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We propose a design of an extremely broad frequency band absorber based on destructive interference mechanism. Metamaterial of multilayered SRRs structure is used to realize a desirable refractive index dispersion spectrum, which can induce a successive anti-reflection in a wide frequency range. The corresponding high absorptance originates from the destructive interference of two reflection waves from the two surfaces of the metamaterial. A strongly absorptive bandwidth of almost 60GHz is demonstrated in the range of 0 to 70GHz numerically. This design provides an effective and feasible way to construct broad band absorber in stealth technology, as well as the enhanced transmittance devices.
©2011 Optical Society of America
1. Introduction
Metamaterials are materials with artificial structures which can achieve properties that may not be found in nature. With exotic properties, metamaterials give rise to many novel inventions and great improvements on classic devices. Various cloaks [1–4] and invisible carpet [5, 6] have been realized by metamaterials with gradient-index based on transformation optics. The perfect lens, first proposed by Pendry [7], was fabricated by metamaterial with negative refractive index, which may breakthrough the resolution limit of the regular optical lens. Recently, the metamaterial is also fashioned to create perfect absorbers by manipulating the resonances in ε and μ [8–20]. However, the strong electric and magnetic resonance simultaneously will of course result in a narrow absorption bandwidth, which may impede its application in practice. In this work, we propose a design of an extremely broad band absorber by using metamaterial based on the destructive interference instead of the strong resonance loss. With a proper refractive index dispersion spectrum, the metamaterial covering on a metal mirror acts as an anti-reflection coating, which can eliminate all incident wave reflected by the mirror in a broad frequency range. We use CST Microwave Studio to explore the absorptance mechanisms in this absorber system and verify that the high absorptance originates from the destructive interference of the reflection waves, but not the intrinsic electromagnetic resonance loss of the SRRs. And the broad absorptive bandwidth is achieved through the joint of the adjacent anti-reflection peaks arising from the destructive interference. An absorptive bandwidth of almost 60GHz is realized in the range from 0 to 70GHz. This design provides an effective way to construct broad band absorber with high absorptance in stealth technology and also a theoretic support for the ongoing experiment.
2. Theory
2.1 Absorber based on the anti-reflection theory
The main loss of a lens originates from the reflection on its surface, as shown in Fig. 1 . (a). Usually, anti-reflection (AR) coating is applied to the surface of the lens in order to enhance the transmittance through the destructive interference of the reflection waves as depicted in Fig. 1(b). On the other hand, a metal plate could be generally regarded as an EM mirror with no transmittance and reflects the entire incident EM wave. In this case, if we choose a suitable coating which can eliminate reflection waves from the two interfaces (air-coating & coating-metal) (Fig. 1(c)) by destructive interference, the anti-reflection effect is equivalent to absorption and the system can be treated as an equivalent absorber.
Fig. 1 Reflections on different coating system: (a) Lens without coating, the transmittance is not very high because of the reflection on the surface of the lens. (b) AR coating on the lens may improve the transmittance. The destructive interference between reflected waves from the front and back interfaces of the AR coating greatly reduces the reflection and enhances the transmittance of the lens. (c) AR coating eliminates all the reflected waves from the metal by destructive interference, which plays a role of absorber. (d) An ideal refractive index spectrum (top) retrieved by anti-reflection theory, which can realize a successive anti-reflection in whole frequency range in theory. And the S11 (reflectance) of a medium with such refractive index spectrum is the envelope of those dispersed anti-reflection peak, as depicted by the short dash line (bottom).
