Wavelength-multiplexed hook nanoantennas for machine learning enabled mid-infrared spectroscopy

Infrared (IR) plasmonic nanoantennas (PNAs) are powerful tools to identify molecules by the IR fingerprint absorption from plasmon-molecules interaction. However, the sensitivity and bandwidth of PNAs are limited by the small overlap between molecules and sensing hotspots and the sharp plasmonic resonance peaks. In addition to intuitive methods like enhancement of electric field of PNAs and enrichment of molecules on PNAs surfaces, we propose a loss engineering method to optimize damping rate by reducing radiative loss using hook nanoantennas (HNAs). Furthermore, with the spectral multiplexing of the HNAs from gradient dimension, the wavelength-multiplexed HNAs (WMHNAs) serve as ultrasensitive vibrational probes in a continuous ultra-broadband region (wavelengths from 6 μm to 9 μm). Leveraging the multi-dimensional features captured by WMHNA, we develop a machine learning method to extract complementary physical and chemical information from molecules. The proof-of-concept demonstration of molecular recognition from mixed alcohols (methanol, ethanol, and isopropanol) shows 100% identification accuracy from the microfluidic integrated WMHNAs. Our work brings another degree of freedom to optimize PNAs towards small-volume, real-time, label-free molecular recognition from various species in low concentrations for chemical and biological diagnostics.

The sensing results of different devices are shown in Fig. S1b, d. The extracted spectrum difference is shown in Fig. S1c, e, representing the sensing performance of each device. The normalized sensitivity of each device is shown in Fig. S1f. In reflection mode, the optimized HNA-1 device improves the sensitivity by 28.2% and 83.6% compared to FRAMM and NA, respectively.
In transmission mode, the enhancement of 2.41 and 17.28 times of sensitivity is demonstrated by the optimized HNA-2 device compared with FRAMM and NA, respectively. From the obvious improvement above, the HNA device is a good candidate for ultrasensitive MIR molecular sensing.
The sensing performance can be optimized from the radiative loss of HNA by tuning the folding degree of the HNA structure (ΔL, defined by L1-L3). According to the optimal loss rates at transmission (f=0.5) and reflection(f=2) modes, two HNA devices with different ΔL are designed as optimized structures for transmission (HNA-2) and reflection (HNA-1) modes. Because the f difference between HNA-2 to control devices is larger than the f difference between HNA-1 to control devices, the improvement of sensitivity in transmission mode is achieved much larger than that in reflection mode (241% to 28.2% for FRAMM, 1728% to 83.6% for NA).  *L1, L2, L3, W: labeled in Fig. S1. Px, Py: the period in the horizontal and vertical direction in Fig. S1. T: the thickness of antennas. S: scaling factor, the ratio between our parameters and original ones in previous papers.

Note S2: Theoretical analysis of nanoantenna sensor using TCMT
The temporal coupled-mode theory (TCMT) 15 is used to describe the coupling behavior between PNA and molecular vibration. We treat the plasmonic resonance (denoted as P) as a bright mode that is coupled to the incident light, while we treat the molecular vibration (denoted as M) as a dark mode, in which coupling efficiency is much lower than PNA and can be ignored in their coupling system. Therefore, we obtain the equations using TCMT as where Therefore, transmission and reflection can be expressed as The Fano-like line shape can be expressed from Equations S9, S10 for both transmission and reflection modes. The plasmonic resonance can be easily obtained when there is no coupling effect from molecules (μ=0).
Equations S9, S10 are used to extract absorptive and radiative loss of HNA by fitting the resonance spectrum in the frequency domain from simulation (Fig. S2). By engineering the HNA structure by changing ΔL with the constant L, the γr and γa can be tuned continuously, and ω0 remains unchanged. To explore the sensing performance, we have made some assumptions to simplify Equation S9 to perform the analytical operation. First, we make ω0=ωm to match the frequency of HNA and molecular vibration since the WMHNA is only designed for the molecular absorption wavelength near the HNA resonance wavelength to have the best enhancement.
Second, we treat μ as a much smaller parameter compared with γm, γr, and γa. Therefore, we apply the difference between Equation S10 and Equation S9 when ω = ω0 = ωm.
Since μ<<γm, 2 is a small real number close to 0. Therefore, we cancel the high order term and simplify Equation S14 as where f = γr/ γa, defining the ratio of radiative and absorptive loss. Similarly, for the reflection spectrum, we get The negative sign in Equation S16 indicates the opposite change in transmission and reflection spectrum induced by molecular vibration. γa refers to the omics loss of material; thus, it is constant in our experiment of HNA made by Au. When changing ΔL of HNA, the electrical field does not change too much among different HNA devices, so that μ is also a constant. Additionally, γm is also unchanged since we fix the absorption peaks of the "C=O" bond from PMMA in sensitivity characterization. By applying the first derivative of f for Equation S15 and Equation S16. We further calculate the maximum enhancement of the T and R spectrum and get the optimal condition that occurs when f equals 0.5 and 2, respectively.

Fig. S2
The fitting curves of simulation results of hook nanoantennas at different ΔL to extract the theoretical parameter (γ a and γ r ) in TCMT. The same fitting method is applied to experimental data for the discussion on sensing performance.

Note S3: Near-field distribution of HNA
To study the near field enhancement of HNA, we perform the FDTD simulation and monitor the electric field intensity and polarity at resonance wavelengths for different devices. The amplitude of the electric field of different devices is plotted in Fig. S2a using the log scale by the equation log(|E/E0| 2 ). The results show that all of the devices have an enhanced field intensity at the magnitude of 10 5 . The extracted field enhancement (|E/E0| 2 ) at two arms of HNAs (position labeled in Fig. S2a) are shown in Fig. S2b. The normalized electric field of each device is characterized by Ex in Fig. S2c, showing a fundamental dipole mode of the resonance and the inverse current induced by the short arm of HNA to tune the radiative loss.   HNA-2 (f) sensors.

Fig. S8
The reference data for different types of nanoantenna devices using machine learning for recognition of alcoholic molecules. a-c, the spectra of NA, NA supercell, and HNA tested by the bare antenna and in water. d-f, the PCA-processed spectra for each device. g-i, the data distribution in PC space.

Note S7: Molecular identification using deep neural network
Our DNN dataset comprises 300×1272 data points and we randomly split these data, in which 80% for training data set, 20% for testing data set. The proposed DNN model is built using the Sequential model of Python's Keras frame. Each fully connected layer followed with ReLu as activation function and the final model was compiled by 'categorical_corssentropy' as the loss function and Adam as the optimizer. We set the batch size as 20. In the 800 epochs, the loss between prediction and ground truth shows excellent convergence in both of training and testing set, and there is no overfitting occurring either. (Fig. S9c) Finally, 100% identification accuracy is obtained for alcohols identification shown in Fig. S9d,e.