# Exploiting Localized Surface Plasmon Resonances in Subwavelength Spiral Disks for THz Thin Film Sensing

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## Abstract

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## Featured Application

**THz thin film sensing.**

## Abstract

^{−4}–10

^{−3}λ) showed good agreement with the simulations. The resonance frequency shift Δf increases with increasing d, while saturating near d = 50 µm. The narrow-band magnetic dark modes excited on symmetrical spiral disks with a 90° C-resonator demonstrated very high figure of merit (FOM) values reaching 1670 (RIU·mm)

^{−1}at 0.3 μm thick analyte. The hybrid high order resonances excited on asymmetrical densely packed spiral disks showed about two times larger FOM values (up to 2950 (RIU·mm)

^{−1}) compared to symmetrical distantly spaced spirals that resembled the best FOM results found in the literature for metasurfaces fabricated with a similar technique. The demonstrated high sensing performance of spiral disks is evaluated to be promising for bio-sensing applications in the THz range.

## 1. Introduction

_{THz}~ 10

^{12}Hz) are several orders of magnitude lower than the plasma frequency of free electrons in metal (ω

_{p}~ 10

^{16}Hz) and their collision frequency (ω

_{c}~ 10

^{14}Hz [11]) and therefore, plasmon resonances cannot formally be excited in this spectral region. To overcome these limitations, Pendry and his colleagues suggested making a periodic corrugation of the flat surface [12] that leads to forming bound surface states with a high confinement of the electromagnetic field, so called “spoof surface plasmon resonances”. It has been shown that sub-wavelength metallic structures [13] are able to support spoof localized surface plasmon resonances (LSPRs) in the long-wave region. This idea was elaborated in detail in the metamaterial community through the concept of plasmonic metasurfaces (PMSs) [14,15], which are understood as thin metallic screens with periodically patterned subwavelength apertures or substrate-backed arrays of subwavelength metallic elements. It is essential that LSPRs excited on a PMS are directly related to the geometry of the PMS unit cells that provides high flexibility in engineering the electromagnetic (EM) properties of the structures both in far- and near-field. Alongside with the feasibility of versatile frequency-selective and polarization-transforming devices, this approach enables creating high-performance PMS-based sensors of thin-film analytes. Exploiting the LSPR-induced effect of near-field confinement, which enhances light–matter interaction, such sensors exhibit high sensitivity to the dielectric environment and allow the determining of analytes with thicknesses several orders of magnitudes smaller than the LSPR wavelength via tracking a frequency shift of the LSPR relative to that of a bare PMS (without a deposited analyte).

_{0}, where n is a total number of grooves. Lately, numerical simulations in the THz region for a periodic structure of azimuthally grooved golden disks on dielectric substrates [18,19,20,21] showed that high-order (multipole) electric and magnetic LSPRs can be excited under oblique illumination or when combining the grooved disk with a C-shaped resonator. As compared to dipole resonances, the multipole ones have higher Q-factors and are more sensitive to the presence of dielectric materials on the structure, i.e., more promising for sensing applications.

_{a}, which depends on the groove depth h and the refractive index n in the groove as f

_{a}= c/(4h·n), where c is the light speed [22]. An increase in the depth h shifts the asymptote frequency (and the resonance spectrum) towards lower frequencies and consequently, enhances the confinement of LSPR modes. Thus, the lowest resonant frequency is governed by the size of the disk. To improve the mode confinement of spoof LSPRs, it was suggested to use long spiral grooves (Figure 1b) [23]. The extension of spirals allows shifting the LSPR resonances towards longer wavelengths, exceeding by far the structure size, which yields a stronger EM field localization near the surface. Thus, a spiral disk design is expected to be very promising for sensing applications at THz, whereas this kind of structures is still understudied. It is worth mentioning that numerical calculations, theoretical analysis and experimental tests of spiral grooves were reported in literature mainly for the microwave region [22] and we know only one paper on the experimental implementation of a simple design of spiral disks in the THz range [24].

## 2. Materials and Methods

**k**in the XYZ coordinate system: the polar angle θ describes the angle between

**k**and the Z axis, while the azimuthal angle φ defines the angle between the orthogonal projection of

**k**on the XY plane measured from the X direction. Since a THz beam was horizontally polarized in our experiments and a rotary stage afforded the rotation of the sample only around a vertical axis, our investigations were limited by TM-polarized excitation. Two marginal cases were considered: φ = 0 and φ = 90°. The former was of primary importance since it enabled the proper excitation of the C-shaped resonator (

**E**

_{in-plane}|| X), as elucidated in Section 3.1.

