#### Abstract

Second-harmonic generation in split ring resonator multilayer nanostructure is studied with the finite-difference time-domain (FDTD) method. The fundamental frequency wave and the second-harmonic generation at the resonant absorption wavelength are highly localized in the dielectric layer, and the absorption peak is sensitive to dielectric constant of the dielectric layer. Under the excitation of the plasmon resonances mode, the strong local field induces an expected increase of the second-harmonic generation with conversion efficiencies 10^{−6}-10^{−7}. The distributions of fundamental frequency electric field and second-harmonic electric field inside the central dielectric layer region are also shown.

#### 1. Introduction

In the area of photonics, two types of materials are being developed: photonic band gap materials and metamaterials [1–8]. Split ring resonator nanostructure is the artificially structured materials that simultaneously possess plasmonic resonance features and low symmetry [9–15]. The first property provides the extraordinary linear optical electromagnetic (EM) properties. The metamaterials nanostructure with controllable permittivity and permeability can exhibit enhanced transmission of incident light involving surface plasmon polaritons (SPPs) and promises many potential applications. The second is a necessary condition for efficient second-harmonic generation (SHG). The large local field induced by the fundamental light plays an important role in the SHG processes. The properties of enhancing SHG in metallic nanostructures with low symmetry have been discussed widely, such as those in single nanoparticle and double plasmonic resonance [16, 17]. Feth et al. experimentally observed strong SHG from planar noncentrosymmetric structures with a variety of unit cell geometries [18]. The results of their experiments are interpreted successfully by a classical theory [19, 20]. When the fundamental frequency wave (FFW) and the second harmonic wave (SHW) are both tuned at the resonant modes or defect states, giant enhancement of SHG will be obtained. Perfect absorbers for refractive index sensing and subsampling infrared imaging were also achieved by three-dimensional electromagnetic metamaterials [21–26].

In this paper, all-optical absorption is realized for the FFW and the SHW in a three-dimensional split ring resonator multilayer nanostructure by introducing resonant cavities to achieve better local field enhancement and perfect absorption. The structure consists of a split ring resonator, a dielectric layer, and a metallic layer on a glass substrate for allowing near-perfect nanostructure absorption. The proposed structure is numerically investigated by the FDTD method. The electromagnetic fields of FFW and SHW are highly localized in the dielectric layer, and the absorption peak is sensitive to dielectric constant of the dielectric layer. Under the excitation of the plasmon resonances modes, the strong local field induces an expected increase of the second-harmonic generation with conversion efficiencies of -. This novel characteristic can find important applications in all-optical integrated photonic circuits for thermal detection, imaging, solar cells, and sensing.

#### 2. Structure and Principles

The numerical calculations presented in this paper have been performed with FDTD method. The method has been described elsewhere [18] and used for the analysis of both the linear response and the second-order nonlinearity response of plasmonic nanostructures [19, 20]. Both the linear response and the second-order nonlinearity response of the split ring resonator multilayer nanostructure can be considered as follows: where is the nonlinear source for second-order nonlinearity. and , and , and and are the electric field, the magnetic flux intensity vectors, and the current density vectors of fundamental and harmonic waves, respectively. is the ion density, is the electron mass, the light speed in vacuum air, and is the elementary charge.

The permittivity of gold has the following form: . The s^{−1} is phenomenological collision frequency, and s^{−1} is the bulk plasma frequency.

The split ring resonator multilayer nanostructure under study is schematically shown in Figure 1, where the three-dimensional unit cell view is depicted. It consists of split ring resonator and gold layer separated by a dielectric layer and a glass substrate under the lower gold layer. Two-dimensional split ring resonator arrays are deposited on the top dielectric layer with the same period in and directions. The perfectly matched absorbing boundary conditions are employed at the bottom and the top of the computational space along the direction, and the periodic boundary conditions are used on the boundaries of and directions. Only one unit cell of the periodic holes array is considered in our computational space. To investigate the absorption properties of the proposed multilayer nanostructure, numerical simulations were performed by the three-dimensional FDTD method.

The multilayer nanostructures have periodic modulation on both the linear and the second-order susceptibility. The lattice periodic and are along the and directions, respectively. To investigate the influences of the structure parameters on the proposed metamaterial absorption, first we use the parameters with the split ring resonator depth nm, dielectric depth nm, below gold layer depth nm, below glass layer depth nm, and structure periods and equal to nm. There is the unit cell of split ring resonator shape with nm, nm, and nm. In the calculation, the incident light wave with polarization along direction is normally illuminated to the split ring resonator multilayer nanostructure.

#### 3. Simulation Results and Discussions

The reflection (), transmission (), and absorption () are calculated and demonstrated in Figure 2. Structure absorption is defined by , thus the key to obtain high absorption is to simultaneously minimize and . From Figure 2, it can be clearly obtained that is zero at all the frequencies. This is because the depth of gold film on the glass substrate is larger than skin depth of light, and the incident light cannot penetrate gold film. In the reflection spectrum, a significant resonant dip occurs at wavelength of 1584 nm, which results in a narrow-band peak as high as 1.0 in the absorption spectrum. The electromagnetic resonance response can be tuned by the structure parameters, and it provides the possibility to match the impedance to free space at a specific frequency [21]. Therefore, when the wave at this frequency propagates to the three-dimensional split ring resonator multilayer nanostructure, no energy will be reflected. As a result, a resonant dip occurs in the reflection spectrum. In this case, the incident optical energy is neither transmitted nor reflected, thereby leading to nearly 100% absorbance of the proposed structure.

