Fig. 1. Schematic illustration of the tunable and reconfigurable EP sensing system on a single plasmonic resonator. The bottom half shows the DP sensor in the absence of particles and the second-order EP sensor with two dynamically movable Rayleigh scatterers. One essential characteristic of the EP is the emergence of a unidirectional propagation traveling wave on the plasmonic resonator. The top half demonstrates the $z$-component of the electric field $E_z$ from standing wave (DP sensor) to traveling wave (EP sensor) of the reconfigurable EPs in five consecutive plasmonic resonance modes.

Fig. 2. (a)–(c) Schematic drawing of the proposed reconfigurable EP sensor based on spoof plasmonic resonator. (d) Experimental measurement setup based on a spoof LSP resonator. (e) Comparison of transmission parameters of DP spoof plasmonic sensors between the simulated and measured results. Nine plasmonic modes are collectively excited, starting from the fundamental mode, and the simulation results exhibit excellent agreement with the experimental observations (Video 1, MP4, 14.9 MB [URL: https://doi.org/10.1117/1.APN.3.5.056004.s1]).

Fig. 3. Schematic diagrams of the reconfigurable EP sensing systems on the single-spoof plasmonic resonator with the relative azimuthal angle between scatterers: (a) ${\alpha }_{m3}=23\mathrm{deg}$, (b) ${\alpha }_{m4}=61\mathrm{deg}$, (c) ${\alpha }_{m5}=50\mathrm{deg}$, (d) ${\alpha }_{m6}=37\mathrm{deg}$, and (e) ${\alpha }_{m7}=34\mathrm{deg}$. Target particles are positioned at the same location (${\alpha }_3=\pi$). (f)–(j) The measured transmission spectra of DP (top panels) and EP (bottom panels) sensors before (blue curves in the left panels) and after (red curves in the right panels) introducing a deep-subwavelength metal target into the vicinity of the spoof plasmonic resonator. Black vertical dashed lines in the right panels highlight the enhancements of sensitivity. The insets depict fully asymmetric reflection coefficients, indicating the occurrences of EPs. The abscissa axes of the inset figures represent frequency detuning (in gigahertz), while the ordinate axes represent the normalized reflection coefficients (in a.u., arbitrary units). (k)–(o) Relationships between the frequency splitting of DP (blue) and EP (red) sensors and the perturbation strength on logarithmic scales. The frequency-splitting responses in EP sensors demonstrate the slope of 1/2, which is proportional to ${\epsilon }^{1/2}$ and consistents with the prediction of Eq. (2).

Fig. 4. Histograms depicting the variations and comparative analysis of the measured frequency-splitting responses (mean values of the experimental results repeated 3 times) induced by the DP and EP sensors with various targets at (a) sextu-, (b) octu-, (c) deca-, (d) dodeca-, and (e) fourteen-pole modes. The whiskers represent the range of results from three measurements. The insets illustrate sensitivity enhancements that refer to the ratio between the frequency splitting of EP sensors and that of DP sensors. The dots in various colors represent the correlation between $|\mathrm{\Delta }{\omega }_{\mathrm{EP}}/\mathrm{\Delta }{\omega }_{\mathrm{DP}}|$ and the perturbation strength $\epsilon$, which conform well to the fitted lines derived from Eq. (1). To be specific, the values of $A_j^{(2)}{e}^{i2m_j\alpha }$ ($j=3,4,5,6,7$) in Eq. (1) of the five proposed reconfigurable EPs are as follows: $-3+11.8\mathrm{i}$, $1.2-10.8\mathrm{i}$, $6.3-7.5\mathrm{i}$, $-2.2+8.6\mathrm{i}$, and $-1.6+7.8\mathrm{i}$, respectively. (f) Variation of the $Q$-factors and minimum resolvable sizes with the EP-mode index of the proposed reconfigurable EP sensors (Video 2, MP4, 12.6 MB [URL: https://doi.org/10.1117/1.APN.3.5.056004.s2]).

Table 1. Scatterer dimensions and positions of the reconfigurable EP sensors.

Table 2. Comparison of the experimental results between the proposed reconfigurable EP-based spoof plasmonic sensor and previous works.