Spatial coherence and optical beam shifts.

A beam of light, reflected at a planar interface, does not follow perfectly the ray optics prediction. Diffractive corrections lead to beam shifts; the reflected beam is displaced (spatial Goos-Hänchen type shifts) and/or travels in a different direction (angular Imbert-Fedorov type shifts), as compared to geometric optics. How does the degree of spatial coherence of light influence these shifts? We investigate this issue first experimentally and find that the degree of spatial coherence influences the angular beam shifts, while the spatial beam shifts are unaffected.

Position measurement of non-integer OAM beams with structurally invariant propagation.

We present a design to generate structurally propagation invariant light beams carrying non-integer orbital angular momentum (OAM) using Hermite-Laguerre-Gaussian (HLG) modes. Different from previous techniques, the symmetry axes of our beams are fixed when varying the OAM; this simplifies the calibration technique for beam positional measurement using a quadrant detector. We have also demonstrated analytically and experimentally that both the OAM value and the HLG mode orientation play an important role in the quadrant detector response. The assumption that a quadrant detector is most sensitive at the beam center does not always hold for anisotropic beam profiles, such as HLG beams.

Observation of orbital angular momentum sidebands due to optical reflection.

We investigate how the orbital angular momentum of a paraxial light beam is affected upon reflection at a planar interface. Theoretically, the unavoidable angular spread of the beam leads to orbital angular momentum sidebands, which are found to be already significant for a modest beam spread (0.05). In analogy to the polarization Fresnel coefficients, we develop an analytical theory based upon spatial Fresnel coefficients; this allows a straightforward prediction of the strength of the sidebands. We confirm this by experiment and numerical simulation.

Radial mode dependence of optical beam shifts.

It is known that orbital angular momentum (OAM) couples the Goos-Hänchen and Imbert-Fedorov shifts. Here, we present the first study of these shifts when the OAM-endowed LG(ℓ,p) beams have higher-order radial mode index (p>0). We show theoretically and experimentally that the angular shifts are enhanced by p while the positional shifts are not.

Role of spatial coherence in Goos-Hänchen and Imbert-Fedorov shifts.

We present a theory for Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts for beams of light with arbitrary spatial coherence. By applying the well-known theory of partial spatial coherence, we can calculate explicitly spatial and angular GH and IF shifts for completely polarized beams of any shape and spatial coherence. For the specific case of a Gauss-Schell source, we find that only the angular part of GH and IF shifts is affected by the spatial coherence of the beam. A physical explanation of our results is given.

Spin Hall effect of light in metallic reflection.

We report the first measurement of the spin Hall effect of light (SHEL) on an air-metal interface. The SHEL is a polarization-dependent out-of-plane shift on the reflected beam. For the case of metallic reflection with a linearly polarized incident light, both the spatial and angular variants of the shift are observed and are maximum for -45°/45° polarization, but zero for pure s and p polarization. For an incoming beam with circular polarization states however, only the spatial out-of-plane shift is present.

Search for Hermite-Gauss mode rotation in cholesteric liquid crystals.

In theory, there are analogous transformations of light's spin and orbital angular momentum [Allen and Padgett, J. Mod. Opt. 54, 487 (2007)]; however, none have been observed experimentally yet. In particular, it is unknown if there exists for the orbital angular momentum of light an effect analogous to the spin angular momentum-based optical rotation; this would manifest itself as a rotation of the corresponding Hermite-Gauss mode. Here we report an experimental search for this effect in a cholesteric liquid crystal polymer, using strongly focussed, spin-orbit coupled light. We find that the relative phase velocities of the orbital modes constituting the Hermite-Gauss mode agree to within 10(-5).

Fiber transport of spatially entangled photons.

Entanglement in the spatial degrees of freedom of photons is an interesting resource for quantum information. For practical distribution of such entangled photons, it is desirable to use an optical fiber, which in this case has to support multiple transverse modes. Here we report the use of a hollow-core photonic crystal fiber to transport spatially entangled qubits.

Transport of orbital-angular-momentum entanglement through a turbulent atmosphere.

We demonstrate experimentally how orbital-angular-momentum entanglement of two photons evolves under the influence of atmospheric turbulence. Experimental results are in excellent agreement with our theoretical model, which combines the formalism of two-photon coincidence detection with a Kolmogorov description of atmospheric turbulence. We express the robustness to turbulence in terms of the dimensionality of the measured correlations. This dimensionality is surprisingly robust: scaling up our system to real-life dimensions, a horizontal propagation distance of 2 km seems viable.

Goos-Hänchen and Imbert-Fedorov shifts of a nondiffracting Bessel beam.

Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts are diffractive corrections to geometric optics that have been extensively studied for a Gaussian beam that is reflected or transmitted by a dielectric interface. Propagating in free space before and after reflection or transmission, such a Gaussian beam spreads due to diffraction. We address here the question of how the GH and IF shifts behave for a "nondiffracting" Bessel beam.

