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Polarization-Controlled Tunable Directional Coupling of Surface Plasmon Polaritons

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Science  19 Apr 2013:
Vol. 340, Issue 6130, pp. 331-334
DOI: 10.1126/science.1233746

Controlling Light Propagation

Surface plasmons are light-induced collective electronic excitations in a metal that offer the possibility of manufacturing optoelectronic devices at nanometer scale. Before such shrinking can be achieved, the propagation direction and lifetime of the plasmonic excitations have to be controlled (see the Perspective by Miroshnichenko and Kivshar). Rodríguez-Fortuño et al. (p. 328) show how this is done using polarized light. Alternatively, using an array of metallic nanoantennae (in this case, slits) patterned into a thin gold film, Lin et al. (p. 331) present a further improvement on current plasmonic coupling schemes that has the potential to encode information contained in both the intensity and polarization of light.

Abstract

Light can be coupled into propagating electromagnetic surface waves at a metal-dielectric interface known as surface plasmon polaritons (SPPs). This process has traditionally faced challenges in the polarization sensitivity of the coupling efficiency and in controlling the directionality of the SPPs. We designed and demonstrated plasmonic couplers that overcome these limits using polarization-sensitive apertures in a gold film. Our devices enable polarization-controlled tunable directional coupling with polarization-invariant total conversion efficiency and preserve the incident polarization information. Both bidirectional and unidirectional launching of SPPs are demonstrated. The design is further applied to circular structures that create radially convergent and divergent SPPs, illustrating that this concept can be extended to a broad range of applications.

Surface plasmon polaritons (SPPs) are propagating excitations that arise from the coupling of light with collective oscillations of the electrons at the surface of a metal (1). The strong dependence of their properties on the composition and structure of the surface has led to many advances in the control of light at the nanoscale (29), holding promise for optical information technology and optoelectronics (10, 11) and for the study and engineering of light-matter interaction (12, 13).

The polarization states of the optical signal that can be coupled to a plasmonic device are often limited by the selectivity of the coupling process. For directional SPP excitation, usually only the component of the incident light that is polarized perpendicularly to either groove- or ridge-like scattering elements (in the case of gratings) or to the metal surface itself (in the case of prism-based schemes) can be coupled into SPPs (1). Light in the orthogonal polarization does not couple to SPPs, leading to a decrease in the SPP signal and a loss of information about the incident polarization state.

Additional challenges arise in controlling the direction of propagation of the generated SPPs. Poor directionality frequently represents a substantial source of noise and reduces efficiency. This has lead to the development of several schemes that couple unidirectionally, albeit with limited dynamic tunability (1416).

We present a directional plasmonic coupler that addresses these challenges by offering polarization-invariant coupling efficiency to SPPs while allowing full control over the distribution of power between two counter-propagating SPP modes. This includes unidirectional coupling and preserves polarization information.

A narrow aperture in a metal film selectively scatters incident light that is polarized perpendicular to it, giving rise to SPPs. This occurs both for light incident on the front and for light incident on the back of apertures that fully perforate the film. In the latter case, SPPs are transmitted through the apertures to the other side of the film, where they are launched across the surface. The SPP emission pattern of a subwavelength aperture is approximately that of an in-plane dipole (17), which is known analytically (18) and plotted in Fig. 1A along with the corresponding orientation of the aperture. When many such dipoles are arranged in a column with a spacing that is smaller than the SPP wavelength (λSPP), the launched SPPs are plane waves that propagate perpendicularly away toward either side of the column (Fig. 1B). This effect is independent of the orientation of the dipoles of the column. We can therefore create a source of SPP plane waves propagating in a fixed direction that can be designed to selectively respond to a polarization component of the incident light determined by the orientation of the apertures of the column.

Fig. 1 Closely spaced subwavelength apertures as polarization-selective SPP plane-wave sources.

(A) The calculated normal component of the SPP electric field launched by an in-plane dipole (in arbitrary units), which is an approximation for a subwavelength aperture in a gold film (overlay) that is scattering incident light polarized perpendicular to its long axis (polarization indicated by a red arrow). (B) The SPP waves generated by a single aperture propagate radially away from it, with wavefronts shown in black. The waves emitted from many apertures arranged in a column with subwavelength spacing interfere constructively along planes parallel to the column, shown as dashed lines. SPP wave vectors (kSPP) are shown as gray arrows. (C) Two columns of apertures (1 and 2) are positioned in parallel with spacing S. The columns couple to the field components Embedded Image (blue arrows) and Embedded Image (green arrows) of the incident field Embedded Image (pink arrow). The resulting combined SPP plane waves propagating away from the column pair (red arrows) have intensities IR and IL.

