Non-dispersive infrared multi-gas sensing via nanoantenna integrated narrowband detectors

Non-dispersive infrared (NDIR) spectroscopy analyzes the concentration of target gases based on their characteristic infrared absorption. In conventional NDIR gas sensors, an infrared detector has to pair with a bandpass filter to select the target gas. However, multiplexed NDIR gas sensing requires multiple pairs of bandpass filters and detectors, which makes the sensor bulky and expensive. Here, we propose a multiplexed NDIR gas sensing platform consisting of a narrowband infrared detector array as read-out. By integrating plasmonic metamaterial absorbers with pyroelectric detectors at the pixel level, the detectors exhibit spectrally tunable and narrowband photoresponses, circumventing the need for separate bandpass filter arrays. We demonstrate the sensing of H2S, CH4, CO2, CO, NO, CH2O, NO2, SO2. The detection limits of common gases such as CH4, CO2, and CO are 63 ppm, 2 ppm, and 11 ppm, respectively. We also demonstrate the deduction of the concentrations of two target gases in a mixture.

To optimize the infrared absorption characteristics of the plasmonic metamaterial absorber, we first used COMSOL, a finite element method based solver to numerically study the optical properties of the absorbers employing periodic boundary conditions and plane wave excitation polarized along the y-axis (Cartesian coordinate system in Fig. 1(c)). Supplementary Fig. 2a shows the configuration of the absorber for parameter tuning: the diameter d of the nanodisk, the lattice constant (period) P of the array, the thickness tSiO2 of the silicon dioxide spacer. The thickness tdisk of the nanodisk and the thickness tbackplate of the backplate are chosen to be 50 nm and 100 nm, respectively. Supplementary Table 1   is the initial temperature. The numerically simulated temperature change ΔT P as a function of the modulation frequency is plotted by the red line in Supplementary Fig. 5.
As a comparison, we also calculate the temperature change Δ using the equation 1, 2 : (1) Where is the mean of the temperature change Δ , =0.82 is the absorption rate of MIM, 1 is the transmission rate of the window of the detector, =3.512 mW is the source power, =4 * * * * * * where =230 μc m -2 k -1 is the pyroelectric coefficient, ω 2π is the angular frequency. The theoretical value of as a function of modulation frequency is plotted in Supplementary Fig. 7a. It is seen that as the modulation frequency increases, the pyroelectric current rises first and then become saturated. When the modulation frequency is 5 Hz, the theoretically calculated temperature change is 0.11 K according to where 80 GΩ, is the total impedance, Rd = 80GΩ, RG = 1TΩ, and 22.95 pF is the parallel plate capacitance of the LT element. As shown in Supplementary Fig. 7b, when the modulation frequency is 5 Hz, the voltage is 3.877 V, and the voltage responsivity is 1103.9 V W -1 . Note that in the main text, the average measured voltage response (90 V W -1 ) is lower than the theoretically calculated value (1103.9 V W -1 ). This can be mainly attributed to the fact that: 1) In the calculation, the LT is assumed to be supported by four Si posts that sit on the substrate (heat sink). The numerical model of the thermal analysis does not include the electrical connections of the LT element. While in experiment, the LT element was directly mounted on the printed circuit board containing the impedance matching circuit. Silver pastes are applied between the bottom electrode of the LT element and the pins on PCB to ensure good electrical connection. Also, the top electrode of the LT element is wire bonded to the PCB for electrical connection. Thus, the heat conduction between the LT element and the PCB board of the packaged detector could be more significant than the simulated case.
2) In the calculation, the area size of the heat source A s in the equation is set to be the area size of the LT element (3.6 mm 2 ). While in the measurement, the spot size of the optical beam arriving at the LT element is about 0.8 mm. Therefore the size of the area heated up by the beam is only π/4× 0.8 2 mm 2 = 0.5024 mm 2 . This is another source of the difference between the calculated and measured voltage response.

b．Calculation of noise
The thermal fluctuation noise and Johnson noise are calculated using the following equations: where is the spectral voltage responsivity, is the Boltzmann constant, is the temperature, Δ is the noise bandwidth, is the voltage gain( 0.99). It is seen that the contribution of the Johnson noise generated by the loss resistance of the lithium tantalate is in general larger than the contribution of the thermal fluctuation noise.

