  Interferometers usually require long paths for the ever-increasing
requirements of high-performance operation, which hinders the miniaturization
and integration of photonic circuits into very compact devices. Slow-light
based interferometers provide interesting advantages in terms of both
compactness and sensitivity, although their optimization is computationally
costly and inefficient, due to the large number of parameters to be
simultaneously designed. Here we propose the design of slowlight-enhanced
bimodal interferometers by using principal component analysis to reduce the
high-dimensional design space. A low-dimensional hyperplane containing all
optimized designs is provided and investigated for changes in the silicon core
and cladding refractive index. As a result, all-dielectric single-channel
interferometers as modulators of only 33 m2 footprint and sensors with 19,200
2pirad/RIUcm sensitivity values are reported and validated by two different
simulation methods. This work allows the design and optimization of slow light
interferometers for different applications by considering several performance
criteria, which can be extended to other photonic structures.
