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An optically transparent frequency selective surface (FSS) based on a nested ring metallic mesh is proposed, whose diffraction distribution is uniform and normalized higher-order diffraction intensity is lower than that of an existing transparent FSS based on metallic meshes. Compared with non-meshed FSSs, the proposed FSS has a remarkably higher optical transmittance, lower −3 dB bandwidth, and higher maximum transmittance in the microwave band. Experimental results indicate that the FSS sample achieved a normalized visible transmittance of 94.84%, uniform diffraction distribution, and stable filtering passband around 31.00 GHz simultaneously, which are attractive properties for transparent FSS applications.
© 2016 Optical Society of America
1. Introduction
A frequency selective surface (FSS) is usually used as a filter in the microwave band to achieve band-pass or band-stop characteristics in the frequency domain [1–3]. Its applications include multiband reflecting antennas and radomes in areas related to communication and protection, etc [1–7]. Currently, developments in band-pass FSSs in the microwave band indicate that optical transparency is increasingly necessary, especially for applications on windows and domes for space observation and communication [8, 9]. Optically transparent FSS also has important applications in optical windows of advanced optical instruments, selective frequency shielding of room windows to prevent radio leakage, train and aircraft windows isolating the unwanted radiation, observation windows of medical electromagnetic isolation rooms, electromagnetic shielding transparent film for displays and transparent microwave antennas [10–15]. Although an FSS fabricated with highly conductive metal has a stable passband, it usually cannot achieve high optical transmittance because of its large metal coverage.
In order to achieve a high transmittance in the optical band and maintain band-pass filtering performance in the microwave band, metallic meshes and traditional FSSs were combined to become transparent FSSs [16–18]. Previously, square and two-dimensional (2D) orthogonal ring metallic meshes have been adopted to improve the optical transmittance of FSSs [17–20]; however, the higher-order diffraction intensity still appears high and non-uniform, which will degrade the imaging quality of optical windows covered with an FSS. To further solve this problem, we propose an optically transparent FSS based on a nested ring metallic mesh. Based on scalar optical diffraction theory, the optical diffractive model has been established for the proposed FSS. Theoretical simulations show that the proposed FSS has a much lower normalized higher-order diffraction intensity compared with existing transparent FSSs. In addition, compared with non-meshed FSSs, after integrating FSSs and nested ring metallic meshes, the normalized zero-order diffraction intensity increased from 2.778 to 91.59%, the maximum normalized high-order diffraction intensity decreased from 1.025 to 0.01208% in the optical band, the −3 dB bandwidth of the FSS decreased from 15.20 to 10.70 GHz, and the maximum transmittance increased from −2.170 to −1.490 dB in the microwave passband. These performance alterations indicate that the proposed transparent FSS not only improves the transparency from nearly opaque to good optical transparency, but also improves its band-pass filtering performance. A transparent FSS sample based on nested ring metallic mesh was fabricated using UV-lithography technology. The experiments show that a highly normalized visible transmittance of 94.84%, stable passband around 31.00 GHz in the Ka-band, and uniform diffraction distribution have been achieved using the FSS sample. This confirms the attractive performance of the proposed transparent FSS.
2. Transparent FSS structure description
Optical transparent FSSs based on a square metallic mesh [17] and a 2D orthogonal ring metallic mesh [20] have been proposed and studied. Through adding sub-rings into ring metallic mesh to construct nested loops, we got a novel metallic mesh and further use it to construct the transparent FSS. Compared with existing transparent FSSs based on meshes, the nested loops increase the diversity of ring diameters and positions, which significantly disperses higher-order diffraction intensity of the new transparent FSS. A schematic of the structure of the proposed optically transparent FSS is shown in Fig. 1, in which a periodic array of cross aperture is added to a nested ring metallic mesh. The nested ring metallic mesh consists of square lattice of basic rings which are arranged in 2D orthogonal intersection array and exteriorly contacted; each basic ring contains three inscribed sub-rings that are mutually tangent to each other and they form a nested loop together. For each FSS unit, a cross aperture is located at its center. The diameters of the basic ring and sub-ring are g and d respectively, and the linewidth of ring is a. The period of cross aperture array is T, the length and width of the cross aperture are L and W, respectively. For the proposed optically transparent FSS, there are two different periods in total: the period of proposed FSS, which is equal to the period of cross aperture array T, and the period of nested ring metallic mesh, which is equal to the diameter of the basic ring g in this design.
