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Chiral nanophotonic waveguide interface based on spin-orbit interaction of light

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Science  03 Oct 2014:
Vol. 346, Issue 6205, pp. 67-71
DOI: 10.1126/science.1257671

Controlling the flow of light with nanoparticles

Light propagating through optic fibers could provide the ultimate in information flow, but controlling the direction of flow is a key requirement. Petersen et al. show that the directional flow of light in a fiber can be controlled by placing a single gold nanoparticle on or near the surface of the fiber. By exploiting the chiral properties of light (the spin-orbit interaction), the authors demonstrate that the “handedness” or polarization state of the light hitting the particle determines in which direction the light flows in the fiber.

Science, this issue p. 67

Abstract

Controlling the flow of light with nanophotonic waveguides has the potential of transforming integrated information processing. Because of the strong transverse confinement of the guided photons, their internal spin and their orbital angular momentum get coupled. Using this spin-orbit interaction of light, we break the mirror symmetry of the scattering of light with a gold nanoparticle on the surface of a nanophotonic waveguide and realize a chiral waveguide coupler in which the handedness of the incident light determines the propagation direction in the waveguide. We control the directionality of the scattering process and can direct up to 94% of the incoupled light into a given direction. Our approach allows for the control and manipulation of light in optical waveguides and new designs of optical sensors.

The development of integrated electronic circuits laid the foundations for the information age, which fundamentally changed modern society. During the past decades, a transition from electronic to photonic information transfer took place, and nowadays, nanophotonic circuits and waveguides promise to partially replace their electronic counterparts and to enable radically new functionalities (13). The strong confinement of light provided by such waveguides leads to large intensity gradients on the wavelength scale. In this strongly nonparaxial regime, spin and orbital angular momentum of light are no longer independent physical quantities but are coupled (4, 5). In particular, the spin depends on the position in the transverse plane and on the propagation direction of light in the waveguide—an effect referred to as spin-orbit interaction of light (SOI). This effect holds great promises for the investigation of a large range of physical phenomena such as the spin-Hall effect (6, 7) and extraordinary momentum states (8) and has been observed for freely propagating light fields (9, 10) in the case of total internal reflection (11, 12), in plasmonic systems (1315), and for radio frequency waves in metamaterials (16). Recently, it has been demonstrated in a cavity-quantum electrodynamics setup in which SOI fundamentally modifies the coupling between a single atom and the resonator field (17).

For vacuum-clad dielectric waveguides, evanescent fields arise in the vicinity of the surface and allow one to locally interface the guided fields with micro- and nanoscopic emitters (18). Because of SOI, these evanescent fields exhibit a locally varying ellipticity that stems from a longitudinal polarization component that points in the direction of propagation of the light and that oscillates in quadrature with respect to the transversal components (19). Surprisingly and in contrast to paraxial light fields, the corresponding photon spin is in general not parallel or antiparallel to the propagation direction of the guided light. In special cases, it can even be perpendicular to the propagation direction and antiparallel to the orbital angular momentum (8, 20).

We have experimentally demonstrated that SOI in a dielectric nanophotonic waveguide drastically changes the scattering characteristics of a nanoscale particle located in the waveguide’s evanescent field. In free space, pointlike scatterers exhibit a dipolar emission pattern (21) in which for the emission of both linearly and circularly polarized light, the intensity distribution of the scattered light is cylindrically symmetric. In particular, this implies that dipolar scattering into any spatial direction perpendicular to the symmetry axis is always accompanied by an equal amount of scattered light into the opposite direction. We demonstrate that SOI breaks this symmetry and show that when light is scattered by the particle into the waveguide modes, the amount of light that is coupled into a given direction of the waveguide can substantially exceed the power that propagates in the opposite direction.

