Interference eraser experiment demonstrated with all-plasmonic which

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Interference eraser experiment demonstrated with all-plasmonic which-path marker based on reverse spin Hall effect of light Aline Pham, Airong Zhao, Quanbo Jiang, Joel Bellessa, Cyriaque Genet, and Aurélien Drezet ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.7b01429 • Publication Date (Web): 15 Jan 2018 Downloaded from http://pubs.acs.org on January 16, 2018

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Interference eraser experiment demonstrated with all-plasmonic which-path marker based on reverse spin Hall eect of light †

Aline Pham,

†

Airong Zhao,

Quanbo Jiang,

†

Joel Bellessa,

‡

¶

Cyriaque Genet,

and

∗,†

Aurélien Drezet

†Institut ‡Institut

NEEL, CNRS-Université Grenoble Alpes, F-38000 Grenoble, France

Lumière Matière, CNRS- Université de Lyon, 69622 Villeurbanne cedex, France

¶ISIS,

UMR 7006, CNRS-Université de Strasbourg, 67000 Strasbourg, France

E-mail: [email protected]

Abstract We report on the reciprocal spin Hall eect of light in T-shaped nanoaperture arrays. Specically, we demonstrate that the information tied to surface plasmons trajectories can be encoded into free-space spin-carrying photons. The functionality of the system to act as a circular polarizer is therefore implemented in an interference eraser experiment where the device is used as a which-path marker. Complementarity between the wave-like and particle-like behavior of surface plasmons is veried, hence further demonstrating the outlook for miniaturized optical elements towards on-chip quantum experiments. This work underscores the high potential of plasmonic devices in the realization of integrated polarization optics hence opening promising prospects for nanoscale optical communications and quantum photonic network. KEYWORDS: Surface plasmon polaritons, interference eraser, spin-orbit coupling, metamaterial, polarization tomography.

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Motivated by the development of new compact and planar devices for photonic integrated circuits, plasmonic metamaterials have emerged as a solution manipulating optical properties with unprecedented degrees of freedom. 1 Plasmonic metamaterials are articial materials engineered on metallic structures at a size scale that is much smaller than the wavelength of interest. A broad spectrum of functionalities ranging from negative refraction, invisibility cloaks, and giant chirality have been reported. 2 Importantly, the design of nanoscale anisotropies and inhomogenenities in plasmonic metamaterials has led to considerably enhanced spin-orbit interaction eects 3,4 including spin Hall eect of light (SHEL) 57 and helicity-dependent optical vortex. 810 Originating from the strong coupling between the intrinsic circular polarization (spin) of light and the spatial degree of freedom of the wave (orbit), such spin-orbit interaction manisfestations are intended to play an essential role in optical communications in which encoding or carrying information on additional degree of freedom has been suggested for increasing the data capacity. 11 Spin-momentum locking, that is transfert of information on the handedness of an incident free-space light into surface waves with opposite trajectories have been demonstrated. 12,13,35 Reciprocally, plasmonic beam propagating in distinct directions are shown to determine the spin of the backconverted photon upon interaction with plasmonic metamaterials. 15 Although the reversed mechanism of SHEL has received much less attention, 16 the conversion process of surface plasmons (SP) back to freely propagating light with controlled polarization is essential not only for plasmonic-based photonic circuits but also shows great potentials for compact on-chip circular polarization manipulation devices. 17 Indeed, circular polarization is conventionally achieved in free-space with bulky waveplates. Experimental demonstration in the THz and visible regimes with metallic nanoantennas reported the decoupling of optical modes guided in dielectric waveguides into circular polarized radiation. 18 Because all-plasmonic devices may simplify the fabrication and integration process while decreasing optical devices footprint, we report here on all-plasmonic circular polarizers for encoding the direction of propagation of SP into spin-carrying photons. In order to fully characterize 2


