We demonstrate a spectrum analyzer with resolution and dynamic range using spectral-hole-burning (SHB) crystals, which are cryogenically cooled crystal hosts lightly doped with rare-earth ions. We modulate a rf signal onto an optical carrier using an electro-optic intensity modulator to produce a signal beam modulated with upper and lower rf sidebands. Illuminating SHB crystals with modulated beams excites only those ions resonant with corresponding modulation frequencies, leaving holes in the crystal's absorption profile that mimic the modulation power spectrum and persist for up to . We determine the spectral hole locations by probing the crystal with a chirped laser and detecting the transmitted intensity. The transmitted intensity is a blurred-out copy of the power spectrum of the original illumination as mapped into a time-varying signal. Scaling the time series associated with the transmitted intensity by the instantaneous chirp rate yields the modulated beam's rf power spectrum. The homogeneous linewidth of the rare-earth ions, which can be at cryogenic temperatures, limits the fundamental spectral resolution, while the medium's inhomogeneous linewidth, which can be , determines the spectral bandwidth.
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