A Pearl Spectrometer.

Information recovery from incomplete measurements, typically performed by a numerical means, is beneficial in a variety of classical and quantum signal processing. Random and sparse sampling with nanophotonic and light scattering approaches has received attention to overcome the hardware limitations of conventional spectrometers and hyperspectral imagers but requires high-precision nanofabrications and bulky media. We report a simple spectral information processing scheme in which light transport through an Anderson-localized medium serves as an entropy source for compressive sampling directly in the frequency domain. As implied by the "lustrous" reflection originating from the exquisite multilayered nanostructures, a pearl (or mother-of-pearl) allows us to exploit the spatial and spectral intensity fluctuations originating from strong light localization for extracting salient spectral information with a compact and thin form factor. Pearl-inspired light localization in low-dimensional structures can offer an alternative of spectral information processing by hybridizing digital and physical properties at a material level.