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the polarization response of the plasmonic device, a complete wavevector-resolved polarization tomography is implemented. Reverse SHEL coupling is thus evidenced by means of a spatial reconstruction of the polarization ellipse of the SP scattering light. Specically, our plasmonic polarizer is shown to convert the incident SP beam into a strongly circularly polarized radiation for on-axis wavevectors on the one hand, and into linear polarization states for o-axis wavevectors on the other hand. Furthermore, the capability of our system to act as a which-path information marker, that is to imprint information about spatially separated SP trajectory into spin components of light, is then implemented into a plasmonic interference eraser experiment. 19 Indeed, eorts to realize quantum optical devices such as ecient single photon sources have motivated the eld of quantum plasmonics which aims at exploring fundamental quantum properties of surface plasmons. 20,21 Generation of single SP, conservation of photon entanglement in SPs and SP wave-particle duality demonstrated that SPs preserve many key quantum features of the photons. 2226 Here, the plasmonic quarter wave plate (QWP) is used as a marker in a platform allowing the investigation of the complementarity between which-path information (SP particle-like behaviour) and visibility of interference fringes (SP wave-like behaviour). 27 Our integrated and all-plasmonic interference eraser apparatus demonstrates that gaining which-way information on the SP trajectories deteriorates the interference patterns, making it an excellent candidate for on-chip quantum optics experiment. Thereby, we envision the reported SHEL reciprocal process to provide new platforms for down-scaled demultiplexing and single photon spin control, thus contributing to the advance of integrated optical devices for quantum optical network applications. SP momentum-to-spin conversion is achieved in plasmonic arrays whose building blocks are made of T-shaped nanoapertures. Scanning electron microscopy images of the samples are depicted in Figure 1. While T-shaped arrays have been widely investigated for their ability to induce spin controlled SP directionality, 12 the reverse process has only been investigated in hybrid plasmonic metamaterials. 18 Here, each of the plasmonic systems under study comprises two out-coupler arrays made of 5 × 10 T-shaped nanoapertures and sepa3


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Figure 1: (a-b) SEM images of the samples. (c) Zoom in on a T-shaped nanoaperture with dimensions L = 200 nm, w = 50 nm, D = 212 nm. n ˆ and m ˆ indicate the electric dipole orientations induced by the slit (1) and (2), respectively. rated by three central slits to form the SP launcher. The nanoholes are milled using focused ion beam on a 200 nm thick opaque gold lm evaporated on a glass substrate. While the T-shaped nanoapertures are milled all the way through the metallic layer, the depth of SP launcher is halfway milled in order to limit the direct transmission of the incident laser beam. It should be noted that the out-couplers on each side of the SP launcher forming the sample A (Figure 1(a)) are identical whereas in the sample B (Figure 1(b)), they are mirror symmetric images with respect to Ox. The present plasmonic systems were designed based on the reverse process introduced in 12,32 which reported that according to the handedness of the light impinging on the T-shaped aperture, the resulting plasmonic beam is directed either to the left or right direction. The key element central to this eect is the ±π/2 phase shift between the SPs emitted from each slit forming the T-aperture, leading to constructive interferences in one direction and destructive interferences of the plasmonic beam in the other direction. The spin-dependent directional coupling is thus ensured if the two rectangular apertures are √

separated by a distance D/ 2 = λSP /4, with the SP wavelength λSP = 603 nm. In addition, the horizontal and vertical periods are taken Λx = λSP and Λy = λSP /2, respectively in order to favor SP unidirectionality along the x direction. Here, we investigate the reciprocal SHEL process which involves three mechanisms as illustrated in Figure 2(a): the coupling of light to SPs, the traveling of SPs on the metallic lm towards the T-shaped out-couplers, and 4


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the scattering of the SPs into free propagating light. To produce SPs, we weakly focus on the SP launcher a laser beam (λ = 633 nm) linearly polarized and normal to the slits. The experimental setup is schematized in Figure 2(b). In order to reveal the SHEL reciprocal mechanism and the polarization conversion, the out-coupled eld is collected in the Fourier plane then imaged on a CCD camera. Along kx , the detection of the scattered light is limited to the three diraction orders n = 0, −1, −2 by the numerical aperture of our collection microscope objective (O2). They correspond to the following wavevectors: kx (n) = kSP + n(

2π ) = ±kSP (n + 1), Λx

(1)

with ±kSP the SP wavevector propagating in ±x directions, respectively. The k-distribution mapping of the exiting states of polarization (SOP) is achieved by means of a quarter wave plate (QWP) and a polarizer (P) enabling the determination of the four Stokes parameters S0 , S1 , S2 , S3 . We recall that they are dened as: S0 = IX + IY , S1 = IX − IY , S2 = IP − IM , S3 = IR − IL , with Ii (i = X, Y, P, M, R, L) the intensity analyzed in the linear X , Y , M √ √ (−45◦ ), P (+45◦ ) and circular R = (X − iY )/ 2, L = (X + iY )/ 2 polarization basis.

