## 5 Applications of 3D-SNOM
### 3D Probing of Near-Fields of Nanostructures
Identical samples annealed at (**b**) 250 \({}^{\circ}\)C; and (**c**) 450 \({}^{\circ}\)C show a decrease in nanoparticle size as the temperature is increased; (**d**) Annealing under atmospheric conditions at 250 \({}^{\circ}\)C shows significantly different morphology consisting of smaller particles 250 nm in size; (**e**) Schematic of _z-x_ c-SNOM scans using an inverted configuration with laser illumination from beneath the substrate; (**f**) Near-field light recorded moving away from the sample surface. Reproduced with permission from [54], Copyright Applied Physics Letters, 2012.  
pixels in panel (b) represent the location of nanoparticles in panel (a) and show regions near the nanoparticles of higher intensity forward-scattered light. Comparing the background signal to that of the copper nanoparticles clearly indicates that very near the sample surface (\(z\approx 0\)), the intensity of light scattered by the bare glass substrate is significantly lower in intensity compared to light scattered from the nanoparticles. From the AFM image the nanoparticle size is significantly smaller than the illumination wavelength, \(\lambda=532\) nm, which means the scattered electric field produced by the nanoparticles is better represented as an infinite superposition of multipoles rather than a purely dipole field [48]. Such a multipolar field is expected to undergo a series of intensity oscillations moving away from the surface showing bands of maxima and minima interval distances z, a property that is not displayed by a purely dipole field [60]. These oscillations are visible (Figure 7c) in an (\(x\), \(z\)) c-SNOM scan of the line A-A' shown in Figure 7b, confirming the multipolar nature of the near-field. The bands of oscillating intensity are found to extend into the far-field up to distances of 5 \(\upmu\)m away from the surface, and possess a nearly uniform intensity along the \(x\)-direction excepting a relatively lower intensity corresponding to the largest particles. This effect is observed because even on a surface where the nanoparticles are not closely packed, they cannot be considered to be isolated when the inter-particle distances remain smaller than the wavelength of probing light. Variations in particle diameter were found to affect the intensity of the first maximum of forward-scattered light as a function of average particle size. Light scattered from nanoparticles with larger diameters is coupled more closely to the surface, which is attributed to the dependence of the cross-section for near-field light absorption and scattering on the particle size [59]. As a consequence of this copper nanoparticles with a diameters of 80 nm or greater exhibit multipolar effects induced by Mie scattering that causes strong coupling of this scattered light to the substrate in the nanoparticle vicinity. Figure 7d presents the integrated intensity of light scattered along the A-A' cross-section labeled in Figure 7b and corresponding to the \(z\)-axis of Figure 7c. Maxima and minima arising from constructive and destructive interference, respectively, are visible on the micron scale moving away from the surface. For the nanoparticles specific to this sample the first intensity maximum of forward-scattered light is  
Figure 7: **(a)** Topographic AFM and (**b**) c-SNOM images obtained simultaneously; (**c**) Light intensity mapping (\(x\), \(z\)) measured along the A–A’ cross-section in panel (**b,d**) the integrated intensity profile in the \(z\)-direction along the A–A’ cross-section showing the positions of constructive (maxima) and destructive (minima) interference of forward light scattered from Cu-nanoparticles in panel (**c**). Reproduced with permission from [48], Copyright Nanoscale, 2015.  
observed 1200 nm above the surface, within the far-field of scattered light. The absolute maxima occurs further away in the far-field at \(\Delta z=4400\) nm.