Surface plasmon polaritons (SPPs) are two-dimensional (2D) electron density oscillations along a metal/dielectric interface resulting from an interaction between free photons in the dielectric and free electrons in the metal . SPPs decay exponentially with distance away from the interface, but propagate along the interface, being subject to ohmic and radiation losses . Since their discovery in the 1950s [3, 4], SPPs have found a broad range of applications, such as waveguiding , light trapping for photovoltaic solar cells [5–9], surface-enhanced Raman scattering (SERS) [10, 11], plasmon rulers , localized surface plasmon resonance bio/chemical sensing [11, 12], and plasmonic circuits , among many others . Accompanying the still-growing number of applications of SPPs is an increased understanding of their underlying physics. Spatial mapping techniques of SPPs are playing a major role in in-depth investigations of SPP properties [15, 16]. Due to the hybrid optical-electronic nature of SPPs, they can be excited by either photons or electrons. This fact leads to two branches of spatial mapping techniques, namely, optical mapping and electrical mapping. Due to the fast speed of SPPs and the relatively slow speed of existing spatial mapping techniques, standing wave patterns (e.g., 2D cavity modes) of SPPs need to be established in order to capture or image their wave nature. Thus, optical and electrical mappings of SPP cavity modes have become the standard techniques for SPP investigations .
We review the state-of-the-art in optical and electrical mapping techniques for SPP cavity modes. We start with a brief summary of SPP excitation schemes in Section 2, given their close relation to detection techniques. We then review in Section 3 near-field scanning optical microscopy (NSOM) as a major spatial mapping technique of SPPs. Several recently published works, including our own contribution of the plasmonic halo effect, are described in some detail to illustrate the NSOM mapping technique. In Section 4, another near-field mapping technique, fluorescence-based SPP mapping, is introduced, along with several engaging examples. Finally, we discuss in Section 5 electrical mapping techniques for SPPs, including electron energy loss spectroscopy (EELS) and cathodoluminescence (CL) microscopy. Other SPP mapping techniques, including leakage radiation microscopy (LRM) [18–22] and dark field imaging  for local SPP field intensity mapping, are not described in this review.
2 Excitation of surface plasmon polaritons
Before delving directly into the spatial mapping techniques of surface plasmon cavity modes, it will be useful to briefly review SPP excitation methods. The hybrid optical-electronic nature of SPPs leads to two branches of excitation schemes, namely, via photon coupling and via electron coupling. We organize this section according to these two schemes in a chronological manner. In general, a particular plasmon mapping technique works well with a specific SPP generation scheme. Typically, a mapping technique is the downstream development of the corresponding SPP excitation technique. In the following, we will give a brief summary of various methods of SPP excitation, including critiques on them and their interfaces with the plasmon mapping techniques, especially the NSOM technique.
2.1 Photon coupling
SPPs cannot be excited directly by injecting photons on a perfectly flat metal/dielectric interface, due to a momentum mismatch between SPPs and freely-propagating photons . Since the early 20th century, various methods have been developed to compensate for this mismatch in order to, in the language of optics, achieve phase-matching.
2.1.1 Prism coupling
Prism coupling provides phase-matching by sending light into a medium with higher refractive index (relative to air or free space, e.g., a glass prism) before engaging the metal/air interface, as shown in Figure 1(A). This scheme is also called attenuated total internal reflection. In 1968, Kretschmann  and Otto  demonstrated their own prism coupling schemes, which are now widely used in optical SPP generation, and SPP-based biosensing . Figure 1(A) shows the Kretschmann scheme on the left, and the Otto scheme on the right. The advantages of the prism coupling technique are that it can achieve very high coupling efficiency between photons and SPPs, and that it can be easily integrated with the NSOM technique to serve as an SPP source for NSOM probes. As a result, it is one of the most widely used SPP generation schemes for NSOM measurements. The drawback is that it is not easy to achieve local SPP excitation by this technique.