^{7}S/m [25,26] placed on top of a 15 µm-thick polypropylene (PP) film with the dielectric permittivity ε

_{pp}= 2.25·(1 − j·10

^{−3}) [25,26]. PP has low absorption in the THz range and was intentionally chosen as a substrate material to minimize the dielectric losses in the structure; we also used the thinnest PP substrate available to diminish interference effects in the PP layer.

_{2}atmosphere to improve the adhesion of Al to PP.

_{a}= 2.65 (n

_{a}≈ 1.63), experimentally evaluated in the spectral range considered [30].

## 3. Results and Discussion

#### 3.1. Symmetric Spiral Disks

_{C}= 204 µm, while the resonator arch angle α was a variable parameter. Figure 2a shows the calculated transmittance spectra of the spiral disks with different α for normal illumination (θ = 0°) by an X-polarized EM wave. Starting from α = 90°, the new dark mode narrow resonances were well excited (see red circles in Figure 2b). With increasing α, the resonances move towards the lower frequencies due to the decrease in the bright mode frequency of the C-resonator. For the following simulations we selected α = 90°, at which there were several narrowband resonances in the region of 0.2–0.5 THz (see the highlighted region in Figure 2a).

**E**-field was parallel to the resonator (φ = 0:

**E**

_{X}≠ 0,

**E**

_{Y}= 0); in the opposite case (φ = 90°:

**E**

_{X}= 0,

**E**

_{Y}≠ 0), the bright mode was not revealed. For both orientations, upon increasing θ, the main resonances shifted a little and became weaker due to the decreasing

**E**-projection on the PMS plane. We may also track new resonances arising above 0.38 THz, whose positions depend on the incidence angle and probably originate from the hybridized nature of these modes.

^{−4}λ to 7 $\times $ 10

^{−3}λ). Depositing thicker layers was not feasible due to the insufficient viscosity of the employed photoresist. The transmittance spectra of the samples measured with the BWO spectrometer are shown in Figure 4b. The simulated spectra (see Figure 4a) are in good accordance with the experiments. With increasing d, all the resonances were gradually shifted towards lower frequencies. We evaluated the resonance shifts Δf (GHz) from the spectra at 0.297, 0.339 and 0.373 THz as a function of the photoresist thickness d (see Figure 5a). The errors for Δf in the experiments and simulations were determined with the inaccuracy (≈0.5–1 GHz) of identifying the resonance frequency for the minima of the transmittance spectra. The experimental errors depended on the step of the frequency scanning (0.5 GHz). The experimental and simulated results were in qualitative agreement. Additional simulations for the larger thicknesses showed that Δf tended to saturation at d > 50 µm, at which the sensor was insensitive to the thickening of the photoresist layer.

_{a}: S = Δf/(d·n

_{a}), with the units of GHz·(the refractive index unit (RIU)·mm)

^{−1}. The dependencies S(d) plotted in Figure 5b are almost consistent with each other, except for d = 0.3 µm at which the experimental value S is larger than the simulated one. The reason for this discrepancy presumably lies in a deviation of the real thickness (averaged over a THz-illuminated area) of the photoresist layer deposited on a flexible 15 µm PP substrate of our PMS sensor.

_{Z}-field distributions simulated at the resonant frequencies at a distance of 2 µm from the metallized layer. According to [22], the magnetic modes potentially have higher Q-factors than the electric ones.

^{−1}. The calculated graphs of the FOM as a function of d depicted in Figure 5d show that magnetic resonances were more sensitive than electric ones, especially for very thin analyte layers. The highest FOM was attained at d = 0.3 µm: FOM ≈ 1670 (RIU·mm)

^{−1}.

#### 3.2. Asymmetric Spiral Disks with Shifted Center

_{Z}-field distribution of two nearby disks at 0.438 THz (Figure 6c) presumably corresponds to an electric sextupole hybrid mode. The FWHM(d) values plotted in Figure 7c are approximately the same as for the distantly spaced disks without shifted centers (see Figure 5c), while Δf(d) and S(d) (Figure 7a,b) are significantly larger. The greater sensitivity can be explained by the high-density arrangement of the disks, which enhances EM field localization near the PMS. The larger sensitivity yields the greater FOM. The highest FOM ≈ 2950 (RIU·mm)

^{−1}is reached at the smallest analyte thickness (d = 0.3 µm), which is ≈77% bigger than in the case of the distantly spaced disks. This result is comparable with the best FOM value (3450 (RIU·mm)

^{−1}) obtained at the same analyte thickness for a labyrinth metasurface absorber implemented with a similar fabrication techniques [16,35].

