Wide angle and narrow-band asymmetric absorption in visible and near-infrared regime through lossy Bragg stacks

Absorber is an important component in various optical devices. Here we report a novel type of asymmetric absorber in the visible and near-infrared spectrum which is based on lossy Bragg stacks. The lossy Bragg stacks can achieve near-perfect absorption at one side and high reflection at the other within the narrow bands (several nm) of resonance wavelengths, whereas display almost identical absorption/reflection responses for the rest of the spectrum. Meanwhile, this interesting wavelength-selective asymmetric absorption behavior persists for wide angles, does not depend on polarization, and can be ascribed to the lossy characteristics of the Bragg stacks. Moreover, interesting Fano resonance with easily tailorable peak profiles can be realized using the lossy Bragg stacks.

Scientific RepoRts | 6:27061 | DOI: 10.1038/srep27061 Finally, it needs to be pointed out that one major obstacle hindering the practical applications of advanced absorbers, particularly those in the visible and infrared region, arises from their elaborate nanostructured surface patterns, which not only lead to high fabrication cost but also limit the sample size. By contrast, the lossy Bragg thin films proposed here are free from elaborate surface patterns and can be conveniently fabricated over a large area using convenient vapor deposition or electrochemical methods 42 .

Structural and theoretical model
The proposed lossy Bragg structure is schematically shown in Fig. 1, consisting alternating Sub-layers A and B, with the "left" surface being a Sub-layer A and the "right" surface being a Sub-layer B. The light propagation directions are also shown in Fig. 1: incident from "left" -light incident on a surface sub-layer of A; incident from "right" -light incident on a surface sub-layer of B. The thicknesses of the sub-layers A and B are denoted as d A and d B . The complex refractive index of the sub-layers A and B are described as ñ A = n A + κ A i and ñ B = n B + κ B i, while the relative permeability of sub-layers A and B is regarded as 1. The period number (i.e., the repeating number of AB or BA in the structure) of the Bragg stack is denoted as m. For simplicity, we set k A d A = k B d B , where k i = ñ i (ω /c) (i = A, B). At resonance wavelengths, In this paper, we used the Transfer Matrix method (TMM) and the finite-difference time-domain (FDTD) method 43 to calculate the optical properties of lossy bragg stacks.

