Compact spectrometer based on disordered multi-mode interferometer

We demonstrate a compact (40 ${\mu}$m $\times$ 260 ${\mu}$m) spectrometer based on multimode interference aided by scattering of light from random SiO$_2$-filled hole arrays on a silicon-on-insulator platform. We characterize the performance of the spectrometer for wavelengths around 1310 nm, and report that the spectrometer can reconstruct a broadband $\sim$ 67 nm source, as well as Lorentzian probes of $\sim$ 1 nm bandwidth. This compact nanometer level resolution spectrometer can be fabricated at a low cost for lab-on-a-chip sensing and imaging applications.