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In this paper, we present a THZ MMs filter with two independent stop-bands based on periodic metallic resonant structures patterned on the top of a flexible polyimide wafer. The optimized geometry parameters were obtained by numerous simulations using full wave finite integration technology of CST 2015. The resonant frequencies of the filter were 126.32 GHZ and 177.32 GHZ with 3-dB bandwidths of 19.3 GHZ and 9.1 GHZ, respectively. The S21 parameters can reach to −47.38 dB and −56.69 dB corresponding to two resonant peaks, which indicate the excellent stop-band performance. The MMs filter in our design is insensitive to the polarization angle of the incident EM waves due to the symmetrical characteristic of the proposed resonance structure. In order to intensively understand the transmission performance of the proposed MMs filter, a large number of simulations were performed based on the different permittivity, period of the unit cell, dielectric thickness, and geometric dimensions. The electric field and surface current distributions were analyzed to understand the mechanism of the EM wave transmission. The proposed MMs filter was fabricated using a surface micromachining process and tested using a THZ-TDS system. Measured terahertz transmission responses of the proposed MMs dual-band band-stop filter have reasonable correspondence with those from simulations.
© 2017 Optical Society of America
1. Introduction
Since the theory and experiment of left-hand materials (LHMs) were first demonstrated [1, 2], comprehensive scientific researches into Electromagnetic (EM) Metamaterials (MMs) have developed in recent decades. MMs is composed of the periodic array of metallic resonant structures with sub-wavelength dimensions on a dielectric substrate, which exhibits unusual EM characteristics that cannot be observed in nature such as negative refraction index, cloaking behavior, backward propagation, and reverse Doppler effects [3–7]. These exotic characteristics can be effectively controlled by adjusting the geometry of sub-wavelength periodic structures. A series of devices such as perfect absorbers [8–12], super-lenses [13, 14], antennas [15, 16], and filters [17, 18] with a wide range of frequencies from microwave towards visible can be realized based upon these unusual characteristics of the MMs. Considerable attentions have been attracted to realize the terahertz (THZ) filters with broad bandwidth, high peak transmission, and excellent stop-band rejection because of the extensive applications in imaging, biological applications, communications, and testing systems and so on [19–21]. Due to the high design flexibility and simple fabrication process, MMs structures have been widely applied in filter’s design. The properties of a MMs filter such as center frequency, bandwidth, transmission, and stop band attenuation are affected by the geometry dimensions of the periodic metallic resonant structures. The bandwidths of the filters are always too narrow due to the strong EM resonant behavior of the MMs. Generally, multi-layer MMs structures are applied to form the multi-band or the broadband transmission, and each layer of the cell structure is formed in different sizes to absorb different frequencies, then the multi-band or the broadband transmission can generate based on the continuous change of the dimensions [22–24]. This method has many limitations for practical application of the MMs filters due to the increase of the overall thickness and the fabrication difficulty. Therefore, the design of single-layer filters with multi-band or broadband, high peak transmission, and excellent stop-band rejection becomes particular urgent. Recently, many research efforts have focused on the frequency tunable MMs filters to realize the stop- or pass-band frequency tuning, so as to indirectly achieve the multi-band performance. Several approaches have been employed to make the design structures with the dynamic tuning ability, for instance, control the depletion layer of the gallium arsenide (GaAs) by using the voltage [25], control the carrier density within the SRR split gap by employing the photo excitation [26], control the effective permittivity by the temperature [27], and control resonance wavelength by changing the doping concentration of the graphene resonance units [28]. Furthermore, it is also extremely significant to develop the flexible MMs filters in order to deploy them on non-uniform surfaces while maintaining the high degree of functionality. Flexible devices have many advantages over their nonflexible counterparts such as much lighter in weight, much smaller in size, and much more durable. One especially outstanding advantage is their flexible and conformal ability when they are placed on unusual surfaces. Flexible MMs filters are typically fabricated by sputtering or depositing of the periodic array of the metallic resonant structures onto a flexible substrate such as MM film, polyimide substrate, and polydimethylsiloxane (PDMS) substrate.
