We present the design and performance of broadband and tunable infrared-blocking filters for millimeter and sub-millimeter astronomy composed of small scattering particles embedded in an aerogel substrate. The ultra-low-density (typically < 150 mg/cm^3) aerogel substrate provides an index of refraction as low as 1.05, removing the need for anti-reflection coatings and allowing for broadband operation from DC to above 1 THz. The size distribution of the scattering particles can be tuned to provide a variable cutoff frequency. Aerogel filters with embedded high-resistivity silicon powder are being produced at 40-cm diameter to enable large-aperture cryogenic receivers for cosmic microwave background polarimeters, which require large arrays of sub-Kelvin detectors in their search for the signature of an inflationary gravitational-wave background.
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