Spectral Characterization of Mid-Infrared Bloch Surface Waves Excited on a Truncated 1D Photonic Crystal

The many fundamental roto-vibrational resonances of chemical compounds result in strong absorption lines in the mid-infrared region (λ ∼ 2–20 μm). For this reason, mid-infrared spectroscopy plays a key role in label-free sensing, in particular, for chemical recognition, but often lacks the required sensitivity to probe small numbers of molecules. In this work, we propose a vibrational sensing scheme based on Bloch surface waves (BSWs) on 1D photonic crystals to increase the sensitivity of mid-infrared sensors. We report on the design and deposition of CaF2/ZnS 1D photonic crystals. Moreover, we theoretically and experimentally demonstrate the possibility to sustain narrow σ-polarized BSW modes together with broader π-polarized modes in the range of 3–8 μm by means of a customized Fourier transform infrared spectroscopy setup. The multilayer stacks are deposited directly on CaF2 prisms, reducing the number of unnecessary interfaces when exciting in the Kretschmann–Raether configuration. Finally, we compare the performance of mid-IR sensors based on surface plasmon polaritons with the BSW-based sensor. The figures of merit found for BSWs in terms of confinement of the electromagnetic field and propagation length puts them as forefrontrunners for label-free and polarization-dependent sensing devices.


Deposited layers surface characterization
The deposited single layers and multilayered structures (ML) have been characterized by atomic force microscopy (AFM). Films with different thickness have been deposited to follow the morphology evolution through the whole deposition process. Figure S.1a, b and c show AFM images of CaF2 layers with increasing thickness (110, 1850 and 2750 nm respectively) evaporated on CaF2 substrates. Initially, the CaF2 layer is homogenous with a grainy like structure of the surface. Increasing the thickness, regular protruding structures emerge: panels S.1b (thickness of 1850 nm shown in plan view) and S.1c (thickness of 2750 nm shown with 3D rendering) show clearly a columnar triangular arrangement, as mentioned in the main text. On the other hand, the ZnS layers deposited on the CaF2 substrates, with the CaF2 adhesion layer, maintain a flat and homogeneous surface even for large thickness, as shown in Figure S.1d and e, were AFM images of 110 and 870 nm thick ZnS layers are reported. Figure S.1f reports the surface morphology of the multilayer with structure from top to bottom ZnS(50nm)/ CaF2(2500nm)/ ZnS(200nm)/ CaF2(2500nm)/ ZnS(200nm)/ CaF2(adlayer)/ CaF2 substrate) (structure B) and the corresponding FIB-SEM section is in the inset (note that the AFM image is shown in 3D rendering). Apparently, the triangular columnar structures, distinctive of the CaF2 layers, are still quite well visible in the multilayered structures, pointing to a conformal coverage of the CaF2 structures, confirmed S2 also by the FIB-SEM analysis (see Figure S.1g). This indicates that the intercalation of the ZnS layers between CaF2 layers do not influence consistently the sample morphology, besides a granular fine structure of the surface essentially due to the presence of the 50 nm thick ZnS cap layer.
The surface morphology evolution can be quantitatively described in terms of the RMS surface roughness analysis, as shown in Figure S.2. It is apparent that upon increasing the thickness the roughness of the deposited CaF2 (black square dots) increases up to a saturation value of about 30 nm. Conversely, the roughness of the deposited ZnS layers (red circle dots) decreases from an initial value of about 3 nm to values between 1-2 nm.  In the same graph, the roughness of the multilayered structure B, described in Figure S.1, is reported (pentagonal light blue dot). This roughness value is compatible with the saturating behaviour of the CaF2 roughness since, as previously pointed out, the deposition of the ZnS layers is essentially conformal.

Voids in the CaF2 thick layers
The Figure   The FIB-SEM cross section morphological analysis permit to obtain an estimation of the void percentage in the CaF2 layers. The images have been processed using the Image J analysis software. Wide enough FIB-SEM images were considered so that the extrapolated value can be representative of the whole sample and the images has been resized in order to account for the sample tilt angle. The Figure S.3b shows an example of the void analysis layer (red/grey frame) superimposed to a FIB-SEM cross section image (in grey scales), with red areas corresponding to the voids.
The area of the voids estimated by this procedure is around 30% of the total area, for both the CaF2 layers in the multi-layered structure. Assuming that the voids visible on the surface section are homogeneously distributed in the volume, we can describe the film as an effective medium made by CaF2 with 30% of voids [1]. This value is quite comparable with that found by fitting the infrared data, though somewhat lower. The discrepancy can be attributed to a partial filling of the voids' cavity due to the redeposition of FIB milled material during the definition of the cross section.