In this paper, we present a flexible THZ dual-band band-stop filter based on the single-layer MMs structure, which consists of symmetrical periodic metallic resonators patterned on a flexible polyimide substrate. The simulation results show the resonant frequencies of 126.32 GHZ and 177.32 GHZ with the 3-dB bandwidths of 19.3 GHZ and 9.1 GHZ. At corresponding resonant frequencies, the S21 parameters can reach to −47.38 dB and −56.69 dB, respectively, which show the excellent band-stop performance. Moreover, the filtering effect is insensitive to the polarization angle of the incident EM wave due to the symmetrical characteristic of the unit cell. The influences of the permittivity, structural periodicity, dielectric thickness, and geometric dimensions on transmission properties of the MMs filter were investigated. The electric field and surface current distributions were analyzed for intensively understanding the EM wave transmission mechanism. At last, the MMs filter structure was fabricated on a polyimide substrate with a surface micromachining process. THZ transmission response measured using the terahertz time-domain spectroscopy (THZ-TDS) system has reasonable correspondence with the simulation results. In comparison with the traditional design of the multi-band or wide-band filters by stacking the resonant structures of the same or different sized sub-units into a multi-layer structure, the proposed dual-band band-stop filter structure is easier to simulate and fabricate. In addition, by comparing with the tunable MMs filter, such as the band-stop filter based on graphene metamaterial at THZ wavelengths presented in [28], the proposed design in this paper based on the single-layer simple resonant structure has the characteristics of dual stop-band properties, polarization insensitivity, and simple fabrication. Furthermore, the flexible MMs filter proposed in this design can be pulled to conform to the unusual surfaces such as cylindrical, pyramid, and spherical and so on.
2. Filter design and simulation
The structure of the proposed MMs filter is shown in Fig. 1, where the array of symmetrical metallic resonant structures is patterned on the top side of the dielectric substrate. We chose the Copper with electric conductivity as metallic pattern and the polyimide with a relative permittivity of as dielectric layer.
Fig. 1 (a) Schematic of the dual-band band-stop MMs filter formed by an array of basic metallic resonance structures on the dielectric layer (b) Schematic of a unit cell represented by the black dotted line in (a).
Numerous simulations were performed using a full-wave electromagnetic simulation software CST based on a finite integration technique. In the simulation process, the propagation wave vector () was perpendicular to the structure plane whereas the electric field (E) and magnetic field (H) were parallel to the incident plane. The periodic boundary conditions were set along the plane, while the open boundary conditions were chosen along the plane to imitate the infinite periodic cells. The optimized geometry parameters of the unit cell are as follows: = 400 μm, = 320 μm, = 80 μm, the length of the periodic array = 1800 μm, the thickness of the dielectric layer = 60 μm, and the thickness of the top metallic structure = 18 μm.
Figure 2 shows the simulated S-parameters of the proposed MMs filter for normally incident EM wave. To explore the band-stop filtering behavior, we mainly focus on the transmission coefficient S21 of the proposed filter structure. The filter behaves as a dual-band band-stop filter with the resonant frequencies of 126.32 GHZ and 177.32 GHZ and the 3-dB bandwidths of 19.3 GHZ and 9.1 GHZ. At 126.32 GHZ and 177.32 GHZ, the S21 parameters can reach to −47.38 dB and −56.69 dB, respectively, which show the excellent band-stop performance.
3. Analyses and Discussions
The polarization behaviors have been researched for the different polarization angles under the normally incident EM waves to further study the transmission performance of the proposed MMs filter. As shown in Fig. 3, on account of the symmetrical characteristic of the metallic resonant structure, the proposed MMs filter is independent of the polarization angle of the incident EM wave, except for the slight changes in the transmission coefficient S21 at the resonant peaks.
Fig. 3 Simulated S-parameters curves for different polarization angles of the normally incident EM waves.
In order to explore the effects of the geometrical parameters on the transmission performance, numerous simulations have been performed based on the varied parameters such as ,,, and .
