Metal-dielectric transitions are important structures that can display a host of optical characteristics including excitation of plasmons. Metal-dielectric discontinuities can furthermore support plasmon excitation without a severe condition on the incident angle of the exciting photons. Using a semi-infinite thin gold film, we study surface plasmon (SP) excitation and the associated electromagnetic near-field distribution by recording the resulting plasmon interference patterns. In particular, we measure interference periods involving SPs at the scanable metal/air interface and the buried metal/glass one. Supported by optical near-field simulations and experiments, we demonstrate that the metal/glass surface plasmon is observable over a wide range of incident angles encompassing values above and below the critical incident angle. As a result, it is shown that scanning near-field microscopy can provide quantitative evaluation of the real part of the buried surface plasmon wavevector.
© 2011 OSA
Photon excitation of surface plasmons [1–3] in nanostructures is the core mechanism by which many plasmonic systems are to be utilized [4–8]. The optical excitation of surface plasmons (SP) may be carried out in prism-based configurations [2,3], or by periodic [9–11] and aperiodic roughness , or by local discontinuities [12–15]. Salomon et al first reported on the local excitation of SP in the vicinity of a gold edge . Using Scanning Near Field Optical Microscopy (SNOM), the aim of our work is to demonstrate the potential of a single gold edge to excite SP modes by characterizing the range of edge-induced plasmon-photon coupling and the ensuing interference at the exposed as well as the buried metal-dielectric interfaces. Near-field microscopy techniques have been utilized to image plasmonic interference patterns in the Kretschmann configuration, between propagative and counter propagative plasmon waves at the scanable interface of a thin continuous film by Passian et al , and of thin metal stripes by Weeber et al . Seidel et al  also reported the observation of interference between SP waves excited with a single groove. Due to the experimental configuration, the observation was restricted to the metal/air SP resonant angle excitation. More recently Aigouy et al  reported on near-field measurements of the same phenomenon using a couple of slits to excite propagative and counter propagative waves. All these works benefit from the subwavelength resolution of the optical scanning near-field microscopy to deepen the understanding of the SPs at the scanable interface.
In this article, by direct and simultaneous observations in the near-field of the SP modes at both interfaces, i.e. the metal/air (m/a) interface and the buried metal/glass (m/g) interface, we study the optical response of both metal-dielectric interfaces of a semi-infinite thin film. We therefore employ a gold edge as in  to excite SPs at both interfaces without incident angle restriction. On the contrary to nanostructured thin films, such as gratings, where the patterning affects the plasmonic response, the presented structure was chosen because of its close similarity with continuous thin films. Numerical simulations and near-field observations are realized for various incident angles, below and above the critical angle in order to obtain a large angular description of the photon plasmon coupling due to the discontinuity. In Section 2, we present the numerical technique employed to describe the various optical modes of the discontinuity. The setup used for the experimental measurements of the modes is described in Section 3 followed by a discussion of the results in Section 4. Concluding remarks are given in Section 5.
2. Numerical work
The scattering of the incident light from the metal-dielectric structure studied can be simulated numerically using the Differential Method (DM) . The solutions provide the amplitude of the diffracted waves as a function of associated wavevectors. Thus, the complex amplitude of the nth diffracted wave in the region above the sample plane may be analyzed as a function of the real part of the tangential wavevector providing information on the nature of the excitations involved. In short, this technique yields the diffracted electromagnetic field [10,12]. Our primary interest here is to obtain a direct estimation of the real part of the resonant wavevectors of the structure. The simulation domain of the DM and the assumed boundary conditions are shown in the inset of Fig. 1 .
Since DM is primarily suitable for simulations of periodic structures, such as gratings, we deliberately choose a very large period (with respect to the excitation wavelength) to neglect SP modes overlapping and resonances introduced by the numerical periodicity. The simulations are performed at λ = 632.8nm (as in the experiment) with a metal/period ratio of 1/2 for a period of 128µm. The dielectric function of gold for a photon wavelength of 632.8 nm is εm = −13.2 + 1.08i obtained by interpolation from reported experimental data in .
