Direct characterization of plasmonic slot waveguides and nanocouplers
Andrei Andryieuski, Vladimir A. Zenin, Radu Malureanu, Valentyn S. Volkov, Sergey I. Bozhevolnyi, Andrei V. Lavrinenko
DDirect characterization of plasmonic slot waveguides and nanocouplers
Andrei Andryieuski, ∗ Vladimir A. Zenin, † Radu Malureanu, Valentyn S. Volkov, Sergey I. Bozhevolnyi, and Andrei V. Lavrinenko DTU Fotonik, Technical University of Denmark,Oersteds pl. 343, DK-2800 Kongens Lyngby, Denmark Centre for Nano Optics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark (Dated: November 7, 2018)We demonstrate the use of amplitude- and phase-resolved near-field mapping for direct charac-terization of plasmonic slot waveguide mode propagation and excitation with nanocouplers in thetelecom wavelength range. We measure mode’s propagation length, effective index and field distri-bution and directly evaluate the relative coupling efficiencies for various couplers configurations. Wereport 26- and 15-fold improvements in the coupling efficiency with two serially connected dipoleand modified bow-tie antennas, respectively, as compared to that of the short-circuited waveguidetermination. [This document is the unedited Author’s version of a Submitted Work that was subse-quently accepted for publication in
Nano Letters , c (cid:13)
American Chemical Society after peer review.To access the final edited and published work see http://dx.doi.org/10.1021/nl501207u .] Keywords: nanocoupler, surface plasmon, slot waveguide, nanoantenna, s-SNOM, near-field microscopy
Great advantages offered by plasmonics to opticalwaveguiding are extreme subwavelength localization ofguided modes close to the metal interface together withelectrical tunability of electromagnetic waves via intrin-sic metallic contacts . Plasmonic waveguides are there-fore considered as a future generation of optical intercon-nects in integrated circuits for datacom technologies . In-evitably, with the appearance of nanoscale waveguides, anew challenge has emerged: how to effectively couple thediffraction-limited optical waves into deep-subwavelengthplasmonic waveguides. Various approaches have beenutilized ranging from lenses to grating couplers . How-ever, the most compact solution is, an antenna basednanocoupler.Antenna is a common tool to capture free-spacepropagating radio-waves with more than a century-long history . Employment of metal-based antennasin photonics started only in the last two decades ow-ing to the progress in high-resolution nanofabricationtechniques . Usage of plasmonic antennas to cou-ple light to plasmonic waveguides has been suggestedtheoretically and then confirmed experimentally withcross-polarization microscopy measurements in the near-infrared and with near-field microscopy in optical ,telecom and mid-infrared ranges. Nevertheless,the amplitude- and phase-resolved measurements of the antenna-excited slot plasmons in the telecom range (withthe free-space wavelength around 1.55 µ m) have not beenreported so far. It should be emphasized that the us-age of phase -resolved near-field mapping is indispensablefor direct characterization of the mode effective index aswell as for revealing the symmetry of excited plasmonicmodes .In this Letter we report, for the first time to our knowl-edge, the amplitude- and phase-resolved near-field char-acterization of plasmonic slot waveguides and antennabased nanocouplers in the telecom wavelength range. Il-lumination with a wide laser beam excites both slot plas-mons confined within a dielectric gap in a metal film andsurface plasmon polaritons (SPP) propagating along themetal film interface perpendicular to the slot, and theresulting near-field interference pattern is mapped witha scattering-type scanning near-field optical microscope(s-SNOM). The observed interference pattern undergoesthen the special filtration procedure in order to extract individual characteristics of the slot mode, including theeffective index and propagation length, and its relativeexcitation efficiency, which is determined as a ratio be-tween the slot mode intensity at the waveguide input andthe average SPP intensity. Experimental characteriza-tion of two serial dipole and modified bow-tie antennasas well as the short-circuited waveguide termination inthe absence of any coupling device is related to mod-elling of these configurations, including calculations ofpropagating mode fields and effective areas.We use a plasmonic slot waveguide (also known asa gap or channel waveguide), representing a rectangu-lar slot of width W WG = 300 nm carved in a gold filmof thickness H = 50 nm. Such a waveguide featuresboth reasonably good mode confinement and propaga-tion length. In a symmetric dielectric environment, thepropagation length can reach