The transmission properties with the thickness of the dielectric layer varied from 40 μm to 80 μm are shown in Fig. 4(a). Two resonant peaks are all shifted towards the higher frequencies when the dielectric thickness is shorter than the reference thickness of 60 μm. In contrast, when the dielectric thickness is longer than 60 μm, two resonant peaks are simultaneously shifted towards the lower frequencies. As shown in Fig. 4(b), the blue shift on the resonant frequencies and the increase of the 3-dB bandwidths in low band can be obtained when the period of the unit cell is smaller than the reference value of 1800 μm. Whereas, the red shift on the resonant frequencies and the decrease of the 3-dB bandwidths in low band can be clearly observed when the period of the unit cell increases to the reference value which is equal to 1800 μm. The 3-dB bandwidths in high band remain unchanged with the variation of the structural periodicity. The red shift on the resonant frequencies of the two independent resonant peaks can synchronously observed from Fig. 4(c) when the length of ‘’ increases from 400 μm to 560 μm with the interval of 80 μm. As shown in Fig. 4(d), when the length of ‘’ is longer than the reference length of 320 μm, the resonant frequencies are synchronously shifted towards the lower frequencies. However, the resonant frequencies are all shifted towards the higher frequencies when the length of ‘’ shorter than the reference length of 320 μm. Therefore, we can adjust the resonant frequency and 3-dB bandwidth to meet our needs in special applications by changing the dielectric thickness, structural periodicity and dimensions of microstructure.
The influences of permittivity on the transmission properties of the MMs filter have been deeply investigated. Figure 5(a) shows the transmission properties of the MMs filter when the middle dielectric is polyimide, FR-4, and porcelain with a relative permittivity of 3.5, 4.4, and 5.7, respectively. The red shift on the resonance frequencies with the increase of the relative permittivity can be clearly observed. Figure 5(b) shows the transmission properties under two different loss conditions (lossy and lossless) of the polyimide dielectric. As observed from Fig. 5(b), the resonant frequencies of the lossy and lossless dielectric remain unchanged, while the S21 parameters can only reach to −21.56 dB and −17.25 dB at corresponding resonant frequencies. It shows the deterioration of the band-stop performance when the middle dielectric is defined as the lossy dielectric.
Fig. 5 Simulated transmission performance for (a) the different relative electric permittivities (b) the different loss conditions.
The filtering mechanism of the MMs filter can be concluded from the distributions of the electric field and surface current, which is quite different from the traditional filter that is formed by the capacitance, inductance, and resistance. For gaining the further insight into the transmission mechanism of the MMs filter with two independent stop-bands, the distributions of the electric field and surface current at 126.32 GHZ and 177.32 GHZ have been investigated.
The simulated electric field distributions are shown in Fig. 6. At 126.32 GHZ, it is observed that the strong electric field uniformly distributes along the edges of the resonant structure. At 177.32 GHZ, the high magnitude of the electric field symmetrically distributes along the left and right sides of the resonant structure, furthermore, the higher electric field concentrates on the corners of the resonant structure. Strong electric field distributions can reflect the strong electric resonant corresponding to the strong coupling between the adjacent resonant structures. For different resonant frequencies, the strong coupling appears in different locations of the resonant structure. The distributions of the surface current on the top resonant structure at the two resonant peaks are illustrated in Fig. 7. For two resonant frequencies, the high account of currents symmetrically distribute along the left and right sides of the resonant structure, resulting in the strong electric resonant. Moreover, the higher current distribution at 177.32 GHZ brings about the stronger resonant at 177.32 GHZ. Due to the strong resonant, almost all incident EM wave energy can be used to maintain the electron oscillation when the frequency of the incident EM wave is equal to the resonant frequency, then the transmission is almost zero. Inversely, when the frequency of the incident EM wave is not the resonant frequency, almost all the energy spreads through the device.
4. Fabrication and measurement
In order to confirm the correctness of the simulated transmission performance of the MMs filter, we have fabricated a prototype sample based on the optimized physical dimensions with a surface micromachining process.
