## 2 Types of SNOM Methods  
Any monochromatic light field can be represented by a vector field \(E(r)\) (similarly for the magnetic component, \(H(r)\) containing components \(A_{m}(r)\) and \(\varphi_{m}(r)\) that represent the spatially dependent amplitude and phase of the vector components of the field (\(m=x\), \(y\), \(z\) in Cartesian coordinates). The field can be represented by a set of waves of the form shown below. \[E(r)=\int\limits_{-\infty}^{+\infty}E_{k}e^{ikr}\mathrm{d}k \tag{1}\]  
where \(r\) represents spatial position, and each wave in the set is defined by its wavevector \(k\) and complex amplitude \(E_{k}\). For a given far-field distribution in a non-absorbing medium with real index of refraction \(n\), wavevector \(k\) is real with an amplitude defined by \(k_{o}=\sqrt{k_{x}^{2}+k_{y}^{2}+k_{z}^{2}}=2\pi n/\lambda\), and wavelength in vacuum, \(\lambda\). However, if \(k_{x}^{2}+k_{y}^{2}>k_{o}^{2}=\omega^{2}/c^{2}\), then \(k_{z}\) must have a non-zero imaginary component. From Equation (1), any imaginary components within the far-field wavevector \(k\) will result in an exponentially decaying amplitude. A light wave defined by such exponential decay is termed an evanescent wave, and it experiences an exponential decay in amplitude moving away from its originating location. The exponential decay in the propagation direction away from the originating surface has the consequence of localizing the near-field to the originating emitter structure or interface (within a distance less than 100 nm from the surface), which also results in the light field near a surface being dominated by evanescent light [8]. A consequence of this is the real part of the wavevectors \(k_{n}\) is larger than \(k_{o}\), resulting in a near-field structure that contains information about the surface beyond the diffraction-limited maximum resolution of the far-field. Figure 1a illustrates the contrast between imaging in the far and near-fields; to make use of near-field light the SNOM probe must be positioned within the near-field, close to the sample surface at a distance \(r\) much less than the wavelength, \(\lambda\), of the incident light. For this reason, SNOM is typically demonstrated in practice coupled to a scanning microscopy system such as AFM. The cantilever system of an AFM allows the SNOM tip to be positioned very close to the surface at a distance of tens of nm (\(r<<\lambda\)), to be within the near-field as shown in Figure 1a,b. The sample is then scanned in a raster pattern to map the near-field distribution while maintaining a tip position very close to the surface. Coupling to an AFM system also allows for simultaneous collection of a topography image and a SNOM image, providing a method to map the surface nanoscale morphology directly to the optical and chemical properties observed in the SNOM image. Two distinct modes of SNOM imaging have been employed, and are classified by the type of tip that is used. Aperture SNOM, also called collection SNOM (c-SNOM), uses hollowed out tips that allow light to shine from the back out of, or up into, the tip as shown in Figure 1b. Aperture tips function by generating near-field light by scattering of far-field light from the nanoscale aperture at the end of the tip. The generated tip near-field is subsequently scattered off the sample surface, into the far-field to be detected. Early versions of the SNOM technique employed a tapered optical fiber with a metallic tip and a subwavelength opening for this purpose [1,8]. The standard aperture tip possesses a circular opening with a typical diameter ranging from 80 to 250 nm, but can be as small as 10-20 nm using advanced nanofabrication procedures. The particular size and shape of the tip and aperture, as well as the tip composition dictate the range of frequencies that can be coupled to or scattered by the sample.