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We report direct observation of the 2D transverse near-field intensity and polarisation distribution of surface plasmon polaritons guided on metal nanowires. Quadrupolar modes are excited on an array of coupled nanowires arranged around the central glass core in a photonic crystal fibre, with lobes whose orientation depends on the polarisation state of the launched core light. The radial electric field is resolved using a polarization sensitive near-field probe in light-collection mode.
©2012 Optical Society of America
1. Introduction
Surface plasmon polaritons (SPPs) arise at metal-dielectric interfaces as a result of collective oscillations of the electron ensemble that couples to an electromagnetic (EM) wave [1–4]. Their evanescent fields penetrate a few tens of nm into the metal and less than a vacuum wavelength into the dielectric. Power dissipation in the metal limits their propagation length to several tens of μm [5, 6]. The sub-wavelength dimensions of the transverse SPP field means that end-fire excitation is very inefficient, so that special techniques such as prism coupling [7, 8], scattering at topological surface irregularities [9, 10] or nanoscale optical antennas [11] are required to excite them. SPPs can be confined or waveguided in nano-scale metallic structures fabricated using techniques such as electron beam lithography or focused ion beam milling. Devices based on guided SPPs, such as splitters [12], switches [13, 14] and couplers [15, 16] provide new design ideas for plasmonic circuitry [17].
Scanning near-field optical microscopy (SNOM) is commonly used to directly measure the intensity distribution of SPPs. It involves bringing a nanoscale aperture [18] or a scattering tip [19] close enough to the metal surface to probe the evanescent field. In recent years polarization and phase sensitive SNOM techniques, suitable for optical characterisation of nanophotonic devices, have been developed [20–23]. These techniques have allowed EM-field distributions on the top surface of two-dimensional (2D) photonic crystal or nanoplasmonic structures to be measured in detail. However, direct measurement of the field profile and local polarisation state in the transverse plane of a SPP waveguide has not yet been reported. The main reason for this is that scanning a nm-scale waveguide perpendicular to its axis in the two transverse dimensions is practically difficult in the near-field microscopes currently used.
In this paper we report the use of SNOM to measure the transverse 2D near-field distribution and polarisation state of SPP modes on the nanoscale. The SPPs are guided on a hexagonal array of gold nanowires incorporated into the cladding of a fused silica photonic crystal fibre (PCF) with a central glass core (Fig. 1(a) ). The sample length was 900 μm, the wire radius was 325 nm and the centre-centre spacing (pitch) was 2.85 μm. A scanning electron micrograph (SEM) of the structure is shown in Fig. 1(b).
Fig. 1 Design of the device. (a) Schematic of the structure. (b) SEM of the polished cross-section of the sample with six rings of gold nanowires, making 120 in total. Dark grey is silica and light grey is gold.
We investigate plasmonic supermodes (pSMs) formed by nearest-neighbour coupling between quadrupolar (azimuthal order m = 2) SPP modes on the nanowires (each individual nanowire actually also supports m = 0 and 1 modes in the wavelength range of interest). We find that one of these pSMs, which is concentrated in the ring of six nanowires nearest the centre, can be excited by launching light into the glass core.
Using an optical fibre-based calibration technique for the near-field tips in collection mode, the local nanoscale polarisation distributions both of a single quadrupolar SPP mode and of the entire coupled nanowire array are measured. All the experimental results are in good agreement with finite-element (FE) modelling.
2. Mode analysis of the sample
The theoretically modelled near-field intensity pattern on an isolated nanowire is shown in the left-hand image of Fig. 2(a) . The wire diameters are more than 10 × larger than the skin depth of the EM-field inside the metal at optical frequencies, so that the guided SPP modes can be approximated by planar SPPs propagating on helical trajectories around the nanowire surface [24]. Guided modes are formed when the azimuthal component of the wavevector multiplied by the circumference equals a multiple of 2π. The effective index of the guided SPP mode can then be written as
where εM and εD are the frequency-dependent dielectric functions of gold and silica, m is the mode order, k0 is the vacuum wavevector and the radius of the wire is ρ. The quadrupolar SPP mode (m = 2, shown as the red curve in Fig. 2(b)) cuts off at 845 nm.Fig. 2 Operation of the gold filled PCF (a) Calculated intensity distributions (vertical polarisation of the core light) at 840 nm for: the quadrupolar SPP mode of an isolated nanowire (left, the white dashed circle indicates the gold-silica interface), the even core-pSM mode (centre) and the odd core-pSM mode (right). The scale-bar corresponds to 0.5 µm for the left-hand panel and 3 µm for the centre and right-hand panels. (b) Refractive index difference (real part) between the simulated even and odd core-pSM modes (blue and black curves) and the glass core mode in the empty PCF (grey curve): Δn = (nSM – nempty). The dashed red curve shows the same quantity for an isolated m = 2 SPP mode; it lies on top of the curve for the even core-pSM mode and cuts off at ~845 nm (red circle). The green dashed vertical line marks the wavelength (785 nm) of the laser diode used in the SNOM experiments. (c) Attenuation of the even and odd modes and of the isolated m = 2 SPP. The odd core-pSM cuts off at 890 nm. (d) Experiment (purple) and modelled attenuation (orange). The dashed purple horizontal line indicates the limit of the dynamic range of the optical spectrum analyser used.
