The state of a two-particle system is said to be entangled when its quantum-mechanical wavefunction cannot be factorized into two single-particle wavefunctions. This leads to one of the strongest counter-intuitive features of quantum mechanics, namely non-locality. Experimental realization of quantum entanglement is relatively easy for photons; a starting photon can spontaneously split into a pair of entangled photons inside a nonlinear crystal. Here we investigate the effects of nanostructured metal optical elements on the properties of entangled photons. To this end, we place optically thick metal films perforated with a periodic array of subwavelength holes in the paths of the two entangled photons. Such arrays convert photons into surface-plasmon waves--optically excited compressive charge density waves--which tunnel through the holes before reradiating as photons at the far side. We address the question of whether the entanglement survives such a conversion process. Our coincidence counting measurements show that it does, so demonstrating that the surface plasmons have a true quantum nature. Focusing one of the photon beams on its array reduces the quality of the entanglement. The propagation of the surface plasmons makes the array effectively act as a 'which way' detector.

We report polarization tomography experiments on metallic nanohole arrays with square and hexagonal symmetry. As a main result we find that a fully polarized input beam is partly depolarized after transmission through a nanohole array. This loss of polarization coherence is found to be anisotropic; i.e., it depends on the polarization state of the input beam. The depolarization is ascribed to a combination of two factors: (i) the nonlocal response of the array as a result of surface-plasmon propagation and (ii) the non-plane-wave nature of a practical input beam. © 2005 Optical Society of America OCIS codes: 230.3990, 240.6680, 260.3910. Currently there is much interest in the optical properties of thin metal films perforated with arrays of subwavelength holes, or nanohole arrays. The optical transmission of these arrays shows a strongly peaked spectrum with anomalously large transmission peak values; this is usually ascribed to resonant excitation of propagating surface electromagnetic waves or surface plasmons (SPs). -3In this Letter we focus on the polarization properties of the anomalous transmission and show that these are strongly inf luenced by the propagating nature of the SPs.So far, polarization properties of nanohole arrays have been studied in a limited context: a beam with a given uniform state of polarization (SOP in ) is transformed by an anisotropic array or an isotropic array with nonspherical holes into a different uniform state of output polarization (SOP out ). 4 -6 This corresponds to a mapping of the Poincaré sphere onto itself; for instance, a rectangular array or a square array with elliptical holes acts as a birefringent and (or) a dichroic element that may convert a linear SOP into an elliptical SOP, conserving polarization coherence. In the present Letter we focus instead on cases where the degree of polarization (DOP) is reduced, DOP out , DOP in , corresponding to a reduction in radius and, in general, a deformation of the Poincaré sphere. 7,8 To underline this point we have chosen for our experiments square and hexagonal arrays, i.e., arrays that, for symmetry reasons, 9 cannot modify the SOP for plane-wave illumination at normal incidence. As we will show, depolarization occurs when two (quite common) conditions are simultaneously fulfilled: (i) the response of the array is nonlocal because of SP propagation, and (ii) the input beam is not a plane wave [but, e.g., a Gaussian beam, with a finite numerical aperture (NA)].In general, depolarization occurs when an optical system acts nonuniformly on polarization within the (spatial or temporal) bandwidth of the incident wave, thereby coupling polarization to other degrees of freedom. Experimentally, a study of depolarization requires a measurement of the Mueller matrix by a tomographic method. 7,8Here we report such polarization-tomography experiments on nanohole arrays and interpret the results in the context of SP propagation.We start by recapitulating the essence of our theoretical model. 9The input and output optical fields ...

We present angle-and polarization-resolved measurements of the optical transmission of a subwavelength hole array. These results give a (far-field) visualization of the corresponding (near-field) propagation of the excited surface plasmons and allow for a simple analysis of their polarization properties.

We present measurements of the wavelength-dependent reflectivity of a subwavelength metal hole array on a glass substrate. We compare the observed resonant structures with those found in transmission and note a nonreciprocity under illumination from the air versus the glass side. This can be used to verify on which interface the surface plasmons are resonantly excited and to estimate the losses in the subwavelength channels.