few tens of micrometers attelecom wavelengths. We, however, select an asymmet-ric configuration (Figure 1a, inset) that allows one to a r X i v : . [ phy s i c s . op ti c s ] S e p FIG. 1. (a) Effective indices of the slot waveguide mode (black solid line), gold-air (green dashed) and gold-silica (blue dotted)SPPs together with the propagation length of the slot mode (red dash-dotted). (b) Effective index (black) and propagationlength (red dash-dotted) of the transmission line waveguide mode depending on the wire width W CO . Two serially connected(c) dipole and (d) modified bow-tie antennas. Insets in (a) and (b) show cross-sections of the correspondent waveguidesgeometry and total electric field magnitude distributions of the plasmonic modes. directly map plasmonic mode-field distributions with asharp probe tip of the s-SNOM. The drawback of suchconfiguration is the energy leakage from the slot modeto the slow SPPs on the silica-gold interface (the effec-tive index of the latter is larger than that of the former).The leakage losses add up to the Ohmic losses in the plas-monic waveguide, resulting in the propagation length of2.5 µ m (Figure 1a). However, simulations indicate thatit is sufficient to fill the slot space and add an additional50 nm thick layer of silica on top in order to eliminatethe leakage losses and increase the propagation length upto ∼ µ m. For comparison, the propagation lengths ofthe air-gold and silica-gold SPPs are 230 µ m and 63 µ m,respectively, at the wavelength 1.55 µ m.In our previous work we showed that the serial con-nection of the antennas provides no benefits for theslot excitation with the tightly focused Gaussian beam,whereas it is an opposite case for the incident plane waveor wide Gaussian beam used in our experimental setup.It is, therefore, important to ensure the optimal connec-tion between the nanoantennas to deliver maximum ofthe incident energy to the waveguide. The effective in-dex and propagation length of the double-wire transmis-sion line depends on the wire width W CO (Figure 1b).Smaller losses correspond to wider wires, but wide wiresconnected to the antenna would prohibit efficient plas-mons excitation. It is therefore better to increase thewidth of the connecting wires in the regions between theantennas, while keeping them narrow otherwise. In orderto check the advantage of wider wires we compare thin-wire-connected dipole antennas (Figure 1c) with mod-ified bow-tie antennas that feature widened wire sec-tions between them (Figure 1d). To prevent the wideregions from out-of-phase plasmons excitation, we tunethe length of the wide sections out of the resonance.Numerical simulation and optimization of thenanocouplers for operation at the wavelength of 1.55 µ m(see Supporting information for details) was carried out in CST Microwave Studio . For the plane wave exci-tation (normal to the substrate in our case), the figure-of-merit of the antenna, which characterizes its couplingefficiency and which is used as an objective function dur-ing optimization, is its effective area defined as the ratioof the power delivered to a waveguide mode to the in-cident power flux A eff = P WG /S inc . The effective areaof one (1DA), two (2DA) and three (3DA) dipole an-tenna couplers was calculated and found being consider-ably and progressively larger than that of the open cir-cuit waveguide termination (0DA) (Figure 2, Table I). Atthe same time, the operation full-width-at-half-maximum(FWHM) bandwidth of the 3DA coupler is smaller thanthat of the 2DA one. This fact agrees with the usual FIG. 2. Effective area of open circuit waveguide (0DA, blacksolid), one (1DA, cyan short-dashed), two (2DA, red dot-ted) and three (3DA, green long-dashed) serial dipoles, short-circuited waveguide (0BA, grey dash-dotted) and two serialmodified bow-tie (2BA, orange dash-double-dotted) antennas.It is seen that the effective area A eff increases with the num-ber of antennas. The values A eff at the wavelength of 1.55 µ mare collected in Table I. TABLE I. Bandwidth of the nanocouplers and their effectivearea at the optimization wavelength 1.55 µ m .Design A eff ( µ m ) Bandwidth ( µ m)0DA 0.00701DA 1.19 0.302DA 2.09 0.393DA 2.61 0.220BA 0.081 0.382BA 1.23 0.62 trade-off between antenna efficiency and bandwidth. Theadvantage of larger plasmon propagation length in widerconnecting wires does not compensate for worse plasmonexcitation due to interaction of metallic bars with theantenna elements and their detuning as well as counter-phase slot plasmons excitation in the modified bow-tie(2BA) antennas, resulting in ∼ ∼ A eff at the wavelength 1.55 µ m (Table I).The nanocouplers were fabricated using standardelectron-beam (e-beam) lithography followed by metal e-beam evaporation and lift-off in acetone (see Supportinginformation for details).Phase- and amplitude-resolved near-field characteriza-tion of the plasmonic antenna nanocouplers was carriedout using the s-SNOM configuration, based on an atomicforce microscope (AFM) with cantilevered tips being em-ployed as near-field probes (NeaSNOM from NeaspecGmbH) (Figure 3). In our experiments, we used stan-dard commercial Si tips covered with platinum (ArrowNCPt, NanoWorld). The AFM was operated in the tap-ping mode, with the tip oscillating at the mechanicalresonance frequency Ω ≈
