Ray tracing through a two ball uniaxial lens system in a single mode fiber-to-fiber coupler

Two ball lens systems are frequently used for single mode fiber-to-fiber coupling. Sapphire is often considered for this type of application due to its high index (for reduced spherical aberration) and its mechanical integrity. However, sapphire is negative uniaxial, and the effect of optical birefringence on coupling loss has not been formally studied for ball lenses. Therefore, the purpose of this study is to determine if Poynting vector walk-off of the e-wave, which leads to beam displacement, contributes adversely to coupling loss (birefringence aberration)