Infrared characterization of the deposited material
In order to assess the quality of the deposited materials, we have measured single layers of ZnS and CaF2 as well as multilayers deposited on flat substrates. Transmission (Reflection) measurements have been performed at (near-) normal incidence. We find that there are small amounts of impurities that are incorporated in the CaF2 layers, yielding some absorption peaks between 1000 and 2000 cm -1 and at about 3000 cm -1 , while no evidence of absorption peaks is found for ZnS layers, as shown in Figure Figure S.5a and b, we show reflection measurements performed at (near-) normal incidence of the multilayers structure C and D compared with the corresponding fit curves. We get refractive index values of n = 1.20 ± 0.05 and 2.20 ± 0.02 for CaF2 and ZnS, respectively, as for the multilayered structure described in the main text confirming that the layers morphological properties described above are highly reproducible.

Transfer Matrix Method
The distribution of the electric field inside each homogeneous layer can be expressed as the sum of an incident plane wave and a reflected plane wave. The complex amplitudes of these waves are the elements of a column vector [2]. The electric field into the external medium in contact with the dielectric stack (1DPC) is related to the field into the incidence medium by the following: For both the relations, λ is the radiation wavelength in µm.
As reported in the main text, the deposited materials are characterized by a porosity that is not neglectable. To take into account the porosity, we used the Maxwell -Garnett mixing rule [5] to calculate the refractive index of the composite material: A multilayer stack characterized by a periodical refractive index function shows the opening of photonic band gaps where the light cannot propagate, as extensively discussed in literature [6]. For two materials with refractive indices nL and nH and thicknesses dL and dH=Λ-dL, where L and H stay for low and high refractive index, respectively, the normalincidence photonic gap is maximized when [ By choosing λ0 = 5.6 µm, as reported in the main text, and θ = 55 deg, equal to the basis angle of the CaF2 truncated prism used for our experiments (see main text), we obtain Λ = 3.1 µm and dH/Λ ratio equal to about 0.65 (quarter-wave stack).
Figure S.6. Reflectance maps (left) and 2D reflectance profiles (right) calculated for different 1DPC structures. In the 2D plots, we plot the reflectance profiles obtained for λ = 4 µm and λ = 5 µm. In the insets, we sketch the simulated structures obtained by increasing the low refractive index material thickness (going from a) to d)).
In Figure S.6., we report some examples about the reflectance map calculated for the structures sketched in the insets. To optimize the structure, we started from the values of dL and dH obtained through the Eqs. (S. 1) and (S. 2). For the sake of simplicity, we report only the reflectance maps obtained by changing the low refractive index layers thicknesses (CaF2). The reflectance maps, as in the main text, are calculated for θ ranging from 40 to 75 deg, whereas the wavelength from 1 to 10 µm. From the reflectance map, we can retrieve information about the dependence of the BSW angular position on the wavelength. By increasing the CaF2 thickness, the BSW dispersion shows a larger slope, thus indicating a larger sensitivity of the BSW angular position to wavelength changes. On the contrary, the 2D reflectance signal plotted by cutting the reflectance maps at λ = 4 µm and λ = 5 µm shows that by increasing the low refractive index layer thickness (going from the figure a) to d)) the BSW resonance appears less deep. Moreover, the BSW dip moves to higher angles, far from θ = 55 deg. By further increasing the thickness of the low refractive index layers, the BSW resonance disappears in the range of angles and wavelength used in our experiments. Similar results are obtained by changing the high refractive index layer thickness. By fixing dL = 2.20 µm, for dH larger than 1.1 µm, the BSW resonance dip disappears from the angular and spectral range of our interest.
In Figure S.7., we report the optimal structure: dL = 2.20 µm and dH = 1.00 µm. The BSW resonance appears deeper because of the maximum field enhancement (see main text). By properly fixing the cap layer thickness to dCL = 200 nm, the BSW angular position is located at θ = 55.2 deg at λ0. A larger cap layer thickness means a larger BSW angular position.
In conclusion, by taking into account the accuracy of the deposition technique, the structure we proposed is dL = 2.25 (±0.15) µm, dH = 0.95 (±0.10) µm and dCL = 0.19 (±0.04) µm, as reported in the main text.  To evaluate the BSW propagation distance by the Eq. (2) and the penetration depth, we found the formula parameters from the reflectance map calculated by TMM and reported in Figure 5(a) in the main text. For each wavelength ranging from 3.5 to 7.5 µm, the BSW resonance dip has been fitted by a Lorentzian curve: The fitting procedure provides the dip central angle ( ‰iŠ ( )) and the dip full width half maximum (FWHM, ∆ ( )).
As an alternative method to evaluate the FoMs, we have resorted to a second possible way to calculate the propagation lengths starting from the definition of quality factor as the ratio between the energy ( ) stored in the oscillating resonator and the energy dissipated per cycle by damping processes ( ). Therefore, we can write = By following the same line of thought, we can estimate the propagation length in this way for the BSW, by considering wavelength and FWHM from our simulations. The results show that WŠrk is larger than what discussed in the paper, yielding higher values of FoMprop, that are however still lower than those of Au at infrared wavelengths. We report in Figure S.9 the comparison among the propagation lengths calculated as reported in the main paper and with this approximation. Figure S.9. Comparison of the propagation length, plotted with respect to the wavelength, calculated either as described in the main paper [7] (dark blue) or with the method described above (light blue).