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We present compact integrated speckle spectrometers based on monofractal andmultifractal scattering media in a silicon-on-insulator platform. Through bothnumerical and experimental studies we demonstrate enhanced optical throughput,and hence signal-to-noise ratio, for a number of random structures withtailored multifractal geometries without affecting the spectral decay of thespeckle correlation functions. Moreover, we show that the developedmultifractal media outperform traditional scattering spectrometers based onuniform random distributions of scattering centers. Our findings establish thepotential of low-density random media with multifractal correlations forintegrated on-chip applications beyond what is possible with uncorrelatedrandom disorder.

High-throughput speckle spectrometers based on multifractal scattering media