250 kHz with the amplitude of ∼
50 nm. Near-field and topography mapping was per-formed by moving the sample across the aligned configu-ration of the oscillating tip and the illumination system.Therefore, in order to continuously excite the antenna,we illuminated the structures from below (transmission-mode s-SNOM ) with a defocused polarized laser beam(the estimated FWHM illumination spot was ∼ µ m).The light, scattered by the tip, was collected by a top FIG. 3. Schematic of amplitude and phase near-field map-ping with the transmission s-SNOM set-up. The sample isilluminated from below with a defocused laser beam (FWHM ∼ µ m) polarized parallel to the dipole antenna. TheAFM metal-covered silicon tip scatters the near field (pre-dominantly its vertical component), and the scattered radi-ation (being collected by the top parabolic mirror) is thenmixed with the reference beam and interferometrically de-tected, yielding amplitude and phase near-field distributionsby scanning the sample. parabolic mirror and directed towards a detector, whereit was spatially overlapped with an interfering referencebeam, yielding both the amplitude and phase of thescattered light via pseudo-heterodyne detection . Back-ground contributions were suppressed by demodulatingthe detector signal at a high-order harmonic frequency n Ω (in our case n = 2), providing background-free near-field amplitude and phase images. It should be pointedout that, in most s-SNOM experiments, the illumina-tion is done in the reflection mode (side-illuminationscheme), where the incident light is focused on the tipwith the same parabolic mirror that collects scatteredlight, a configuration that creates many problems for ob-taining clear near-field images due to strong tip-samplecoupling and phase-retardation effects . However, inour transmission-mode configuration, the sample was il-luminated from below with an in-plane direction of po-larization, allowing us to achieve uniform illuminationand efficient excitation of the plasmonic antenna whileavoiding the direct tip excitation . Due to a dom-inating dipole moment of the tip along its axis (i.e.,along the z -axis), the recorded s-SNOM images repre-sent mostly a distribution of the amplitude and phase ofthe z -component of the electric field, E z . In order toenhance this selectivity, a polarizer in front of the de-tector was set to select the out-of-plane z -polarization oflight scattered by the tip. Finally, the recorded data weretreated with free (scanning probe microscopy) softwareGwyddion .The recorded optical amplitude and phase images (Fig-ure 4b,c) exhibit a complex interference pattern, pro- FIG. 4. Pseudocolor s-SNOM images, representing (a) topography, (b) amplitude, (c) phase, and (d) real part of the rawoptical near-field distribution. Amplitude, phase, and real part of the decomposed contributions of (e-g) SPP background and(h-j) slot mode fields.FIG. 5. Pseudocolor s-SNOM images, representing (a) topography, filtered (b) amplitude, and (c) real part of measured near-field data, and filtered (d) amplitude and (e) real part of simulated field for all three types of nanocouplers: 2DA (left), 2BA(middle) and 0BA (right). Electric field of the slot mode is normalized to the average amplitude of the background SPP. Thescale bar is equal to 1 µ m. duced mainly by the slot waveguide mode and SPPs. Thelatter are excited with the incident wave being diffractedon the slot, and propagate away from and perpendicularto the slot waveguide. Due to the large (defocused) exci-tation laser spot, adjusted with the AFM tip during thescan, the SPP amplitude and phase do not significantlychange along the waveguide, as opposed to those of theslot mode. One can therefore decompose the recordedraw near-field data (Figure 4b-d) in the half-space con-taining the waveguide into the SPP background (Fig-ure 4e-g) and slot mode (Figure 4h-j) fields by fitting thedata along the waveguide as a sum of propagating modeand a constant background (see Supporting informationfor details). Thus filtered images reveal the propagat-ing slot mode with the decreasing amplitude (Figure 4h)and linearly advancing phase (Figure 4i) of E z field. Asexpected from the mode field distribution (Figure 