Letter pubs.acs.org/NanoLett
Polarization Tailored Light Driven Directional Optical Nanobeacon Martin Neugebauer, Thomas Bauer, Peter Banzer,* and Gerd Leuchs Max Planck Institute for the Science of Light, Guenther-Scharowsky-Straße 1/Bldg. 24, 91058 Erlangen, Germany Institute of Optics, Information and Photonics, University Erlangen−Nuremberg, Staudtstraße 7/B2, 91058 Erlangen, Germany ABSTRACT: We experimentally demonstrate all-optical control of the emission directivity of a dipole-like nanoparticle with spinning dipole moment sitting on the interface to an optical denser medium. The particle itself is excited by a tightly focused polarization tailored light beam under normal incidence. The position dependent local polarization of the focal field allows for tuning the dipole moment via careful positioning of the particle relative to the beam axis. As an application of this scheme, we investigate the polarization dependent coupling to a planar twodimensional dielectric waveguide. KEYWORDS: Nanoantenna, tight focusing, transversally spinning dipole, dielectric interface, waveguide
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(e.g., in a tightly focused, linearly polarized Gaussian beam).18 In this work, we choose a tightly focused radially polarized beam, which exhibits a strong longitudinal electric field on axis, surrounded by transverse field components.20 Due to this strong position dependence of the local polarization of the focal field, the particle’s dipole moment can be easily and sensitively tuned via careful positioning of the subwavelength particle relative to the optical axis of the tightly focused beam. The additional feature of cylindrical symmetry of the chosen beam enables full control over the angle of the directive emission in the full azimuthal range of 2π. The focal field distribution of the deployed radially polarized beam focused tightly onto the dielectric interface is plotted in Figure 1. For the calculation, we use vectorial diffraction theory21,22 with the same parameters as in the experiment discussed later. As expected, the amplitudes and relative phases of the components of the electric field Ex, Ey, and Ez vary strongly with respect to the lateral position in the focal plane.20 The strongest component of the electric energy density for the chosen input beam configuration is |Ez|2 (Figure 1d). In addition, the z component of the electric field is ± π/2 out of phase compared to the transverse components Ex and Ey (Figure 1b,c). As mentioned above, this ± π/2 phase difference between longitudinal and transverse electric field components of the incoming beam is required to excite a spinning electric dipole in the nanoparticle (with its axis parallel to the interface) and achieve maximum directivity of the scattered light.16 The ellipticity of the induced dipole then depends on the radial distance of the nanoparticle relative to the beam center. If the particle is sitting in the center of the focal spot, meaning on the optical axis, it is excited by the longitudinal electric field component only. For this position, a symmetric far-field pattern
n the past decade, directional emission and coupling of nanophotonic devices have gained increasing attention. Using optical nanoantennas to couple light selectively to plasmonic or dielectric waveguides on the nanoscale is one of the main ingredients for on-chip or interchip integrated photonic circuits.1−5 To enhance this coupling, a huge variety of different complex antenna designs have been proposed and experimentally examined. Examples include the well-known concepts of Yagi-Uda6−8 or graded antennas9 at the nanoscale and other designs to achieve directional emission.10−15 Recently, sensitive optical control over the emission directionality has been reported for a polarization dependent near-field effect.16,17 By employing an elliptically polarized spinning dipole emitter, it was shown, that the evanescent components of the dipole’s near-field result in angular dependent constructive and destructive interference. This leads to directional emission and coupling into a waveguide when the spinning axis of the dipole is oriented parallel to the waveguide interface. This coupling was demonstrated experimentally by shining circularly polarized light under grazing incidence onto a plasmonic slit, resulting in the excitation and directional propagation of surface plasmon polaritons.16 Here, we show that a full two-dimensional optically controllable directionality (nanobeacon) based on this effect can be achieved. We address and tune the dipole moment of a spherical subwavelength nanoparticle (radius ≪ λ) sitting on a dielectric interface by excitation with a tightly focused vector beam under normal incidence. Because of its small size, the particle senses most dominantly the local electric field, with its induced dipole moment being proportional to the latter, p ∝ E(x, y, z).18 For generating a transversally spinning electric dipole with maximum directivity, we therefore require an excitation beam with suitable polarization properties, that is, a local electric field vector with ± π/2 phase difference between the longitudinal and the transverse component.19 When focusing spatially coherent light to a tight spot, this required phase difference is directly given in many beam configurations © 2014 American Chemical Society
Received: January 28, 2014 Revised: April 7, 2014 Published: April 11, 2014 2546
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Figure 1. Focal field distribution at an air-glass interface for an incoming radially polarized beam. (a) The total energy density of the electric field |Etot|2 and (b−d) the components of the electric energy density |Ex|2, |Ey|2, |Ez|2 are plotted including the relative phases Φx, Φy, Φz as insets. All distributions of the electric energy density are normalized to the maximum value of |Etot|2.