To highlight both polarization conversion and its evolution in the k-space, the SOPs are represented with polarization ellipses which are characterized by their ellipticity ε, orientation θ and helicity h derived from the Stokes parameters such as sin(2ε) = S3 /S0 , tan(2θ) = S2 /S1

and h = sign(S3 ). Let us start with the demonstration of the reverse SHEL with a thorough characterization of the SOP transformation induced in the systems displayed in Figure 1. Upon the incident light, the SP launcher generates two counter propagating SP beams which then re-radiate from both out-couplers located on each side of the launcher (see Figure 2(b)). In order to reconstruct the SOP of the eld that is independently re-emitted by each out-coupler, a spatial beam blocker (M) is placed in the direct plane to lter out the signal radiated either by the right or left out-coupler. In Figure 2(c), we show the k-space intensity distribution

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Figure 2: (a) Side-view illustration of the k-resolved polarization analysis method on individual T-shaped aperture array: SP are excited from the central grating via the laser beam (1), then progagate towards the T-plasmonic arrays (2), on which they scatter into free propagating radiation (3). A beam blocker M can be inserted in the direct plane to prevent the recording of the scattered light emerging from the second outcoupler. (b) Experimental setup scheme: O1 input microscope objective (40 ×, NA= 0.75), O2 immersion microscope objective (100 ×, NA= 1.45), TL, L1, L3 converging lenses, M removable beam blocker placed in the direct plane (DP), FL removable Fourier lens used to image the back focal plane of O2, quarter waveplate (QWP) and polarizer (P) used for polarization analysis. (c) Fourier plane image of the scattered light when M is placed in the DP such that only the radiation emitted from the left outcoupler is recorded. The white circle indicates the maximum NA of O2 of radius k0 . of the scattered light out of the sample A, in the case the beam blocker obstructs the light exiting from the right out-coupler. This is equivalent to study the emission from the T-shaped array when stricken by a SP beam coming from the right direction. Along the kx direction, the numerical aperture of our microscope objective allows the recording of three beams corresponding to the nth diraction orders as previously discussed, while in the ky direction, the vertical pitch of the array prevents the detection of the o-axis orders which scatter out of the collection aperture of O2. We stress that for SPs propagating in −x direction, the orders n = 0, −1 and −2 are detected at kx (n = 0) = −kSP , kx (n = −1) = 0 and kx (n = −2) = +kSP , respectively. Conversely, for SPs coming from the left direction (−x), the diraction

orders are now located at kx (n = 0) = +kSP , kx (n = −1) = 0 and kx (n = −2) = −kSP (illustration in Figure 2(a)). The intensity dierence among the three scattered signals in 6


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Figure 3: Polarization analysis of the sample A: Experimental intensity proles corresponding to the -2th, -1st, 0th diraction orders resulting from the scattering of an incident SP beam on the T-shaped aperture arrays coming from the right (a-d) and from the left (e-h) as schematized in (a) and (e). Left bottom insets: corresponding simulation data. Polarization ellipses are superimposed on the data: red and black colors stand for +1 (left circular polarization) and -1 (right circular polarization) helicity, respectively. Scale bar value: 3k0 N.A./8. Bottom (right-hand side) color scale: Experimental (simulations) intensity in arbitrary units. Figure 2(c) is due to the fact that most of the light is scattered in the 0th order. Indeed, the grating being excited by SPs coming from the right, the left spot corresponds to the n = 0 scattering order, so it appears brighter. Now, to evidence the SHEL reciprocal coupling, we record a serie of six images for each polarization states, resulting in the determination of the Stokes parameters and subsequently in a reconstruction of the polarization ellipses of the eld. In Figure 2, we display a zoom in on each diraction order from the sample A of the k-dependent SOP features. The top row corresponds to the scattering from the left out-coupler (Figure 3(a-d)) and the second row to the right out-coupler (Figure 3(e-h)). We recall that n refers to the diraction orders as illustrated in Figure 2(a). Remarkably, we observe that both congurations are shown to induce k-sensitive polarization transformation with circular polarization conversion for kx ≈ 0 direction (n = −1) and linear polarization