2.1.2 Grating coupling
Another route to achieve phase-matching is by gratings on metal surfaces. For a 1D grating with periodicity a, the reciprocal vector (G=2π/a) provides the needed momentum for SPP launching, as sketched in Figure 1(B). The pioneering work of Ebbesen et al. of extraordinary optical transmission through subwavelength hole arrays  can actually be explained by the excitation of SPPs on the periodic arrays . Devaux et al. used 2D subwavelength holes on a metal film for SPP generation and detection . Gratings can also be used as out-couplers for SPPs to freely-propagating photons. Park et al. have shown out-coupling of SPPs to photons using a dielectric grating with few-nanometer depth with an efficiency of about 50% . Radko et al. systematically studied the efficiency of local SPP excitation on 1D periodic ridges . Like the prism coupling scheme, the grating coupling scheme is a mature technique now widely adopted as an SPP source in NSOM experiments. Compared to prism coupling, the grating coupling scheme allows one to define a much better confined region as the SPP source. However, it is still not well focused enough for many nanoplasmonic applications. In the following, we show several more localized optical coupling schemes.
2.1.3 Highly focused beam coupling
A microscope objective of high numerical aperture (NA) together with immersion oil can be used to generate SPPs at its focal point . As shown in Figure 1(C), incident photons are focused by the lens with NA=1.4, through immersion oil index-matched to the metal surface, where SPPs are generated and propagate out. A lens with NA>1 is used to ensure that the lateral component of the wave vector of the incident photon matches that of the excited SPPs, i.e., to achieve phase-matching. This works in the reverse way of leakage radiation microscopy. The advantage of this coupling scheme is that it conveniently works for white (broadband) incident light , although usually a single frequency laser is used as light source. The measurement techniques for SPPs generated by a highly focused beam are usually fluorescence mapping and LRM , due to the possible issue of an NSOM probe blocking the incoming beam.
2.1.4 Near-field coupling
While the above coupling schemes are, in principle, subject to the diffraction limit of light, the spatial extent of near-field coupling of SPPs with a sharpened metallic tip or tapering metal aperture is defined by the dimensions of the excitation tip itself, which can be made to be much smaller than the excitation wavelength . By squeezing photons through an aperture smaller than the SPP wavelength, they acquire enough lateral momentum to couple to SPPs. Figure 1(D) shows a typical setup for near-field coupling of SPPs, where photons are first coupled to the metallic aperture via an optical fiber, then converted to SPPs on the sample surface. As will be discussed in Section 3, the transmission-mode NSOM works in the reverse process of near-field coupling .
2.1.5 End-fire coupling
Instead of providing a phase-matching mechanism, end-fire coupling couples photons into SPPs by matching their spatial field profiles. In doing so, it maximizes the probability of photons coupling to SPPs. Figure 1(E) shows a schematic of the end-fire coupling method. This scheme can reach high coupling efficiency , and is also highly compatible with the conventional fiber optics technique . Chang’s theoretical work shows single photon coupling to SPP by this scheme [35–37]. Maier also demonstrated wave guiding with a tapered optical fiber and metal nanoparticle chains with 75% efficiency .
2.1.6 Step-gap leakage coupling
As a special case of a leakage coupling scheme, Ye et al. (present authors) recently developed a step-gap leakage coupling method . As shown in Figure 1(F), the step-gap structure consists of a dielectric support layer with refractive higher than 1 (here, PMMA), an optically-thick top metal layer (Ag) and a base metal layer connected by an optically-thin metal film, forming a step-gap. Photons are injected from the bottom side of the structure. Optically-thick top and base metal layers preclude the direct transmission of photons through the device, such that the only path is through the step-gap. When photons from the dielectric side leak through the step gap, they acquire enough momentum to excite and couple to SPPs along the top surface of the base metal layer. Thus, the step-gap leakage scheme defines a localized SPP source, with minimum requirements for collimation of the input light source. It also naturally separates input photons from the out-coupled SPPs, optimizing the signal-to-noise ratio in subsequent SPP measurements . As will be discussed in detail later, the step gap leakage scheme can be easily designed to excite SPP cavity modes. As a result, the step-gap leakage scheme of SPP generation works seamlessly with a conventional NSOM under collection mode.
An advantageous aspect of the step-gap leakage structure is ease of fabrication. By using the photoresist PMMA as the supporting dielectric step layer, a lengthy PMMA lift-off process was avoided, and by utilizing the quasi-directional nature of sputter deposition to form the thin metal layer along the step-gap, multiple metal depositions were avoided. The fabrication procedure is thus succinct, with ~1/2 h of sputtering, and electron beam lithography (EBL) dominating the total time consumption (several hours for large area writing patterns). For testing purposes, with relatively small EBL patterns (~1 mm2 writing area), the fabrication process takes <2 h.
