Mid-infrared laser frequency combs are compelling sources for precise and sensitive metrology with applications in molecular spectroscopy and spectro-imaging. The infrared atmospheric window between 3-5.5 $mu$m in particular provides vital information regarding molecular composition. Using a robust, fiber-optic source of few-cycle pulses in the near-infrared, we experimentally demonstrate ultra-broad bandwidth nonlinear phenomena including harmonic and difference frequency generation in a single pass through periodically poled lithium niobate (PPLN). These $chi^{(2)}$ nonlinear optical processes result in the generation of frequency combs across the mid-infrared atmospheric window which we employ for dual-comb spectroscopy of acetone and carbonyl sulfide with resolution as high as 0.003 cm$^{-1}$. Moreover, cascaded $chi^{(2)}$ nonlinearities in the same PPLN directly provide the carrier-envelope offset frequency of the near-infrared driving pulse train in a compact geometry.
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