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states for kx 6= 0 (n = 0, −2). On the one hand, considering the situation in which the T-shaped array is excited from the right by the SP beam (Figure 3(a-d)), the analysis of the order along the optical axis (n = −1) yields to a predominance of lefthanded circular state, thus revealing the ability of the plasmonic device to couple the incident SP direction into spin-carrying photons for a given k. On the other hand, the right outcoupler, that is excited by an impinging SP beam coming from the left (Figure 3(f-h)), feature opposite helicity now with a right-handed circular polarization state in the kx ≈ 0 region. During the reciprocal SHEL process, upon interaction with the medium, the surface wave acquires a spin angular momentum along the optical axis direction. The SP direction-to-spin conversion can be quantied via the degree of circular polarization dened as DCP =| S3 | /S0 . The high mean value of < DCP >= 0.88 measured in our all-plasmonic system conrm its ability to act as a circular polarizer. Furthermore, opposite spins resulting from the excitation of the arrays by SPs with opposite trajectories clearly manifest the eects of the reverse process of spin-control directional coupling. While the previous studies 12 have reported on the conversion of an incident circular polarization into directional SP propagation, our work unprecedentedly evidences in a compact and all-plasmonic metamaterial the reciprocal SHEL mechanism, attesting that the direction of SP waves can be encoded into spin. 2830 We thus expect the plasmonic device to be applicable to the manipulation of quantum source SOP. 31 In addition, the plasmonic system is also shown to transform SPs into linear states for kx 6= 0. The o-axis SOP emanating from the left (Figure 3(b,d)) and right plasmonic array (Figure 3(f,h)) exhibit quasi-linear orthogonal states and manifests mirror-symmetric behavior with respect to Oy . Our characterization method, which combines k-space mapping and polarization analysis thus allows us to resolve the SOP conversion as function of k, and to reveal linearly polarized states along X and Y for the 0th and −2nd orders, respectively. Physical interpretation of the underlying reciprocal SHEL and k-dependent polarization conversion occuring in the plasmonic metamaterial is achieved by the well-established multidipole description as introduced in. 32 Let us consider the case of an incident SP beam 8


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Figure 4: Polarization analysis of the sample B: Experimental intensity proles corresponding to the -2th, -1st, 0th diraction orders resulting from the scattering of an incident SP beam on the T-shaped aperture arrays coming from the right (a-d) and from the left (e-h) as schematized in (a) and (e). Left bottom insets: corresponding simulation data. Polarization ellipses are superimposed on the data: red and black colors stand for +1 (left circular polarization) and -1 (right circular polarization) helicity, respectively. Scale bar value: 3k0 N.A./8. Bottom (right-hand side) color scale: Experimental (simulations) intensity in arbitrary units. traveling in the ±x direction and scattering on a single T-shaped aperture. Each rectangular slit forming the T subsequently radiates light in the far eld and is modeled as an electric dipole moment oriented normally to the long edge of the aperture as indicated in Figure 1(c). The backconverted eld is expressed as:

E(k) ∝ (ˆ n.E SP (r1 ))ˆ ne−ik.r1 + (m.E ˆ SP (r2 ))me ˆ −ik.r2 ,

(2)

e∓ikSP .ri

(µ.xˆi )xˆi describes the plasmonic eld, ri the position of the slit |xi | ˆ = √12 (1, 1)T the normal vectors to the slit 1 and 2, respectively i = 1, 2, n ˆ = √12 (−1, 1)T , m

where E SP (ri ) = p

(T stands for the transpose operator). The coordinate origin is taken at the SP launcher position. Because the distance separating the SP launcher and the T-shaped aperture is 9


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√

much greater than D/ 2 = λSP /4, the radiated eld E ± (kx ) resulting from the excitation with a SP beam propagating in ±x direction then simplies as:

E ± (kx ) ∝

under the approximation

√ e−i(kx ∓kSP )x1 p [(ˆ x − yˆ) + (ˆ x + yˆ)ei(kx ∓kSP )D/ 2 ], |x1 |

(3)

p p |x1 | ≈ |x2 |. Following Eq.1, we thus retrieve the informa-

tion on the k-dependent properties of the polarization transformation according to the nth diraction order: n = 0 −→ E ± (kx ≈ ±kSP ) ∝ X √ n = −1 −→ E ± (kx ≈ 0) ∝= (X ∓ iY )/ 2

(4)

n = −2 −→ E ± (kx ≈ ∓kSP ) ∝ Y

(6)

(5)

Thereby, the reverse SHEL coupling is theoretically demonstrated along the optical axis (n = −1) with circularly polarized radiation. We also recover the linear SOP features in the 0th and −2nd order with a scattered light polarized along X and Y , respectively. Including the eects of the imaging system as detailed in, 33 the analytical simulations of the k-distributed SOPs are displayed in insets of Figure 3. In agreement with our experimental results, this simple analytical model well predicts a re-emission of the SP into spin-carrying photons for on-axis directions and linear SOP for increasing kx . It should be noted however that discrepencies are detected, especially between the linearly polarized side beams: while the theoretical data predict linear states aligned along X and Y , we experimentally observe slight ellipticity and rotation of the linear axis in Figure 3(b), (d), (f) and (h). In addition to experimental errors coming from misaligments and the polarizers, it has been reported that subbtle imperfections in the shape of the nanostructures due to fabrication errors can lead to optical activity and dichroism as a result of break of symmetry in the system. 3436