2.2 Electron coupling
2.2.1 Fast electron coupling
The fact that fast electrons (with energy usually above 1 keV) bombarding metal thin films generate bulk and surface plasmons played an important role in the early stages of understanding SPPs. A typical fast electron SPP generation process is sketched in Figure 2(A). Powell and Swan’s observation using EELS of fast electrons bombarding on aluminum thin films  served as the first experimental proof of Ritchie’s theory of surface plasmons . Later, Teng and Stern coupled fast electrons to a periodically-corrugated metallic surface for more efficient SPP launching, with the metallic gratings also serve as photon couplers for SPPs . Heitmann also demonstrated similar effects in 1977 . In recent years, as a highly localized SPP generation scheme, fast electron coupling has attracted increasing attention. Bashevoy et al. demonstrated the excitation of SPPs by electron beam bombardment in 2006, coupling the SPPs out as photons by a grating some distance apart . García de Abajo et al. have demonstrated SPP generation by energetic electron incidence [42–44]. A more recent work by Liu et al. in 2012 demonstrated SPP generation by coupling fast electrons to metal surfaces with a grazing incident angle , as sketched in Figure 2(B).
2.2.2 Electron tunneling
In contrast to the high-energy bombardment method for SPP launching, a low-energy route based on inelastic electron tunneling was first reported by Lambe and McCarthy, with roughened metal-insulator-metal (MIM) junctions . The reason tunneling electrons with very low energy electrons (on the order of 1 eV) can still excite SPPs is that the highly localized tunneling process is inelastic . The inelastic tunneling process generates localized surface plasmon gap modes, which then couple into propagating SPPs , as sketched in Figure 2(C). Scanning tunneling microscopy (STM) turned out to be the ideal tool to explore this effect. A major difference between STM and optical excitation of SPPs is that STM generates a wide range of frequencies ν (with hν smaller than tunneled electron energy) at once, while optical excitation usually works at a single frequency . Gimzewski  and Coombs  were the first to observe light emission from tunneled electrons in STM. Recently, Palash et al. demonstrated propagating SPPs along a gold nanowire excited on one end by tunneling electrons from the STM tip . Generally speaking, metallic NSOM probes can be used to generate SPPs anywhere on conducting surfaces, through the electron tunneling scheme. The electron tunneling scheme, together with the near-field optical coupling scheme, makes the NSOM technique the preferred generator of SPPs on all sorts of surfaces.
2.2.3 Hot electron coupling
Recent theoretical work by Kempa shows that hot electrons generated in a semiconductor  can couple their excess free energy into an adjacent metal surface in the form of SPPs . By comparing electron-phonon and electron-plasmon coupling probability amplitudes, he concluded that hot electrons are more probable to couple to surface plasmons. Thus, hot electrons can also serve as potential SPP sources. The schematic drawing of the hot electron-SPP coupling process is shown in Figure 2(D).
3 Mapping surface plasmon cavity modes by near-field scanning optical microscopy
3.1 Background and theory
Near-field scanning optical microscopy (NSOM) is a powerful technique to investigate SPPs along a metal-air interface, due to its sub-diffraction limited spatial resolution . The acronym NSOM was proposed by Lewis , but the technique is also called scanning near-field optical microscopy (SNOM) . When working in so-called collection mode, with SPPs excited by the Kreschtmann configuration, NSOM is also referred to as photon scanning tunneling microscopy (PSTM) . The latter term emphasizes the similarity with the electron scanning tunneling microscope (STM) . A comprehensive review of the different existing near field configurations can be found in books by Novotny  or Courjon .
In a typical NSOM measurement, a sharp optical probe (with or without an aperture) is first brought into close proximity with a metal sample surface, then raster scanned across the surface while keeping a constant distance (usually below 100 nm) to map out the local electric field intensity over the scanned area. Typical NSOM scans therefore map out the local electric field intensity distribution. Recent work by Denkova et al. also demonstrated the mapping of magnetic near field distributions, via plasmonic nanoantennas by an aperture-less probe  (details of this work will be discussed in Section 3.2).