Fig. 1 (a) Schematic of the structure of the proposed optically transparent FSS. (b) The FSS unit. (c) The nested loop.
The period of FSS T, i.e. the period of cross aperture array, plays a decisive role for the passband center frequency of the FSS. The period of nested loops g, i.e. the period of the nested ring metallic mesh, is designed to be smaller than the period of the FSS T to decrease higher-order diffraction intensity. In order to maintain the same transmittance, the diameter of basic ring in nested loops must be enlarged because of the added sub-rings, thus the diffraction intensity caused by basic ring array are decreased. In addition, the sub-rings have smaller diameter than the basic ring and are distributed in different positions, which makes their diffraction intensity have low superposition probability with that caused by basic ring array. Thus the diversity of ring diameters and positions further disperses higher-order diffraction intensity of the proposed FSS.
The parameters can be expressed by the following equations:
where t, l, and w are positive integers.3. Diffractive characteristic comparison with existing transparent FSS structures based on metallic meshes
Decreasing and homogenizing higher-order diffraction intensity of optically transparent applications based on mesh structures is very important work [21, 22]. Metallic meshes behave as 2Ddiffraction gratings at optical frequencies; thus, optically transparent FSSs based on metallic meshes will also diffract. The optically diffractive characteristic of the proposed FSS can be modeled by using scalar diffraction theory and the distribution of diffraction intensity can be given by the modulus squared of the Fourier transform of the pupil functions [23, 24].
In this work, a novel metallic mesh structure, i.e. the nested ring metallic mesh, shown in Fig. 1, has been applied to construct the transparent FSS. The pupil function t1(x, y), of the nested ring metallic mesh can be expressed as:
where ** represents the 2D convolution symbol, is a 2D comb function which is used to describe 2D orthogonal intersection array of nested loops when combing with 2D convolution operation, and n and m are integers. rect() is a 2D rectangular function which represents the square aperture of a FSS unit. 1-t0 in Eq. (4) is used to describe an opaque basic ring with three sub-rings, i.e. nested loop.A circle function can be used to represent pupil function of a circular aperture [23], and the difference of two circle functions can be used to describe the pupil function of a circular ring aperture. Then according to the diameters and position relations of sub-rings and basic ring, t0 can be expressed as:
where △circ() represents the pupil function of a circular ring aperture with its circle center at coordinate (d1, d2). where circ() represents the circle function; h is the number of sub-rings in one basic ring, which is 3 in this design; and θ is the angle between the centers of two adjacent sub-rings to the basic ring.The pupil function t2(x, y) of the cross aperture in Fig. 1 can be expressed as [20]:
Based on Eqs. (4)–(9), the pupil function t3(x, y), of the proposed transparent FSS in Fig. 1 can be expressed as:
where p and q are integers. The circle function circ() here represents a circular aperture with diameter MT, where M is the number of FSS units in a diameter direction of the circular aperture. The circular aperture is used to observe the diffraction intensity distribution.Based on Eq. (10) and the Fourier transform method for diffraction [23, 24], the distribution of diffraction intensity can be given by the modulus squared of the Fourier transform of the pupil functions. The normalized diffraction intensity distribution of the proposed FSS was simulated through MATLAB and shown in Fig. 2. The incident wavelength was chosen as 632.8 nm and the incident angle is 90° in the simulation, which are consistent with our measurement equipment to make it easy to compare the simulation and experimental results.
Fig. 2 Diffraction distribution and normalized diffraction intensity of the proposed FSS, g = 360 μm, a = 2.50 μm, T = 9g = 3.24 mm, L = 7g = 2.52 mm, W = g = 360 μm.
