Computational spectrometers are pivotal in enabling low-cost, in-situ and rapid spectral analysis, with potential applications in chemistry, biology, and environmental science. However, filter-based spectral encoding approaches typically use filter arrays, complicating the manufacturing process and hindering device consistency. By capitalizing on the polarization separation effect under oblique incidence (PSEOI), we pioneer the use of a single filter for highly efficient spectral encoding, and propose a novel computational spectrometer spanning visible to mid-infrared wavelengths by combining the Single-Spinning Film Encoder (SSFE) with deep learning-based reconstruction algorithm. The particle swarm optimization (PSO) method is employed to optimize the film configuration of SSFE, achieving low-correlation and high-complexity spectral responses under different polarizations and spinning angles, thereby enhancing both spectral resolution and accuracy of reconstruction across diverse spectral ranges. Spectral resolutions up to 0.5 nm, 2 nm, 10 nm can be realized for single-peak narrowband spectra, and 3 nm, 6 nm, 20 nm for dual-peak narrowband spectra, over the visible, near-, and mid-infrared wavelength ranges, respectively. Moreover, the proposed spectrometer demonstrates an overall 81.38% precision for the classification of 220 chemical compounds, confirming its robustness and precision in practical scenarios, along with the capability for compact, cost-effective spectroscopic solutions.