A more complex polarization response can be achieved by fabricating multiple columns on the metal surface, resulting in interference of the SPP waves created by individual columns. We consider two parallel columns (Fig. 1C) that are spaced a distance S apart and are made up of apertures with width W and length L, such that W << L < λSPP. The apertures of one column are spaced a distance D apart, with D < λSPP. The columns are offset by half a period (D/2) along their axes to reduce near-field coupling and scattering of the SPPs by neighboring apertures. With this geometry, simulations showed both effects to be negligible (19). The apertures of the first and second column are oriented at angles θ1 and θ2 with respect to the y axis. If light with an electric field Embedded Image is normally incident on the metal surface, the respective columns will then couple to the components of the incident field Embedded Image and Embedded Image that are polarized at angles 90° + θ1 and 90° + θ2. The conversion efficiency Ci of a column scales as Ci ∝ cos2 θi because the SPP emission pattern of the individual apertures is anisotropic (Fig. 1A) and only the component of the wave that is launched perpendicular to the column is not cancelled by the fields of the surrounding dipoles (Fig. 1B).

The field components Embedded Image and Embedded Image can have a relative phase δ that is preserved by the coupling process and transferred to the SPPs. If the propagation loss of the SPPs over the small distance S is neglected, interference of the SPP waves launched by each column results in time-averaged SPP field intensities propagating to the right (IR) and the left (IL) to the pair of columns (19): Embedded Image(1)where the intensities are calculated in the dielectric. E1 and E2 denote the amplitudes of the field components coupled to the respective columns and Embedded Image the SPP wave number. If Embedded Image, then Embedded Image. We make the particular choice of θ1 = 45° and θ2 = 45° + 90° = 135°, in which case the coupling coefficients of the two columns C1 = C2 = C. If we adjust the lateral spacing S of the columns with respect to the SPP wavelength to Embedded Image, Eq. 1 becomes

Embedded Image(2)

Notably, the combined intensity of the coupled SPP fields Embedded Image is proportional to the intensity of the incident light but is independent of δ and of the relative magnitude of the coupled field components E1 and E2. The total power that is converted to SPPs can thus be made independent of the polarization of the incident light. Moreover, the polarization dependence in Eq. 2 can be used to adjust the fraction of the total converted power that is propagating in the SPP waves launched either toward the left or toward the right side of the column pair by changing the polarization state of the incident light. The distribution of the intensities in the counter-propagating SPP modes as a function of polarization as predicted by Eq. 2 is shown in Fig. 2A. Here, we expressed the polarization state of the incident light in complex number representation (20) in terms of ψ and δ according to Embedded Image(3)where Embedded Image and Embedded Image are the complex amplitudes of the field components Embedded Image and Embedded Image, respectively. Unidirectional coupling occurs when the incident light is circularly polarized (E1 = E2; Embedded Image), with the direction determined by the handedness. In this way, the two circular polarization states represent two separate channels that can selectively address structures to either side of the coupler. Switchable unidirectional coupling is possible by changing the handedness of the incident light (Fig. 2A). The structure is analogous to a polarizing beam splitter with two SPP output channels because the SPP fields propagating to the left and the right correspond to the circularly polarized components of the incident light. The polarization state of the incident light is then fully encoded in the amplitude and relative phase of the SPPs.

Fig. 2 Changing the incident polarization enables continuous tuning of the directionality of the launched SPPs.

(A) Distribution of power between the SPP waves propagating to either side of the coupler as a function of the polarization state of the normally incident light according to Eq. 2. The incident polarization states are expressed in complex number notation in terms of the angles Ψ and δ (Eq. 3) and additionally shown as a black overlay. (B) Multiple parallel column pairs are spaced λSPP apart. The structure is shown such that right (left) CPL is coupled to the right (left) when it is incident from the top. (C) FDTD simulation of the near-field intensity (arbitrary units) above a coupler made up of five column pairs (white overlay) under illumination by incident light with linear and circular polarizations (pink arrows).

The cross-section of the coupler can be increased by placing several column pairs an SPP wavelength apart in the manner of a second-order grating (Fig. 2B). The side of the structure toward which each circularly polarized state is routed relative to the observer is shown in Fig. 2B.

We performed full-wave finite-difference time-domain (FDTD) simulations of the SPPs created by a group of five column pairs patterned on a gold surface for various incident polarizations. This structure was designed for operation at λ = 633 nm, corresponding to λSPP ≅ 606 nm. The geometrical parameters of the structure are S = 150 nm, D = 300 nm, W = 40 nm, and L = 200 nm. The column pairs are spaced 600 nm apart, and the thickness of the Au film is 200 nm. The results show good agreement with the predictions of Eq. 2 (Fig. 2C). Further simulation results can be found in (19).

