Large-area split ring resonators (SRRs) array is fabricated by laser micro-lens array (MLA) lithography on flexible Polyethylene Naphthalate (PEN) substrates. Multi-layer metamaterials are formed by stacking and bonding several layers of the laser fabricated metamaterials together. The resonance of the multi-layer metamaterials is enhanced significantly as compared to the single-layer metamaterials. The roll-off value of the half-wavelength resonant dip, which reflects the strength of resonance, increases significantly from 4.9 to 11.2 as the layer number increases from 1 to 5. A logarithm relationship between the amplitude of the resonant dip and the layer number is also studied, which indicates a flexible method to tune the strength of resonance by changing the layer number. The multi-layer metamaterials with the enhanced resonance can be used to make narrow band terahertz filters.
© 2011 OSA
Terahertz wave, which is loosely defined between 0.1 and 10 THz, has drawn dramatic research interest in the recent decades due to its various potential applications [1,2]. However, terahertz wave is not developed sufficiently as compared to the other electromagnetic frequency regions such as infra-red and microwave. One of the main problems is the lack of terahertz functional devices since majority of nature materials do not show response to terahertz wave. Recently with the rapid development of terahertz metamaterials [3,4], various types of terahertz devices are realized [5–14]. The functions of metamaterial devices are typically realized by their resonance properties dominated by the metamaterial structures. In practical applications, the stronger resonance is preferred. The strength of resonance is characterized by the sharpness of the resonant dip in the transmission spectra, which can be represented by the roll-off value [15,16]. In previous studies, the strength of resonance can be tuned by various means in the two dimensional (2D) plane [17–21]. However, the amplitude drop of the resonant dip is limited to 1 order because the tuning effect is saturated when the thickness of SRRs exceeds the skin depth of the metal. Since the optical properties have been demonstrated successfully in 2D metamaterials, three dimensional (3D) metamaterials with strong resonance are proposed . There are several methods to realize 3D metamaterials [23–25]. The intricate helices metamaterials were fabricated on the polymer slab by laser direct writing, which provides a method to realize the 3D metamaterials with arbitrary designs. However, it takes a long time to fabricate large-area metamaterials. The fabrication of metamaterials on curved spaces also employs complicated multi-step process. Multi-layer metamaterial by bonding 2D metamaterials is an easier fabrication method to realize 3D metamaterials with the flexible polymer substrates [25,26]. In this paper, 2D split ring resonators (SRR) metamaterials are fabricated firstly on Polyethylene Naphthalate (PEN) substrates by laser micro-lens array (MLA) lithography, which is a parallel fabrication method for large-area terahertz metamaterials. Laser MLA lithography can fabricate SRRs patterns in the area of 6 mm × 10 mm with one processing cycle of less than 1 minute, which is a high speed process. The substrate is a flexible PEN film with the thickness of 100 μm, the same as the period of the SRRs array, which realizes a homogenous distribution of SRRs in three dimensions. Multi-layer metamaterials with different layer numbers are then formed by stacking and bonding the 2D metamaterial layers together flexibly. The laser fabricated multi-layer metamaterials with different layer numbers are characterized by a Terahertz Time Domain Spectroscopy. The resonant dips in the transmission spectra are found to drop 10,000 times as the layer number increases, which illustrates a stronger resonance. Numerical simulation is carried out to study the electric field distribution of the multi-layer metamaterials consisting of 5 layers when the terahertz wave propagates, showing the interaction between the terahertz wave and the multi-layer metamaterials at LC and half-wavelength resonance frequencies. The multi-layer metamaterials can be used as narrowband high-performance terahertz filters, absorbers, and polarizers etc with tunable resonance properties.