Similarly, the normalized diffraction intensity distributions of the optical transparent FSS based on a square metallic mesh [17] and a 2D orthogonal ring metallic mesh [20] are simulated and shown in Figs. 3 and 4, respectively, which are the most typical optical transparent FSS based on metallic meshes ever reported in literatures at present. In Fig. 3, the higher-order diffraction intensity is high and concentrated along the two axes for the FSS based on square metallic mesh, while for the FSS based on a 2D orthogonal ring metallic mesh, the higher-order diffraction intensity is more uniform than that based on square mesh, however still high, as shown in Fig. 4. Compared with these two existing transparent FSS structures based on meshes, the higher-order diffraction intensity of the proposed optically transparent FSS is more uniformly distributed, as shown in Fig. 2. When their normalized zero-order diffraction intensities are similar and near 91.6%, the maximum normalized higher-order diffraction intensities in Fig. 2 are 74.10% and 41.13% lower than that in Figs. 3 and Fig. 4, respectively. This comparison confirms the idea that using nested loops in the design of optical transparent FSS can effectively disperse higher-order diffraction intensity, and thus, has lower degradation of imaging quality of optical windows, which is much more favorable for transparent FSS applications.
Fig. 3 Diffraction distribution and normalized diffraction intensity of the FSS based on square metallic mesh, g = 360 μm, a = 4.70 μm, T = 9g = 3.24 mm, L = 7g = 2.52 mm, W = g = 360 μm.
Fig. 4 Diffraction distribution and normalized diffraction intensity of the FSS based on 2D orthogonal ring metallic mesh, g = 360 μm, a = 6.00 μm, T = 9g = 3.24 mm, L = 7g = 2.52 mm, W = g = 360 μm.
4. Performance comparison with non-meshed FSSs
Setting the pupil function t1 = 0, Eq. (10) can also be used to simulate the diffraction distribution and normalized diffraction intensity of non-meshed FSS having only a cross aperture unit; the simulation results are shown in Fig. 5. Compared with that in Fig. 2, the normalized zero-order diffraction intensity of the non-meshed FSS is only 2.778% and that of the proposed FSS based on the nested ring mesh is 91.59%. This indicates the FSS improves the optical transparency from almost none to a very good optical transparency when the nested ring mesh is combined with the FSS. On the other hand, the maximum normalized high-order diffraction intensity decreases from 1.025% in the non-meshed FSS to 0.01208% in the meshed FSS, which means the FSS based on nested ring metallic mesh has very small imaging quality degradation compared with non-meshed FSS.
Fig. 5 Diffraction distribution and normalized diffraction intensity of non-meshed FSS, T = 3.24 mm, L = 2.52 mm, W = 360 μm.
In the microwave band, the optically transparent FSS based on nested ring metallic mesh behaves as a band-pass filter, similar to a non-meshed FSS. The band-pass filtering performances in the microwave band for the meshed and non-meshed FSSs were simulated using CST Studio Suite. The frequency band used was the Ka-band (26.5 to 40 GHz) and the simulation results are shown in Fig. 6. The passband center frequency is shown to possess a shift of 4 GHz after integrating the FSS and nested ring metallic mesh. In addition, after integrating the nested ring mesh, the −3 dB bandwidth of FSS decreases from 15.20 to 10.70 GHz, and the maximum transmittance increases from −2.170 to −1.490 dB. This indicates that the meshed FSS has a narrower −3 dB bandwidth and maximum passband transmittance, i.e., the band-pass performance is improved in the microwave band compared with the non-meshed FSS.
Fig. 6 Comparison between the non-meshed FSS (black) and meshed FSS (red) for microwave band-pass filtering performance, T = 3.24 mm, L = 2.52 mm, W = 360 μm. The right plot is an enlarged version of the left in order to visualize the peak transmittances.
5. Experimental verification of performance of a FSS based on nested ring mesh
5.1 Transparent FSS fabrication
As shown in Fig. 7, a transparent FSS sample based on a nested ring mesh was fabricated using UV-lithography technology on a 0.8-mm-thick quartz-glass substrate; the rings and cross aperture edges were made of a 0.4-µm-thick aluminum layer. Considering the trade-offs between optical transmittance and band-pass performance in the microwave band, the parameters of the proposed FSS were chosen as follows: g = 360 μm, d = 168 μm, a = 2.50 μm, T = 9g = 3.24 mm, L = 7g = 2.52 mm, W = g = 360 μm.