Now, the dependences of the absorption spectra on the split ring resonator multilayer nanostructure parameters are investigated. When enlarging the structure period along direction or the structure period along direction from 700 nm to 770 nm and 840 nm, while maintaining other structure parameters the same as the design in Figure 2, the absorption spectra of FFW through a split ring resonator multilayer nanostructure are calculated in Figures 3(a) and 3(b). It illustrates that the absorption peak can be linearly tuned by the multilayer nanostructure period along direction and along direction. When the multilayer nanostructure period along direction is increased, a red shift of absorption peak is observed. When the multilayer nanostructure period along direction is increased, a blue shift of absorption peak is observed.

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The influence of the wide of split ring resonator along direction on the absorption of FFW through a split ring resonator multilayer nanostructure is shown in Figure 4, where the period is fixed at 700 nm and the wide of split ring resonator is changed from nm to 140 nm and 210 nm, respectively. When the wide of split ring resonator is nm, a significant resonant dip occurs at the wavelength of 1517 nm, which thereby results in a narrow-band peak as high as 0.8 in the absorption spectrum. When the wide of split ring resonator is increased, a blue shift of absorption peak is observed. It can be clearly obtained that the wide of split ring resonator will strongly influence the position and intensity of absorption peak. The reason is that increasing the wide of split ring 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.

The influence of the wide of split ring resonator arms on the absorption of fundamental frequency wave through a split ring resonator multilayer nanostructure is shown in Figure 5, where the period is fixed at 700 nm and the wide of split ring resonator arms is changed from nm (black line) to 224 nm (blue line) and 238 nm (red line), respectively. It can be obtained that the wide of split ring resonator arms will strongly influence the position of absorption peak. The reason is that increasing the wide of split ring will minimize the interactions regions of upper and lower metallic layers and thus the structure absorption phenomenon will be deteriorated.

The influence of the dielectric constant of the dielectric layer on the absorption of fundamental frequency wave through a split ring resonator multilayer nanostructure is shown in Figure 6(a), where the period is fixed at 700 nm and the dielectric constant of the dielectric layer is changed from (black line) to 1.2 (blue line) and 1.4 (red line), respectively. It can be obtained that the dielectric constant of the dielectric layers will strongly influence the position of absorption peak but will not reduce the absorption peak. In Figure 6(b), sensitivity of the absorption peak to the dielectric constant of the dielectric layer is plotted. When is changed from 1.0 to 1.6, the absorption peak varies almost linearly from 1583.8 nm to 1688.2 nm and 1787.1 nm, respectively. The results in Figures 6(a) and 6(b) indicate two properties of the proposed structure, that is, the electromagnetic field is highly localized in the dielectric layer, and the absorption peak is sensitive to dielectric constant of the dielectric layer. These two novel characteristics ensure us to actively tune the all-optical metamaterial absorption.

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To obtain the absorption spectra of SHG of the three-dimensional split ring resonator multilayer nanostructure, the input light wave , , is polarized along the direction with wavelengths , and the is amplitude.

The absorption spectra of fundamental frequency field , second-harmonic field , and second-harmonic field are calculated in Figures 7(a) and 7(c) for the wide nm of split ring along direction, while maintaining other structure parameters the same as the design in Figure 2. When the continuous wave at incident wavelengths nm is incident through the split ring resonator, one can see absorption spectra of fundamental frequency wave at the wavelength 1518 nm in Figure 7(a). The absorption spectra of the second-harmonic field and the component at the wavelength 759 nm are also shown in Figures 7(b) and 7(c), respectively. The second harmonic conversion efficiencies in the second-order nonlinear optical process are defined as follows: , where is the frequency of the incident FFW. The -polarized second harmonic conversion efficiencies are about while the -polarized SH conversion efficiencies are about 10^{−7} for the -polarized fundamental frequency wave incident at the wavelength 1518 nm.

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The transmission of the FFW results from an enhancement of the local field. The strong local field and noncentrosymmetry induce an increase of second harmonic nonlinearity signals. A strong electromagnetic field is established at the resonant wavelength and localized in the dielectric layer region. The electric field distributions of and for fundamental frequency field inside the central dielectric layer region at wavelength 1518 nm are shown in Figures 8(a) and 8(b), respectively.And the second-harmonic electric field distributions of and for SHG inside the central dielectric layer region at wavelength 759 nm are also shown in Figures 8(c) and 8(d), respectively. The distributions of fundamental frequency electric field along the BC (red line) and along the AB direction (black line) at wavelength 1518 nm are shown in Figure 9(b). The distributions of the second-harmonic electric field along the BC direction (red line) and along the AB (black line) at wavelength 759 nm are shown in Figure 9(c).

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#### 4. Conclusions

In summary, we have numerically investigated a three-dimensional split ring resonator multilayer nanostructure. The structure consists of split ring resonator and metallic layers for allowing near-perfect absorption of the fundamental frequency wave and the second-harmonic generation. The electromagnetic field is highly localized in the dielectric layer, and the absorption peak is sensitive to dielectric constant of the dielectric layer. These characteristics ensure us to tune the metamaterial absorption. Under the excitation of the plasmon resonances modes, the strong local field induces an expected increase of the second-harmonic generation. The second harmonic conversion efficiency is about -. 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.

#### Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

#### Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grants nos. 11247003, 51175172, and 11304094, the Open Research Fund of National Laboratory for Infrared Physics (GJKF20130027 and GJKF20130028), the Chinese Academy of Sciences, and the Scientific Research Fund of Hunan Provincial Education Department (12A045, 12C0143, and 13C323). The authors would especially like to thank Dr. Yong Zeng for the discussion of FDTD simulations.