The effective index of an isolated m = 2 SPP mode comes close to that of the glass core mode of the empty PCF, but cuts off before they can match (Fig. 2(b)). Since the coupling rate between SPP and dielectric mode strongly dominates over the dephasing rate, a pronounced anti-crossing (blue and black curves in Fig. 2(b)) forms at 840 nm. The blue branch corresponds to even modes of the coupled core-pSM system and the black branch to odd modes (Fig. 2(a) shows the intensity pattern of the even and odd). An animation of the wavelength dependence of the intensity patterns of the core-pSM modes is available online.
The attenuation of even and odd core-pSMs (see Fig. 2(c)) is a result from energy dissipation in the metal and share the same value of loss at the centre of the anti-crossing (~90 dB/mm at 840 nm). There is a decrease in loss for the odd core-pSM at long wavelengths because it cuts off at 890 nm.
All the dispersion plots and field distributions were calculated using the modal analysis package of the FE software COMSOL, including tabulated complex dielectric functions for gold [25] and silica [26].
3. Nearest-neighbor coupling model
In the previous section numerical modelling indicated that the pSMs that couple most strongly to the core have fields that are concentrated in the first ring of nanowires. To understand this behaviour better, we use a simple scalar nearest-neighbour coupling model to analyse a structure consisting of eighteen nanowires placed around a dielectric core. An inter-wire coupling constant κSPP and a core-wire coupling constant κPCF are assumed – a knowledge of the field profiles of individual core and guided SPP modes is not needed. Assuming that the core and individual guided SPP modes are phase-matched (this will occur at their anti-crossing), and that each mode couples only to its nearest neighbors, we can express the rate of change of the field amplitude in the k-th waveguide as:
where αk is the loss of the k-th mode and κkp the coupling constant between the k-th mode and its p-th neighbor. The eigenvalues of Eq. (2) yield the corrections to the propagation constant for each supermode and the values of |ak|2 yield the modal power distribution.It turns out that only two of these supermodes have a significant fraction of power in the core, and that for both these modes the cladding light is concentrated in the first ring of wires (see Fig. 3 ), all six of which are synchronous. The lowest index mode shows a phase flip of π ± ~0.01 between core and the first ring of wires, and between the first ring of wires and the second. For the highest index mode, however, all the modes are in phase to within ~100th of a radian.
Fig. 3 Solutions of the nearest-neighbour coupling model for 18 nanowires plus core. The numbers represent the percentage of modal power at each site, the color code represents the phase (red is zero, black is π): (a) the quasi-even supermode (all nodes approximately in phase); (b) the quasi-odd supermode (each ring approximately π out of phase with its neighbour).
4. Experiments and discussion
4.1 Sample fabrication
The PCF was drawn from a fused silica preform fabricated using the stack-and-draw method [27, 28]. It had a hexagonal array of sub-micrometer diameter hollow channels surrounding a central solid glass core and running along the entire length of the fiber. The nanowire array was formed by pumping molten gold into the hollow channels using pressure-assisted melt-filling [29]. A 900 μm long sample was prepared by cleaving and polishing using focused ion beam milling.
4.2 Loss measurement
The loss of the gold-filled sample (purple curve in Fig. 2(d)) was experimentally estimated by comparing its transmission spectrum [29], using a supercontinuum (SC) source, with that of an empty PCF (cut-back was not possible because the sample was only 900 µm long). This was necessary because of variations in SC intensity with wavelength. The theoretical attenuation (orange curve) is based on a superposition of the even and odd core-pSM modes, weighted so that the power in the pSM mode is zero at the fibre input, assuming a Gaussian beam incident on the core [30]. It deviates noticeably from a Lorentzian shape at the long wavelength side of the resonance, where the odd core-pSM mode cuts off. Comparing theory to experiment shows that the measured resonance position at ~840 nm is in excellent agreement with the FE simulations. The transmitted signal on-resonance was however so low that it could not be detected by the optical spectrum analyser within the range 800 to 880 nm, indicated by the horizontal dashed purple line. The width of the resonance is greater in the experiment, which we attribute to inhomogeneous broadening caused by the wire diameters not being perfectly equal. The overall increase in attenuation towards longer wavelength results from the increasing overlap of the glass core mode with the metal.