1a, in- set), E z field magnitude is zero in the middle and oppo-site in sign on both sides of the waveguide (Figure 4j).The filtering procedure was applied to all measure-ments (see Supporting information for more details)made in the telecom range (1.425-1.525 µ m) and to allthree types of antenna nanocouplers: 2DA, 2BA, and0BA (Figure 5b-c). Numerically simulated E z field dis-tribution at the height of 50 nm above the structure (theaverage position of the s-SNOM tip) was filtered withthe same procedure (Figure 5d-e), signifying very reason-able agreement with the experimental results. We shouldmention that phase images not only allow observing slotplasmon phase evolution, but also reveal information onthe impedance matching of the antennas to the waveg-uide.The filtered images of the slot mode allowed us to es-timate the effective mode index, propagation length and FIG. 6. (a) Wavelength dependence of the coupling efficiencyof different type of antennas: 0BA (grey, circles), 2BA (or-ange, stars), and 2DA (red, rhombs), represented as effec-tive area for numerical calculations (lines) and as normalizedintensity for experimental results (points). (b) Wavelengthdependence of the experimentally measured effective modeindex (black circles) and propagation length (red squares),compared with numerical simulations (lines). intensity of the slot mode at the waveguide entrance (Fig-ure 6) normalized to the average intensity of the SPPbackground, which does not significantly depend on thewavelength in the range of 1.425-1.525 µ m. Thus normal-ized slot mode intensity is expected to be proportionalto the nanocoupler effective area I slot at x =0 ∼ P WG ∼ A eff .The validation of such approach is supported by thecomparison of simulation results (lines) with experimen-tal results (points), shown in Figure 6a. The effective in-dices determined from the experimental (filtered) phaseimages (Figure 5c) were found in good correspondencewith the calculated ones (Figure 6b), while the exper-imentally obtained propagation lengths turned out be-ing slightly smaller than the calculated ones (Figure 6b),most probably due to the fabrication imperfections. Onemay notice small oscillations in the experimentally mea- sured values, which, we believe, represent a systematicerror due to degradation or a drift in our setup, sincea sequence of measurements for each antenna was 1475-1425-1525-1500-1450 nm, which correlates well with theerror in propagation length and effective index (Fig. 6b).In conclusion, we have demonstrated the useof amplitude- and phase-resolved near-field mappingfor complete characterization of the complex plas-monic waveguide configuration including antenna-basednanocouplers and slot waveguides. The s-SNOM charac-terization allowed us not only to make relative compar-ison of the efficiencies (in terms of the effective area) ofdifferent couplers, but also to measure the effective in-dex and propagation length of the slot waveguide mode.All experimental data were found being in a very goodcorrespondence with the numerical simulations. We havealso confirmed that the serially connected dipole anten-nas represent the most efficient (for the excitation witha wide light beam) and simple design of nanocouplers.We would therefore anticipate that the serial antennasnanocouplers will become efficient optical interfaces be-tween macroscopic light sources and nanoscale waveg-uides. We also believe that the s-SNOM-based character-ization procedure described here will become a standardrobust technique for the plasmonic waveguide character-ization due to its high resolution, reliable measurementsand efficient data filtration procedure. Acknowledgments
A. A. acknowledges financial support from the DanishCouncil for Technical and Production Sciences throughthe GraTer project (Contract No. 0602-02135B). V. A.Z., V. S. V. and S. I. B. acknowledge financial sup-port from the Danish Council for Independent Research(the FTP project ANAP, Contract No. 0602-01507B)and from the European Research Council, Grant No.341054 (PLAQNAP). The authors also acknowledge J.Rosenkrantz de Lasson for a useful discussion on numer-ical simulations, G. Biagi, T. Holmgaard, J.-S. Bouillardand A. V. Zayats for discussions on near-field character-ization and an anonymous reviewer for useful comments.
Supporting Information Available
Details on numerical simulation and optimization, thefabrication procedure, filtration procedure for experi-mental and simulated field distributions. This mate-rial is available free of charge via the Internet at http://pubs.acs.org . Author Contributions
A. A. and V. Z. contributedequally. ∗ [email protected] † [email protected] Gramotnev, D. K.; Bozhevolnyi, S. I.
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