in the optically denser medium is expected because of the orientation of the induced dipole.23 If the particle is just slightly shifted away from this position, an asymmetric far-field pattern will be observed with its directionality opposite to the chosen direction of the transverse displacement. Hence, the chosen symmetry of the focal field distribution allows for tuning both the emission direction as well as the directivity of the nanobeacon. The angle of emission depends on the azimuthal position of the particle in the beam. In contrast, the amplitude ratio between transverse and longitudinal field components, providing the directivity of the scattered field, depends on the radial position of the particle. After explaining the basic concept for the excitation and tuning of the dipole moment, we now want to introduce the actual experimental implementation. A scheme of our setup (similar to the one used in a previous work24) is depicted in Figure 2a. An incoming radially polarized paraxial beam (Figure 2b) with wavelength λ = 530 nm is focused onto the sample by a high numerical aperture microscope objective (NA = 0.9). The sample consists of a nanoparticle with dipole-like scattering behavior (radius = 40 nm), sitting on a glass substrate (n = 1.5). The air−glass interface of the sample coincides with the focal plane of the impinging beam. The sample itself is attached to a 3D piezo stage, which allows for positioning of the particle relative to the incoming tightly focused beam with nanometer resolution. Below the sample, an aplanatic immersion-type microscope objective (NA = 1.3), index-matched to the glass substrate, is mounted confocally with the upper objective. Via imaging the back focal plane of the immersion-type objective, it is possible to measure the far-field emission pattern I(kx, ky) of the dipole-like particle in k-space.25 Here, the NA of 1.3 limits the maximum measurable transverse k-vectors k⊥ = (k2x + k2y )1/2
Figure 2. Scheme of the experimental setup. (a) An incoming radially polarized paraxial beam (white arrows indicate the polarization in (b)) is focused onto the sample by a microscope objective with NA = 0.9. The sample consists of a subwavelength gold nanosphere (radius r = 40 nm) sitting on a glass substrate (n = 1.5). An immersion-type microscope objective (NA = 1.3) is mounted below the sample. It collects the transmitted beam and the light scattered off the particle in forward direction. A camera is used to image the back focal plane of the second objective. (c) Illustration of the aperture angles. The incoming and transmitted beam is indicated by the green area. The gray area marks the angular region, where only light scattered off the particle is detected by the immersion-type microscope objective and the dotted white line marks the critical angle. (d) Sketch of the experimental concept. The gold nanosphere can be moved through the focal plane of the tightly focused incoming beam. In the far-field, the light of the incoming beam (green) and the evanescent fields coupled to the medium are separated.
(Figure 2c). In the angular region with k⊥/k0 < 0.9, a mixture of the light scattered off the particle and the transmitted beam is detected in the far-field. Therefore, to measure only the light 2547
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Figure 3. The Nanobeacon. (a−i) Measured far-field patterns for nine different positions (see insets) of the gold particle in the focal plane of an incoming tightly focused radially polarized beam. All distributions are normalized to the maximum value of (e). The far-field pattern in (e) corresponds to the particle sitting on the optical axis of the beam. For (a−d) and (f−i), the particle is displaced by 250 nm into different directions.