The occurrence of the destructive interference requires half wavelength phase difference between the two reflection waves. As a result, the equivalent optical path in the AR coating is at least quarter wavelength and the characteristic frequency of the AR coating is determined by the thickness (d) and refractive index (n) of the AR coating [21]:
where c is the speed of light; fAR is the characteristic frequency of the anti-reflection; λAR is the characteristic wavelength of the anti-reflection; and m is any positive odd integer, which implies that the anti-reflection occurs periodically. As shown in Fig. 1(d), there are minimums with the same frequency interval in the S11 (reflectance) spectra, due to the periodic anti-reflection. Because of the index dispersion of the AR coating, the anti-reflection behavior generally occurs in a small frequency band around fAR, especially at low frequencies (e.g. microwave). Accordingly, the absorptive bandwidth of absorber based on this mechanism would be also rather narrow. However, the proper refractive index dispersion is able to produce a successive anti-reflection which may broaden the bandwidth of the absorber greatly.2.2 Successive destructive interference induced by proper refractive index dispersion
According to Eq. (1), we propose an ideal refractive index dispersion spectrum, producing a successive anti-reflection in a wide frequency region, as shown in Fig. 1(d). Considering the coating in Eq. (1) with a fixed thickness (d), the characteristic frequency fAR varies with the refractive index (n), as shown in Fig. 1(d, bottom). Put the reflection curves of AR coating with different refractive index in the same graph, and then we find that all the minimum peaks join with each other and occupy the whole frequency range. Accordingly, the optimal index spectrum in Fig. 1(d, top) can be retrieved by associating the refractive indices with the fAR of each corresponding minimum peaks. Then, the effective reflection spectra can be roughly described by the envelope of dash line in Fig. 1(d, bottom). Moreover, the periodic index dispersion may expand the operating region to much higher frequency range, which, theoretically, forms a broad band absorption range in the whole spectrum (Fig. 1(d, top)).
3. Design
It is rather difficult to find a natural material with the refractive index dispersion spectrum in Fig. 1(d). Fortunately, metamaterials of artificial engineering structures give an opportunity to realize such an index spectrum. Here, we use metamaterial with multilayered SRRs to obtain the desirable refractive index at frequencies required by the anti-reflection. The optimized structure contains four layers of dielectric substrate and three SRRs with different size. SRRs are arranged between two substrates as shown in Fig. 2(a) . The typical size of each SRR and the thickness of the substrate are presented in Table 1 . The refractive index of the top layer is 1.5 + 0.13i and the other three are 2 + 0.15i.There is also a back plate of copper behind the last dielectric substrate. The three SRRs with different size create suitable refractive index in the corresponding frequency regions. Lossy material is chosen as the substrate purposely, however, the lossy material cannot function as a good absorber by itself [22].
Fig. 2 (a) Fabrication of this absorber structure and (b) the typical size of the SRRs and layers’ thickness
Table 1. Typical size of the metamaterial structure
4. Simulation results and discussion
Here we use CST Microwave Studio to explore the absorption mechanism and the performance of this metamaterial absorber in Fig. 2. A TEM wave is incident to the metamaterial vertically (y-axis), with E field polarized along the x-axis (Fig. 3(a) ). The spectra of S11 (reflection) with different thickness of the top layer are shown in Fig. 3(b). Because of the copper backplate, the S21 (transmission) of this system is zero. Consequently, each minimum of the curves corresponds to an absorption peak. It should be noted that the value of S11 less than −10dB means an >90% absorptance (A = 1-|S11|2 -|S21|2). The frequency range with absorptance larger than 90% in the green curve (d4 = 2.25 mm) is almost 20GHz, ranging from 10GHz to 30GHz (Fig. 3(b)).
Fig. 3 (a) The simulation model of the metamaterial absorber; (b) S11 of this model is calculated by CST with different thickness of the top layer thickness d4. Peaks resulted from the anti-reflection theory shows redshift with the increase of d4, but there is almost no change on the peaks resulted from the resonance loss, as shown in the inset.
This wide absorption range is consisted of several adjacent absorption peaks, which can be divided into two types. Peaks in the higher frequency range (>10GHz) show red shift with the increase of the top layer thickness, obeying the rules of Eq. (1). Yet the frequency points of the three peaks in the lower frequency region (<10GHz) hardly change with the decrease of d4, as shown in the inset of the Fig. 3. Further model calculation reveals that the two types of peaks can be attributed to different mechanisms. Peaks of red shift result from the anti-reflection theory, by means of the suitable refractive index provided by the three SRRs in the metamaterial (see the details in the supplementary). And the other three are produced by the electromagnetic resonance loss of SRRs, as described in Ref [8].