4.3 Near-field mapping of the intensity distribution
As a next step we probed the near-field distributions. The silica matrix serves as a mechanical support to hold the nanowires in place, uniquely permitting integration of the sample into a SNOM without needing to bend the nanowires upwards from a planar substrate. The SNOM used was an aperture-based customized WITec alpha300 S [31] and is sketched in Fig. 4(a) . Polarised light from a continuous-wave laser diode (785 nm, 2 mW) was launched into the glass core using a microscope objective (40x, 0.65 NA). This wavelength used represented a good compromise between too-strong loss on-resonance and too-weak core-wire coupling off-resonance. Both in-coupling objective and sample were mounted on a piezo-controlled x-y-z scanning table. The light source was not attached to the scanning table, so constant in-coupling conditions were maintained over the scanning area (10 × 10 µm) by over-filling the input aperture of the objective. Evanescent and propagating field components were collected at the output end of the sample using a nanoscale aperture (<60 nm diameter). This probe (a silicon cantilever with a hollow pyramid [31]) was brought into physical contact with the sample surface. The sample was then scanned laterally, permitting the near-field to be probed with 60 nm spatial resolution. After tunnelling through the hollow channel in the cantilever, light was converted to far-field radiation, collected by another objective (20x, 0.45 NA) and finally detected using an avalanche photodiode (APD). Optionally, we could place an additional linear analyser between output objective and APD.
Fig. 4 Experimental setup, SNOM results and FE-modeling of the near-field without analyser. (a) Sketch of the experimental set-up for the SNOM measurements (for details see text). LD: laser diode, P: polariser, λ/2: half-wave plate, O1-O2: microscope objectives, C: cantilever, A: analyser, L: lens, I: iris, APD: avalanche photo-diode. Experimentally measured near-fields and simulated FE results at 785 nm for (b) vertical and (c) horizontal polarisation of the PCF core mode (indicated by the white double-headed arrows). The white dashed circles show the gold-silica interface and the white dashed squares indicate the position of the nanowires. The purple arrows on the FEM plots show the direction of the local transverse electric field at a fixed moment in time (upper and lower plots taken together). The color bars show the correct scale for the lower images only. The upper images are saturated for a better contrast.
Transverse scans of the near-field at the end-face of the fibre for vertical and horizontal input polarisation are shown in Figs. 4(b) and 4(c) for 785 nm excitation wavelength without analyser. For both polarisation states, quadrupolar mode patterns are clearly seen on each nanowire in the first ring. The residual light between the nanowires results from cladding modes excited at the input of the sample. According to the above discussion, the quadrupolar patterns result from excitation of a pSM consisting of six coupled quadrupolar SPP modes. Depending on the input polarisation state, the lobes of these SPP modes are rotated relative to each other in a particular arrangement, in perfect agreement with the FE simulations.
The close-ups in Figs. 4(b) and 4(c) show the patterns of the same wire for the two polarisation states. It can be seen that for the vertical case, the lobes of the SPP mode are aligned along the line connecting the centres of PCF core and wire, while for horizontal polarisation the lobes are rotated by 45° relative to this line.
Some nanowires show an intensity pattern on the surface of the wires, e.g., see the top left-hand image in Fig. 4(c). These patterns may be caused by excitation of standing-wave SPP resonances on the end-faces of the wires.
Between 820 nm and 880 nm no light was observed either in the core or on the nanowires – a result of the large on-resonance attenuation (>70 dB over the sample). For λ < 750 nm light was observed only in the glass core, the wires remaining dark, as expected since the pSM mode is not phase-matched to the core mode in this range.
When we repeated the same experiment without a cantilever, light was observed only in the glass core mode, the nanowires remaining dark. This is as expected, since the very fine nano-scale features in the near-field are unable to radiate into the far-field.
