An infrared spectrometer for operation in the mid-infrared spectral range is disclosed, where the spectrometer includes a Bragg-mirror-based spectral filter that is operative for providing an output optical signal whose spectral content is spatially dispersed along a first direction, where the Bragg mirrors include low-refractive-index layers comprising a polymer material that is transmissive across the mid-infrared spectral range and is characterized by less than ten absorption peaks with the operating spectral range of the spectrometer.