Tolerances of the alignment of fibers to photonic integrated circuits

This work presents the solutions to the alignment of two Gaussian beams representing two sides of the optical connection between a fiber and a photonic integrated circuit (PIC). The focus is to use these solutions to derive equations that allow for the straightforward calculation of alignment tolerances for displacement in all three directions, as well as two axes of rotations. These equations can be used to aid in the design of photonic packages by allowing the determination of precision necessary for fabrication of mechanical alignment features, in addition to packaging process development.