4.4 Polarisation-resolved experiment
As a next step we measured the local polarisation state of the near-fields both for the whole structure and for the m = 2 mode on a single nanowire. Before making these measurements, we first determined the polarisation properties of the hollow SNOM-cantilevers in collection mode using a fibre-based calibration technique. To determine the polarisation eigen-axes, modes with predefined polarisation states were generated by replacing the gold filled sample with a polarisation maintaining (PM) PCF. The total transmission for both modes (i.e., without analyser) was then measured to check if the tips had a preferred transmission axis. In a second step, an analyser was inserted between cantilever and APD to establish whether the polarisation state of the PM-fiber mode was maintained along this axis in the far-field. The polarisation properties of the tip depended strongly on the actual shape of the aperture – an effect that has also been reported for transmission-mode SNOMs [32]. We found that 10% of the cantilevers maintained the local near-field polarisation in the far-field, while all of them had a preferred polarisation axis. The cantilever used had a polarisation discrimination of 50:1 with a difference in transmission between the two orthogonal polarisation axes of 50%.
When such a polarisation-maintaining cantilever was used, we found that the local transverse near-field polarisation state could be directly transferred into the far-field without any scrambling. We then repeated the near-field measurements on the gold filled sample for vertical input polarisation state, an additional analyser being inserted between output objective and detector (see Fig. 4(a)).
Figure 5 shows the measured and calculated near-field intensity distributions at the end-face of the fibre. When the transmission axes of analyser and input light are parallel (Fig. 5(a)), the pSM patterns in the ring are strongly modified compared to those in Fig. 4(b), while the glass core mode remains almost unchanged. A close-up scan of the top wire (same as in Fig. 4(b)) shows that light is transmitted only from the upper and lower field lobes, while the left- and right-hand ones are blocked. This means that the electric field vectors in the upper and lower lobes are either parallel or anti-parallel, i.e., they oscillate either in- or out-of-phase. When the analyser is rotated by 90° relative to the vertical input polarisation (Fig. 5(b)), the core mode vanishes (some residual light is seen, resulting from cladding modes), distinct near-field features remaining in the vicinity of the wires. These features are linked to the evanescent fields of the left- and right-hand lobes of the SPP modes, as visible in the close-up in Fig. 5(b). The two weak additional lobes below the nanowire result from the excitation close to resonance, and are not present in an isolated m = 2 nanowire mode. All the measured near-fields (even the weak lobes just mentioned) are in excellent agreement with FE-simulations.
Fig. 5 Polarisation-resolved near-field measurements and FE results at 785 nm for vertical input polarisation. The logarithmic intensity profiles of the modes are shown for two orientations of the analyser relative to the vertical input polarisation: (a) parallel configuration (b) orthogonal configuration (indicated by the yellow double-headed arrows). The modes shown in this figure correspond to the one shown in Fig. 4 (white dashed circles/squares, white double-headed arrows and color scale are the same).
To obtain the local polarization of the near-field an additional measurement was performed with the analyser oriented at 45° to the horizontal axis. This measurement, together with the patterns from two other analyser positions (Fig. 5), gave sufficient information for unambiguously determining the transverse polarization state of the SPP modes. The orientations and amplitudes of the electric field vectors are shown in Fig. 6(a) as white double-headed arrows overlaid on the intensity pattern of Fig. 4(b). Inside one lobe the electric vectors are oriented approximately radially, their length being longest in the regions of highest intensity. This is in very good agreement with the simulations (Fig. 6(b)), and shows that we are able not only to reliably super-resolve the near-field of a SPP mode, but can also measure its local transverse polarisation state. Note that the axial field component of the SPP cannot be resolved because the cantilever is an aperture sprobe and to first order transmits only the local transverse fields.
Fig. 6 Spatially resolved polarisation state of the near-field of a quadrupolar SPP mode. (a) The white double-headed arrows show the orientation of the electric field vectors (90 nm spacing) for the SNOM measurement, their lengths being proportional to the absolute value of the transverse electric field. For clarity, no arrows are shown at regions where the intensity is low. The red double-headed arrow shows the input polarisation state. (b) FE-simulations showing the local transverse electric field at a fixed moment in time. The underlying intensity patterns are the same as the two upper left-hand images in Fig. 3(b).
4. Conclusion
In conclusion, gold-filled PCF offers the possibility of measuring near-fields across nanowires, and allows easy excitation of SPP modes in nanowire arrays. By careful characterisation of hollow cantilever tips, it is possible to measure the local polarisation state of light in the near-field well below the Rayleigh resolution limit. The polarisation-resolved near-field technique described is likely to be useful in many areas of nanophotonics.
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