scattered off the particle, the solid angle with k⊥/k0 ∈ [0.95, 1.3] is experimentally considered and imaged. Essentially, this makes the technique similar to an inverse dark field microscopy approach.26 In our experiment, we utilize the discussed technique to investigate the emission of the nanoparticle exemplarily for nine different positions of the particle in the focal plane, that is, nine different local polarization states and induced dipole moments.27 The measured far-field distributions are shown in Figure 3. The corresponding particle positions relative to the tightly focused beam are plotted as insets. When the particle is in the center of the tightly focused radially polarized beam (Figure 3e), we see, in fact, the expected axial symmetric farfield distribution caused by the emission of the excited longitudinally oriented dipole. Figure 3a−d and f−i show the far-field distributions for the particle displaced by 250 nm away from the optical axis in the focal plane for different displacement directions (see corresponding insets). On the basis of the cylindrical symmetry of the input beam, all those plotted emission patterns reveal approximately the same asymmetric distribution, but with changing directionality depending on the chosen direction of the particle displacement. To validate the near-field interference as the origin of the directed emission, we calculate the theoretical far-field distributions.18,28 Choosing kx and ky as Cartesian coordinates in k-space (see coordinate system in Figure 2d), the far-field intensity of a point-like dipole sitting on a glass substrate, emitted into the substrate in an angular region above the critical angle, is described by
⎛ E TM ⎞ ⎟ I (k x , k y ) ∝ ⎜ ⎝ E TE ⎠ ∝
2
n2k 02 − k⊥2 |k z |
2
e
−|kz| d
M̂ (kx , k y) ·p (1)
with the transformation matrix ⎛ ı|k z |k x f ı|kz|k y fTM k⊥ f ⎞ TM ⎜ − TM ⎟ ⎜ |k |⃗ k⊥ |k |⃗ k⊥ |k |⃗ ⎟ M̂ (kx , k y) = ⎜ ⎟ kx fTE ⎜ k y fTE ⎟ 0 ⎟ ⎜ − k⊥ k⊥ ⎝ ⎠
The matrix M̂ is derived from a rotation matrix and includes the Fresnel coefficients f TM(kx, ky) and f TE(kx, ky) corresponding to the transverse magnetic and transverse electric polarization components ETM and ETM in the far-field. As distance between the dipole and the interface, we use the radius of the particle d = r = 40 nm. Above the critical angle, the z component of the k-vector reads kz = ı|kz| = ı(k2⊥ − k20)1/2. Here, we see that the evanescent near-fields of the TM-component can interfere for a transversally spinning dipole with dipole moment p = (px, py, ıpz) and px, py, pz ∈ ℝ. To compare the theoretically calculated scattering patterns with the experimental results, we investigate three particle positions along the x axis (Figure 3d−f), which correspond to three different dipole moments of the particle. From the theoretically calculated focal field distribution (see Figure 1) we 2548
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Figure 4. Theoretically calculated far-field patterns equivalent to the measurements in Figure 3d−f and comparison of the measured and predicted integrated polar emission. The insets in (a−c) indicate the corresponding particle position relative to the incoming beam. The respective dipole moment used for the calculation was deduced from the local polarization state depicted in Figure 1. As estimate for the distance between the pointlike dipole and the substrate we used the radius of the particle d = 40 nm. The integrated polar emission plots in (d−f) show the intensity emitted into the region above the critical angle (k⊥/k0 ∈ [1, 1.3]), with the solid red and the dotted black lines denoting the theoretical and experimental results.
know, that Ey is zero along the x axis, and Ex and Ez have a relative phase of ± π/2. Because we assume the dipole moment to be proportional to the local electric field, we can write the dipole moment as p = (px, 0, ıpz) with px, pz ∈ ℝ for all possible particle positions on the x axis. Inserting this simplified dipole moment into eq 1, the ratio Pxz = px/pz determines the directivity. For the lateral positions chosen in the experiment, x = −250 nm, x = 0 nm, and x = +250 nm, we yield Pxz = +0.46, Pxz = 0, and Pxz = −0.46. The respective far-field distributions are calculated for these values (see Figure 4a−c). The theoretical far-field images also include the region with k⊥/k0 < 0.95. For the given scheme, this illustrates that the asymmetry of the k-spectrum (directive emission) occurs only for the evanescent fields. In addition, the integrated polar emission into the region with (k⊥/k0 ∈ [1, 1.3]) is plotted in Figure 4d-f for a direct comparison of the experimental (dotted black line) and theoretical (solid red line) results. If the particle is placed in the center of the tightly focused radially polarized beam, a symmetric far-field distribution is observed, as in the experiment (see Figure 4e and compare Figures 3e and 4b). Figure 4a (Figure 4c) shows the far-field distribution for the particle shifted by −250 nm (+250 nm) along the x axis and the corresponding integrated polar emission is plotted in Figure 4d (Figure 4f). Because all three theoretically calculated distributions are in very good agreement with their experimental counterparts in Figure 3d−f, we validate the constructive or destructive near-field interference as origin of the far-field directivity. Furthermore, this directivity of the particle’s emission is subwavelength displacement dependent. In the shown experimental results, we investigated specifically particle positions leading to maximum asymmetry in the farfield. Nevertheless, even for smaller displacements of only 25 nm, an asymmetry is already observable (not shown here). Thus, the presented experimental scheme might additionally be applied for high precision position sensing, where the displacement of the dipole-like particle relative to the beam is
