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This paper presents the experimental study on an inductive mesh composed of contiguous metallic rings fabricated using UV-lithography on quartz glass. Experimental results indicate that, at the same period and linewidth as square mesh, ring mesh has better transmissivity for its higher obscuration ratio, stronger electromagnetic shielding performance for its smaller maximum aperture, and less degradation of imaging quality for its lower ratio and uniform distribution of high order diffraction energy. It is therefore concluded that this kind of ring mesh can be used as high-pass filters to provide electromagnetic shielding of optical transparent elements.
©2007 Optical Society of America
1. Introduction
Metallic meshes are widely used as filters and beam splitters [1–3], and square meshes with a submillimeter period can be used as high-pass filters to achieve electromagnetic shielding of optical transparent elements for their capability to transmit visible light and reflect microwave [4–7]. However, good transmissivity and strong electromagnetic shielding can not be gained at the same time due to their inherent conflict for square meshes [4, 5], and their high order diffraction energy is mainly distributed along the two axes in the visible band [5], which causes the concentration of stray light, and thus degrades the imaging quality. As electromagnetic environments get more and more complex, it is of great significance to use new mesh structures to achieve high transmissivity, strong electromagnetic shielding and high imaging quality for optical windows of medical facilities, communication devices and space astronomy observation instruments. Ring elements have attracted much attention in recent years because they can be used to achieve band-pass or band-stop filtering through separated arrangement of rings [8–11], but to the best of our knowledge, not much work has been done on fabrication of meshes with contiguous metallic rings to achieve high-pass filtering. Therefore we conducted experimental study on an inductive mesh composed of contiguous metallic rings fabricated using UV-lithography on quartz glass, and compared ring and square meshes for their transmissivity and electromagnetic shielding performances.
2. Structural description and fabrication of ring meshes
As shown in Fig. 1, shown in bold lines are contiguous metallic rings with high electrical conductivity, arranged in a 2D orthogonal intersection array and electrically interconnected by a small piece of metal placed at tangent points of adjacent rings.
The mesh sample fabrication process is as follows: 1) sputter 50 nm titanium(Ti) as a bonding layer and 450 nm aluminium(Al) as a conductive layer to prepare a metal film on a clean quartz glass substrate; 2) coat a 1.1 μm FUJIFILM 6400 photosensitive resist on the surface of the aluminium film; 3) align the mesh mask made by electron beam direct writing upon the resist layer; 4) expose the sample to a KARLSUSS MA/BA6 lithography machine and then degum and etch it. The ring and square meshes obtained in this way are as shown in Figs. 2 and 3, they both have a period of 320.00 μm, but for a fabricated error the measured linewidth is 3.52 μm for the ring mesh and 2.31 μm for the square mesh.
3. Transmissivity analysis and experiments
3.1 Model used for transmissivity analysis
The pupil function of a ring mesh with a circular aperture shown in Fig. 1 can be expressed as:
where rect(x)rect(y) is a 2D rectangle function, circ(r) is a circle function, ** is a 2D convolution, is a 2D comb function.
The intensity point spread function (PSF) of an optical system is the modulus squared of the Fourier transform of its pupil function [5, 12], so the normalized intensity PSF of a ring mesh can be given by:
where r= (g-2a)/g, J1(ρ) is the first-order Bessel function.
The pupil function and normalized intensity PSF of a square mesh with a circular aperture can be expressed as:
According to the scalar diffraction theory, the total energy transmittance of a mesh is approximately equal to its obscuration ratio i.e. the fraction of the area without metal [5], so the total energy transmittance of the ring mesh and the square mesh i.e. the normalized intensity PSF values of Eq. (2) and Eq. (4), can be expressed respectively as:
For imaging applications in medical facilities, communication devices and space astronomy observation instruments, only zero order diffraction light is useful, and high order diffractions cause stray light that degrades imaging quality. According to Eq. (2) and Eq. (4), the normalized zero order diffraction intensity or the zero order transmittance for ring and square meshes can be expressed respectively as:
So, the total energy ratio of high order diffractions or the total stray light ratio for ring and square meshes can be expressed respectively as:
3.2 Transmissivity analysis and experiment
It can be seen from Fig. 4 that Tr and Tr (0, 0) are greater than Ts and Ts (0,0) respectively, i.e. ring mesh has better transmissivity than square mesh at the same period and linewidth. Shown in Fig. 5, Sr is smaller than Ss for a practical application transmissivity range (at least a/g<0.1). Ring mesh has a better transmissivity and less stray light than square mesh because ring mesh has a smaller metal covering area on its surface, i.e. a higher obscuration ratio.