Results and Discussion
It is set that = = = . Note that the ratio between the real and imaginary parts of the refraction indexes is set to be the same here is for the calculation convenience, but not a necessity. The TMM produces the complex wavelength-dependent parameters reflectivity, r, and transmissivity, t. Reflection, transmission and absorption are defined as = R r 2 , = T t 2 , and A = 1 − R − T, respectively. It is assumed that the lossy Bragg structure is thick enough to make T equal to near zero, for simplicity, we assumed A = 1 − R, indicating the equivalence of the reflection asymmetry and the absorption asymmetry. Figure 2 shows that the reflection asymmetry depends on the parameters n A , v and u. The color scale in Fig. 2 represents the degree of asymmetry (DoA) which is defined as DoA = R right /R left . When v is increased, the maximum value of DoA is decreased. Meanwhile, this maximum tends to appear at high value of n A . The maximum value of DoA was found when n A = 4.9, u = 0.01, v = 1.08. Unless otherwise stated, the default parameters are set as follows: ñ A = 4.9 + 0.049 i, ñ B = 5.3 + 0.053 i, m = 30, d A = 25.5 nm, and d B = 23.6 nm.
The reflection, transmission and absorption spectra of typical lossy Bragg stack were shown in Fig. 3(a,b) for different light propagation directions. The finite-difference time-domain (FDTD) method was also adopted to calculate the absorption spectra. For FDTD simulation, we have used periodic boundary conditions along the x and y axes, and PML boundary conditions along z axis (the light propagation direction). Unlike otherwise stated, the structural periodicity of the lossy Bragg stack is set as 30. The absorption spectra of a lossy Bragg structure calculated using  the TMM and FDTD method are shown in Fig. 3(c,d). At the Bragg resonance wavelength of 500 nm, an absorption peak and dip are observed for light propagating from "left" and from "right", respectively (see Fig. 1 for the "left" and "right" sides). It should be pointed out that the Bragg resonance wavelength can be easily controlled by adjusting the structural or optical parameters of the Bragg stack, e.g., by tuning the thickness of the sub-layers. Notably, little absorption/reflection asymmetry is observed for the rest of the spectra. Therefore, a novel thin-film type of optical device whose two surfaces are able to exhibit dramatically different optical response selectively only within an exceptionally narrow band of several nanometers Fig. 3(d) in the visible and near-infrared spectrum can be achieved using the design proposed in this study. Furthermore, the DoA peak appears to be sensitive to the changes of the refractive index, indicating the potential optical sensing applications of the lossy Bragg structures. For example, when ñ A is changed from 4.90 + 0.049 i to 4.95 + 0.049 i, and ñ B changed from 5.30 + 0.053 i to 5.35 + 0.053 i, a notable red-shift of the DoA peak is resulted in Fig. 3(e). Considering the high similarity of the mathematic models between the lossy and dielectric Bragg stacks, the tolerance of the optical responses of the proposed lossy Bragg stacks to the structural or optical parameter imperfection should be at a very similar level as the conventional dielectric Bragg stacks.
One may ask why the lossy Bragg structure displays the above-discussed absorption asymmetry at the resonance wavelength, whereas the dielectric Bragg structure does not. To explain this discrepancy, let us consider one period first. Its corresponding transfer matrix can be written as 44 :  For a Bragg stack with the number of periodicity, m, the corresponding transfer matrix can then be written as: where F R is the real part of F, F I the imaginary part of F, and η is piecewise defined as The respective reflection for forward and backward directions is: It is obvious that the difference between the forward and backward reflection is correlated with the difference between G and G * .  ≠ 0), the models of G and G* are different, leading to reflection asymmetry. It should be pointed out that, by carefully designing the optical parameters of the lossy Bragg stack proposed in this study, it is potentially feasible to accomplish the recently reported asymmetric Bragg reflection that was realized in the complex crystals and PT-symmetric periodic structures [39][40][41] .
The electric field distribution (at λ = 500 nm) for the lossy Bragg stack was simulated using the FDTD method (Fig. 4). When propagating from "left", most light enters the structure and gets absorbed; On the contrary, most light is reflected when propagating from "right".
The asymmetric absorption/reflection behaviors of the lossy Bragg structures are found insensitive to TE polarization (Fig. 5a) and TM polarization (Fig. 5b) and possess good tolerance to wide incident angles. When light propagating from "left", an absorption efficiency of 50% is observed at the incident angle of 60° and 85° for the TE and TM polarization, respectively. For light propagating from "right", low absorption (high reflection) is sustained up to 90° for the TE polarization, while for the TM polarization low absorption is observed up to 60°. The high absorption emerges at high angles (~82°) for the TM polarization can be explained by the Brewster's law.
Interestingly, by changing the thickness of the top Sub-layer in the lossy Bragg stack, the profile of the resonance absorption/reflection spectrum can be varied precisely from symmetric to asymmetric (Fig. 6), i.e., the Fano resonance can be induced. Remarkably, by adjusting the thickness of the top sub-layer of the lossy Bragg structure, the peak profile can be rotated from 0° to 360° continuously (Fig. 6). The Fano resonance observed here is possibly resulted from the interference between the radiative mode and the localized mode (Tamm states). The radiative mode originates from the periodic multilayered structures. Previous studies 45,46 have shown that the Tamm states are localized at the interface between a truncated periodic multilayer and a semi-infinite homogeneous medium (e.g., air). Here in this study, when the surface layer (taking Sublayer A for example) of a lossy Bragg stack is truncated, the wavevector of Tamm states for TE and TM polarizations can be respectively written as 45 : Here, k a is the wavevector in Sub-layer A, M 11 and M 12 the elements of the transfer matrix of one period, σ ∈ [0, 1] the thickness portion of the truncated Sub-layer A, K the Bloch wave vector, d the thickness of one period, and d a the length of Sub-layer A. The Tamm states (localized mode) exist when and only when there is a truncated surface sublayer, so do the Fano-type profiles in the absorption spectra, confirming that the presence of Fano resonance is due to interference between the localized mode (Tamm states) and the radiative mode (originated from periodic structures).
For practical applications, porous metals (e.g. Pt, Ni, Pd, Cr) can be used to construct the proposed lossy Bragg structures. Regarding the manufacturing method, the lossy Bragg structures can be potentially constructed by the convenient vapor deposition or electrochemical method. The Lorentz-Drude (LD) model was used to describe  distribution (at λ = 500 nm) of the typical lossy Bragg stack for light propagating from "left" to "right" (upper) and from "right" to "left" (lower).  metals with the relative complex permittivity 47,48 (the relative permeability is 1). The effective permittivity of the porous metal sub-layers can be tuned by controlling its porosity. For example, let us set the porosities of Sub-layers A and B, p A and p B , 0.4 and 0.3, respectively (i.e. the metal volume percentage of Sub-layers A and B, fa and fb,is 0.6 and 0.7, respectively), the thickness of each sub-layer 100 nm, and the periodicity 15. In the condition of the porous metallic feature sizes of the porous sub-layers significantly smaller than the light wavelength, each sub-layer can be treated as a homogeneous material with the effective permittivity, ε eff . According to the Maxwell-Garnett effective medium theory (MGEMT), The absorption behaviors of metal-based lossy Bragg stacks are simulated (Fig. 7a). Among the different metals simulated (Pd, Ni, Cr, and Pt), Pd shows the most dramatic absorption/reflection asymmetry with highest value of DoA (Fig. 7b). The porous Pd-based Bragg stack displays a near-perfect (99.6%) absorption peak for light propagating from "left" , and an absorption dip (45% efficiency) for light propagating from the opposite direction.
In order to enhance the relatively low DoA value observed for pure metal-based lossy Bragg stacks, other material systems are further investigated. Encouragingly, for practical applications at the telecom wavelength of 1550 nm, the composite material of Al nanoparticles-embedded Al 2 O 3 has been identified as a promising candidate for constructing the proposed lossy Bragg stacks. Experimentally, the Al/Al 2 O 3 based Bragg stacks can be constructed through either the convenient vapor deposition (e.g., by co-sputtering Al and Al 2 O 3 ) or electrochemical (e.g., by electrodepositing Al in the anodic Al 2 O 3 template) methods. When the Al particle sizes are significantly smaller than the light wavelength, each sub-layer can be treated as a homogeneous material. The Lorentz-Drude (LD) model was used to describe metals with the relative complex permittivity (the relative permeability is 1). The effective permittivity (ε eff ) of Sub-layer A or B can be tuned by adjusting the Al volume percentage (f) in the corresponding sublayer (Fig. 8a). According to the Maxwell-Garnett effective medium theory (MGEMT), when the refractive index of Al 2 O 3 = 1.76, Al vol% = 70% for Sublayer A, Al vol% = 75% for Sublayer B, d A = 73.5 nm, d B = 70 nm, and m = 100, the desired asymmetric absorption behaviors are clearly observed (Fig. 8b) with a sharp DoA peak located at the resonance wavelength of 1550 nm (Fig. 8c).