determined with subwavelength accuracy by a single image of the back focal plane. Further investigation of this sensing ability and a determination of the experimentally achievable resolutions would get beyond the scope of this letter but will be discussed elsewhere soon. The results in Figure 3 demonstrate conclusively that we are able to control the dipole moment of a subwavelength plasmonic particle and its directional emission into the dielectric substrate it is sitting on. In a next step, we investigate a possible application of this technique for directional coupling of the emission of a dipole-like particle to a dielectric waveguide. For the nanobeacon, we now utilize a plasmonic gold cylinder (radius = 100 nm, height = 45 nm), located above the waveguide interface. This choice of particle shape is based on the utilized fabrication technique (e-beam lithography). Basically, the directional emission could be demonstrated for a huge variety of different waveguide geometries and dielectric materials. Here, the core of the two-dimensional waveguide is a thin layer (thickness d = 40 nm) of high refractive index material. We have chosen Nb2O5 with refractive index nco = 2.3 because of easy layer fabrication via sputter deposition. The surrounding medium (glass and immersion oil) has a refractive index of ncl = 1.5. For the given waveguide parameters and a wavelength of λ = 710 nm, only the fundamental modes for TE (electric field transverse to the interface) and TM (magnetic field transverse to the interface) polarization with the effective k-vectors kTE and kTM are supported and guided by the waveguide. Because of the large difference of the refractive indices of core and cladding, a sufficiently high amount of power is coupled to the waveguide via the evanescent fields. As in the aforementioned experiment, the cylinder is excited by a tightly focused radially polarized light beam under normal incidence. Again because of the small size of the particle compared to the wavelength of the excitation beam, its response can be approximated by that of a point-like dipole.18 For the experimental investigation of the polarization depend2549
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Using the described experimental setup, the polarization dependent coupling of the central dipole-like scatterer to the waveguide is measured. To suppress the statistically distributed imperfections of our sample (varying shape, size and quality of the cylinders), each recorded image of the field probes shown in Figure 6 is an average of 14 single measurements for different structures. Here, we investigate three particle positions in the focal plane of the impinging tightly focused beam (Figure 6a− c). The beam reflected by the waveguide surface and the light backscattered directly by the central particle are blocked in each image. If the central particle is placed exactly on the optical axis (Figure 6b), we observe nearly equal scattering intensities from all surrounding nanoparticles. This indicates an isotropic coupling of the central particle to the waveguide, as expected in this configuration. Residual differences between the scattering strength of individual particles on the ring originate from their varying dimensions caused by the fabrication process. In contrast, if we shift the particle exemplarily by 240 nm to the left (Figure 6a) or to the right (Figure 6c), effectively stronger scattering to the far-field from the righthand or left-hand outer particles is observed, respectively. This becomes particularly clear when comparing the magnified images of the outer particles near the x axis (see white framed insets). Consequently, Figure 6a, c indicates the directional coupling of the central particle into the waveguide, depending on the relative position of the particle in the excitation beam and, thus, on the local electric excitation field. For a quantitative description of the directivity, we compare the intensity scattered by the outer particles on the right- and left-hand side of the ring (we choose the seven particles closest to the x axis, respectively). To minimize the influence of background fluctuations of the examined image, the signals originating from those particles are weighted with a Gaussian distribution with its barycenter at the respective particle positions. For our experimental data, this results in a maximum directivity ratio of 6:1, roughly four times stronger than in previous experiments concerning the directional emission of a spinning dipole.16 In conclusion, we presented a feasible experimental scheme to verify the polarization dependent coupling of a point-like dipole to an optically denser medium and control its directivity within the full azimuthal angle. We tuned the dipole moment of a subwavelength particle via position dependent excitation with a tightly focused polarization tailored beam of light. In particular, we demonstrated, that the directive scattering of the dipole-like particle is position dependent on the subwavelength scale. This could find application in nanoscopic position sensing.
ent coupling to a planar waveguide, we utilize a slightly modified setup depicted in Figure 5. Here, the radially polarized
Figure 5. Scheme of the experimental setup, slightly altered in comparison to Figure 2. (a) The incoming radially polarized paraxial beam is now focused by an oil immersion microscope objective with NA = 1.3 onto the sample, consisting of a subwavelength gold nanoparticle sitting on a dielectric planar waveguide (Nb2O5 with thickness 40 nm and refractive index nco = 2.3). The sample is embedded in immersion oil, index matched to the glass substrate. In reflection, the sample is imaged onto a CCD camera. (b) Sketch of the sample. The central particle (exemplary electron micrograph included as inset) is utilized for coupling to the waveguide. The particles sitting on a ring with radius r = 20 μm are used as local field probes.
