Polarizing beam-splitter rotation in Martin-Puplett interferometers for spectroscopic measurements at millimeter wavelengths

The spectroscopic measurement of the Cosmic Microwave Background at mm and sub-mm wavelengths received significant attention recently, aimed at measuring tiny spectral distortions of the Cosmic Microwave Background (CMB) relevant for cosmology. Several experiments, including OLIMPO (Masi et al. 2003), PRISM (André et al., 2014), MILLIMETRON (Smirnov and Baryshev, 2012), PIXIE (Kogut and Fixsen, 2011) are based on a Martin-Puplett Fourier-transform spectrometer. Its differential capabilities are the key to success in these difficult measurements. The polarizing beam splitter is the optical core of a Martin-Puplett interferometer. In this paper we analyze, analytically and experimentally, the systematic effects induced by a beam splitter orientation different from the canonical 45°. These effects are potenitally important for the delicate measurements of CMB spectral distortions. We find an analytical formula describing the effect, and verify experimentally, in the range 150-600 GHz, that our formula correctly describes the results (with a C.L. of 88%). We also demonstrate that the rotation of the beam splitter does not induce distortions in the measured spectra.