1. Introduction

Electromagnetic metamaterials are usually defined as a class of artificially structured materials composed of arrays of subwavelength “meta-atoms”. They provide the possibility of creating an effective medium with controllable permittivity and permeability, which exhibits exotic electromagnetic properties and promises many potential applications such as perfect lenses [1], electromagnetic cloaks [2,3], and negative refractive index materials [4]. Engineering the absorption properties of the metamaterial is very important in practical applications. For example, Zhang et al. have theoretically suggested that, by taking advantage of the coupled dark and bright resonant modes in planar metamaterials, classical electromagnetically induced transparency (EIT) can be realized and zero absorption can be achieved [5]. Quite recently, Giessen et al. have experimentally demonstrated a plasmonic EIT at the Drude damping limit using a stacked optical metamaterial composed of an upper gold strip and a lower pair of gold strips with a dielectric spacer [6]. EIT with zero system absorption allows for the realization of ultracompact optical delay lines and buffers, thus attracting a great attention in various kinds of structures, such as metallic metamaterial composed of asymmetric double bars [7], two-dimensional lattice of metallic spheres mounted on an asymmetric dielectric waveguide [8], nanoscale plasmonic resonator antennas coupled by means of a single-mode silicon waveguide [9]. The aforementioned researches all aimed to depress the structure absorption, while for some applications absorption with high efficiency can be put to advantage. The concept of perfect absorbers was first proposed by Padilla et al. [10]. They pointed out that nearly unit absorption was possible in a metamaterial by properly engineering the electric and magnetic responses. The proposal of perfect absorbers initiated a new research area, and many efforts have been later made to achieve perfect absorbers with polarization-insensitive [11], wide-angle [12], and broad-band performance from terahertz to optical frequency [14,15]. Perfect absorbers were also achieved by three-dimensional array of plasma spheres [16], photonic crystals consisting of gold nanoparticles [17], and metallodielectric non-overlapping silver spheres [18]. As useful applications of perfect absorbers, namely, refractive index sensing [19] and subsampling infrared imaging [20], have been experimentally achieved quite recently.

In this paper, by incorporating perfect absorption with Kerr-nonlinearity in a multilayer metamaterial structure, all-optical absorption switching is realized for the first time to our best knowledge. The proposed structure is numerically investigated by the finite-difference time-domain (FDTD) method. Our simulations demonstrate that by simply adjusting the incident optical intensity, the structure absorption performs with different values, and can be flexibly and actively tuned from unity to zero. This novel characteristic can find important applications in all-optical integrated photonic circuits and networks for thermal detection, imaging, solar cells, and sensing [19–22].

2. Structure and principles

The structure under study is schematically shown in Fig. 1 , where the three-dimensional unit cell and the corresponding two-dimensional side view are both depicted. It consists of two gold (Au) layers separated by a Kerr dielectric spacer, and a glass substrate under the lower gold layer. Two-dimensional air hole arrays are perforated on the top gold layer with the same period in x and y direction. To investigate the absorption properties of the proposed structure, numerical simulations were performed by the three-dimensional FDTD method. The permittivity of gold in optical frequency can be described by Drude model ε _m = 1-w _p ²/(w ² + iwγ). Here, w _p = 2π × 2.175 × 10¹⁵ s⁻¹ is the plasma frequency, and γ = 2π × 1.95 × 10¹³ s⁻¹ is the damping constant [19]. The dielectric constant of the Kerr dielectric is decided by

 

Fig. 1 Kerr-nonlinearity-assisted multilayer metamaterial to achieve all-optical absorption switching. (a) Schematic unit cell of the three dimensional nanostructure consisting of two gold layers separated by a layer of Kerr dielectric. An air hole is engraved on the top gold layer, and a glass substrate lies under the lower gold layer. (b) Side view of the structure unit cell. The proposed structure has the same period in x and y direction.