beam is tightly focused by an immersion-type microscope objective (NA = 1.3) onto the sample, which is now fully immersed in oil. A sketch of the whole sample and an electron micrograph of the central particle is shown in Figure 5b. The sample is designed to consist of 61 identical cylindrical gold particles sitting on the Nb2O5 waveguide. Sixty particles are placed equidistantly on a circle with radius r = 20 μm around one central particle. Because of the fabrication via e-beam lithography and the subsequent lift-off process, some of the outer particles are missing. Furthermore, they vary in size and shape. This has to be taken into account for the evaluation of the experimental data. The radially polarized input beam is focused onto the central particle, which mediates the directional coupling into the waveguide. The surrounding particles act as local field probes, scattering the light propagating in the waveguide partially into the far-field. Via imaging of the surrounding particles by using a CCD camera in reflection, the directionality of the light coupled to the waveguide by the central particle can be measured. The sample itself is again attached to a 3D piezo stage. Equivalent to the case discussed before, the dipole moment of the central particle can be tuned by its position relative to the incoming tightly focused beam.
Figure 6. Averaged images of the field probes for three different positions of the central particle relative to the excitation beam (see insets). (a) The particle is shifted 240 nm to the left of the optical axis, (b) the particle is in the center, and (c) the particle is shifted 240 nm to the right. Each image is background corrected via subtraction of a reference measurement, and resulting negative values of the intensity are omitted to increase the visibility. For better illustration of the directional coupling, the particles close to the x axis are plotted again in a magnified view in the center of each experimental image (white frames). 2550
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(16) Rodríguez-Fortuño, F. J.; Marino, G.; Ginzburg, P.; O’Connor, D.; Martnez, A.; Wurtz, G. A.; Zayats, A. V. Science 2013, 340, 328− 330. (17) Mueller, J. P. B.; Capasso, F. Phys. Rev. B 2013, 88, 121410. (18) Novotny, L.; Hecht, B. Principles of Nano-Optics; Cambridge University Press: Cambridge, 2006. (19) Banzer, P.; Neugebauer, M.; Aiello, A.; Marquardt, C.; Lindlein, N.; Bauer, T.; Leuchs, G. J. Eur. Opt. Soc., Rapid Publ. 2013, 8, 13032− 13037. (20) Quabis, S.; Dorn, R.; Eberler, M.; Glöckl, O.; Leuchs, G. Opt. Commun. 2000, 179, 1−7. (21) Debye, P. Ann. Phys. (Berlin, Ger.) 1909, 335, 755−776. (22) Richards, B.; Wolf, E. Proc. R. Soc. A 1959, 253, 358−379. (23) Lee, K. G.; Chen, X. W.; Eghlidi, H.; Kukura, P.; Lettow, R.; Renn, A.; Sandoghdar, V.; Götzinger, S. Nature Photon. 2011, 5, 166− 169. (24) Banzer, P.; Peschel, U.; Quabis, S.; Leuchs, G. Opt. Express 2010, 18, 10905−10923. (25) Lieb, M. A.; Zavislan, J. M.; Novotny, L. J. Opt. Soc. Am. B 2004, 21, 1210−1215. (26) Gebhardt, W. Z. Wiss. Mikrosk. Mikrosk. Tech. 1898, 15, 289− 299. (27) Rodríguez-Herrera, O. G.; Lara, D.; Bliokh, K. Y.; Ostrovskaya, E. A.; Dainty, C. Phys. Rev. Lett. 2010, 104, 253601. (28) Lukosz, W.; Kunz, R. E. J. Opt. Soc. Am. 1977, 67, 1615−1619. (29) Hancu, I. M.; Curto, A. G.; Castro-López, M.; Kuttge, M.; van Hulst, N. F. Nano Lett. 2014, 14, 166−171.
In addition, we extended our studies to the investigation of light emitted by a nanoparticle and coupled to a planar dielectric waveguide. Also in this scheme, we were able to precisely control the dipole induced in the particle via position dependent excitation with a polarization tailored beam. The near-field interference effect discussed in this paper is therefore promising for polarization dependent optical switching, for example in nanophotonic devices. For that purpose, the local polarization of the induced dipole could also be adapted within different near-field geometries, e.g. via suitably excited plasmonic waveguides or polarization switched and tailored fields at the tip of a tapered fiber. In general, the described experimental setup and concept is an excellent and very convenient tool to investigate more complex antenna designs. Especially, by introducing particles or antennas, which support higher order multipoles,29 even stronger directivity could be achieved via excitation with appropriately polarization tailored light fields under normal incidence.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank O. Lohse, I. Harder, and U. Mick for the inspiring discussions of the design and the fabrication of the samples utilized for the waveguide coupling experiment.
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REFERENCES
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