Broadband Absorption Tailoring of SiO2/Cu/ITO Arrays Based on Hybrid Coupled Resonance Mode

Sub-wavelength artificial photonic structures can be introduced to tailor and modulate the spectrum of materials, thus expanding the optical applications of these materials. On the basis of SiO2/Cu/ITO arrays, a hybrid coupled resonance (HCR) mechanism, including the epsilon-near-zero (ENZ) mode of ITO, local surface plasmon resonance (LSPR) mode and the microstructural gap resonance (GR) mode, was proposed and researched by systematically regulating the array period and layer thickness. The optical absorptions of the arrays were simulated under different conditions by the finite-difference time-domain (FDTD) method. ITO films were prepared and characterized to verify the existence of ENZ mode and Mie theory was used to describe the LSPR mode. The cross-sectional electric field distribution was analyzed while SiO2/Cu/ITO multilayers were also fabricated, of which absorption was measured and calculated by Macleod simulation to prove the existence of GR and LSPR mode. Finally, the broad-band tailoring of optical absorption peaks from 673 nm to 1873 nm with the intensities from 1.8 to 0.41 was realized, which expands the applications of ITO-based plasmonic metamaterials in the near infrared (NIR) region.


S1.2 Drude model
Drude-Sommerfeld model is usually used to describe the optical constants of metal and metal-like dielectric films [1]: ( ) = 1 ( ) + 2 ( ) = ∞ − 2 2 + (1) ε ꝏ is the background dielectric constant (high frequency limit), ω p is the plasma frequency, and Γ represents the charge carrier collision rate, which directly affects the optical loss of materials. The plasma frequency ω p can be described as: Here, ε 0 is the dielectric constant in free space, n is the carrier concentration, e is the electron charge, and m* is the effective mass of the electron. The change of plasma oscillation frequency will directly affect the optical coupling mode between light and material or microstructures, thus modulating the position and intensity of optical absorption peaks.

S1.3 Surface plasma coupling effect
In optical microstructural arrays, the sizes of structures and materials are in the sub-wavelength range, where metals exhibit extraordinary local surface plasmon resonance (LSPR) effect. Based on Drude model, the LSP oscillation frequencies of lossless dielectrics in dielectrics and Drude metals are obtained as follows： Here, is for SPR peak frequency, is SPs frequency, the negative dielectric constant of the metal at this time is = 2 , n is the refractive index of environmental medium. According to reference [2,3]，the resonant wavelength is finally calculated by the relationship between 0 and n shown as follows: In this formula， is the dielectric constant of environmental medium. It shows that the extinction spectrum wavelength is determined by L (the size of metal nanoparticles), n (the refractive index of environmental media) and p  (the equivalent wavelength of metal materials).
In addition, the strength and occurrence conditions of LSPR effect will vary following with the change of size and shape of metal nanoparticles, It can be described by Mie-Theory and Gans-Theory [4][5][6].
Mie-Theory is described as follows: E( ) is the extinction spectrum，χ is for shape factor, is external dielectric constant, is real metal dielectric constant and is imaginary metal dielectric constant. The increase of diameter a can lead to the redshifts of the resonance wavelength ( ).
Gans-Theory extends the influence of shape on material extinction to nano-ellipsoid and nanorod [7]. The extinction coefficient is expressed as: Here，V is the spherical particle volume and ε is the dielectric constant of the surrounding medium (assumed to be frequency independent).
Among them, the polarization factor is shown as follows: Among them, A represents the long axis of the ellipsoid, B and C are related to the short axis, respectively. There are two maxima in extinction ratio spectra, corresponding to two resonance modes: longitudinal mode and transverse mode.

S1.4 Nonlinear ENZ Mode and Gap Coupled Resonance Mode
When the light is incident on the periodic metal/dielectric optical microstructures, the Epsilon-Near-Zero (ENZ) mode of ITO is excited by the incident light on the film surface. Then, the surface plasmon resonance (SPR) effect is produced with the light passing through ITO film to the metal layer.
At the same time, the gap in the structure shows a certain local effect on light.
When the light and microstructures are coupled and resonated, the strong electromagnetic field is confined to the gap region between the microstructures. The gap plasma mode is coupled and repulsed with ENZ mode in sub-wavelength microstructures. When they are coupled together, the absorption enhancement and the coupling of light field will be stimulated.
When they are mutually exclusive, the coupling mode will be detuned and the mixed coupling mode will split into two separate resonance modes. The ENZ mode has a great influence on the resonance in short near infrared wave, and the gap coupling resonance has a great influence on the long wave range of near infrared. In addition, the ENZ mode has a very large density of states. In our work, we choose ITO nano-films with sub-wavelength thickness as the top layer, whose near infrared plasma frequency can meet the generation of ENZ mode.

S2.2 FDTD simulation process
Before FDTD simulating, the original film and structure system were needed to be chosen in advance, and also the relevant material parameters.
The specific steps included shape design, material selection, size setting, light source and optical detector addition, scanning setting, mesh addition, optical simulation area setting, material or memory checking, simulation and data preservation. The following figure shows the material parameters used in the experiment. The ITO data were from our coating experiment. Figure S1. Material index data used in the simulations (including model data and material data of Cu and ITO).      Table S1. 16nm and 20 nm. Finally, the position and intensity of absorption peaks in S-NIR and M-NIR bands were obtained, as shown in Table S2.