Resonant microtaper leaky-mode computational spectropolarimetry with tens of femtometers spectral resolution and full Stokes measurement.

Emerging computational measurement techniques for acquiring multi-dimensional optical field information, such as spectrum and polarization, are rapidly advancing and offer promising solutions for realizing high-performance miniature systems. The performance of these computational measurement approaches is critically influenced by the choice of random media, yet a general framework for evaluating different implementations remains absent. Here, we propose a general analytical model for computational measurement systems and reveal that the system resolution is fundamentally determined by the maximum optical path difference (OPD) permitted within the random medium. Building on this theoretical foundation, we present a resonant leaky-mode (RLM) spectropolarimeter that achieves a record high resolution-footprint-product metric. The RLM spectropolarimeter leverages the complex coupling between leaky modes in a tapered coreless optical fiber and whispering-gallery modes of microsphere to significantly enhance the maximum OPD within a compact footprint. We simultaneously achieve an ultrahigh spectral resolution of 20 fm, a spectral measurement bandwidth of 150 nm, and full-Stokes polarization measurement with a mean squared error of 4.732 × 10