We used an air-clad silica nanofiber as an optical waveguide and positioned a single spherical gold nanoparticle on its surface. We illuminated the particle with a focused paraxial laser beam from the side (Fig. 1A) and characterized the scattering properties of the particle into the optical waveguide. The emission rate of the particle into a given nanofiber eigenmode is proportional to Embedded Image, with the induced electric dipole moment d of the particle and the profile function of the electric part of the fiber mode (22). For spherical scatterers, the dipole moment is d = α · exc, where α is the complex polarizability and exc is the positive-frequency envelope of the excitation field, which is related to the real value of the electric field by Eexc = 1/2[excexp(–iωt) + c.c.]. Here, ω/2π is the frequency of the light, and c.c. is the complex conjugate. The total power of the light scattered into a given fiber mode is given by Embedded Image(1)where (r, ϕ) denotes the position of the scatterer in the nanofiber transverse plane. As a consequence, the emission rate is directly proportional to the overlap between the field of the excitation light and the fiber mode at the particle’s position.

Fig. 1 Experimental setup.

(A) A single nanoparticle on a silica nanofiber surface is illuminated with light propagating in –x direction. The polarization of the light can be set with a quarter-wave plate. The light scattered into the nanofiber is detected by using SPCMs at the left and right fiber output ports. (B) Modification of the intensity distributions for an incident field polarized along y (bottom half) and z axis (top half) owing to the presence of the nanofiber. (C and D) Scanning electron microscope images of the nanofiber and the nanoparticle used in our experiments. From the images, we determine diameters of 2a = (315 ± 3) nm for the fiber and 2r = (90 ± 3) nm for the nanoparticle.

For a single-mode nanofiber, all guided light fields can be decomposed into the quasi-linearly polarized fiber eigenmodes (19) Embedded Image and Embedded Image, where the z axis coincides with the nanofiber axis and the ± sign indicates the propagation direction (±z) of the light in the fiber. We choose Embedded Image and Embedded Image so that their main polarization component points along the x (ϕ = 0°) and y (ϕ = 90°) directions, respectively. The normalized total power of the light scattered into the Embedded Image and Embedded Image modes is shown in Fig. 2, according to Eq. 1, as a function of the position of the scatterer in the fiber transverse plane. The calculations were performed for circularly Embedded Image and linearly π = ex polarized excitation light. Here, the x axis is the quantization axis, and ex,y,z are the unit vectors along the corresponding axes. The predicted asymmetry of the scattering originates from the fact that the local polarization depends both on the position in the fiber transverse plane and on the propagation direction of the mode—a consequence of SOI of the nanofiber-guided light. For a particle located at the top (ϕ = 90°) of the nanofiber, the polarization overlap between the Embedded Image mode and σ is maximal and reaches 93%, and the overlap between the Embedded Image mode and σ is minimal and reaches 7%. This means that the field is nearly perfectly circularly polarized. Because the emission probability of the particle into the fiber is directly proportional to this overlap, a strong asymmetry of the scattering into the left (+z) and right (­–z) direction of the fiber results, which can be tuned by the polarization of the incident light field and the position of the nanoparticle. In particular, the asymmetry reverses when switching the polarization of the excitation light from σ to σ+ or when changing the position of the particle from (x, y) to (x, –y).

Fig. 2 Scattering in the presence of SOI (theoretical predictions).

(A) When the nanofiber-guided light is quasi-linearly polarized along the y axis, longitudinal polarization components occur. For light traveling in +z direction, this leads to nearly circular σ polarization on the top of the fiber and σ+ polarization on the bottom of the fiber (circular green arrows). For light propagating in ­–z direction, Embedded Image and Embedded Image are interchanged. At these positions, the spin angular momentum of the light (yellow arrows) is oriented perpendicular to the propagation direction and antiparallel to the orbital angular momentum (red arrows), defined with respect to the z axis (8). (B) Intensity, Embedded Image, of the Embedded Image modes, normalized to its peak value on the fiber axis. (C) Position-dependent power, scattered into the Embedded Image mode for σpolarized excitation light and into the Embedded Image mode for σ+ polarized excitation light. (D) Power scattered into the Embedded Image mode for σ polarization and Embedded Image mode for σ polarization. (E) Power scattered into the Embedded Image modes for π = ex polarization. (F to I) Same as (B) to (E) but for the fiber modes Embedded Image. The calculations assume our experimental parameters, and the scattered powers are normalized to the peak value on the fiber axis in (I). On top of the fiber (x = 0, y = a), we find a normalized power of 0.88, 0.06, and 0 in panels (C) to (E), respectively.

