One-dimensional gradient-index metrology based on ray slope measurements using a bootstrap algorithm

The refractive index profile of one-dimensional gradient-index (GRIN) samples can be measured using the incident and exit beam angles of multiple beams passing through the sample at different positions along the index gradient. Beginning from a region of known refractive index, the collective angular deflection measurement of multiple beams is boot-strapped to compute the index profile of the entire sample. An alternative method using an approximate beam displacement model and a corrective algorithm is also presented. The two techniques are used to measure the index profile of a thick GRIN sample, and experimental results show good agreement with a maximum discrepancy of 1.5 × 10 −3 in the calculated index. An index accuracy of 5 × 10 −4 is predicted for the bootstrap method employing typical micron-level spatial measurements. 1 Introduction Recent developments in the fabrication of gradient-index (GRIN) materials make it possible to create increasingly complex refractive index distributions. Several of these fabrication techniques are reported and discussed in Ref. 1. These GRIN materials are proving to be useful in a variety of applications. Fibers pulled from GRIN preforms can be designed to reduce modal dispersion and thereby increase the bandwidth and repeater distance of optical communication systems. Lenses made using GRIN profiles find application in telecommunications and compact imaging, where their small size and flat faces give them attractive packaging properties. GRIN elements can also be combined with conventional homogeneous glass elements to broaden the design space of imaging lenses. In particular, GRIN lens materials often have unique dispersion characteristics, making them useful for chromatic aberration correction. 2 Finally, in recent studies, GRIN materials have shown utility in coherent mode conversion and beam shaping applications.