We fabricated 10 column pairs, with S = 150 nm, D = 300 nm, W = 50 nm, and L = 200 nm in a 150-nm-thick gold film using focused ion beam milling (FIB). The devices were back-illuminated with polarized 633-nm laser light, and the SPPs were measured using near-field scanning optical microscopy (NSOM) (19). The observed field distributions are in good agreement with the theoretical model (Fig. 3). The NSOM micrographs exhibit fringe patterns that result from the interference of the SPPs with incident light directly transmitted through the film, confirming that the measured optical signal corresponds to the near-field (19). Figure 3, B to D, shows in particular that circularly polarized light (CPL) of opposite handedness generates counter-propagating SPP beams, whereas linearly polarized light (LPL) launches SPP beams of equal intensity toward either side of the coupler.

Fig. 3 Measurement of the SPPs launched by a fabricated coupler.

(A) Scanning electron microscope (SEM) image of a structure fabricated in a gold film for operation at λ = 633 nm. (B to D) NSOM images of the structure under illumination from the back by LPL (B), right CPL (C), and left CPL (D). The state of incident polarization is shown by white arrows.

This coupling scheme can be generalized by adding curvature to the column pairs on the metal surface. A coupler bent into a circle can be used to achieve radial unidirectional coupling (Fig. 4A). Depending on the handedness of the structure, the two circular polarization states result in SPPs that propagate radially toward the center of the circle (Fig. 4B) or outward (Fig. 4C). In case of unidirectional inward coupling, a high-intensity standing wave is formed within the circle, whereas the field intensity is minimal in the case of unidirectional outward coupling. LPL, as an equal superposition of left and right circularly polarized waves, results in SPPs propagating equally inward and outward (Fig. 4D). SPPs emanate from sections of the coupler oriented at all angles with respect to the incident polarization, demonstrating the polarization-invariant coupling efficiency for LPL. This feature becomes clear by comparing the properties of our structure with those of a ring-shaped groove (Fig. 4E), which is functionally equivalent to conventional SPP couplers. The NSOM image of the SPP field above the latter shows that SPPs can only be generated where the incident polarization is perpendicular to the groove (Fig. 4F).

Fig. 4 Curved structures and polarization-invariant coupling efficiency.

(A) SEM image of a circular coupler based on our design. (B) NSOM images of the coupler under right CPL, resulting in radially inward coupling, which creates a high-intensity standing wave within the circle. (C) NSOM image under left CPL, resulting in radial unidirectional coupling away from the circle and low intensity within the circle. (D) NSOM image of the coupler under LPL, which results in equal power propagating inward and outward. SPPs are generated by sections of the coupler oriented at all angles with respect to the incident polarization. (E) SEM image of a circular groove of the same radius, representative of a conventional plasmonic coupler. (F) NSOM image of the circular groove under LPL, showing generation of SPPs only where the groove is perpendicular to the incident polarization.

Our couplers may form the basis for novel plasmonic devices and can be used to both improve efficiency and lower cross-talk in plasmonic networks. The possibility of encoding the polarization information in SPPs is particularly relevant based on recent evidence that SPPs preserve quantum coherence (21), which suggests that the structure may be used to reversibly convert polarization-encoded photon qubits to SPPs. This could help to further harness the unique properties of SPPs for applications in quantum information.

Supplementary Materials

www.sciencemag.org/cgi/content/full/340/6130/331/DC1

Materials and Methods

Figs. S1 to S7

Table S1

References (22, 23)

References and Notes

  1. See supplementary materials on Science Online.
  2. Acknowledgments: Part of this work was performed at the Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Infrastructure Network (NNIN), which is supported by the NSF (under award ECS-0335765). CNS is part of Harvard University. This research is supported in part by the Air Force Office of Scientific Research under grant FA9550-12-1-0289. J.L. acknowledges the fellowship support from the Agency for Science, Technology and Research (A*STAR), Singapore. X.-C.Y. acknowledges the support given by the National Natural Science Foundation of China under grants 61036013 and 61138003, the Ministry of Science and Technology of China under grant 2009DFA52300 for China-Singapore collaborations, and the National Research Foundation of Singapore under grant NRF-G-CRP 2007-01. The authors express thanks to M. Kats (School of Engineering and Applied Sciences, Harvard University), K. A. C. Lee and Y. Zhou (Singapore Institute of Manufacturing Technology), and L. Du (Nanyang Technological University) for their assistance in the preparation of the manuscript. Data are available upon request.
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