4.1 Anti-reflection absorption in this system
In order to demonstrate the fact that the peaks of redshift are produced by the anti-reflection theory, we explore the transmittance enhancement property of the multilayered metamaterial, which is treated as a uniform coating film. The copper backplate in Fig. 2 is replaced by a dielectric medium with a high refractive index (n = 13). Accordingly, air, multilayered metamaterial together with the high index medium compose a transmittance enhancement system, which can increase the transmission of the high index medium. And the anti-reflection theory can be demonstrated by analyzing both the refraction and the transmission properties of such a system. The whole anti-reflection system is illustrated in Fig. 4(a) , where the total reflection is the superposition of the reflection at two interfaces. The Fresnel coefficients are written as [22]:
where r12, t12, r21, t21 and r23 are Fresnel coefficients at two interfaces as illustrated in Fig. 4(a), ζ = ψ12 + ϕ23 + ψ21 + 2β, β = −nk0h/cos(θ2), k0 is the free space wave number, and n is the refractive index of the AR coating. Then, we can obtain the reflectance:in which ϕ12-ζ is the phase difference of the reflected waves from the two interfaces (air-AR film & AR film-medium). For the quite high refractive index of the medium (n = 13), the reflection coefficient at the second interface is almost one (r23≈1). If we assume: in which N can be any nonnegative integer. The value of cos(ϕ12-ζ) is −1, and then the Eq. (4) can be written as:According to Eq. (5), the reflectance is zero, namely, R = 0. Consequently, we can conclude the Eq. (5) and (6) as the anti-reflection conditions.Fig. 4 (a) Illustration of multiple transmissions and reflections in the enhanced transmittance system. ψ12 implies the phase change brought by transmission from air (1) to AR-film (2). ψ21 implies the phase change brought by transmission from AR-film (2) to air (1). ϕ12 implies the phase change resulted by the reflection at the interfaces between air (1) and AR-film (2). ϕ23 implies the phase change resulted by the reflection at the interfaces between AR-film (2) and medium (3). r12, r23, t12, t21 are amplitudes of Fresnel coefficients and they are real positive numbers. (b) The S parameters of the transmission enhanced system formed by the metamaterial structure. (c) The phase difference of the reflective wave from the two interface of the metamaterial. The vertical dashed lines (green, orange, red and blue) indicate that the phase different is π when the destructive interference occurs.
We use CST to compute the S parameters and the total phase difference (ϕ12-ζ) of the system formed by the metamaterial with d4 = 2.5mm. Lossy material parameters are set to tune the value of t12 and t21 in order to satisfy the Eq. (5) and the results are shown in Fig. 4(b). There are seven transmittance maximums on the spectrum of S21. The phase difference of the four transmittance peaks marked by the dashed lines with different colors is π, which satisfies the condition of Eq. (6). Thus, these four peaks belong to the anti-reflection peaks. Furthermore, the frequencies of these four peaks are 10GHz, 12.5GHz, 15.2GHz and 22.8GHz, in good agreement with the frequencies of those with red shift at 9.8GHz, 12.5GHz, 15.5GHz and 23GHz, respectively, in Fig. 3(b, d4 = 2.5mm). Therefore, it is demonstrated that the four peaks in Fig. 3(b) can be attributed to the anti-reflection theory. On the contrary, although the reflectance values at 2.8GHz, 4.1GHz, and 7GHz (marked by the black dash line) are relatively low, the phase difference (ϕ12-ζ) of them is not π, demonstrating that no destructive interference occurs at these three frequency points. Moreover, these three frequency points correspond to those of the three peaks in the inset of Fig. 3, which again shows that the mechanism of the three absorption peaks is not anti-reflection.
4.2 Resonance loss absorption in this system
The absorption at the lower frequencies (<10GHz) is caused by the resonance loss of the SRRs. SRR with simultaneously large electric and magnetic resonance loss may result in a strong absorption, which is the main mechanism of the perfect metamaterial absorber [8]. As shown in Fig. 5(a) , a ring resonator together with a metal plate and the substrate between them composes an absorber system, which looks similar with our design, but totally different from ours in theory. By manipulating the resonances in ε and μ of the metamaterial independently, it is able to absorb both the incident electric and magnetic fields. Therefore, it requires a SRR of certain size and quite low loss substrates [8–10] with favorable thicknesses (h1, h2). Any deviation from the favorite thickness may aggravate the performance of the absorber. Figure 5(b) shows S11 spectra of three perfect metamaterial absorbers with SRR1, SRR2 and SRR3 of typical size in Table 1, respectively. By choosing the suitable h1, h2, as shown in Table 2 , all the three minimum values of S11 are below −25dB due to the strong resonance absorption from each SRR. The frequency point at each minimum is in satisfactory agreement with that in the inset of Fig. 3, which reveals that the peaks at lower frequencies are resulted by the matched electromagnetic resonance loss. In the multilayered system, because of the use of lossy substrate and the unsuitable substrate thickness, the resonance absorption peaks are rather small (Fig. 3).
