Interferometric optical path measurement of a glass wedge with single photons and biphotons.

We have measured the phase structure of a glass wedge with single photons and biphotons in a Mach-Zehnder interferometer using parametric downconverted light from a Hong-Ou-Mandel particle interferometer as the source. By scanning the wedge through the focus of a microscope objective we find a doubling of the period of the interference pattern in the coincidence counts for biphotons compared to the single-photon experiment. We compare our measurement setup with classical ones and discuss some of the problems of superresolution in quantum lithography.

Beam mixing with a pinhole.

After a small aperture the spatial information of a complex optical wavefront is lost, but amplitude and phase information is mixed and transferred to the smoothed wave that emerges from the pinhole. This mixing effect is described in the case of a wavefront with a phase step, which is shifted over the input plane of an optical processor with a pinhole as spatial filter in the Fourier plane. We constructed a polarizing interferometer to demonstrate this continuous phase shift and show that it can be used as a variable retardation wave plate similar to a birefringent compensator, but without crystalline wedges.

Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle.

We observe the spinning and orbital motion of a microscopic particle trapped within a multiringed light beam that arises from the transfer of the spin and orbital components of the light's angular momentum. The two rotation rates are measured as a function of the distance between the particle and the axis of the trapping beam. The radial dependence of these observations is found to be in close agreement with the accepted theory.

Nonlinearity of Pancharatnam's geometric phase in polarizing interferometers.

Earlier investigations show a time-variable nonlinear shift of the fringe pattern in a polarizing interferometer while rotating a polarizer at the exit. This effect was identified as Pancharatnam's geometrical phase and proposed for applications in interferometry and fast optical switching devices. A heterodyne analysis attributes moving fringes to a frequency difference between the interfering beams; thus changing fringe velocities point to a dynamic frequency development within the period of the uniformly rotating analyzer. This explanation offends the intuition and we undertake an experimental and theoretical investigation of the effect to solve the paradox. We determine, e.g., the complete frequency and mode spectrum of an arbitrary state of polarization P0 behind a rotating linear analyzer and behind a rotating arbitrary linear birefringent plate. We find that, in spite of a fast changing phase in the interferometer, no other (higher) frequency components appear in the spectral distribution of the intensity at the exit than the double of the rotary frequency of the analyzer: phase nonlinearities are compensated for by intensity changes. Only a phase-sensitive detector like an array of photodetectors is able to observe the nonlinearity of Pancharatnam's geometrical phase. A single detector only finds a sinusoidal intensity variation. Our insight into these relations leads us to two new applications of Pancharatnam's phase: supersensitivity of a polarizing double beam interferometer with a video camera acting as a phase detector and external tuning of a Fizeau interferometer.

Polarization-based tunable interferometric filter.

A polarization-based tunable interferometric filter essentially consisting of a two-beam interferometer with birefringence elements is described. The analysis of the filter is done through the concept of a geometric phase in optics-namely, the Pancharatnam phase. The transmission characteristics of the filter can be controlled through three parameters: the thickness of the birefringent elements, the optical path difference, and the orientation angle of an analyzer placed at the interferometer output. It is demonstrated theoretically that, with a particular choice of these parameters, the chromatic dispersion of the filter is compensated in a given spectral range. Some properties of the device are confirmed by an experimental demonstration.