Generalized Brewster-angle effect in thin-film optical absorbers and its application for graphene hydrogen sensing

Generalized Brewster angle (GBA) is the incidence angle at which polarization by reflection for p- and s-polarized light takes place. Realizing s-polarization Brewster effect requires a material with magnetic response which is challenging at optical frequencies since the magnetic response of materials at these frequencies is extremely weak. Here, we experimentally realize GBA effect in the visible using a thin-film absorber system consisting of a dielectric film on an absorbing substrate. Polarization by reflection is realized for both p- and s- polarized light at different angles of incidence and multiple wavelengths. We provide a theoretical framework for the generalized Brewster effect in thin-film light absorbers. We demonstrate hydrogen gas sensing using a single layer graphene film transferred on a thin-film absorber at the GBA with ~1 fg/mm2 aerial mass sensitivity. The ultrahigh sensitivity stems from the strong phase sensitivity near point of darkness, particularly at the GBA, and the strong light-matter interaction in planar nanocavities. These findings depart from the traditional domain of thin-films as mere interference optical coatings and highlight its many potential applications including gas sensing and biosensing.


Sample fabrication
Thin-film absorbers: To fabricate the thin film absorber, 500 nm thick MMA copolymer from MICROCHEM (8.5MMAEL 11) was spin coated at 3000 rpm on 700 µm thick Si substrates and 30 nm thick Ge layer deposited glass substrates. The Ge layer was deposited by thermal evaporation (Oerlikon Leopold vacuum system) of Ge pellets at a deposition rate of 0.2 Å/s and a base pressure of <5 x 10 -6 mbar.
Thin-film meta-surface light absorber: Films were deposited on a glass substrate (Micro slides, Corning) using electron-beam (e-beam) evaporation of Ni and TiO2 pellets (Kurt J. Lesker). The deposition rate of Ni and TiO2 were 0.5 and 1 10 A. s −1 .
Graphene-based thin-film absorbers: To fabricate the graphene based thin film absorber, the graphene was grown on 25 µm thick copper foil using the conventional chemical vapor deposition method. Prior to deposition of graphene, copper foil was cleaned thermally at 1000 C in the presence of 2 SCCM hydrogen. Thereafter, 10 SCCM CH4 injected into the chamber to deposit the graphene at 1000 C for one hour. After deposition of graphene, the copper foil was rapidly cool down to room temperature. 500 nm thick MMA was spin coated on the graphene/Cu at 3000 rpm. MMA/graphene deposited on copper foil was transfer to the Si substrates using the wet chemical etching technique. The MMA/graphene/Cu was immersed in the FeCl3 solution with its MMA/graphene facing upward for 2 hours. After copper etching, remaining MMA/graphene, was transferred to the deionized water to remove the unwanted impurities from the FeCl3 solution. The cleaning process was repeated for 3 times with 1-liter fresh deionized water. The cleaned MMA/graphene was transfer to the Si to design the graphene/MMA/Si hetero-structure.

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Thereafter, the designed graphene/MMA/Si was kept in the 60 C preheated oven for 6 hours to evaporate the deionized water. The designed structure was used for the hydrogenation using plasma.

Angular reflection measurements
Angular reflection was measured using Variable-angle high-resolution spectroscopic ellipsometer (J. A. Woollam Co., Inc, V-VASE). The transmittance is zero for all wavelengths and angles. Since we are dealing with thin films, perfect light absorption corresponds to near zero reflectance. We consider ≤ 5 ×10 -4 to be zero reflectance since this is the noise limit of the detector which is determined by considering an incident p-polarized light on a non-chiral film and measuring the sto-p reflectance which gives us the detector noise level for the parameters adopted in our measurements.

Hydrogenation of graphene-based thin-film absorbers
Hydrogenation of graphene transferred on the graphene/MMA/Si were performed low power capacitively coupled RF plasma of the hydrogen and argon gas. The graphene/MMA/Si heterostructure was place in the quartz tube and evacuated to 10 -3 mbar prior to the hydrogenation. To perform hydrogenation, RF plasma was generated between the two copper electrodes on the quartz tube. To this end, the 30-Watt RF plasma was generated by flowing 2 SCCM hydrogen and 15 SCCM argon gas while maintaining the chamber pressure of 0.13 mbar. The sample was placed in between the electrodes separated by a safe distance of 15 cm from the discharge zone to avoid the direct exposure. The graphene/MMA/silicon was exposed to three different time duration of RF plasma i.e. 1, 2 and 5 minutes. The plasma exposure will attach the hydrogen to the surface of the graphene. The hydrogenation of graphene in the graphene/MMA/Si structure was investigated by S4 measuring the intensities of D and G peak of the hydrogenated graphene as a function of the plasma exposure using the Raman spectra (Renishaw Invia spectrometer, 632.8 nm excitation wavelength). The estimated distance between the defects after first hydrogenation (for 1 min) is,  which is far below the low-defect density regime 1 .