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Source of deviations could then arise from structural defects in the sample. Nevertheless, the conversion of SP with opposite trajectories into free-space radiation of opposite helicity with high DCP strongly conrms the reverse SHEL coupling occurring in our plasmonic system. Let us now turn to the analysis of the sample B (Figure 1(b)). The latter is formed by two mirror-symmetric plasmonic arrays: the left outcoupler is similar to that of sample A while the right outcoupler is made of mirror imaged T-apertures with respect to Ox . As previously, the measurements in the rst and second rows presented in Figure 4 are associated with SP excitation beams coming from the right and left directions, respectively. We now compare the SOP of the light scattered from each outcouplers with that of measured in the sample A (Figure 3). First of all, we observe strong similarities between the experimental data depicted in the top row of Figure 3(a-d) and Figure 4(a-d). This veries both the SHEL reciprocity and the robustness of the k-selected polarization conversion achieved in the plasmonic system: the impinging surface wave is transformed into free-space radiation of left-handedness at kx ≈ 0 and to linear states for kx 6= 0. As far as the right outcoupler is concerned, symmetry considerations predict that photons will be scattered with opposite helicity from the mirror-symmetric T-shaped apertures while the linear SOP retain their orientations along X and Y . The SOPs displayed in the bottom rows of Figure 3(e-h) and Figure 4(e-h) manifest indeed counter handedness and Figure 4(g) exhibit now left-handed spin-carrying photons for on-axis kx . In agreement with the analytical simulations, the oaxis SOP are conserved with X and Y for 0th and −2nd orders, respectively. Thereby, we have shown that plasmonic metamaterials can be designed to transform surface waves with given directionality (here +x), to right (Figure 3(g)) or left (Figure 4(g)) circular polarized radiations. Relying on reverse SHEL coupling, we thus demonstrated the ability of our allplasmonic 2D polarizer to decouple surface waves into free propagating light with controlled polarization at selected wavevectors. Since it enables the information on the direction of the incident SP beam to be encoded in the handedness of the exiting radiation, the plasmonic arrays can serve as which-path markers for SPs which we now propose to implement into a 11


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Figure 5: (a), (b) K-space images recorded from the sample A and B respectively. No spatial beam blocker is used nor polarization analysis is achieved. (c) K-space image recorded from the sample A after a linear polarizer is inserted in the path of the scattered light. (d) Blue and red curves are intensity crosscut proles achieved along the white dashed lines on experimental measurments in (a) and (b), respectively. (e) Theoretical intensity crosscut proles simulating the blue and red curves obtained for (a) and (b), respectively. (f) Intensity crosscut prole achieved along the white dashed lines on the experimental measurment in (c). Scale bar value: k0 N.A./16 plasmonic analog to the quantum eraser experiment. Attempts to deepen our understanding of fundamental quantum properties of SP have led to a wide range of plasmonic circuits operating at the quantum levels, thus oering new opportunities for integrated quantum photonic systems to be built. 20 In particular, SP waveparticle duality has been probed with the demonstration of both particle-like and wave-like behaviour from self-interfering single SP. 2325 Quantum eraser experiment intends to demonstrate the complementarity principle between which-path information and the observation of interference fringes. 19 Any accessible information on the path taken by the photons is predicted to induce vanishing of the fringe visibility of the interfering beams. Here, we report on a plasmonic interference eraser demonstrating that any distinguishability of the directions followed by the SP is associated with a smearing of the fringes. In the following study, the spatial beam blocker M is removed from the apparatus such that the waves resulting from the SP scattering on both left and right outcouplers can be recorded at the same time. Let