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In the calculation, the optical wave with polarization along x direction is normally illuminated to the structure. To investigate influences of the structure parameters on the proposed metamaterial absorption, first we neglect the nonlinearity of Kerr dielectric, i.e., χ^{( 3)} is zero in Eq. (1). With the lower gold depth t ₁ = 60 nm, Kerr dielectric depth t ₂ = 70nm, upper gold depth t ₃ = 30 nm, air hole diameter d = 120 nm, and structure period of 340 nm, the reflection (R), transmission (T), and absorption (A) are calculated and demonstrated in Fig. 2 . Structure absorption is defined by A = 1-R-T, thus the key to obtain high absorption is to simultaneously minimize R and T. From Fig. 2, it can be clearly obtained that T is zero at all the frequencies. It is because that the depth of the lower gold film is larger than the typical skin depth of light in optical frequency, and the incident light cannot penetrate the structure. In the reflection spectrum, a significant resonant dip occurs at wavelength of 722 nm, which thereby results in a narrow-band peak as high as 0.96 in the absorption spectrum. The reason for the resonant dip in the reflection spectra is that when light normally incidents to the structure, antiparallel currents will be excited in the upper and bottom gold layer, which leads to a magnetic resonance response [10,19,20]. The magnetic resonance response can be tuned by the structure parameters, and it provides possibility to match the impedance Z = (μ/ε)^0.5 to free space at a specific frequency [10]. Therefore, when the wave at this frequency propagates to the structure, no energy will be reflected. As a result, a resonant dip occurs in the reflection spectrum.

 

Fig. 2 Spectral properties of the proposed multilayer metamaterial: reflection (R), transmission (T), and absorption (A).

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3. Simulation results and discussions

Now, the dependences of the absorption spectra on the structure parameters are investigated. When enlarging the structure period from 320 nm to 340 nm and 360 nm, while maintaining other structure parameters the same as the design in Fig. 2, the absorption spectra are calculated in Fig. 3(a) . It illustrates that the absorption peak can be linearly tuned by the metamaterial period. When the metamaterial period is increased, the length of the metallic regions where antiparallel charges exist will be increased. As a result, a red shift of absorption peak is observed. The behavior resembles the phenomenon of increasing the metallic cut-wire length in composite cut-wire structure as reported in [13]. The influence of air hole diameter on the absorption is shown in Fig. 3(b), where the period is fixed at 340 nm and the air hole diameter is changed from 120 nm to 200 nm, 260 nm, respectively. It can be clearly obtained that the air hole diameter will not influence the position of absorption peak, but will reduce the absorption peak. The reason is that increasing the air hole diameter will minimize the interactions regions of upper and lower metallic layers, leading to the impedance mismatch, and thus the structure absorption phenomenon will be deteriorated. If the air hole diameter is further increased to the value of the period, i.e., the upper metallic layer is removed, almost all the incident light will be reflected, and absorption will not happen any more.

 

Fig. 3 (a) Absorption spectra with the structure period (from left to right) of 320 nm, 340 nm, and 360 nm, respectively. The inset shows that the resonant wavelength varies linearly with the structure period. (b) Absorption spectra with air hole diameter of 120 nm, 200 nm, and 260 nm, respectively. Electric filed |E| in the central dielectric spacer at the non-resonant wavelength 1000 nm (c) and the resonant wavelength 722 nm (d), respectively.

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The electric filed |E| in the central dielectric spacer at non-resonant wavelength of 1000 nm and resonant wavelength of 722 nm (See the absorption spectra in Fig. 2) are plotted in Fig. 3(c) and (d), respectively. From Fig. 3(c), we can see that when the incident wave is locating at the non-resonant wavelength, almost all the energy is reflected and no electromagnetic field exists in the dielectric spacer. In contrast, a strong electromagnetic field is established at the resonant wavelength and localized in the dielectric spacer, as indicated in Fig. 3(d). In this case, the incident optical energy is neither transmitted nor reflected, thereby leads to nearly 100% absorbance of the proposed structure.

In Fig. 4 , sensitivity of the absorption peak to the refractive index n _d is plotted. When n _d is changed from 1.5 to 1.55, 1.6, and 1.65, the absorption peak varies almost linearly from 722.2 nm to 740.5 nm, 759.7 nm, and 790.5 nm, respectively. The results in Fig. 3(d) and Fig. 4 indicate two properties of the proposed structure, i.e., the electromagnetic field is highly localized in the dielectric layer, and the absorption peak is sensitive to refractive index of the dielectric layer. These two novel characteristics ensure us to all-optical actively tune the metamaterial absorption by a low incident power when the dielectric materiel ε_d has a Kerr nonlinear response.