It can be seen from Fig. 6 that, the measured transmittance of ring mesh with linewidth of 3.52 μm is lower than that of square mesh with linewidth of 2.31 μm, which proves the correctness of the theoretical model and ring mesh has a higher transmittance than the square mesh when they have the same fabricated linewidth.
Fig. 6. Comparison of transmittances measured with SPEX 1000M spectrum analyzer for ring and square meshes with simulation results obtained using Eqs. (5) and (6).
3.3 Analysis and experiment of diffraction spots distribution
It can be seen from Figs.7, 8, 9 and 10 that the good agreement between experimental observations and simulation results further proves the correctness of the model used for analysis. Both simulations and experiments show that, the high order diffraction energy concentrates along the two axes for a square mesh but distributes uniformly for a ring mesh, i.e. less degradation of imaging quality results from the stray light caused by high order diffractions of ring mesh.
4. Electromagnetic shielding performance analysis and experiment
The equivalent circuit model is an effective method for electromagnetic shielding performance analysis of square mesh since it is first proposed by Ulrich [13]. To get a higher analysis accuracy, Lee et al., [14] and Withbourn et al, [15] developed and optimized Ulrich’s model. A further work done by Kohin et al, [5] expanded the scope of application of the equivalent circuit model to the electromagnetic wave oblique incidence by introducing an equivalent film. However, in recent researches, we find that all the methods described above have a lower accuracy when the electromagnetic shielding performance at low frequency is analyzed for a high transparency mesh with micron magnitude linewidth. Therefore, based on these methods, we proposed a more accurate equivalent refractive index model [16], which can be given by:
where n0 and ng are the refractive indexes of the topstrate and substrate of a mesh, λ is the electromagnetic wavelength, de is the equivalent film thickness, X/Z0 is the normalized equivalent reactance and R0/Z0 is the normalized equivalent resistance for a mesh, which can be expressed as:
where ω=g/λ is the normalized incident frequency, ω0≈1-0.41a/g is the normalized resonant frequency, ε0 is the dielectric constant of free space, c is the speed of light and σ is the bulk DC conductivity of mesh metal.
As a matter of fact, only the effects of period and linewidth on the electromagnetic shielding performance analysis of a mesh are take into consideration in almost all the equivalent circuit methods [5, 13–16], but it can be seen from Fig. 11 that, the RF attenuations measured for square mesh are close but smaller than the simulation results, while the measurements of ring mesh are much larger than the simulation results, i.e. the electromagnetic shielding performance of ring mesh is better than that of a square mesh when they have the same period and linewidth, which indicates the effect of another structural parameter: the maximum mesh aperture, that was ignored in the past on the shielding performance analysis, it is the length of the diagonal line for a square mesh and the diameter g for a ring mesh, and can be easily satisfied for a practical application of high transparency meshes with small linewidth a. A smaller maximum aperture of ring mesh leads to a shorter cutoff wavelength at a low frequency, but a better shielding performance.
Fig. 11. Comparison of RF attenuations measured using Agilent E8363B PNA Seires Network Analyzer with simulation results obtained using Eq. (11) and standard thin-film analysis techniques[5, 16].
5. Conclusion
Ring metallic mesh with a submillimeter period has better visible light transmissivity and microwave shielding performance than square mesh, at the same period and linewidth, ring mesh has better transmittance for its larger obscuration ratio, and stronger electromagnetic shielding ability for its smaller maximum aperture, so ring mesh can be used to strike a better balance between transparent ability and shielding ability than square mesh. In addition, ring mesh has less degradation of imaging quality than square mesh for its lower ratio and uniform distribution of high order diffraction energy. It is therefore concluded that this kind of ring mesh can be used as filters to provide electromagnetic shielding of optical transparent elements, while it can also be used as beam splitters or a new type of metallic photonic crystal.
Acknowledgments
We would like to thank “211 Projects” Foundation from Ministry of Education of China and the National Natural Science Foundation of China (Grant No.50675052) for their financial support, Prof. Dacheng Zhang and Dr. Ting Li for mesh samples fabrication, Prof. Yinglin Song and Prof. Xiaoyu Wang for transmittance measurement.
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