The simulations are performed for different incident angles from 30° to 65°. The modulus of the complex amplitude of nth transmitted wave versus the normalized value of the parallel wavevector ( with ) is plotted in Fig. 1 for three different incident angles (40°, θSP, and 60°). In this work, we refer to θSP, as it is defined following the Kretschmann configuration for thin fully continuous films, and theoretically estimated and shown in the inset of Fig. 2 . With the representation in Fig. 1, peaks are associated with the resonant response of the structure. Several peaks are observable and clearly identified in Fig. 1. The peaks are associated with the real part of the SP wavevectors at both interfaces, implying propagating in the positive and negative directions (each value is pointed at a fixed position for the different incident angles). The SP wavevector values are analytically evaluated from the dispersion relation of a single boundary metal/dielectric interface :Fig. 1, is associated with the incident beam wavevector projected on the sample plane. The value calculated from shifts to the large positive wavevectors with an increase of the incident angle. The real part of the SP modes wavevectors are estimated for uncoupled interfaces. The peaks obtained from the numerical simulations presented here confirm that the system supports resonant waves associated with the SP modes at both interfaces are excited without incident angle restriction. In fact, due to the diffraction phenomenon at the local discontinuity, the wavevector is no longer conserved. Hence SP modes at both interfaces are resonant, excited without critically depending on the incoming wave wavevector.
3. Experimental setup
In order to carry out measurements of the scattered fields using a scanned probe, we consider the collection of information on the manner by which the metal-glass transition, that is, the change in the measured field over the glass area versus that over the metal, contributes to the scattering. This constitutes the optical response of the metal-dielectric transition. The structure considered here is fabricated by vacuum evaporation of a 55 nm thick gold semi-infinite film on a glass substrate. The resulting m/a edge is made by optical lithography followed by lift-off. As depicted in Fig. 2, the sample is illuminated through a hemicylindrical glass prism (n = 1.46), with a collimated He-Ne laser beam (λ = 632.8 nm). The incident beam polarization is controlled by the combination of a linear polarizer with a half-wavelength plate, allowing the m/a edge to be illuminated with either a p-polarized (perpendicular to the edge) or s-polarized (parallel to the edge) light. The incident beam angle θ with respect to the normal is controlled by a precise micromechanical rotational stage. Incident angles in the range from 30 degrees (below the critical angle) to 60 degrees are studied.
Thereafter, a near-field probe, in form of a pulled optical fiber with a 20 nm apex, is brought and scanned in the vicinity of the sample utilizing a scanning near-field optical microscope (SNOM) with shear force feedback. This feedback allows one to maintain a constant probe-sample distance as indicated by the z-direction in Fig. 2. Here we note that in general the shear force feature requires a close approach to the surface in comparison to techniques with direct optical feedback as in Photon Scanning Tunneling Microscope (PSTM) [16,17]. The optical signal is then collected via the near-field optical probe and directed to a photomultiplier tube (PMT).
4. Results and discussions
The described probe-sample configuration allows a simultaneous measurement of the topography and the optical fields. The probe position with respect to the m/a edge can thus always be readily determined. To experimentally determine θSP measurements were carried out far away from the edge taking into account the roughness of the structure, as well as the near-field probe influence . Figure 3 illustrates near-field measurements at different incident angles including θSP.
In Figs. 3(a) and 3(b), we present images of both the glass and gold surfaces at an incident angle of 60 degrees. The topographic image Fig. 3(a) confirms the 55 nm thickness of the film well and further analysis of selected profiles from this image yields an average roughness of about 1 nm. In the associated optical image given in Fig. 3(b), a maximum intensity is detected at the m/a edge, with various oscillations of distinct periods observed on both glass and gold sides. These periods in the range of a few hundreds of nanometers up to tens of micrometers can be predicted from calculation, which will be described thereafter. To capture the various observed periods, the scan sizes, and therefore the spatial resolution, were adjusted accordingly. To enhance the image contrast, the measurements were carried out a few micrometers away from the discontinuity, where the diffractive contributions due to the discontinuity  are less. These contributions arise due to scattering of the portion of the light, which lack the appropriate properties to couple to the edge plasmons. While not the focus of this work, we anticipate that some excited plasmons may couple to radiations due to the presence of the edge contributing to the total diffracted components.
Figures 3(c) and 3(d) show measurements for a p-polarized incident beam with angles of 55 degrees and θSP, respectively. Moreover, we record images for s-polarization as illustrated in Fig. 3(e) at θSP, in order to assure excitation of plasmon. Figure 3(c) highlights periods close to 4.5 µm and Fig. 3(d) a period around 1 µm, whereas Fig. 3(e) gives no particular periods. Fourier transform analysis of the images and image line profiles were used to quantitatively obtain the periods of the observed oscillations. We note that, at θSP, we expect to observe a higher degree of the thin film plasmon response in the measurements. This can indeed be seen in Fig. 3(d) at the spatial location indicated by the arrow, where a small bump had been observed in the topographic image (not shown). The optical near-field is very sensitive to the sample surface properties due to the confinement of the plasmons at the interfaces. The slight distortion seen in the interference pattern at this location can thus be due to the plasmon scattering at the location of the bump.