The probe-sample distance is a key factor in near field microscopy . Probe-sample distance is controlled by a feedback system based on interaction forces normal and/or lateral to the sample surface, borrowing from now standard atomic force microscopy (AFM) techniques . Unlike most commercial AFMs, NSOM generally cannot introduce an optical auxiliary feedback mechanism, due to its sensitivity to environmental illumination. Mechanical feedback methods for NSOM include the shear-force methods  and the piezoelectric force detection by quartz tuning fork techniques . In both cases, the probe is excited at its mechanical resonance frequency and caused to approach the sample surface. When the lateral/normal force between the probe and the sample surface is large enough to be sensed, an abrupt change in the amplitude or phase of oscillation of the probe serves as a good reference for subsequent control of the probe-sample distance . A more detailed summary of the feedback methods is given in the book by Novotny .
The most common NSOM probes are uncoated fiber probes , aperture probes , sharp-tipped metal probes  and metallic nanoparticle probes . The optical fiber probes are usually fabricated by heating and pulling  or chemical etching  of optical fibers. Metallic probes are usually chemically etched using techniques taken from the STM field . The optical resolution of NSOM can beat the diffraction limit of light being, in principle, restricted only by the physical dimensions of the probe end . Uncoated optical fiber probes can be made to 80 nm in diameter , and aperture probes typically have 40 nm-diameter aperture sizes . Some reports showed that the resolution can be as high as 15 nm in the case of metallic probes .
Conventional SPP excitation schemes for NSOM measurements include prism coupling (Kreschtmann configuration) , grating coupling , NSOM probe coupling , and interactions between a metallic probe and a sample . As introduced in Section 2, the step-gap leakage SPP generation scheme provides a controllable localized SPP source for NSOM probes, without strict requirements on the incident light source. Due to the slow scanning speed of NSOM, to capture the wave nature of SPPs along a metal surface, one needs to find ways to create SPP cavity modes [74–76], also called SPP standing waves. Otherwise, the detected signal will be smoothed out by the time averaging of the fast-propagating SPPs. In many cases, obtaining an NSOM scan of the SPP cavity modes can serve as direct proof of the existence of SPPs in the studied system.
3.2 Experimental realization
In recent years, the rapid development of near-field scanning techniques has facilitated the emergence of high-level research activities on NSOM mapping of SPP cavity modes. When choosing the application examples among thousands, we focus on the recent progress of NSOM mappings of SPP cavity modes, with clear measured NSOM data, and/or novelty and importance in the experiments carried out. We also try to cover a wide variety of problems studied by NSOM, presenting one example in each aspect. We provide here only a brief summary of the many selected works, leaving a more detailed discussion of the authors’ recent work on NSOM mapping of SPP cavity modes within a circular step-gap  to the next section.
Kwak et al. imaged SPP standing waves between periodic nano-holes on a metal surface . Shortly after that, Gao et al. showed that by varying the metal film thickness, the SPP standing wave pattern changes from SPP-SPP interference to SPP-photon interference , thus giving direct evidence for the SPP as the origin for the observation of extraordinary optical transmission through subwavelength holes discovered by Ebbssen et al. . Figure 3 shows the NSOM mapping of SPP standing wave patterns. Figure 3(B) shows the SPP-SPP interference pattern that arises when the gold film is 125-nm thick, with negligible direct tunneling of photons through the film. Figure 3(C) shows the SPP-photon interference pattern when the gold film is thin enough (75 nm) for direct photon tunneling through the film.
Liu et al. studied SPP cavity modes inside an area defined by symmetric circular and elliptical slits , demonstrating that such structures can behave as plasmonic lenses for SPP focusing, as shown in Figure 4. They also found that the measured electric field by NSOM is primarily the parallel component of the SPP, and confirmed their results by numerical simulations. Figure 4(C) shows the NSOM mapping of an SPP cavity mode inside a circular slit 14 μm in diameter fabricated on a Ag layer of 150 nm thickness. Figure 4(D) is an AFM scan of the plasmonic lithography pattern (recorded in photoresist under 365 nm UV exposure) of an elliptical slit with a 4 μm long axis and a 2.5 μm short axis, milled in an Al layer with 75 nm thickness.
Later, Babayan et al.  proposed an optical version of the quantum corral [80, 81]. By measuring the fields inside circular and elliptical corrals using an NSOM system, they found that the fields depend on the geometry and local dielectric environment of such corrals. In the circular corrals, only certain wavelengths produced constructive interference, creating a bright spot in the center, while in the elliptical corrals, the eccentricity was said to have suppressed or enhanced the focal points. Figure 5(A) shows an SEM image of the elliptical corral with different eccentricities, e=0.60 and 0.75, from top to bottom, respectively. Figure 5(B) shows the measured fields by NSOM inside the elliptical corrals for different wavelengths, 457 nm circularly polarized light incidence. Figure 5(C) is the calculated fields inside the corrals using these same eccentricities and wavelength.
