# Broadband Plasmonic Metamaterial Optical Absorber for the Visible to Near-Infrared Region
## 3 Results Analysis
### Performance Evaluation for Solar Application  
A solar thermos photovoltaic (STPV) system needs three main components to work effectively. First component is broadband absorber that can absorb the entire solar spectrum, second one is narrowband emitter that converts absorbed energy from the absorber into heat and photons in a specific range above the PV cell's bandgap, and the last component is low bandgap PV cell to generate electron-hole pairs without thermalization losses. Metamaterials can be used to create the narrowband emitter and broadband absorber [32]. The efficiency of the emitter and absorber is given in Equation (10). \(A_{ab}\) and \(A_{em}\) represent the area of the absorber and emitter. The ratio of the area is \(\beta\). \(P_{sol}\), \(P_{ab}\) and \(P_{em}\) is Thermal irradiance of the Sun, absorber, and emitter. \(P_{sol}\) can be defined as input power. \(P_{ab}\), \(P_{em}\) and \(P_{sol}\) is described in Equations (11)-(13). T and N\({}_{\text{s}}\) is the temperature in kelvin and solar concentration, respectively. \(\varphi\) is the polarization angle, \(\theta\) is the incident angle, \(\varepsilon_{em}\) is emitter emittance, \(\varepsilon_{am}\) is absorber emittance, \(\lambda\) is the wavelength, \(I_{BR}\) is the equilibrium temperature blackbody radiation, and \(I_{sol}\) is solar radiation spectrum. \(P_{ab}\) at \(T\) temperature is given at Equation (14). \[\eta_{int}=\frac{A_{em}P_{em}}{A_{ab}P_{sol}}=\beta\frac{P_{em}}{P_{sol}} \tag{10}\]  
\[P_{ab}(T)=\int\limits_{0}^{2\pi}d\omega\int\limits_{0}^{\frac{\pi}{2}}\sin( \theta)\cos(\theta)d\theta\int_{0}^{\infty}\varepsilon_{ab}(\lambda,\theta, \varphi)I_{B}(\lambda,T)d\lambda \tag{11}\]  
Figure 12: The MA is bending (**a**) toward the inside (**b**) toward the outside. \[P_{em}(T)=\int\limits_{0}^{2\pi}d\omega\int\limits_{0}^{\frac{\pi}{2}}\sin(\theta) \cos(\theta)d\theta\int_{0}^{\infty}\varepsilon_{em}(\lambda,\theta,\varphi)I_{ B}(\lambda,T)d\lambda \tag{12}\]  
\[P_{sol}(T)=\int\limits_{0}^{2\pi}d\omega\int\limits_{0}^{\frac{\mu}{2}}\sin( \theta)\cos(\theta)d\theta\int_{0}^{\infty}\varepsilon_{ab}(\lambda,\theta, \varphi)I_{sol}(\frac{B}{\lambda M1.5})(\lambda)d\lambda \tag{13}\]  
\[P_{ab}(T)=P_{sol}(N_{s})-\beta P_{em}(T) \tag{14}\]  
The proposed MA can be used as a broadband absorber that absorbs the solar spectrum completely. Using Equation (14) in (10), the equation Equation (15) can be attained, which is independent of the emitter's thermal irradiance, making the absorber independent from the emitter. \[\eta_{int}=\frac{P_{sol}-P_{ab}}{P_{sol}}=1-\frac{P_{ab}}{P_{sol}} \tag{15}\]  
Figure 13 shows the position of MA in the STPV system. Variations of the absorber unit cell structure can result in different absorption in the solar spectrum. The solar spectrum universal characterization method (\(A_{AM1.5}\)) has been used to characterize terrestrial power generation of the MA universally. This method indicates the MA's feasibility for solar cell applications. Also, photon conversion is proportional to conversion efficiency values, which results in significant electron mobility. Given below is the expression mentioned in [29] for \(A_{AM1.5}\) calculation. \[A_{A.M1.5}=\frac{\int_{W_{1}}^{W_{2}}A(W)N(W)dW}{\int_{W_{1}}^{W_{2}}N(W)dW} \tag{16}\]  
Here in Equation (16), W is the wavelength of light, \(A(W)\) is the absorption of the proposed design, and \(N\) (\(W\)) is the allocation of photon numbers in the \(AM1.5\) solar illumination, a function of wavelength and is expressed as  
\[N(w)=\frac{S(w)}{E(w)} \tag{17}\]  
In Equation (17), \(E(W)\) is the energy of photon and \(S(W)\) is the solar spectral irradiance. ASTM G173-03 reference solar spectral irradiance (global tilt) has been used to calculate \(N(W)\). After deriving \(N(W)\)and \(A(W)\), the \(A_{AM1.5}\) has been calculated using Equation (16). The final structure of the MA unit cell obtained 90.76% \(A_{AM1.5}\). High value of \(A_{AM1.5}\) is an indicator of high solar cell photon conversion efficiency [33].