Optical sensors are indispensable in diverse applications, ranging from detecting nanoscale thin films and nanoparticles to identifying biomolecules, viruses, and cells. Elevating sensor efficacy, particularly by intensifying the interaction between light and matter and enhancing sensitivity, holds the potential to unlock groundbreaking applications. Metamaterials (MMs) are artificial periodic structures with sub-wavelength features. Their response to electromagnetic radiation can be controlled by their structural design and the materials they are composed of. The strong local electric field enhancement by the subwavelength mode concentration makes MMs ideal candidates for sensing analytes. The exploration of applications of MMs for sensing has been flourishing in the last two decades.

Although terahertz (THz) sensors based on metallic MMs have shown advantages in terms of contact- and label-free detection, they still have disadvantages in terms of sensitivity and detection limits compared to existing mature and standardized biochemical diagnostic methods such as enzymatic immunoassays. It is widely accepted that optimized MM sensors should exhibit a strong local electric field enhancement at the location of the analyte, a high quality factor (Q-factor) to ensure a narrow spectral resonance for reliable identification of a resonance shift, and a small mode volume—an aspect recently recognized as a key parameter—in order to achieve a large overlap of the electric field with the analyte. However, a systematic and practical optimization strategy that coherently considers all the parameters for the rational design of MM sensors has been missing until now.

Another shortcoming in this field of sensor research relates to the performance indicators usually employed. For the assessment of the relative performance of MM sensors, two parameters find application. The first is the refractive index sensitivity, often denoted by the letter S, which is calculated as the resonance frequency shift resulting from a change in the refractive index of the analyte by unity (and hence is measured in units of 'GHz/RIU', RIU standing for 'refractive index unit'). The second indicator is the figure of merit (FOM), calculated as the ratio of S to the full width at half maximum (FWHM) of the resonance line in the power spectrum (and hence is measured in units of 1/RIU. The problem with these parameters is that they only allow the comparison of sensitivities among various sensors if the analyte is applied at the same location and in the same amount, which means thin films should be applied with the same layer thickness.

To address these two issues, Associate Professor Lei Cao from Huazhong University of Science and Technology, in collaboration with Professor Hartmut G Roskos's team from the Johann Wolfgang Goethe-Universität Frankfurt am Main, Professor Peter Haring Bolívar's team from the University of Siegen and Professor Shihab Al-Daffaie from the Eindhoven University of Technology, propose a class of highly sensitive interdigitated THz MMs sensors based on the dielectric perturbation theory. Relevant research results were recently published in Photonics Research, Volume 12, No. 6, 2024. [Lei Cao, Fanqi Meng, Esra Özdemir, Yannik Loth, Merle Richter, Anna Katharina Wigger, Maira Beatriz Pérez Sosa, Alaa Jabbar Jumaah, Shihab Al-Daffaie, Peter Haring Bolívar, Hartmut G. Roskos, "Interdigitated terahertz metamaterial sensors: design with the dielectric perturbation theory," Photonics Res. 12, 1115 (2024)].

Regarding the first issue, the research team applies the dielectric perturbation theory to quantitatively guide the rational design of planar MM sensors. The interdigitated electric split-ring resonator (ID-eSRR) with mini-gaps, integrates interdigitated fingers with split-ring MM resonators, proving to be an optimized structure for thin-film detection. The ID-eSRR not only significantly enhances the detection sensitivity, but also boosts the Q-factor compared to the eSRR without fingers. With regard to the second issue, it also becomes apparent that it is often unconvincing to compare sensors using only those two conventional performance parameters (S and FOM). One should design different sensors for different types of analytes and employ different performance parameters. For analytes brought onto the sensor in the form of continuous thin films, the research team suggests a third performance indicator obtained by normalizing the FOM by the thickness of the film. We term this indicator a TN-FOM (abbreviation for 'thickness-normalized FOM').

To demonstrate the advantages of the proposed interdigitated MM sensors, the research team fabricated two kinds of sensors based on electric split-ring resonators (eSRRs): one with interdigitated fingers (ID-eSRR) and one without. The scanning-electron-microscope (SEM) image of a single ID-eSRR resonator is shown in Fig.1(a). In Fig. (b) and (c), the simulated and measured transmittance spectra are presented, respectively, for both types of MM sensors. The agreement between the resonance frequencies, the amplitudes, and the shapes of the simulated and measured spectra is quite satisfactory. The remaining discrepancies may stem from the different illumination conditions in the simulations and measurements: The simulations assume a plane wave with a well-defined wave-vector, while the measurements are performed with a focused THz beam with an angular spread of wave-vectors, for which the MM's response may vary. Additional deviations may arise from different values of the substrate permittivity and the metal conductivity in the experiment and simulations, as well as by fabrication tolerances, particularly with regard to the metal fingers.

Fig.2(a,b) presents the measured transmittance spectra for the empty and analyte-loaded ID-eSRR and eSRR structures. Data for five distinct values of the SiO₂ layer thickness are shown. These are for the ID-eSRR sensor 23 nm, 47 nm, 71 nm, 95 nm and 150 nm, and for the eSRR sensor 20 nm, 43 nm, 68 nm, 90 nm and 155 nm. In the case of the ID-eSRR sensor, this is simply the frequency position of the transmission minimum (marked by an upwards-pointing black arrow in Fig.2(a)). For the eSRR sensor, the minimum is difficult to identify directly. The research team determine it by fitting the resonance curve with a Lorentzian function around the broad transmission valley. It is obvious that the presence of the analyte leads to a much stronger shift of the resonance frequency in the case of the ID-eSRR MM as compared with the eSRR MM. Fig.2(c) displays the resultant frequency shifts for the two structures. Both theory and experiment confirm the superior sensitivity of the ID-eSRR structure. At a thickness of about 150 nm, the Q-factor, sensitivity, and FOM (TN-FOM) value of the ID-eSRR sensor are higher by factors of 6.6, 8.4, and 55.3, respectively, compared to the eSRR sensor.

Figure 1 (a) SEM image of an ID-eSRR structure fabricated by electron beam lithography, (b) simulated transmittance spectra of both the ID-eSRR MM (G = 12 μm, w = g = 0.6 μm) and the eSRR MM (G = 12 μm) without analyte, (c) measured transmittance spectra of the ID-eSRR and eSRR MMs without analyte

Figure 2 (a) Measured transmittance spectra of the ID-eSRR structure loaded with a SiO2 layer of varying thickness (from 23 to 150 nm). (b) Likewise, but for the eSRR structure SiO2 layer thickness varying from 20 to 155 nm). (c) Simulated and measured resonance frequency shift in dependence of the SiO2 layer thickness.

The research team observed a remarkable improvement of the FOM by more than a factor of fifty, which lets the ID-eSRR outperform existing MM-based THz sensors for thin-film detection in terms of sensitivity and FOM. Lei Cao commented that, "The reported optical sensors based on interdigitated MMs provides a high-performance platform and holds promise for label-free and amplification-free detection of trace amounts of analytes, particularly biomolecules such as DNA and proteins. Currently, we are conducting biosensing measurements on the ID-eSRR sensor."

Lei Cao acknowledges support from the HUST Overseas Training Program for Outstanding Young Teachers. This research work was funded by DFG projects RO 770/46-1, RO 770/50-1 and HA3022/15 (the latter two being part of the DFG-Schwerpunkt "Integrierte Terahertz-Systeme mit neuartiger Funktionalität'' (INTEREST -- SPP 2314)).