Design study of random spectrometers for applications at optical frequencies

Compact spectrometers based on disordered planar waveguides exhibit a rather high resolution with a relatively small footprint as compared to conventional spectrometers. This is achieved by multiple scattering of light which - if properly engineered - significantly enhances the effective optical path length. Here a design study of random spectrometers for TE- and TM-polarized light is presented that combines the results of Mie theory, multiple-scattering theory and full electromagnetic simulations. It is shown that the performance of such random spectrometers depends on single scattering quantities, notably on the overall scattering efficiency and the asymmetry parameter. Further, the study shows that a well-developed diffusive regime is not required in practice and that a standard integrated-optical layout is sufficient to obtain efficient devices even for rather weakly scattering systems consisting of low index inclusions in high-index matrices such as pores in planar silicon-nitride based waveguides. This allows for both significant reductions in footprint with acceptable losses in resolution and for device operation in the visible and near-infrared frequency range.