Interferometric Evanescent Wave Excitation of a Nanoantenna for Ultrasensitive Displacement and Phase Metrology

We propose a method for ultrasensitive displacement and phase measurements based on a nanoantenna illuminated with interfering evanescent waves. We show that with a proper nanoantenna design, tiny displacements and relative phase variations can be converted into changes of the scattering direction in the Fourier space. These sensitive changes stem from the strong position dependence of the orientation of the purely imaginary Poynting vector produced in the interference pattern of evanescent waves. Using strongly confined evanescent standing waves, high sensitivity is demonstrated on the nanoantenna’s zero-scattering direction, which varies linearly with displacement over a wide range. With weakly confined evanescent wave interference, even higher sensitivity to tiny displacement or phase changes can be reached near a particular location. The high sensitivity of the proposed method can form the basis for many metrology applications. Furthermore, this concept demonstrates the importance of the imaginary part of the Poynting vector, a property that is related to reactive power and is often ignored in photonics.

Figure 1

(a). A dipolar nanoparticle is illuminated by two counterpropagating TM polarized evanescent waves. The scattering of the particle is measured at the back focal plane of a lens, i.e., in the Fourier $k$ space. (b),(c) The purely imaginary Poynting vector (color represents its magnitude and white arrows its orientation) of the standing wave due to the interference of two evanescent waves with opposite transverse wave vectors $\pm k_{\parallel }=\pm 2k_0$ (b) and $\pm k_{\parallel }=\pm 1.01k_0$ (c), where the phase difference between the two waves is set to $\mathrm{\Delta }\varphi =0$.

Figure 2

(a) The $y$ dependence of ${\theta }_s$ [the angle from $+\widehat{\mathbf{y}}$ to the purely imaginary Poynting vector of the interfering evanescent field shown in Fig. 1] and $\theta$ (the angle from $+\widehat{\mathbf{y}}$ to the particle’s zero scattering direction). The scattering patterns of a dipolar particle are shown [the ED and MD coefficients fulfil $a_1=(-\mathrm{i}/\sqrt{3})b_1$] placed at various locations: (b) $y=0$, (c) $y=\lambda /4-\lambda /40$, (d) $y=\lambda /4$; (e) $y=\lambda /4+\lambda /40$. The green solid arrows represent the Poynting vectors, the blue solid arrow represents the fixed zero scattering direction $-\widehat{\mathbf{z}}$, the blue dashed arrows represent the other zero scattering direction, while the insets in (b)–(e) show the scattering pattern (logarithm ${\log }_{10}$ scale, dark red for maximum while deep blue represents zero scattering) in the $k$ space of the Fourier lens above the nanoparticle.

Figure 3

(a). The dependence of the purely imaginary Poynting vector angle ${\theta }_s$ on the relative phase difference $\mathrm{\Delta }\varphi$ at a fixed location $y=0$ of the interferometric evanescent field with $\pm k_{\parallel }=\pm 2k_0$ and $\pm k_{\parallel }=\pm 1.01k_0$, respectively. The scattering patterns are shown for a dipolar particle placed at $y=0$ of the interfering fields with different relative phases: (b) $\mathrm{\Delta }\varphi =0$ and (c) $\mathrm{\Delta }\varphi =\pi /25$. The radiation patterns plotted in colors correspond to nanoparticles with a fixed electric dipole but different magnetic dipole Mie coefficients: $b_1=i({\gamma }_z/k_0)a_1$ (blue), $b_1=2i({\gamma }_z/k_0)a_1$ (red) and $b_1=3i({\gamma }_z/k_0)a_1$ (magenta), where ${\gamma }_z=0.142k_0$.