 

Fig. 4 (a) Dependence of the absorption spectra on the refractive index of the dielectric spacer. (b) Sensitivity of absorption peak to the refractive index of the dielectric spacer.

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Now, we investigate the Kerr-nonlinearity-assisted all-optical absorption switching of the proposed structure. Here, the third-order susceptibility χ ⁽³⁾ of the nonlinear material in the dielectric spacer is assumed to be 9 × 10⁻¹² m²/v² [23,24]. Conventionally, two technical methods can be used to investigate property of the optical switching. One is that the incident light is continuous, and the spectra at a certain wavelength will vary with the incident light intensity [24]. The other is the pump-probe technique [25], i.e., the incident light has two beams, one is continuous probe beam and the other is pulsed pump beam. In this paper, the two methods are both considered, and their corresponding results are plotted in Figs. 5 and 6 , respectively. First we evaluate the required intensity of the incident light for exciting the Kerr-nonlinear effect. As illustrated in Fig. 4(a), when the refractive index of the dielectric spacer is increased from 1.5 to 1.55, the absorption spectra demonstrate an obvious red-shift. Therefore, to ensure the dielectric spacer to have a refractive index of 1.55 as the Kerr nonlinearity is considered, the required |E|² should reach 1.7 × 10¹⁰ V²/m² according to Eq. (1). However, attributing to the SPP effect there are enhanced and localized electric filed in the Kerr dielectric spacer. So the required |E|² of the incident light to realize absorption switch should be smaller than 1.7 × 10¹⁰ V²/m². When |E|² of incident light is 1 × 10⁸ V²/m² (i.e., 13 W/cm²), the absorption at wavelength of 722 nm is as large as 0.91 as demonstrated in Fig. 5. In this case, no nonlinear effect happens. While |E|² is increased to 1 × 10⁹ V²/m² (i.e., 1.3 × 10² W/cm²) and 8 × 10⁹ V²/m² (i.e., 1.04 × 10³ W/cm²), the refractive index of the dielectric layer will be enlarged due to the Kerr nonlinear response according to Eq. (1), and the absorption is actively tuned to 0.55 and 0.15, respectively. Apart from the red-shift of the absorption peak as shown in Fig. 5, there is a dramatic change in the shape of the peak. It is because that the electric filed in the Kerr dielectric layer is position dependent [26]. At different positions, the induced dielectric constant ε_d will be different, which may deteriorate the impedance match.

 

Fig. 5 Nonlinear properties of the all-optical absorption switching excited by a single continuous wave with |E|² of 13 W/cm², 1.3 × 10² W/cm², and 1.04 × 10³ W/cm², respectively.

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Fig. 6 Dynamic response of the structure absorption to a 10 fs ultrashort Gaussian pulse. The green solid line is the absorption response of the probe beam, and red dotted line is the incident pump |E|² in time domain.

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The pump-probe technique to realize absorption switching is demonstrated in Fig. 6. The probe beam is continuous with wavelength of 722 nm. The pump beam is an ultrashort Gaussian-temporal-profile pulse with 10 fs Full-Width-Half-Maximum (FWHM), 1000 nm central wavelength, and 2 × 10¹⁰ V²/m² (i.e., 2.6 × 10³ W/cm²) peak value of |E|². Due to the positive third-order susceptibility of the Kerr dielectric, the metamaterial absorption responses instantaneously to the pump pulse. The structure absorption decreases from the maximum value of 0.94 to the minimum value of 0.08 when the pump pulse transmits to the structure, and then returns to the maximum value when the pump pulse passes through. The absorption spectra possess of rapid rise and drop time according to the pump pulse, and the absorption switching contrast reaches as large as 86%.

4. Conclusions

In summary, we have proposed and numerically investigated a Kerr-nonlinearity-assisted multilayer metamaterial. Owing to the third-order susceptibility and nonlinear response of the Kerr dielectric, the metamaterial performs a novel property of all-optical absorption switching. Two types of methods are utilized to investigate the absorption switching phenomenon of the proposed structure. Our results demonstrate that the metamaterial absorption can be actively tuned from near unit to near zero by adjusting the incident optical intensity. This highly nonlinear behavior of the absorption switching structure can find potential applications in all-optical integrated photonic circuits and networks, such as thermal detectors and imaging, solar cell, and plasmonic sensing.