1. Introduction

Structure with high absorption is important at present for various nanotechnologies such as solar cells, thermal detectors [1], and time-reversed lasers [2]. Perfect absorber is a recent concept proposed by Padilla et al. in the year of 2008 [3]. They demonstrated that near-unity absorption was achievable in metamaterials by properly engineering electric and magnetic responses to satisfy the impedance-match. With above ideal, successively, many attention are paid to realize polarization-insensitive [4], wide-angle [5], dual-band [6], and broad-band metamaterial absorbers [7] from terahertz to optical frequencies. Based on the perfect abosrption, refractive index sensors [8], all-optical switches [9], and subsampling infrared images [10] have been recently achieved.

Optical Tamm states (OTSs) are a kind of surface mode occurring at the interface inside one-dimensional photonic crystal (PhC) heterostructures [11]. Comparing with traditional surface waves, it can be directly formed in both the TE- and TM-polarizations and occurs even at normal incidence, thus attracts a great attention both theoretically and experimentally [12–14]. The OTSs have been applied in polariton lasers [15], optical switch [16], and enhancement of Kerr nonlinearity [17], Faraday rotation [18], polariton integrated circuits [19], and excitation of hybrid one-dimensional plasmon-polariton modes [20], etc. Different with the physical mechanism of the absorbers reported in [3–10], in this paper, taking advantage of the OTSs in a plasmonic metal-dielectric-metal (MDM) waveguide we present a novel design of perfect absorber. With the transfer-matrix-method (TMM) and the finite-difference time-domain (FDTD) method, the proposed absorber spectra and filed distributions are investigated. The results demonstrate that the OTSs locating at the wavelength near the central stopband of the PhC are excited at the boundary between the TML and PhC, which makes the light wave to be trapped in the MDM waveguide core and leads to near-unity absorption of the incident energy. The proposed structure has compact size and high absorption, thus is a promising candidate for highly integrated photonic circuits.

2. Design of the OTSs-assisted near-unity absorber

The proposed absorber is based on a two-dimensional plasmonic MDM waveguide and is schematically shown in Fig. 1(a) . An air core with width of w is sandwiched by an upper and lower semi-infinite metallic claddings, and thin metallic layer (TML) with length of L_m followed by a dielectric PhC is inserted in it. The PhC is consisted by alternately staking two dielectric layers of A and B with N periodic. The refractive indexes and lengths for each layer A and B are n_a and n_b, L_a and L_b, respectively.

 

Fig. 1 (a) Schematic diagram of the proposed perfect absorber. A TML is arranged in the air core of the two-dimensional MDM waveguide, and a PhC with N periodical dielectric layers of A (TiO ₂) and B (PSiO ₂) is adjacent to it. (b) The real and (c) imaginary parts of the effective refractive indexes for SPPs propagating in the dielectrics A (red solid line) and B (blue dotted line), respectively.

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The MDM waveguide is one of the most used structures in plasmonic nanodevices due to its strong localization with an acceptable propagation length [21], and zero bend loss as well as relatively simple fabrication [22]. When a TM-polarized light wave is illuminated to the MDM waveguide as shown in Fig. 1, SPPs are excited and propagating along the dielectric core [21]. While the SPPs penetrate the TML and travel to the dielectric layers, they possess an effective refractive index n_eff determined by the dispersion relation of [21,23–25]

Here, k_{d , m} = (β_spp ²-ε_d,mk₀ ²)^0.5 and n_eff = β_spp/k₀. The β_spp is the propagation constant. The ε_d and ε_m are the permittivity of the dielectric and metal, respectively. The k₀, k_d and k_m are the propagation constants in the vacuum, dielectric and metal, respectively.

In our design, the metal is chosen as silver whose permittivity can be characterized by the Drude model of [24]

In our simulations, the structure geometric parameters are chosen as: L _m = 22 nm, L _a = 140 nm, L _b = 220 nm, and N = 10. Since the optical wave incident to the structure propagates only in the mutilayers of the MDM waveguide core, the spectra of MDM structure can be calculated by the TMM [25,26]. Taking into account both the real and imaginary parts of n_eff (as shown in Figs. 1(b) and 1(c)) in the TMM, the structure reflection (R), transmission (T), and absorption (A = 1-R-T) are calculated as shown in Fig. 2 . Figure 2(a) displays the R and T for the MDM waveguide with single TML or (AB)₁₀ in the core, respectively. It illustrates that when a TML is in the MDM waveguide core, the R is almost unity in the whole wavelength ranges. It is due to that the L _m approaches to skin depth of the silver. While the PhC of (AB)₁₀ is in the MDM waveguide core, the structure acts as Bragg gratings and a stopband from about 1240 nm to 1700 nm is generated. The optical wave locating in the stopband will be totally reflected.

 

Fig. 2 (a) Reflection (R) and transmission (T) spectra for the plasmonic MDM waveguide with single TML or (AB)₁₀ in the core, respectively. (b) Transmission, reflection, and absorption spectra calculated by the TMM and FDTD method for the MDM waveguide with the TML followed by the (AB)₁₀ in the core, respectively. The structure geometric parameters are: w = 80 nm, L _m = 22 nm, L _a = 140 nm, L_b = 220 nm, n_a = 2.13, and n_b = 1.23.