Fig. 5 (a) Perfect metamaterial absorber system with a certain size of SRR and favorable thickness of substrate (h1, h2). Moreover, the material (n = 2 + 0.01i) of the substrate is quite low loss. (b) The three SRRs with the typical sizes in Table 1 produce three absorption peaks at frequencies of 2.8GHz, 4.15GHz and 7.15GHz, which is in agreement with the peaks at 2.8GHz, 4.1GHz and 7GHz, respectively, as shown in the inset of Fig. 3.
Table 2. Favorite values of h1, h2 when strong resonant absorption occurs for each SRR
4.3 Periodic property of the AR coating
According to Eq. (1), the anti-reflection behavior may periodically appear at , which can be used to broaden the absorption range. Figure 3 just shows the first period in the frequency range of 0~30GHz. Here, by simulating the metamaterial structure in Fig. 2 in the frequency range from 0 to 70GHz, we explore the periodic effect on the absorption bandwidth and the results of S11 & absorptance are shown in Fig. 6 . This frequency range contains three anti-reflection periods divided by the intrinsic anti-reflection peaks of the substrate around 12GHz, 32GHz and 60GHz. With the increase of the top layer thickness d4, the peaks show redshift, which is consistent with Eq. (1). The interval frequency region between the three intrinsic peaks are occupied by other peaks created by SRR resonance, forming an absorptive bandwidth of almost 60GHz (absorptance>90%) except for a small flaw at 42GHz, as illustrated in Fig. 6(b). And the structure with d4 = 2.25mm can result in a better absorptive performance than that of the other four values of d4.
Fig. 6 Simulation results of S11 (a) and absorptance (b) at the frequency range of 0 to 70GHz with increased d4. Arrows in (a) show the redshift of the intrinsic anti-reflection peaks with the increase of d4. Bandwidth of absorptance >90% in (b) ranges from 10GHz to 70GHz.
5. Conclusion
In conclusion, we propose a design to realize an extremely wide frequency bandwidth absorber based on the anti-reflection theory. Metamaterial with multilayered SRRs structure is used to form a required refractive index dispersion, which can realize a successive anti-reflection in a wide frequency range. The destruction interference mechanism is demonstrated by analytical derivation and numerical calculation.
Despite of the use of SRR resonance, the resonance itself is not lossy enough to realize a perfect absorber, but able to supply an optimal refractive index required by the destructive interference. So this metamaterial absorber is different from the perfect absorber based on the simultaneously strong electric and magnetic resonance loss. Notably, the broadened absorption bandwidth is achieved by the successive anti-reflections, in contrast to the coherent effect of among SRRs in the perfect metamaterial absorber [23–26].
On the other hand, the refractive index, formed by the resonance of SRR and substrate together, is responsible for the anti-reflection, which is different from the previous design of the THz metamaterial AR coating [22]. In that design, the SRR, mesh and the spacer works independently, to tailor magnitude and phase of waves reflected and transmitted at boundaries of metamaterial coating in order to satisfy the condition of the anti-reflection [22]. Thereby, metamaterial absorber proposed here is a new design different from the former schemes.
The performance of this metamaterial absorber is also simulated by CST and an absorptive bandwidth of almost 60GHz is achieved in the range of 0 to 70GHz. This design provides a feasible way to broaden the band of absorber. Meanwhile, it also shows light on the application as enhanced transmittance devices in even higher frequency region like THz and infrared.
Acknowledgments
This work is supported by the National Science Foundation of China under Grant Nos. 90922025, 51032003, 50921061, and 10774087.
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