The single-layer metamaterials are fabricated by laser MLA lithography, E-beam evaporation, and followed by the lift-off process [27–29]. Figure 1 (A) shows the microscopic image of the large-area split ring resonators (SRRs) metamaterials fabricated. The SRR array is made by Cu, which can be treated as perfect electric conductor (PEC) in the terahertz range. The dimensional parameters of the SRRs metamaterials are as follows: the period is 100 μm, the outer dimension 40 μm, the line width 6 μm, and the thickness 100 nm. The PEN film is flexible as compared to other substrates, such as quartz, silicon, and GaAs. Meanwhile, the thickness of the PEN films (100 µm) is the same as the period of the SRRs array (100 µm). Therefore, the periods are kept the same in the three dimensions if the metamaterials layers are attached closely. This indicates a potential way to realize 3D bulk metamaterials with homogeneously distributed unit cells. The multi-layer metamaterials with the same design on PEN substrates are stacked and bonded together into 1, 2, 3, 4, and 5 layers to form the multi-layer metamaterials. Figure 1 (B) illustrates the stacking process of the sample with the 5 layers design. The SRRs in different layers are aligned in the same orientation. The interaction between SRRs in different layers is not an important factor as the coupling is weak. Therefore, the misalignment of unit cells in each layer and the distance between different layers do not affect the experimental results. The metamaterials consisting of 5 layers are shown in Fig. 1 (C). The samples are characterized by a Terahertz Time Domain Spectroscopy (THz-TDS, TPS3000, Teraview Inc.) in transmission mode at a normal incidence. The electric field of the incident terahertz wave is aligned parallel to the gap-bearing side of the SRRs as illustrated in Fig. 1 (B). All the transmission spectra of the samples with different layer numbers are normalized against the reference transmission spectrum of Nitrogen gas environment .
3. Results and Discussion
The transmission spectra of 1, 3, and 5 layers metamaterials are shown in Fig. 2 . In the transmission spectra, three resonant dips are observed in each transmission curve. They are the LC resonance at 0.5 THz, half-wavelength resonance at 0.75 THz, and the higher mode resonance above 2.0 THz. All the three resonance dips do not show frequency shift. The LC resonance results from the inductive current circulating in the SRR structure with the capacitive charge accumulation at the gap. The dipole resonance and higher order mode resonance are due to antenna-like couplings between the SRRs conductors parallel to the electric field of the incident terahertz wave. All the three transmission dips increases gradually as the layer number increases from 1 to 5, especially for the LC resonance and half-wavelength resonance. The larger transmission dips indicate enhanced resonances. This result shows that the multi-layer terahertz metamaterials can flexibly tune the strength of resonance by the layer number, which shows potential applications of the terahertz devices with the flexible transmission tunability. The half-wavelength resonant dip in the multi-layer metamaterials consisting of 5 layers reaches to 1.9 × 10−4 at 0.75 THz, which is small enough for applications as terahertz filters or attenuators. Meanwhile, the transmission in the non-resonance frequency band does not drop significantly. It is less than 1 order smaller than the incident terahertz wave when the 5 metamaterials layers are bonded together, which is a much smaller amount as compared to the amplitude drop of the resonant dips. This result demonstrates that the PEN film is a suitable substrate for multi-layer metamaterials or bulk metamaterials with low loss in terahertz range.The amplitudes of the resonant dips at the LC and half-wavelength resonance frequencies versus layer number is presented in Fig. 3 (A) . Experimental data fitting shows that the amplitudes of the LC and half-wavelength resonant dips are in the logarithm relationship with the number of the metamaterials layers as:
where N is the number of metamaterial layers. The fitting curve of the half-wavelength resonance has a bigger slope than that of the LC resonance, which reflects a stronger damping effect at resonance frequencies. If the single-layer metamaterial is treated as the damping medium, the damping factors αLC and αHalf-wavelength can be extracted as 0.172 (10-0.7650) and 0.405 (10-0.3924). It indicates that the LC resonant transmission and half-wavelength resonant transmission drop 0.172 and 0.405 times, respectively, as one more metamaterials layer is bonded. The amplitude drop of the half-wavelength resonance is stronger than that of the LC resonance. The relationship presented in Eqs. (1) and (2) can be varied by tuning the structural parameters of the SRRs design, as well as the period of the SRRs array  to achieve the desired damping factors and resonance frequencies. This logarithm relationship also provides a convenient way for the design of terahertz devices based on multi-layer metamaterials. The sharpness of the resonant dip can be used to describe the strength of resonance, which is characterized as the roll-off value. The roll-off value is defined as the change of transmission at the resonance frequency, which is shown in Eq. (3) [32,33],
where fR is the resonance frequency and f0 is the frequency of transmission maximum. Figure 3 (B) shows the roll-off values of the LC and half-wavelength resonant dips of the multi-layer metamaterials. For both the LC and half-wavelength resonances, the roll-off values increase significantly. The roll-off value of the half-wavelength resonance increases from 4.9 to 11.2 when the layer number increases from 1 to 5. It shows that the transmission reduces almost 10,000 times. Besides the LC and half-wavelength resonances, it can be observed from Fig. 2 that the higher order mode resonant dip also increases as the layer number increases. However, it is difficult to characterize the strength of resonance as this resonance is relatively weak.