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us consider the sample A in Figure 1. The total radiated intensity, i.e. without polarization analysis, is displayed in Figure 5(a). We observe that each of the three recorded diraction orders exhibit a blurred interference pattern. Upon performing intensity crosscut proles (Figure 5(d)), we measure a low visibility of the interference pattern with a mean value of < VA >= 0.16 ± 0.01 for the central beam. By analogy to a double-slit experiment in which each slit is replaced by a plasmonic array, the weakness of the observed interference fringes arises from an increasing knowledge concerning which outcoupler the photons are radiated from. Although no spatial beam blocker nor external polarizing lter is used here, information on the SP trajectory is stored in the handedness of the free propagating light along kx ≈ 0 by means of the T-shaped array: surface wave of opposite direction scatter spin-carrying photons of opposite helicity. Therefore, the eld emanating from each outcoupler are orthogonal so their amplitudes add destructively. Based on the above study, these results conrm the orthogonality of polarization for the emerging waves. We thus demonstrate that information on the particle-like nature of the SP can be extracted thanks to the T-shaped apertures which act as which-path markers and cause the disappearance of the interference pattern. Note however that the peaked signal observed at n = 0 and −2 results from a residual leakage of the SPs through the metallic lm which appears at ±kSP . The intensity imbalance among the three spots is assigned to a slight misalignment of the laser beam incident on the SP launcher which yields to an unequal generation of SPs, hence of the scattered light between left and right. Now, following the complementarity principle, gaining information on the wave-like behavior of photons implies a loss in the which-path information. We could thus expect the interference pattern to reappear for kx ≈ 0. To experimentally verify this, we now turn to the analysis of the sample B. As seen previously, SP propagating to the left or to the right direction should be indistinguishable along the optical axis given that both arrays radiate left-handed circular polarization (Figure 4(c), (g)), hence allowing the recovery of the interference fringes. In Figure 5(b), the scattered light indeed features fringes with remarkably higher mean visibility of < VB >= 0.82 ± 0.01 in the central 13


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beam (measurement from the cross-section in Figure 5(d)). One then veries that for this on-axis diraction order, part of information on the particle-like behavior, i.e. on the SP trajectory, is lost during the scattering process on the mirror-symmetric outcouplers that is subsequently accompanied by the retrieval of the fringes. Interestingly, the which-path information is not totally destroyed since part of it is still contained in n = 0, −2 orders. The red curve in Figure 5(d) clearly demonstrates that absence of fringes in the side diraction orders in contrast with the high visibility in the central region. The plasmonic beam scatters into photons of identical spins for n = −1 (indistinguishable SPs) but into orthogonal and linearly polarized beams along X (Y ) for the 0th (−2nd ) order (indistinguishable SPs). It prohibits the observation of interference fringes in the side beams such that the SP trajectories could still be identied. As a result, only a fraction of information on the particle-like behavior of SP has been lost in the sample B. These observations are conrmed theoretically in Figure 5(e) based on our analytical model. In the central beam, the which-path markers in the sample A prevents the formation of interferences fringes whereas the fringe eraser, that is the sample B, restores them. One also veries the absence of the fringes in the side orders for both congurations. Total erasure of the which-path information, i.e. for the three orders, is now achieved by inserting in the path an external linear polarizer oriented at 45◦ with respect to X . As seen in Figure 5(c ,f), the introduction of a polarizer after the sample A restores the interference pattern with well-dened fringes for the three orders. The SOP of all the photons is now polarized in a unique direction along this external polarizer such that they can add constructively. The which-path information is erased so it is no longer possible to determine the trajectory followed by the SP. Therefore, based on the reverse SHEL process, we have realized which-path and interference eraser operations that we expect to be benecial to the manipulation of single SP, hence yielding to further understanding of fundamental SP quantum properties and applications in quantum nano-optics. To conclude, we have experimentally demonstrated a SP direction-to-spin converter in planar and all-plasmonic structures. SHEL reciprocity is revealed by means of a complete 14


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polarization tomography enabling k-resolved mapping of the local polarization ellipses, thus the evidence of high circular polarization conversion by the plasmonic device. In addition, we also show that the handedness of the emerging light stores the trajectory information taken by the SP, thus driving us to use the device in which-path and interference eraser operations. Complementarity of particle-like and wave-like nature of SPs is successfully demonstrated, albeit here in the classical regime, which emphasizes the potential of plasmonic devices in single photon manipulation and polarization control for quantum nano-optics applications.

Acknowledgments This work was supported by Agence Nationale de la Recherche (ANR), France, through SINPHONIE Grant No. ANR-12-NANO-0019 and PLACORE Grant No. ANR-13-BS10-0007. C.G. also thanks the support from the ANR Equipex Union (ANR-10-EQPX-52-01) and the Labex Nanostructures in Interaction with their Environment Projects (ANR-11-LABX0058-NIE). The Ph.D. grant of A. P. by the Ministère de l'enseignement et la recherche scientique, of A. Z. by the China Scholarship Council are gratefully acknowledged. We thank J.-F. Motte and G. Julie, from NANOFAB facility in Neel Institute, for the sample fabrication.

References (1) Yao, K.; Liu, Y. Plasmonic metamaterials.

Nanotechnology Reviews

210.

15


2014, 3(2), 177-

ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 21

(2) Monticone, F.; Alù, A. Metamaterial, plasmonic and nanophotonic devices. Reports on Progress in Physics

2017, 80(3), 036401.