A 2 in. silicon wafer was used as the supporting substrate after cleaning using acetone, absolute ethyl alcohol and DI water, respectively, and drying using nitrogen on the drying plate. The liquid polyimide as dielectric substrate of the structure was spun coated on the silicon wafer at 1700 rpm with thickness of 60 μm and solidified in an oven at 80°C, 120°C, 180°C, and 250°C for 2 hours, respectively. Then the sample was naturally cooled down to the room temperature. The AZ6112 positive photo-resist was spun coated on a polyimide wafer. The soft bake was carried out on a horizontal hot plate. The sample was then exposed under Contact Aligner by using a photo mask. The post bake was performed on a hot plate. After the above process being accomplished and the sample being naturally cooled down to the room temperature, it was dipped into the photo-resist developer for the development of the structure. A Copper film was sputtered on the surface of the structure under the argon environment with 99% purity Copper target. By controlling the sputtering power, argon pressure and sputtering time, the thickness of the Copper film can be effectively controlled. Since the photo-resist under the metal film needs to be removed, the sample was firstly immersed in the acetone solution for about 1 min, and then was cleaned using the ultrasonic cleaning method, the residual acetone was finally washed using the alcohol and DI water. At the end of the fabrication, the sample was immersed in the HF solution for 30 min, and the MMs filter fabricated on the polyimide substrate was carefully peeled off the silicon substrate. By far, the sample of dual-band band-stop filter is completely fabricated.
The flow diagram of the manufacture process is shown in Fig. 8. Figure 9 shows the fabricated filter structure.
To verify the validity of the simulation and fabrication, the THZ-TDS system was applied to test the transmission performance of the fabricated MMs filter. The transmission value of the filter can be calculated by the following formula.
where and are the energy of THZ wave transmitted through the filter and in the vacuum.During the testing process, a part of energy of the incident EM wave will get through the sample and the other part energy will be used to maintain the inner electron motion, and then absorbed by the device. Figure 10 illustrates the comparison of the simulated and measured transmission performance for the normally incident EM wave. It can be observed that the fabricated MMs filter sample displays a dual-band band-stop filter with the resonant frequencies of 124.86 GHZ and 175.43 GHZ and the 3-dB bandwidths of 18.8 GHZ and 7.9 GHZ. At 124.86 GHZ and 175.43 GHZ, the S21 parameters can only reach to −27.38 dB and −17.89 dB, respectively. The significant differences between the simulated and measured results for the resonant frequencies, bandwidths, and transmissions are mainly caused by the irregular thickness of the Copper film because of the tolerance of the sputtering machine, the inaccurate size of the sample because of the precision of the fabrication, and the inaccuracy from the measurement system.
5. Conclusions
A THZ dual-band band-stop MMs filter based on the periodic array of the metallic resonant structures patterned on the flexible polyimide substrate has been presented. The resonant frequencies of the filter are 126.32 GHZ and 177.32 GHZ with 3-dB bandwidths of 19.3 GHZ and 9.1 GHZ. At resonant frequencies, the S21 parameters can reach to −47.38 dB and −56.69 dB, respectively, which show the excellent band-stop performance. Due to the symmetrical characteristic of the resonant structure, the transmission performance of the filter is independent of the polarization angle of the incident EM waves. In addition, the effects on the transmission properties which are generated by the geometrical parameters, structural periodicity, dielectric thickness and material characteristics have been analyzed. The distributions of the electric field and surface current have been investigated for understanding the mechanism of the EM wave transmission. The MMs filter structure was fabricated on a polyimide substrate with a surface micromachining process and measured by the THZ-TDS system. Measured THZ transmission response of the proposed MMs dual-band band-stop filter has good correspondence with the simulation. In this design, the periodic metallic resonance structures were patterned on the flexible polyimide substrate, so it can be conformed to the unusual surfaces such as cylindrical, pyramid, spherical and so on. In comparison with the traditional design of the multi-band or wide-band filters by stacking the resonant structures of the same or different sized sub-units into a multi-layer structure, and the tunable MMs filter design, the proposed dual-band band-stop filter structure is easier to simulate and fabricate based on the single-layer simple resonant structure.
Funding
National Natural Science Foundation of China (51475438); National Natural Science Foundation of China (61401405); Natural Science Foundation of Shanxi Province (2012011021-4); Joint Funds of the National Natural Science Foundation of China Key Program (Grant No. U1637212).
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