Supplementary Note 6 The output power of the light sources as a function of wavelength
The details about the light sources used in the experiment can be found from the following webpages:

Comparison of the narrowband detectors with commercial LT detectors 3
Reference  [3] (20 μm and 5 μm) and the narrowband detectors in this work are not vacuum packaged, it is expected that the specific detectivity can be further improved by using thinner LT elements and implementing vacuum package.

Supplementary Note 9
The configuration of NDIR system The gas cell used in this work is a White type multipass cell 4, 5 with an effective optical length of 5m. Its physical length is about 40 cm. Supplementary Fig. 9(a) illustrates the arrangement of the components in the NDIR system, including the Globar light source with the built-in beam collimating capability, the optical chopper, the multipass gas cell, the reflective objective and the narrowband detector that is mounted on an x-y-z translation stage. Supplementary Fig. 9(b) shows the optical configuration of White cell.

Supplementary Note 10 The calculation of the effective absorption coefficient
In the main text, the value of k in Equation 1 is calculated as followed 6, 7 : and (9) Here keff represents the effective absorption coefficient of the target gas; I0 is the optical length; x0 is the gas concentration. The integration is from λ min = 0.5 µm to λ max = 9 µm.   Fig. 5(b) In practice, the parameters span and c are fitting parameters used to match the fitting curves to the measured data as close as possible. They are adjusted to account for the changes in experimental conditions due to the mounting and unmounting of narrowband detectors in each round of measurement.

Mixed gas experiment
To turn the problem around and see whether our model allows the calculation of the gas concentrations x1 and x2 from the detector responses D1 and D2, we first write a computer program based the following mathematical model. span * span * (10) span * span * The values of the coefficient span ij , k ij , c ij are listed in the following  Fig. 6

(b)
We then define ΔD 1 = |D 1-calculated -D 1-measured | and ΔD 2 = |D 2-calculated -D 2-measured |, where D 1-calculated and D 2-calculated are the calculated detector responses, and D 1-measured and D 2-measured are the measured detector responses. Therefore, ΔD1 and ΔD2 represent the absolute difference between the the calculated response and measured response of the two detectors. We further define ΔD = ΔD ΔD as the standard deviation of ΔD 1 and ΔD 2 .
To work out the best values of the gas concentrations x 1 and x 2 for the given D 1-measured and D 2-measured , the program initiates a two-level iteration that varys both x1 and x2 from 1 ppm to 12500ppm, with a step size of 2 ppm. In each iteration, the program finds the calculated detector responses D 1-calculated and D 2-calculated from the combinations of x1 and x2 using Supplementary Equation 10 and Supplementary Equation 11, and then calculate ΔD 1 , ΔD 2 and ΔD respectively. Finally, the program selects the combination of x 1 and x 2 that corresponds to the minimized ΔD (ΔDmin) as the best values for the given D1-measured and D2-measured.
We select five cases from the mixed gas experiments, as shown by the measured data points A, B, C, D, and E in Supplementary Fig. 10, to implement the program. The experimental input gas concentrations, the measured detector responses, the minimized ΔD (ΔD min ), and the calculated gas concentrations are listed in Supplementary Table 6.
Ideally, if all the measured detector responses (purple squares) strictly follow the red dash lines in Supplementary Fig. 10, the calculated concentrations shall be the same as the experimentally used concentrations. However, it is seen that there are discrepencies between the calculated concentrations and the experimental concentrations. For example, case A in Supplementary Fig. 11 Another way to determine the values of x 1 and x 2 for the given D 1-measured and D 2-measured , is to set a certain error range of Δ and Δ , and search for the combinations of x 1 and x 2 whose corresponding Δ and To minimize the thermal cross-talk, the basic idea is to thermally isolate each narrowband detection element using its own heat sink. For example, the current 75μm thick LT substrate with built-in MIMs can be cut into separate narrowband detection elements. The separate detection elements can then be mounted on a PCB board via the pins that provide electrical connections, as shown in Supplementary Fig. 12. In this case the pins provide heat conduction to the PCB boards and thermally isolate each detection elements.

Supplementary Figure 12 | Packaging and thermal isolation of narrowband detectors using a PCB board
We also plan to fabricate MIMs on 700 nm thick LT thin film on silicon substrate (LTOI). To create themal isolation, one can fabricate deep trenches in the LT substrate between adjacent MIMs to reduce the thermal conduction, as shown in Supplementary Fig. 13.