In 2010, Fang et al. demonstrated plasmonic focusing in symmetry-broken circular corrals with NSOM observation . They demonstrated that it is possible to focus the SPP into a spot smaller than the diffraction limit using a symmetry-broken corral under linearly polarized incidence because of SPP interference. The interference pattern can be controlled by changing the polarization and the degree of symmetry-breaking. Figure 6 shows an SEM image of the symmetry-broken corral (left) and the near field image acquired by NSOM in the same structure (right), when linearly polarized light is interacting with the structure. The direction of the electric field is indicated by the arrow.
Recently, Lin et al. demonstrated polarization-controlled tunable directional coupling of SPPs . Using a special set of apertures arranged in a specific geometry, they showed that it is possible to control the propagation direction of the generated SPPs by controlling the polarization of the incident light. Photons with circular polarization couple to unidirectional SPPs, launching the SPPs to the left for clockwise polarization, and to the right for counter-clockwise polarization . Their specific geometry also allows recovering the common bidirectional SPP coupling for linearly polarized light. Figure 7(A) shows an SEM image of the proposed coupler winding in a circular shape. Figures 7(B) and (C) show the measured field by NSOM for clockwise and counter-clockwise circular polarizations, respectively. Figure 7(D) is the case for linear polarization with direction indicated by the arrow.
Finally, Denkova et al. demonstrated the mapping of lateral magnetic near field distributions of plasmonic nanoantennas . Using aperture probes in NSOM, they used the strong coupling of the probe-sample system to induce an effective magnetic dipole that generates surface plasmon resonances only at lateral magnetic field maxima. In the experimental results appears a spectral mismatch that can be explained by the difference between real conditions of the experiment, i.e., geometry, dielectric constants and roughness in both the sample and probe, compared with the ideal case used in the numerical simulations. Figure 8 shows a comparison between experimental and numerical results, top and bottom, respectively, for a 1120 nm long nanoantenna using the wavelengths indicated by the number above each image. The labels l=2, l=3, l=4 and l=5 are the predicted modes in each wavelength.
3.3 Plasmonic halos: mapping of the SPP drumhead modes via NSOM
As introduced in Section 2, the step-gap leakage SPP coupling scheme provides a convenient way to locally excite SPPs with a macroscopic light source. As a specific example, let us consider curving the step-gap into a circular shape. The metal surface surrounded by the step-gap then forms a circular drumhead for 2D SPP waves. By scanning the NSOM tip on the surface of the metal drumhead, one can map out the SPP drumhead modes .
The drumhead mode profiles can be calculated from the 2D Helmholtz equation governing the dynamics of SPPs: (∇2+kSPP2)Ez=0, with Ez the vertical electric field, kSPP=k0(ε0εAg/(ε0+εAg))1/2 the SPP propagation constant in the x−y plane, and k0 the free space wavenumber. By separation of variables, we obtain the resonant condition for the SPP drumhead modes: Ro=ρm, nλSPP/2π, with ρ≡rkSPP, ρm, n being the mth zero-crossing of the nth Bessel function of the first kind: Jn(ρ). The resonating dimensionless normalized radius ρm, n can be calculated for various m, n combinations, e.g., for m=1, n=0, ρ10=2.40.
We first showed the excitation of SPP drumhead modes on the SPP drumheads implicitly via the effect of SPP modulated transmission. As shown in Figure 9(A) and (B), the transmission minima of a circular step-gap array form branches as one increases the radius of the circular cavity. The fact that these branches of transmission minima coincide with the SPP drumhead mode branches indicates that the transmission spectra are modulated by SPP drumhead modes. This transmission modulation by SPP drumhead modes produces color tuning of the circular step-gaps, yielding attractive “plasmonic halos” , some of which are shown in Figure 9(C).
We then carried out NSOM scans to selected SPP drumheads along the SPP drumhead mode branches, with a linearly polarized 660 nm laser as the excitation source. Due to the polarization property of our laser, the n=1 drumhead modes are excited. As shown in Figure 9(D) and (E), the theoretical calculations match well with the measured electric field intensities. These NSOM mappings give direct proof of the excitation of SPP drumhead modes.