(3) Bliokh, K. Y.; Rodríguez-Fortuño, F. J.; Nori, F.; Zayats, A. V. Spin-orbit interactions of light. Nature

Photon.

2015, 9(12), 796-808.

(4) Ling, X.; Zhou, X.; Huang, K.; Liu, Y.; Qiu, C. W.; Luo, H.; Wen, S. Recent advances in the spin Hall eect of light. Reports

on Progress in Physics

2017, 80(6), 066401.

(5) Yin, X.; Ye, Z.; Rho, J.; Wang, Y.; Zhang, X. Photonic Spin Hall Eect at Metasurfaces. Science

2013, 339, 1405-1407.

(6) Shitrit, N.; Bretner, I.; Gorodetski, Y.; Kleiner, V.; Hasman, E. Optical spin Hall eects in plasmonic chains. Nano

Lett.

2011, 11(5), 2038-2042.

(7) Hosten, O.; Kwiat, P. Observation of the spin Hall eect of light via weak measurements. Science

2008, 319(5864), 787-790.

(8) Yu, N.; Genevet, P.; Kats, M. A.; Aieta, F.; Tetienne, J. P.; Capasso, F.; Gaburro, Z. Light propagation with phase discontinuities: Generalized laws of reection and refraction. Science 2011, 334, 333-337 . (9) Gorodetski, Y.; Drezet, A.; Genet, C.; Ebbesen, T. W. Generating far-eld orbital angular momenta from near-eld optical chirality. Phys. Rev. Lett. 2013 110(20), 203906. (10) Karimi, E.; Schulz, S. A.; De Leon, I.; Qassim, H.; Upham, J.; Boyd, R. W. Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface. Light:

Science and Applications

2014, 3(5), e167.

(11) Guan, B.; Scott, R. P.; Qin, C.; Fontaine, N. K.; Su, T.; Ferrari, C.; Cappuzzo, M.; Klemens, F.; Keller, B.; Earnshaw, M.; Yoo, S. J. B. Free-space coherent optical communication with orbital angular, momentum multiplexing/demultiplexing using a hybrid 3D photonic integrated circuit. Opt. 16

Express

2014, 22(1), 145-156.


Page 17 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

(12) Lin, J.; Mueller, J. B.; Wang, Q.; Yuan, G.; Antoniou, N.; Yuan, X. C.; Capasso, F. Polarization-controlled tunable directional coupling of surface plasmon polaritons. Science

2013, 340(6130), 331-334.

(13) Petersen, J.; Volz, J.; Rauschenbeutel, A. Chiral nanophotonic waveguide interface based on spin-orbit interaction of light. Science 2014, 346(6205), 67-71. (14) Gorodetski, Y.; Bliokh, K. Y.; Stein, B.; Genet, C.; Shitrit, N.; Kleiner, V.; Hasman, E.; Ebbesen, T. W. Weak measurements of light chirality with a plasmonic slit. Phys. Rev. Lett.

2012, 109(1), 013901.

(15) O'connor, D.; Ginzburg, P.; Rodríguez-Fortuño, F. J.; Wurtz, G. A.; Zayats, A. V. Spin-orbit coupling in surface plasmon scattering by nanostructures.

Nat. Commun.

2014, 5, 5327.

(16) Ren, J. L.; Wang, B.; Pan, M. M.; Xiao, Y. F.; Gong, Q.; Li, Y. Spin separations in the spin Hall eect of light. Phys.

Rev. A

2015, 92(1), 013839.

(17) Yu, N.; Aieta, F.; Genevet, P.; Kats, M. A.; Gaburro, Z.; Capasso, F. A broadband, background-free quarter-wave plate based on plasmonic metasurfaces. Nano Lett. 2012, 12(12), 6328-6333. (18) Rauter, P.; Lin, J.; Genevet, P.; Khanna, S. P.; Lachab, M.; Davies, A. G.; Lineld, E. H.; Capasso, F. Electrically pumped semiconductor laser with monolithic control of circular polarization. Proceedings

of the National Academy of Sciences

2014, 111(52),

E5623-E5632. (19) Scully, M. O.; Drühl, K. Quantum eraser: A proposed photon correlation experiment concerning observation and "delayed choice" in quantum mechanics. 1982, 25(4), 2208.

17


Phys. Rev. A

ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 21

(20) Tame, M. S.; McEnery, K. R.; Özdemir, S. K.; Lee, J.; Maier, S. A.; Kim, M. S. Quantum plasmonics. Nature

Phys.

2013, 9, 329-340.