Fig. 7 (a) Transparent FSS sample photograph. (b) Micrograph of the proposed FSS sample taken using a Nikon SMZ1500 stereomicroscope.
5.2 Optical performance
In the visible band, the wavelength of the visible light is much smaller than the periods (both for FSS and nested loops) and diameters (for all rings) of the proposed FSS. According to the scalar diffraction theory, though diffraction happens, the total transmittance is nearly not changing with wavelength and can be calculated by obscuration ratio of the proposed structure, which is used to indicate the fraction of the area without metal [24]. Therefore, the total transmittance, Tm, of the proposed FSS shown in Fig. 1 can be expressed as:
The total transmittance of the proposed FSS calculated by Eq. (11) is 95.67% using the aforementioned design parameters. The total transmittance of the fabricated FSS sample in the wavelength range 400–700 nm was measured using a Fourier transform spectrometer (UV-3101PC). The theoretical and experimental results are plotted in Fig. 8. We find that the measured normalized transmittance has an average value of 94.84% and the maximum comes up to 95.36%. The experimental result clearly agrees well with the theoretical result; the small reduction of measured transmittance is caused by the slight deviation between the designed linewidth and the fabricated linewidth, and not all the diffraction spots can be collected by the spectrometer due to its small collection cone angle.
Fig. 8 Normalized theoretical (red) and experimental (black) optical transmittances of FSSs based on nested ring mesh.
The diffraction distribution of the fabricated FSS was measured, as shown in Fig. 9. The diffraction image was captured using a high-resolution Sony ILCE-6000 camera with a 632.8-nm-wavelength He-Ne laser perpendicularly incident on the FSS sample. The agreement between the experimental observations and the simulation results in Fig. 9 indicates the high accuracy of our simulation method. We see from Fig. 9 that the diffraction distribution is very uniform for the fabricated FSS sample, which further confirms the effectiveness of the homogenizing diffraction distribution by the transparent FSS designed in this study.
5.3 Microwave band-pass filtering performance
The Ka-band band-pass filtering characteristics of the FSS sample have been measured using a microwave transmittance measurement system, which contains an Agilent E8363B PNA series network analyzer, a transmitter antenna, and a receiver antenna. Limited by the size of the fabricated FSS sample and the effective measurement frequency range of the experimental setup, only the microwave transmittance in Ka-band has been measured. The measured transmittance curves at the Ka-band and simulated results at 0-50 GHz are shown in Fig. 10. The two curves have similar trends in the Ka-band and the curves indicate that the measured passband center frequency is approximately 31.00 GHz, which is extremely close to the simulated result.
6. Conclusion
In this work, an optically transparent FSS based on nested ring metallic mesh has been proposed and fabricated using UV-lithography technology. Simulation results indicate that the maximum normalized higher-order diffraction intensities of the FSS based on nested ring metallic mesh are 74.10% and 41.13% lower than those based on a square mesh and 2D orthogonal ring mesh, respectively. In addition, compared with non-meshed FSS, after integrating nested ring metallic meshes, the proposed transparent FSS not only improves the optical transmittance from nearly opaque to greater than 90%, but also improves its band-pass filtering performance. Experimental results show a normalized visible transmittance of 94.84%, a stable passband in the Ka-band with the center frequency at approximately 31.00 GHz, and a uniform diffraction distribution have been achieved simultaneously using the FSS sample. The proposed optically transparent FSS based on nested ring metallic mesh may have applications in various areas, such as multi-mode communication windows, space observation facilities, and transparent car antennas.
Funding
National Natural Science Foundation of China (NSFC) (61575075); Fundamental Research Funds for the Central Universities (HIT.NSRIF.2014020); Natural Science Foundation of Heilongjiang Province (F2016014); the Postdoctoral Science-Research Development Foundation of Heilongjiang Province (LBH-Q13078).
Acknowledgments
The authors would like to thank Professor Ting Li in Peking University for her help in fabricating the transparent FSS sample. We would like to express our sincere gratitude to CST Ltd. Germany, for providing the CST Training Center (Northeast China Region) at our university with a free package of CST MWS software.
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