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Abstract
This comment addresses errors in J. Opt. Soc. Am. A 33, 2066 (2016) [CrossRef] and corrects the material parameters and simulated field distributions of the carpet cloak.
© 2022 Optical Society of America
The proposed theory in [1] is neither feasible nor efficient. The noteworthy issues supporting this opinion are as follows.
First, according to Fig. 1, there is no doubt that the two ground corners must be located on the opposite sides of the mutual line to avoid overlaps. A revision is needed since in the case studies, both values $a$ and $b$ are larger than $c$ simultaneously [1].
Fig. 1. (a) Scheme of the proposed triangular carpet cloak in the paper. (b) Overlapping triangles with two corners at the same side of the mutual line.
The linear mapping between the physical space ($x,y,z$) and virtual space ($x^\prime ,y^\prime ,z^\prime $) is as follows:
Eventually, the material properties of the cloak shell are derived as
where the Jacobian matrix $\rm A$ isThe equations and coefficients for the second linear mapping corresponding to the green section of the cloak shell are mathematically similar. Therefore,
After defining the arbitrary cloaked region or defining $a$, $b$, $c$, and $d$, the remaining geometric parameters corresponding to the cloak shell, i.e., $e$ and $f$, are derived using invasive weed optimization (IWO) to obtain near-isotropic material properties [1]. Then, the material properties are calculated by substituting the geometric parameters in Eqs. (2)–(5). According to Table 1, each cloaked region can be positioned in two conditions where $a$ and $b$ have opposite signs. Therefore, each asymmetrical cloaked region can be covered with two cloak shells.
Table 1. Properties of the Carpet Cloaks
Second, consider the questionable part of the paper. According to Table 1, the noticeable difference between the diagonal elements of permittivity/permeability tensors leads to significant anisotropy. In other words, the proposed method in the paper cannot give near-isotropic parameters, which is the ultimate goal of the paper. Moreover, ignoring the effect of the minimized anisotropy is controversial.
Generally speaking, the difference between the derived values here with those given in the paper is intangible. The key point is if the material properties should be derived according to optimum geometric parameters, any deviations from optimum values will inevitably cause errors and therefore result in poor performance. In other words, further optimizations or simplifications are meaningless and deleterious. For instance, due to asymmetry (symmetry), the difference between the material properties of the left and right cloak parts is reasonable (unreasonable) for the first (third) case study. In the second and third case studies, the permittivity and permeability are unequal, which is in contradiction with Eq. (3).
Third, in carpet cloak strategy, regardless of the amount of the scattered field for the flat ground, the cloaked object should mimic the behavior of the reflecting flat ground. The more it resembles the behavior, the better the performance [2]. Numerical simulations as well as scattering patterns proposed in the paper indicate noticeable differences between the cloaked objects and the flat ground behaviors. The simulations are performed using COMSOL Multiphysics commercial software, which is based on the finite element method (FEM). It is evident in Figs. 2–5 that the scattered fields of the cloaked objects and the flat ground are not in the same direction. Therefore, the carpet cloaks cannot resemble the flat ground behavior and exhibit poor performance.
Fig. 2. Electric field distributions of the first case study (at first possible position) at frequency 2 GHz for the (a) anisotropic carpet cloak, (b) proposed carpet cloak in the paper, (c) flat ground, and (d) object.
Fig. 3. Electric field distributions of the first case study (at second possible position) at frequency 2 GHz for the (a) anisotropic carpet cloak, (b) proposed carpet cloak in the paper, (c) flat ground, and (d) object.
Fig. 4. Electric field distributions of the second case study at frequency 10 GHz for the (a) anisotropic carpet cloak, (b) proposed carpet cloak in the paper, (c) flat ground, and (d) object.
Fig. 5. Electric field distributions of the third case study at frequency 10 GHz for the (a) anisotropic carpet cloak, (b) proposed carpet cloak in the paper, (c) flat ground, and (d) object.
Fig. 6. In addition to the discrepancy between the scattering patterns of the cloaked object and the flat ground, the pattern of the uncloaked object at the scattered angle (45 deg) is closer to the flat ground pattern [1].
Take the following quoted sentence from the paper for further explanation: “The magnitude of the far field pattern decreases by 20.55 dB, so that the cloak cannot be detected by the radars” [1]. This sentence is not reason enough for supporting the presented method since more important criteria should be taken into consideration for verifying the proper performance of a designed carpet cloak. For carpet cloaks, calculating the similarity between the scattered fields of the cloaked object and the flat ground is an evaluation method for efficiency [3].
Consider the important scattering pattern lobe at 45 deg for the third case study. According to Fig. 6, the uncloaked object has closer behavior to the flat ground compared to the cloaked object. In other words, using the designed cloak deteriorates the condition and increases the signature of the object in the scattered direction. Therefore, pointing out the 20.55 dB decreased magnitude of the far field pattern in support of having perfect performance is misleading. This problem can be seen in all case studies.
Finally, as the last visible issue, the uncloaked object is different from the cloaked one in the first case study (see Fig. 7). This questionable difference makes the comparisons in the paper more ambiguous.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this comment are available from the author upon reasonable request.
REFERENCES
1. Z. Sharifi and Z. Atlasbaf, “New procedure to design low radar cross section near perfect isotropic and homogeneous triangular carpet cloaks,” J. Opt. Soc. Am. A 33, 2066–2070 (2016). [CrossRef]
2. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008). [CrossRef]
3. J. Xiong, T. Chen, X. Wang, and J. Zhu, “Design and assessment of an acoustic ground cloak with layered structure,” Int. J. Mod. Phys. B 29, 1550191 (2015). [CrossRef]