We investigated this directional scattering using a tapered optical fiber (TOF) with a nanofiber waist (23) [diameter, 2a = (315 ± 3) nm], which enables almost lossless coupling of light from a standard optical fiber into and out of the nanofiber section. A single spherical gold nanoparticle [diameter, 2r = (90 ± 3) nm] positioned on the nanofiber surface (22) acts as a polarization-maintaining scatterer (24, 25). The particle is illuminated with a laser beam propagating in the –x direction (Fig. 1A) with a wavelength of 532 nm, which is close to the measured resonance of the nanoparticle at 530 nm (full width at half maximum, 50 nm). The nanofiber can be rotated around the z axis, which because of its cylindrical symmetry amounts to changing the azimuthal position ϕ of the nanoparticle around the fiber (Fig. 1A). The polarization of the incident light field is set by means of a quarter-wave plate. The angle θ between its optical axis and the y axis can be adjusted at will. Before passing through the waveplate, the polarization of the light is aligned along z. Thus, we can set the polarization to linear along z (θ = 0°, 90°) and circular, σ (θ = 45°) or σ+(θ = 135°). For intermediate angles, the polarization is elliptical, with the major axis along z. The excitation laser beam has a waist radius of around w = 150 μm at the position of the nanoparticle, assuring a homogeneous spatial intensity distribution with negligible longitudinal polarization components. A single-photon counting module (SPCM) at each output port of the TOF detects the light scattered into the nanofiber. After completion of all measurements, we analyzed the fiber surface with a scanning electron microscope (Fig. 1, C and D) to check that only a single nanoparticle was present and to measure the diameters of fiber and nanoparticle.

The measured photon fluxes at both fiber outputs are shown in Fig. 3, A and B, as a function of the azimuthal position of the nanoparticle and the polarization of the excitation light field, and the theoretical predictions are shown in Fig. 3, C and D, calculated according to Eq. 1 under the assumption that the polarization and intensity distribution of the incident light field are not modified by the presence of the optical fiber (22). We find qualitative agreement between measurement and theoretical prediction. In particular, we observed the expected maximum of the left-right asymmetry for the case of circular input polarization with the particle located at the top or the bottom of the fiber. However, scattering and refraction of the excitation light field by the nanofiber led to an appreciable modification of the polarization and intensity of the field close to the nanofiber surface (Fig. 1B) (26). Including these effects, we obtained the theoretical predictions shown in Fig. 3, E and F, where we used two fit parameters: the angular offset ϕ0 = 6.3° ± 0.1° of the nanoparticle from the expected deposition position of ϕ = 90° and the amplitude κf = (21.0 ± 0.1) × 106 s–1 of the photon flux detected with the SPCMs (22). This model agrees well with the measured data. The main differences to the simple model are an increase of the scattering rate around ϕ = 180° owing to the focusing of the incident light field by the fiber and the emergence of a shadow region around ϕ = 120° and ϕ = 240°, with a concomitant decrease in the scattering rate.

Fig. 3 Chiral waveguide coupling: experiment and theory.

(A and B) Measured photon flux (raw data, only corrected for the nonlinear response of the SPCMs) of the light scattered into the (A) left and (B) right direction as a function of the azimuthal position of the nanoparticle ϕ and the polarization of the excitation light field set by the angle θ of the quarter-wave plate. The ticks on the right mark the azimuthal positions for which data have been acquired with a stepsize of θ of 5°. The data are interpolated in between the measured points. The dashed lines indicate the data sets plotted in Fig. 4. (C to F) Theoretical prediction for the photon fluxes when [(C) and (D)] neglecting and [(E) and (F)] including the effect of the nanofiber on the incident light field. The model uses the angular offset of the nanoparticle and the overall amplitude of the photon flux as free parameters, which are obtained from a fit of (E) and (F) to the data in (A) and (B) (22).