The transmission modulation effect is perhaps better illustrated by the full wave electromagnetic simulations, where one sees that when SPP drumhead modes are excited, far field radiation is minimized, as demanded by energy conservation. In contrast, when SPP drumhead modes are not excited, far field radiation is maximized. For more detailed discussions on transmission modulations of the circular step-gap structures, the reader is referred to the paper by Ye et al. .
3.4 Summary and outlook
NSOM is a scanning probe-based technique for spatial mapping of the near electric field profile of relatively planar samples. NSOM has been proven to be a powerful technique for direct mapping of the near field profiles of SPP cavity modes. SPPs excited by different schemes, confined in various cavity shapes, such as circular, elliptical, asymmetrical, and rectangular, have been measured by NSOM. Our proposed step-gap coupling scheme for SPPs is shown to be a convenient way to generate SPP cavity modes with different cavity geometries, and highly compatible with the NSOM measurement technique. The step-gap design combined with the traditional bottom illumination scheme gives a controllable local SPP source, enhancing the signal-to-noise ratio of detected SPPs.
It is important to note that although the NSOM technique is a unique and powerful tool, it can be very time consuming, and the measurements are rather complicated using research or commercial systems. In this framework, it would be advantageous to develop techniques that allow access to the information contained in the near field by indirect methods in an inexpensive and real-time way. Our group is working in this direction, by integrating leakage radiation microscopy with the step-gap SPP generation scheme. Progress on that front will be published elsewhere.
4 Mapping surface plasmon cavity modes by fluorescence techniques
Unlike the previously described techniques (NSOM), nano-sized emitters such as semiconductor quantum dots or fluorescent molecules can be directly placed in the vicinity of the enhanced electric field of SPPs, to serve as real time local indicators of the SPP field intensity. A prominent advantage of the fluorescence techniques is a short image acquisition time (as compared to scanning-based techniques such as NSOM), enabling one the ability of capturing real time dynamics of SPPs [84, 85]. Two counteracting processes occur when fluorescent molecules are in the vicinity of metal structures: (1) enhanced fluorescence emission by the enhanced local electric field and (2) quenched fluorescence by non-radiative decay in the metal. Kramer et al. observed the first process by showing fluorescence enhancement for molecules placed near metal nanotips . Dulkeith et al. showed the quenching effect of gold nanoparticles . Anger et al. provided a comprehensive description of these two processes, by investigating the fluorescence rate of a single molecule as a function of its separation from a spherical gold nanoparticle . They concluded that when the separation is too small, the quenching effect dominates, killing the fluorescence; when the separation is too large, the near-field enhancement is too weak to enhance fluorescence. There is thus an optimum separation between fluorescent molecules and metal surfaces for maximized fluorescence enhancement. This separation is usually achieved by coating a thin dielectric layer on the metal surface before fluorescent molecule engagement.
By using the above dielectric spacer technique, Ditlbacher et al. demonstrated the fluorescence mapping of propagating SPPs generated by focusing a laser beam on metal nanowires and nanoparticles . As shown in Figure 10(A) and (B), Ag nanoparticles and nanowires were fabricated by EBL on a 70 nm thick Ag film; a 10 nm SiO2 layer was coated on top to serve as the dielectric spacer to prevent quenching; a sub-monolayer of Rhodamine 6G fluorescent molecules was then coated on top of the SiO2 layer to map the SPP field profiles in real time. Figure 10(C) and (D) show the fluorescence mapping of the interference between SPPs generated by two Ag nanoparticles, aligned parallel and perpendicular, respectively, to the polarization direction of incident light.
Recently, Xu’s group has shown beautiful applications of fluorescence mapping of SPP modes along single-crystal metal nanowires [85, 89, 90]. By using CdSe@ZnS quantum dot emitters (QDs) with 30 to 50 nm Al2O3 spacer layer, Wei et al. demonstrated interferometric optical logic gates based on intersecting Ag nanowires (NWs) . By tuning the relative phases between two highly focused incident laser beams on two joining Ag NWs, controllable ON-OFF states on the far end of one of the NWs are achieved. Subsequent work by Wei et al. showed good control of the SPP mode profiles along Ag NWs by tuning the radius of the Ag NW, the thickness of the Al2O3 layer, and the embedding environment, as shown in Figure 11 . Based on the same technique, Zhang et al. have demonstrated the excitation of SPP chiral modes along Ag NWs . Fluorescence images of various SPP chiral modes were obtained along a Ag NW with tuned input polarization. They concluded that the SPP chiral modes are a result of interference between different orders of plasmonic modes along the Ag NW. Since for Ag NWs with small enough radii, only the first order SPP mode (TM0) is supported, with higher order modes cutting off, the excitation of SPP chiral modes can only be seen on relatively thick Ag NWs (about 150 nm in radius).