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When both the TML and the (AB)₁₀ are both arraged in the MDM waveguide core as shown in Fig. 1(a), zero reflection appears at 1550 nm as plotted in Fig. 2(b). The reflection dip arises from excitation of the OTSs at the boundary between the TML and the (AB)₁₀, and locates in the stopband of the PhC while a litter longer than the central wavelength of the stopband, which is similar to the phenomena in two specially designed periodic dielectric structures reported in [11]. At the frequencies far away the OTS mode, the TML is opaque and the incident optical light is almost totally reflected. At the frequencies near the OTS mode, due to the excitation of OTSs the optical wave is trapped in the TML/(AB)₁₀ boundary and decays significantly in the (AB)₁₀ and thereby no transmission occurs either. Therefore, the transmission is almost zero in all the wavelengths as shown in Fig. 2(b). As a result, a sharp absorption peak with value of 0.991 happens at the zero reflection dip. The designed absorber has a FWHM of 20 nm which is smaller than that of the absorbers reported in [8,10], thus are more attractive for sensing and imaging applications. The curve with black circle in Fig. 2(b) demonstrates the structure absorption spectrum obtained by the FDTD method. It shows that the TMM results agree well with that of the FDTD, which validates the TMM model for dealing with the proposed structure. To investigate the effect of the metal loss on the structure properties, the structure spectra at different value of collision frequency γ are plotted in Fig. 3 . It indicates that as the γ is decreased, the reflection spectrum have a higher but narrower trend. When the γ is decreased to zero, the reflection is near-unity and perfect absorption will not happen anymore.

 

Fig. 3 (a) Reflection, transmission and (b) absorption spectra for the proposed plasmonic absorber under different value of electron collision frequency γ. The other geometric parameters are: w = 80 nm, L _m = 22 nm, L _a = 140 nm, L_b = 220 nm, n_a = 2.13, and n_b = 1.23.

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To investigate how the OTSs behave in generation of the perfect absorption, the structure filed distributions are simulated by the two-dimensional FDTD method. In the calculations, perfect matching layer are set along x and y directions at edges of the structure. The spatial sizes are Δx = Δy = 2 nm, and the temporal cell size is Δt = Δx/(2c), where c is the velocity of optical wave in vacuum. The incident optical wave is continuous and its amplitudes is supposed to be 1. The field distributions of H_z for the proposed structure at wavelength of 1300 nm are plotted in Fig. 4(a) . It shows that since 1300 nm is far away from the wavelength of the OTSs as shown in Fig. 2(b), the optical wave decays inside the TML and strong reflection occurs at its entrance face. The field distributions of H_z and the curve of |H_z| along y = 0 at wavelength of 1550 nm are depicted in Figs. 4(b) and 4(c), respectively. We can see that due to excitation of the OTSs, the optical wave has a strong local-field enhancement at the TML/(AB)₁₀ boundary with the maximum value three times higher than the incident optical wave. Meanwhile, the optical wave has litter refection and decays significantly in the (AB)₁₀. As a result, perfect absorption of the incident energy is achieved.

 

Fig. 4 Field distributions of H_z for the proposed structure at the wavelengths of (a) 1300 nm (Media 1) and (b) 1550 nm (Media 2), respectively. (c) Field amplitudes of |H_z| along y = 0 at wavelength of 1550 nm. The TML/(AB)₁₀ boundary is at x = 0 μm.

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3. Influence of the structure geometric parameters to the absorber peak

The dependence of the absorption spectra on the structure geometric parameters is considered. Since the OTSs occur in the stopband of the PhC as indicated in Fig. 2(b), the absorption peak can be flexibly tuned by varying the stopband by means of adjusting the L _a and L _b. When the L _a is 140 nm and the L _b is 220 nm, the absorption peak locates at the telecommunication wavelength as shown in Fig. 2(b). While they are changed to 110 and 70 nm, 100 and 60 nm, 90 and 50 nm, 80 and 40 nm, the absorption peak is effectively tuned to visual frequencies of 844 nm, 758 nm, 676 nm, and 594 nm, respectively, as clearly demonstrated in Fig. 5 .

 

Fig. 5 Absorption spectra versus the L _a and L _b when w = 80 nm and L _m = 22 nm.

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The influence of the core width w to the absorption spectra is shown in Fig. 6(a) . It is noted that decreasing w will give rise to the red-shift of the absorption peak. The reason is that when w is decreased the n_eff of SPPs in dielectrics A and B are enlarged as shown in Fig. 6(b), thereby the stopband of PhC as well as the absorption peak is shiftted to the longer wavelength. Absorption evolution with the L _m and wavelength is plotted in Fig. 7 . As the L _m increases, the maximum absorption increases and the peak performs a blue-shift until the L _m reaches to 22 nm. When the L _m is further increased, the position of the absorption peak is almost unchanged, while its value decreases clearly. Therefore, there exists an optimal L _m for achieving the maximum absorption.

 

Fig. 6 (a) Absorption spectra versus the w. (b) The n_eff for SPPs propagating in the dielectrics A and B for different w. The other structure parameters are: L _m = 22 nm, L _a = 140 nm, and L _b = 220 nm.

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Fig. 7 Absorption evolution with the L _m and wavelength when w = 80 nm, L _a = 140 nm, and L _b = 220 nm.

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4. Conclusions

In summary, we have proposed a perfect absorber based on the plasmonic MDM structure with a TML and a dielectric PhC in the waveguide core. The spectral properties of the perfect absorber are investigated by the TMM and the FDTD method. It is found that the OTSs whose wavelength locating near the central stopband of the PhC will be excited at the TML/PhC boundary, which results in near-unity absorption of the incident energy. It is also demonstrated that by varying the structure geometric parameters, the absorption peak can be flexibly tuned. The novel absorber is a promising candidate for highly integrated photonic circuits.