For closer comparison, Fig. 4, A to D, shows the polarization dependence of the measured photon flux in the fiber for selected azimuthal positions of the nanoparticle together with the theoretical prediction. For the cases of the nanoparticle positioned near the top and the bottom of the nanofiber, we also plot the directionalityEmbedded Image (2)of the scattering process together with the theoretical prediction (Fig. 4, E and F), where c+ is the photon flux detected by the left detector and c is the photon flux detected by the right detector. We observed a maximum directionality of D = 0.88 for a particle near the top of the fiber, which corresponds to a ratio of 16:1 between the photon flux scattered to the left and right, and D = 0.95 for a particle near the bottom of the fiber, which corresponds to a ratio of 40:1 between the photon flux scattered to the right and left. When the particle is located near the side of the fiber, the overlap of the fiber eigenmodes with any polarization of the excitation light is independent of the propagation direction, and zero directionality is expected. In the experiment, we indeed observed only a small variation with the incident polarization (Fig. 4, A and B). The residual modulation most probably is due to the small angular deviation of the nanoparticle position from the ideal point.

Fig. 4 Directionality of the scattering process.

(A to D) Measured photon fluxes at the left (blue circles) and right (purple squares) fiber output ports as a function of the angle θ of the quarter-wave plate. Here, θ = 0°, 90°, ... corresponds to linear polarization along z (dashed orange lines), θ = 45°, 225° corresponds to σ polarization of the incident light field, and θ = 135°, 315° corresponds to σ+ polarization of the incident light field (dash-dotted green lines). (A) to (D) correspond to the azimuthal positions (ϕ = 358°, 178°, 84°, and 264°) of the nanoparticle (green dot) around the fiber (gray disk), as indicated in the insets. The solid lines are the predictions of our theoretical model. The statistical error bars are too small to be visible in the plot. The measured photon fluxes to the left (yellow diamonds) and right (green triangles) also are shown in (C) for the nanofiber without the nanoparticle, scaled up by a factor of 10. (E and F) Directionality  of the scattering process into the fiber for the data in (C) and (D).

The underlying physical mechanism that enables the directional scattering is spin-orbit interaction of light, which universally occurs in light fields that are strongly confined in the transversal direction. Our method is thus highly versatile, and we expect it to find application in various scenarios of nanophotonic systems. There is no fundamental limit to the directionality: By setting the polarization of the excitation field orthogonal to the polarization of the fiber eigenmodes that copropagate into the left/right direction, unity directionality can always be realized (22). Moreover, at the inside of the waveguide, the quasi-linearly polarized guided modes of our silica nanofiber exhibit a perfectly circular polarization at two specific positions in the fiber transverse plane. Thus, a particle at such a position that is excited with circularly polarized light will couple light exclusively into one direction of the waveguide. Apart from their usefulness for optical signal processing and routing of light, our findings have important consequences for the interaction between atoms and light in evanescent fields (27, 28) or strongly focused laser beams. Moreover, they may enable novel nanophotonic sensors that allow one to detect and identify, for example, scatterers with an intrinsic polarization asymmetry (22, 29). In the course of preparing this manuscript, we became aware of two related theoretical works (30, 31) discussing effects based on directional emission in photonic crystal waveguides.

Supplementary Materials

www.sciencemag.org/content/346/6205/67/suppl/DC1

Materials and Methods

References (3235)

References and Notes

  1. Materials and methods are available as supplementary materials on Science Online.
  2. Acknowledgments: We gratefully acknowledge financial support by the NanoSci-ERA network “NOIs” and the European Commission (IP Simulators and Interfaces with Quantum Systems, 600645). J.V. acknowledges support by the European Commission (Marie Curie Intra-European Fellowship grant 300392). The scanning electron microscope imaging has been carried out by use of facilities at the University Service Center for Transmission Electron Microscopy, Vienna University of Technology, Austria.
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