5 Mapping surface plasmon cavity modes by electron beams
As introduced in Section 1, electron impinging is another major method (besides optical excitation) for SPP generation. As a result, scanning-mode electron microscopes (both SEM and STEM), combined with electron energy loss spectroscopy (EELS) or cathodoluminescence (CL) analysis, are becoming more popular for SPP cavity mode mapping. Due to rapid development in the precise control of electron beam emission, electron microscopes now reach unprecedented spatial resolution (sub-Angstrom) and energy span (from ~1 eV to 300 keV) . Thus, no other existing technique can match EELS or CL in combined space-energy resolution . A recent comprehensive review on this subject by Garcia de Abajo is available . Here we give a brief summary focusing on the spatial mapping aspect of EELS and CL.
5.1 Electron energy loss spectroscopy
Since the first demonstration by Hillier and Baker , EELS has become standard in electron microscopy, in both TEM and SEM. EELS detects material properties by engaging electron beams with the sample, and recording the energy loss spectra of the incident beams. When an energetic electron beam passes through a thin metal film, parts of its energy and momentum couple to the free electron gas, forming bulk and surface plasmon modes [3, 4]; parts of those couple to core electrons, exciting electron-hole pairs, while parts couple to very-low-energy excitations (e.g., phonon modes), resulting in the major zero-loss peak (ZLP) of unscattered electrons . Excitations of bulk plasmons and SPPs belong to the low energy loss region of EELS. In the early stage of the development of SPP theory, EELS of aluminum thin film  served as the first experimental proof of Ritchie’s surface plasmon theory .
EELS has been used to detect SPPs since the mid-20th century. However, the application of EELS to spatial mapping of SPP cavity modes has only emerged in recent years , thanks to maturing techniques in precise control of emission and detection of electron beams. As shown in Figure 12(A), conventional EELS works in transmission mode, by sending energetic electron beams through thin-film samples. EELS can also work in reflection mode (when integrated with a SEM and detecting thick samples), called REELS [94–96], as shown in Figure 12(B).
Nelayah et al. demonstrated the EELS mapping of SPP cavity modes on a Ag nanoprism for frequencies ranging from infrared to ultraviolet in 2007 . The EELS experiment was done in an STEM, on a 10 nm-thick single-crystal Ag triangular nanoprism with side length of 78 nm, supported by a mica layer. Figure 13(A) and (B) show the measured and simulated SPP cavity modes on the Ag nanoprism, at three different frequencies. Each SPP spatial map consists of 32×32 resolutions, with each resolution point corresponding to an EEL spectrum subtracted by the ZLP. For a mapping at a selected frequency, the EELS signal is translated to a color at each resolution point. Figure 13(C) shows spatial mapping with the EELS fitted by Gaussian parameters, showing a better localized spatial distribution.
EELS is also shown to be an ideal tool for measuring dark (nonradiative) SPP modes . Figure 14(A) schematically shows the dark and bright modes within a symmetric metallic dimer as a result of plasmon hybridization. While the lower energy bright modes can be directly excited by incident photons, the higher energy dark modes can only be excited electrically due to their anti-symmetry properties. By measuring EELS on a Ag nanoparticle dimer, Koh et al. showed the excitation of both bright and dark modes. As shown in Figure 14(B), when electron beam is incident on position A, both bright and dark modes are excited, resulting in two peaks at 2.2 and 3.3 eV. When electron beam is incident on positions B1 and B2, bulk plasmon modes are excited, with energy of 3.8 eV. When electron beam is at position C, only dark modes are excited, with energy 3.4 eV, as the bright mode is symmetry-forbidden.
First discovered in the mid-19th century as light emission stemming from cathode (electron) rays impacting a glass substrate, cathodoluminescence (CL) is now widely used as a material characterization technique in mineralogy, semiconductor physics, and many other fields . The most extensive industrial application of CL was as the emission source in CRT monitors, before the LCD, LED, etc. display eras .
