time, a fabrication process was proposed. We managed to get the optimum parameters (the bath stop time, temperature, and length) to make a quarter pitch lens. As a result, some samples of the GRIN lens were fabricated and tested successfully. Theoretical considerations and experimental results are presented.