In order to discern the various resonant wavevectors of the fields contributing to the formation of the measured interference patterns, we rely on the numerical investigations for the used structure.
To compare the experimental and numerical results, we begin by noting that the oscillations in the field intensity measured by the probe over the sample may be linked to interference between the various resonant waves induced by the discontinuity (see Fig. 2). Four different waves are discerned; the incident wave of wavevector the back reflection of the incident wave at the prism/air interface (), the m/a and m/g SP waves ( respectively). The values of and are defined by and the two SP wavevectors with Eq. (1). The intensity calculated using the above four waves, exhibits modulation terms due to the interferences between the waves . An analysis of this modulation shows that the intensity variations are due to six periods. However, even though the interferences between the waves associated with and are identified over the glass (one of the above six periods) and are still observable over the metal, the other predicted interferences from the reflection of the incident wave and the different SP waves are not detected. This is explained by the very low amplitude associated with the reflection of the incident wave. We therefore experimentally detect only four periods, labelled by and given by where is the difference between the real part of the considered wavevectors projected on the sample plane. These periods are given by:Fig. 4 present the interference periods calculated as a function of the incident angle. In this figure, the measured periodicities for selected angles (symbols) have been superimposed on the theoretically predicted curves. As one can clearly see, each experimental point appears in good agreement with those obtained from calculations.
Furthermore, we note that Λ4 provides a true calibration of our experimental setup including the piezoelectric scanner and the precision on the angle position control. Moreover, the results demonstrate the SNOM capability to register the shortest periodicities of about 300 nm expected in this experiment. As  reports m/a SP excitation at incident angles higher than θSP, we complement the previously reported results showing the m/a SP excitation (Λ1) at incident angles below θSP.
In addition, the interference periods Λ2 and Λ3 are both associated with the m/g SP mode propagating at the buried interface. At the precise angle θSP, we clearly observe a specific interference period around 1 µm marked in Fig. 4. Note that under this condition, becomes equal to consequently the interference period Λ1 becomes infinite and Λ2 equals Λ3, corresponding to the case of a fully continuous thin film. Therefore, at θSP, these particular interference forms allow the experimental determination of the period of the interference associated with the m/g SP mode. However, the Fourier transform analysis of experimental data and the numerical simulations confirm that the interference between both SP modes is realized over the whole range of incident angles.
Finally, we demonstrate that the interference period measured at θSP, associated with Λ2 and Λ3, results from interferences involving the buried m/g SP. This is a “true” experimental observation of a buried SP, that also permits the experimental estimation of the real part of the to be (1.63 ± 0.08) which is comparable to the theoretical value of 1.59 calculated from Eq. (1).
In conclusion, by scanning near-field optical microscopy of a semi-infinite thin film, we have clearly imaged surface plasmon modes of both interfaces; the accessible surface and more interestingly the buried metal/glass interface. Various interference periods associated with the metal/air surface plasmons are demonstrated over a large angular domain, below and above the critical angle. Similar to other symmetry breaking scattering processes, the investigated discontinuity provides the conditions for “broadening” the range of available momenta for the plasmon-photon coupling. As a result, plasmon excitation can also occur below the critical angle that is normally associated with the case of fully continuous film, that is, one without the studied discontinuity. Moreover, at the metal/air plasmon resonance angle, a specific period stands out for the buried metal/glass surface plasmon. Wavevectors corresponding to angular value of θSP permit an experimental observation and a quantitative evaluation of the real part of a buried surface plasmons wavevector using near-field technique. This approach opens up new opportunities to deepen studies on the surface plasmon dispersion relation in semi-infinite and continuous thin films and on the possible coupling between surface plasmons of both interfaces. The Surface Plasmon Resonance (SPR) sensing, while a fairly mature technology, might benefit from the presented results. SPR, as an analytical tool for many biological and chemical investigations such as reaction rate measurements, antigen-antibody reactions etc can potentially profit from similar well-designed discontinuity structures that may provide complementary information on the changes associated with the index of refraction of the biological/chemical coating. The ability to analyze the buried plasmons may help achieving better sensing since the m/g plasmons are not exposed to the coating environment but rather coupled to the m/coating interface plasmons.
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