Conclusion
Lossy Bragg structures have been theoretically investigated as a novel type of asymmetric absorber/reflector in a narrow bandwidth, insensitive to the incident angle and polarization. The reflection coefficient of the lossy Bragg stacks has been derived by the Transfer Matrix method, revealing that the asymmetry is mainly due to the lossy characteristics of the stacks. Interestingly, Fano resonance can be potentially realized using the lossy Bragg structures as well. For realistic device construction, Al embedded Al 2 O 3 can be used to construct the proposed lossy Bragg structures. Furthermore, According to the Kirchhoff 's law 49 , the proposed Bragg absorbers may also be used as asymmetric thermal emitters, enabling greatly improved emitter performance by selectively suppressing emission from the non-active surface. Moreover, the novel metal-based Bragg absorbers can fully utilize the many desirable attributes of metals, (e.g., high conductivities), and enable novel multi-functional optical devices for sensing, logic gates, unidirectional thermal emission, and photovoltaic cells. For example, ultra-sensitive optical sensors, or photocatalytic thin-film electrodes with the two surfaces having dramatically different catalytic efficiencies at targeted wavelengths, can be realized. Another potential photovoltaic application based on the Thomson effect involves irradiating the lossy Bragg thin films to produce a temperature gradient and further induce a voltage across the two film surfaces. Furthermore, the concepts and structural designs proposed in this study may potentially be applied in phononic crystals, to realize wavelength-selective asymmetric phonon responses 50 .