A high resolution anharmonic λ/2 fringe spacing interferometer

Abstract

Two-beam interferometry is a widely spread tool for high precision measurement, whose ultimate resolution is directly linked to the fringe spacing of the interferogram. All usual two-beam interferometers show a fringe spacing equal to a wavelength of the laser light. Here we present an interferometer where the fringe spacing is reduced by a factor of two and where the width of a fringe can be extremely narrow, leading to potential applications in very precise displacement measurement. Our interferometer is based on elementary aspects of atomic physics. The laser wavelength is tuned to an atomic transition J=1/2→J=1/2 (i.e. two-fold degenerate two level system). The laser field is initially polarized at 45° and sent to a polarizing beam splitter. Vertical and horizontal polarizations experience a relative phase shift φ and are recombined at the output. Then the resulting beam is sent into an atomic vapour and the fluorescence is recorded. When φ = 0 or π, the resulting polarization is linear (at 45° and 135° respectively) and the atom experiences continuous cycles of absorption-fluorescence. When φ = π/2 or 3π/2, the resulting polarization is circular and the atom is optically pumped onto one of the dark states |mJ = +/− ½≫ and the fluorescence vanishes. Therefore the fluorescence has a periodicity of π with the phase shift, contrary to an usual interferometer where the period is 2π. When the laser power is increased above the saturation intensity of the transition, a simple rate equation model shows that the variation of the fluorescence with φ becomes strongly anharmonic and follows an Airy function behaviour. An extremely sharp variation of the fluorescence is obtained in the vicinity of φ = π/2 and 3π/2 (Fig. 1 left). When the propagation of the laser beam is taken into account both the emitted fluorescence and the transmission of the laser field present anharmonic variations with the phase (Fig. 1 right).