CL includes direct and indirect emission processes. The main direct emission processes involved in CL are Cherenkov radiation and transition radiation. Cherenkov radiation happens when a charged particle (electron) moves in a transparent medium, with speed v faster than the phase velocity of light in that medium (v>c/n), and is thus mainly observed in dielectrics and not in metals . Transition radiation is emitted if a charged particle passes through a boundary between two media with different dielectric constants . It is generated by the time-dependent interaction between the incident charge and its image charge in the other dielectric. This effect was first predicted by Ginzburg and Frank  and observed by Goldsmith and Jelly  for metals.
The observation of bulk and/or surface plasmons via electron bombardment is an indirect process of CL. Bulk plasmons and/or SPPs are excited when traveling electrons couple to the free electron gas of a metal. SPPs then couple out as free-propagating photons through properly designed gratings on metal surfaces. Thus, this electron-SPP-photon process is an indirect CL process. The first observations of light emission from SPPs were done by Teng and Stern .
A schematic of a typical electron microscope coupled with a CL collection system is shown in Figure 12(B). The parabolic mirror has a through hole on the top for electron beam passage. It is designed to be confocal with the electron beam, so as to maximize the collected optical signal. Out-coupled light is usually detected by a spectrometer . For the purpose of spatial mapping of SPP cavity modes, an optical signal at a selected wavelength suffices. Spatial mapping is realized by scanning the electron beam across the measured sample. CL usually has a poorer signal-to-noise ratio than EELS, but it has the unique property of probing local optical properties of a sample . Several examples of CL SPP cavity mode mapping have been presented over the last few years. The following includes some representative examples.
Barnard et al. imaged the hidden modes of ultrathin plasmonic strip antennas by CL  in 2011. A 30 keV electron beam is injected on a 20 nm thick Ag wedge with tuning width from 200 to 700 nm. The Ag wedge is deposited on a silicon-on-insulator substrate. CL image corresponding to a free-space wavelength of 700 nm is shown in Figure 15. The formation of the measured SPP cavity mode pattern is attributed to the interference between the short-range SPPs and the long-range SPPs, with simulation details shown in Figure 15(C) and (D).
Yu’s group has been using CL to map out SPP cavity modes within ultra-smooth metal cavities with various shapes [104–106]. As shown in Figure 16, plasmonic triangular nanocavities with ultra-smooth surfaces were fabricated by a template stripping method . High quality CL mappings were obtained due to the smoothness of the SPP cavities. Using the same technique, Zhu et al. mapped SPP cavity modes within open circular cylinder cavities for SPPs via CL . They also investigated the control of SPP cavity modes by tuning of the height of the cylindrical cavity. Later, they also measured the vertical SPP cavity modes within a vertical nanocavity .
Vesseur et al. measured the SPP whispering gallery modes via CL within circular grooves in a gold surface [107, 108]. Such resonators with various geometries were fabricated by focused-ion-beam milling. A 30 keV electron beam was used to generate CL spectra. SPP whispering gallery mode mappings with angular quantum numbers m=0, 1, and 2 are obtained. More recently, by measuring the asymmetric SPP cavity modes within elliptical metal cavities via CL, Schoen et al. have demonstrated that surface plasmon physics can be employed to realize a planar broadband unidirectional parabolic antenna at optical frequencies . The CL SPP cavity mode mapping is also shown to be representing the local density of optical states (LDOS) across the Ag wedge. Sapienza et al. have recently shown the determination of the LDOS of dielectric (Si3N4) photonic crystals by CL .
Beginning with various excitation schemes for SPPs, we have reviewed current mapping techniques for SPP standing wave cavity modes. We have also shown the connection between the excitation schemes and mapping techniques for SPPs. SPPs can be excited by both photon and electron injection, and thus can be spatially-mapped by both optical and electrical methods. Optical schemes include NSOM mapping, fluorescence mapping, LRM mapping, dark-field mapping; electrical schemes include EELS mapping and CL mapping. SPP spatial mapping techniques provide direct evidence and fundamental information toward a deepening understanding of surface plasmon physics. With the continued development of nanofabrication and nanocharacterization techniques, SPP spatial mapping will continue to play an important role in the plasmonics community.
This work was supported by the W.M. Keck Foundation.
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