  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.