Numerical simulation is carried out to understand the electric field distribution in the multi-layer terahertz metamaterials when terahertz wave propagates by CST Microwave Studio 2009. The terahertz wave incidents the multi-layer metamaterials at a normal incidence as shown in Fig. 4 (A) . The incident terahertz wave polarization is parallel to the gap-bearing side of the SRRs. Figures 4 (B) and (C) present the cross-sectional views of the electric field distribution in the 5-layer metamaterials at the LC and half-wavelength resonance frequencies. There is no significant interaction between the SRRs in the adjacent layers. When the terahertz wave passes through the 5-layer metamaterials, each metamaterial layer interacts with the incident terahertz wave in sequence. At the LC resonance frequency, the circular current is induced inside the SRRs and a large amount of charges accumulate resonantly at the gaps of the SRRs. As shown in Fig. 4 (B), the first metamaterial layer shows the strong charge accumulation at the LC resonance frequency. When the terahertz wave reaches the second metamaterial layer, the interaction between the terahertz wave and the second layer metamaterials occurs. The charges accumulate at the gaps of SRRs in the second layer. The charge intensity is lower than that in the first layer. The transmitted terahertz wave is further reduced due to the LC resonance as the terahertz wave goes through more metamaterial layers. Along the terahertz wave propagation direction, the charge intensity at the gaps of SRRs in different layers decreases. The terahertz wave at the LC resonance frequency of 0.5 THz is damped significantly when going through one layer of SRR metamaterials, which follows the relationship presented in Eq. (1). The damping of the half-wavelength resonant transmission dip is presented in Fig. 4 (C). The dipole resonance is induced by the coupling between the terahertz wave and the conductive components of SRRs parallel to the incident polarization. The terahertz wave with the dipole frequency of 0.75 THz is resonantly reduced along the propagation direction. As the 5 metamaterials layers are bonded together, the resonant dip drops 10,000 times at the half-wavelength resonance frequency due to the resonance in each layer. This multi-layer metamaterials can be applied to make narrow band terahertz filters, absorbers, and polarizers etc with tunable resonance enhancement properties by setting the layer number or changing the SRRs designs.
The multi-layer terahertz metamaterials on the flexible PEN substrates are designed, fabricated, and studied experimentally and theoretically. The amplitude of the transmission dips at the resonance frequencies decreases gradually as the layer number increases, which is in the logarithm relationship at the LC and half-wavelength resonance frequencies. For the half-wavelength resonance, the transmission decreases 10,000 times in a logarithm relationship as the layer number increases from 1 to 5. The increase of the roll-off value from 4.9 to 11.2 indicates a strong resonance enhancement. The simulation result also demonstrates the interaction between the terahertz wave and metamaterials in each layer at the LC and half-wavelength resonance frequencies. The multi-layer metamaterials can realize a tunable resonance enhancement by varying the number of metamaterials layers flexibly. The multi-layer metamaterials can be applied as high narrowband high-performance value terahertz devices with resonance strength tunability.
This work is supported by National University of Singapore Start-up Grant (Project No. R-263-000-515-133) and ASTAR/SERC Metamaterials Program: Meta-Antenna (Grant number: 0921540097.)
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