## 4. Conclusions

^{−4}λ) photoresist coatings increased with d, while approaching a constant at d = 50 µm. Dark magnetic modes excited on symmetric spiral disks with 90° C-resonators demonstrated very high FOM values, especially for the smallest thicknesses (1670 (RIU·mm)

^{−1}at d = 0.3 µm) due to a narrow resonance width. The hybrid high order mode resonances of asymmetrical densely packed spiral disks (with a shift of the disk center) showed about two times larger FOMs (up to 2950 (RIU·mm)

^{−1}) then symmetrical spirals, which is comparable with the best FOM values obtained for alternative metasurfaces with densely packed unit cells fabricated with a similar technique. The attained results allow us to highlight the spiral disks design as promising for bio-sensing applications in the THz range.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Four different designs of plasmonic metasurfaces (PMSs) with the metal disk elements (the unit cells are shown; p is the lattice constant): (

**a**) the azimuthally patterned disk; (

**b**) the spiral disk; (

**c**) the spiral disk with a C-shaped resonator (α is the resonator’s arch angle); (

**d**) the spiral disk with a C-shaped resonator and a shifted center (δr is center shift).

**Figure 2.**(

**a**) Transmittance spectra of the distantly spaced (p = 768 µm) spiral disks with different C-resonator angles α. Normal incidence (θ = 0°),

**E**|| X; (

**b**) The resonance frequencies vs. α (n—number of resonances), the red circles—the resonances produced by the bright mode of the C-resonator.

**Figure 3.**TM-transmittance spectra of the distantly spaced spiral disks with a 90° C-resonator under oblique illumination: θ = 0, 20 and 40°: (

**a**) the simulations and (

**b**) the experiments. Azimuthal angles φ = 0 and φ = 90° correspond to the zero projections of the incident

**E**-field on the Y and X axes, respectively.

**Figure 4.**Transmittance spectra of the distantly spaced (p = 768 µm) spiral disks with a 90° C-resonator and photoresist coatings of different thicknesses: (

**a**) the numerical simulations; (

**b**) the experiments; (

**c**) the E

_{Z}-field distributions at the resonances (0.297 THz–natural electric dipole mode (ED), 0.339 THz and 0.373 THz–magnetic dipoles (MDs)). Normal incidence (θ = 0°),

**E**|| X.

**Figure 5.**Sensor parameters for the distantly spaced (p = 768 µm) spiral disks with 90° C-resonator, evaluated from the transmittance spectra in Figure 4: (

**a**) the frequency shifts Δf of resonances at 0.297, 0.339 and 0.372 THz vs. photoresist thickness d (left—simulations, right—experiments); (

**b**) the sensitivity of S vs. d; (

**c**) the full width at the half minimum (FWHM) vs. d; (

**d**) figure of merit (FOM) vs. d.

**Figure 6.**Transmittance spectra of the closely spaced (p = 408 µm) spiral disks with centers shifted at δr = 35 µm, covered by photoresist films of different thicknesses: (

**a**) the numerical simulations; (

**b**) the experiments; (

**c**) the E

_{Z}-field distribution at resonance (0.438 THz). Normal incidence (θ = 0°),

**E**|| X.

**Figure 7.**Sensor parameters for the closely spaced (p = 408 µm) spiral disks with centers shifted by δr = 35 µm, evaluated from the transmittance spectra in Figure 7: (

**a**) the frequency shift Δf of resonance at 0.438 THz vs. the photoresist thicknesses d (left—simulations, right—experiments); (

**b**) the sensitivity S vs. d; (

**c**) FWHM vs. d; (

**d**) FOM vs. d.

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**MDPI and ACS Style**

Gerasimov, V.V.; Hafizov, R.R.; Kuznetsov, S.A.; Lazorskiy, P.A. Exploiting Localized Surface Plasmon Resonances in Subwavelength Spiral Disks for THz Thin Film Sensing. *Appl. Sci.* **2020**, *10*, 3595.
https://doi.org/10.3390/app10103595

**AMA Style**

Gerasimov VV, Hafizov RR, Kuznetsov SA, Lazorskiy PA. Exploiting Localized Surface Plasmon Resonances in Subwavelength Spiral Disks for THz Thin Film Sensing. *Applied Sciences*. 2020; 10(10):3595.
https://doi.org/10.3390/app10103595

**Chicago/Turabian Style**

Gerasimov, Vasily V., Ruslan R. Hafizov, Sergei A. Kuznetsov, and Pavel A. Lazorskiy. 2020. "Exploiting Localized Surface Plasmon Resonances in Subwavelength Spiral Disks for THz Thin Film Sensing" *Applied Sciences* 10, no. 10: 3595.
https://doi.org/10.3390/app10103595