Spectroscopic characterizations:
Variable-angle high-resolution spectroscopic ellipsometer (J. A. Woollam Co., Inc, V-VASE) was used to determine the thicknesses and optical constants of MMA and Ge layers. The polarized reflectance spectra as a function of wavelength and incident angle were acquired using the same instrument with a wavelength spectroscopic resolution of 2 nm and an angular resolution of 1°. The ellipsometry parameters (ψ and Δ) as a function of incident angle were acquired using the VASE ellipsometer with an angular resolution of 1°. All the ψ and Δ spectra were acquired by selecting high accuracy mode in the ellipsometer. Furthermore, the complex refractive indices of MMA, Ni, and TiO2 were obtained by fitting the ellipsometry parameters.
Numerical simulations: Numerical reflection spectra and ellipsometry parameters spectra were generated using a transfer matrix method-based simulation model written in Matlab. The calculated reflectance spectra of Graphene-MMA-Si device and the calculated power dissipation distribution in the thin-film stack was performed using the commercially available finitedifference time-domain software from Lumerical ® . The simulation was performed using a 2D model with incident plane wave at zero incidence angle. Periodic boundary conditions were used in the x-direction and perfectly matched layers where used in the y-direction (normal to the sample). The mesh was tailored to each layer with a mesh step of 0.0005 µm for the graphene layer and 0.005 µm for the rest of the structure.

Theoretical framework
We investigate the proposed design, i.e., a lossless dielectric film on a substrate with optical losses.
Our system consists of a superstrate (refractive index 0 ), a dielectric layer (refractive index , thickness d), and a lossy substrate (refractive index + ). Using transfer matrix theory 2 , one can express the complex reflection coefficient of this system as where are the entries of the transfer matrix for the dielectric layer, In Eqs. (3) where 0 is the incident angle and the two results in each case correspond to and polarized incident light. The angle Φ ≡ 2 −1 √ 2 − 0 2 sin 2 ( 0 ) in Eq. (2) is the phase thickness of the dielectric layer, where is the wavelength of the incident light. Note that 0 and are both real, while = + is complex when > 0, with real and imaginary parts and , respectively.

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Zero reflectance occurs when the numerator of Eq. (1) is equal to zero, which is equivalent to requiring that the real and imaginary parts of the numerator separately equal zero. This gives two equations defining the conditions for zero reflectance,   case, field is tightly confined inside the MMA layer for s-polarization at s-polarized Brewster angles. Also note that low intensity field is confined inside the MMA layer even with ppolarization. This is because the reflected light intensity for p-polarization at s-polarized Brewster angle is only around 40 % and 20% at 450 nm and 752 nm, respectively (see Fig. S3 e, f). The remaining field intensity is confined inside MMA layer and absorbed in the Si layer. It is clear from Fig. S4e & Fig. S4g.    Figure S9. The isolated absorptance of graphene layer calculated on an MMA-Si stack (a) and of graphene on glass (b) which shows the enhanced absorptance of graphene due to destructive interference. Clearly, the absorption in graphene increased by an order of magnitude when it is a part of the thin-film stack. Note that this is the isolated absorptance of graphene and not the absorptance of the entire system. S12 Figure S10. The calculated phase upon reflection from an MMA-Si stack vs. graphene-MMA-Si stack as a function of angle for (a) s-polarized light and (b) p-polarized light. The addition of graphene changes the angular reflection phase for both s-and p-polarizations. Figure S11. The calculated (a) ψ (b) Δ spectra at the Brewster angle for an MMA-Si stack vs. graphene-MMA-Si. Both ψ and Δ values, which determine the Brewster angle, change by adding graphene layer. S13 Figure S12. Raman D peak change with hydrogenation time. Figure S13. FDTD calculation of the power dissipation density inside the graphene-MMA-Si structure at 73° incidence angle. S14 Figure S14. Reversible hydrogenation of graphene-MMA-Si stack: As graphene is hydrogenated, it transitions from a semi-metal to an insulator. Accordingly, hydrogenation is associated with increase in the measured resistance across the graphene sheet as we see in (a). As we anneal the sample at 150 o C, the measured resistance drops as shown in (b) indicating that graphene is becoming a semi-metal. Note that here we used higher plasma exposure time because the sample was placed in between the electrodes separated by a distance of 20 cm.