Quadrant detector calibration for vortex beams.

This Letter reports an experimental and theoretical study of the response of a quadrant detector (QD) to an incident vortex beam, specifically a Laguerre-Gaussian (LG) beam. We have found that the LG beam response depends on the vorticity index ℓ. We compare LG beams with hard-ringed beams and find that at higher ℓ values, the QD response to LG beams can be approximated by its response to hard-ringed beams. Our findings are important in view of the increasing interest in optical vortex beams.

Demonstration of a quasi-scalar angular Goos-Hänchen effect.

We show experimentally that the angular Goos-Hänchen (GH) effect can be easily observed, also without employing its resonant enhancement at Brewster incidence. An s-polarized beam was used to decouple the polarization from the propagation dynamics of the beam. We found that, in this case, the angular GH effect can be strongly enhanced by increasing the angular aperture of the Gaussian beam. Our experiments suggest a route toward observing the angular GH effect for true scalar waves, such as acoustic waves and quantum matter waves.

Goos-Hänchen shift for a rough metallic mirror.

We investigate experimentally the dependence of the Goos-Hänchen shift on the surface properties of an air-metal interface. The shift depends on the microscopic roughness of the metal surface but it is insensitive to the large-scale variations associated with surface non-flatness. Both an effective medium model of roughness and the Rayleigh-Rice theory of scattering are used to interpret the observed phenomenon.

Brewster cross polarization.

We theoretically derive the polarization-resolved intensity distribution of a TM-polarized fundamental Gaussian beam reflected by an air-glass plane interface at Brewster incidence. The reflected beam has both a dominant (TM) and a cross-polarized (TM) component, carried by a TEM(10) and a TEM(01) Hermite-Gaussian spatial mode, respectively. Remarkably, we find that the TE-mode power scales quadratically with the angular spread of the incident beam and is comparable to the TM-mode power. Experimental confirmations of the theoretical results are also presented.

Shannon dimensionality of quantum channels and its application to photon entanglement.

We introduce the concept of Shannon dimensionality D as a new way to quantify bipartite entanglement as measured in an experiment. This is applied to orbital-angular-momentum entanglement of two photons, using two state analyzers composed of a rotatable angular-sector phase plate that is lens coupled to a single-mode fiber. We can deduce the value of D directly from the observed two-photon coincidence fringe. In our experiment, D varies between 2 and 6, depending on the experimental conditions. We predict how the Shannon dimensionality evolves when the number of angular sectors imprinted in the phase plate is increased and anticipate that D approximately 50 is experimentally within reach.

Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts.

We derive the polarization-dependent displacements parallel and perpendicular to the plane of incidence for a Gaussian light beam reflected from a planar interface, taking into account the propagation of the beam. Using a classical-optics formalism we show that beam propagation may greatly affect both Goos-Hänchen and Imbert-Fedorov shifts when the incident beam is focused.

Loss-induced transition of the Goos-Hänchen effect for metals and dielectrics.

We report a unifying approach to the Goos-Hänchen (GH) shifts on external optical reflection for metals and dielectrics in particular for the case of high losses, that is for a large imaginary part of the dielectric constant. In this regime metals and dielectrics have a similar GH shift which is in contrast to the low-loss regime where the metallic and dielectric forms of the GH shift are very different. When going from the low-loss to the high-loss regime we find that metals show a much more prominent transition; we present a condition on the dielectric constant which characterizes this transition. We illustrate our theoretical analysis with a realistic example of seven lossy materials.

Characterization of scattering in an optical Fabry-Perot resonator.

Roughness-induced scattering affects the performance of a resonator. We study the scattering of a single mirror first and compare the result with the losses of a two-mirror Fabry-Perot resonator. Besides some standard tools to characterize the losses, a new method based on the spectrally averaged transmission is introduced.

Mode counting in high-dimensional orbital angular momentum entanglement.

We study the high-dimensional orbital angular momentum OAM) entanglement contained in the spatial profiles of two quantum-correlated photons. For this purpose, we use a multi-mode two-photon interferometer with an image rotator in one of the interferometer arms. By measuring the two-photon visibility as a function of the image rotation angle we measure the azimuthal Schmidt number, i.e., we count the number of OAM modes involved in the entanglement; in our setup this number is tunable from 1 to 8.

Observation of Goos-Hänchen shifts in metallic reflection.

We report the first observation of the Goos-Hänchen shift of a light beam incident on a bare metal surface. This phenomenon is particularly interesting because the Goos-Hänchen shift for p polarized light in metals is negative and much bigger than the positive shift for s polarized light. The experimental result for the measured shifts as a function of the angle of incidence is in excellent agreement with theoretical predictions. In an energy-flux interpretation, our measurement shows the existence of a backward energy flow at the bare metal surface when this is excited by a p polarized beam of light.