(21) Cuche, A.; Mollet, O.; Drezet, A. and Huant, S. Deterministic quantum plasmonics. Nano Lett.

2011, 10, 4566-4570 .

(22) Altewischer, E.; van Exter, M. P. and Woerdman, J. P. Plasmon-assisted transmission of entangled photons. Nature 2002, 418, 304-306 . (23) Kolesov, R. et al. Wave-particle duality of single surface plasmon polaritons. Phys.

Nature

2009, 5, 470-474 .

(24) Fujii, G.; Segawa, T.; Mori, S.; Namekata, N.; Fukuda, D.; Inoue, S. Preservation of photon indistinguishability after transmission through surface-plasmon-polariton waveguide. Opt.

Lett.

2012, 37(9), 1535-1537.

(25) Di Martino, G.; Sonnefraud, Y.; Tame, M. S.; Kéna-Cohen, S.; Dieleman, F.; Özdemir, . K.; Kim, M. S.; Maier, S. A. Observation of quantum interference in the plasmonic Hong-Ou-Mandel eect. Phys.

Rev. Applied

2014, 1(3), 034004.

(26) Siampour, H.; Kumar, S.; Bozhevolnyi, S. I. Nanofabrication of Plasmonic Circuits Containing Single Photon Sources. ACS

Photonics

2017, 4(8), 1879-1884.

(27) Ajimo, J.; Marchante, M.; Krishnan, A.; Bernussi, A.A. and Grave de Peralta, L.;. Plasmonic implementation of a quantum eraser for imaging applications. J. Appl. Phys 2010, 108(6), p.063110.

(28) Bliokh, K. Y.; Nori, F. Transverse spin of a surface polariton.

Phys. Rev. A

2012,

85(6), 061801. (29) Canaguier-Durand, A.; Cuche, A.; Genet, C.; Ebbesen, T. W. Force and torque on an electric dipole by spinning light elds. Phys. 18

Rev. A

2013, 88(3), 033831.


Page 19 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

(30) Aiello, A.; Banzer, P. The ubiquitous photonic wheel. J.

Opt.

2016, 18(8), 085605.

(31) Dheur, M. C.; Devaux, E.; Ebbesen, T. W.; Baron, A.; Rodier, J. C.; Hugonin, J. P.; Lalanne, P.; Greet, J.-J.; Messin, G.; Marquier, F. Single-plasmon interferences. Science advances

2016, 2(3), e1501574.

(32) Jiang, Q.; Pham, A.; Berthel, M.; Huant, S.; Bellessa, J.; Genet, C. and Drezet, A. Directional and singular surface plasmon generation in chiral and achiral nanostructures demonstrated by leakage radiation microscopy.

ACS Photonics

2016, 3 (6), pp 1116-

1124. (33) Berthel, M.; Jiang, Q.; Chartrand, C.; Bellessa, J.; Huant, S.; Genet, C.; Drezet, A. Coherence and aberration eects in surface plasmon polariton imaging.

Phys. Rev. E

2015, 92(3), 033202.

(34) Caneld, B. K.; Kujala, S.; Laiho, K.; Jemovs, K.; Turunen, J.; Kauranen, M. Chirality arising from small defects in gold nanoparticle arrays. Opt. Express 2006, 14(2), 950-955. (35) Gorodetski, Y.; Lombard, E.; Drezet, A.; Genet, C.; Ebbesen, T. W. A perfect plasmonic quarter-wave plate. Appl.

Phys. Lett.

2012, 101(20), 201103.

(36) Pham, A.; Jiang, Q.; Zhao, A.; Bellessa, J.; Genet, C.; Drezet, A. Manifestation of planar and bulk chirality mixture in plasmonic Λ-shaped nanostructures caused by symmetry breaking defects. ACS

Photonics

19

2017, 4(10), 2453-2460.


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Graphical TOC Entry

For Table of Contents Use Only

Interference eraser experiment demonstrated with all-plasmonic whichpath marker based on reverse spin Hall eect of light. Aline Pham, Airong Zhao, Quanbo Jiang, Joel Bellessa, Cyriaque Genet, Aurélien Drezet. The present Table of Content (TOC) Graphic depicts the reconstruction maps of the polarization ellipses of the eld resulting from the scattering of surface plasmons on T-shaped plasmonic arrays. It points out the ability of the plasmonic metamaterial to induce reciprocal spin Hall eect of light used to encode the information on the surface plasmon trajectory into spin-carrying photons.

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281x108mm (96 x 96 DPI)


Interference eraser experiment demonstrated with all-plasmonic which

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