  We demonstrate a new scheme of infrared spectroscopy with visible light
sources and detectors. The technique relies on the nonlinear interference of
correlated photons, produced via spontaneous parametric down conversion in a
nonlinear crystal. Visible and infrared photons are split into two paths and
the infrared photons interact with the sample under study. The photons are
reflected back to the crystal, resembling a conventional Michelson
interferometer. Interference of the visible photons is observed and it is
dependent on the phases of all three interacting photons: pump, visible and
infrared. The transmission coefficient and the refractive index of the sample
in the infrared range can be inferred from the interference pattern of visible
photons. The method does not require the use of potentially expensive and
inefficient infrared detectors and sources, it can be applied to a broad
variety of samples, and it does not require a priori knowledge of sample
properties in the visible range.
