Research Article: Controlling Energy Radiations of Electromagnetic Waves via Frequency Coding Metamaterials

Date Published: May 26, 2017

Publisher: John Wiley and Sons Inc.

Author(s): Haotian Wu, Shuo Liu, Xiang Wan, Lei Zhang, Dan Wang, Lianlin Li, Tie Jun Cui.


Metamaterials are artificial structures composed of subwavelength unit cells to control electromagnetic (EM) waves. The spatial coding representation of metamaterial has the ability to describe the material in a digital way. The spatial coding metamaterials are typically constructed by unit cells that have similar shapes with fixed functionality. Here, the concept of frequency coding metamaterial is proposed, which achieves different controls of EM energy radiations with a fixed spatial coding pattern when the frequency changes. In this case, not only different phase responses of the unit cells are considered, but also different phase sensitivities are also required. Due to different frequency sensitivities of unit cells, two units with the same phase response at the initial frequency may have different phase responses at higher frequency. To describe the frequency coding property of unit cell, digitalized frequency sensitivity is proposed, in which the units are encoded with digits “0” and “1” to represent the low and high phase sensitivities, respectively. By this merit, two degrees of freedom, spatial coding and frequency coding, are obtained to control the EM energy radiations by a new class of frequency‐spatial coding metamaterials. The above concepts and physical phenomena are confirmed by numerical simulations and experiments.

Partial Text

Metamaterials are artificial structures composed of periodic or nonperiodic subwavelength unit cells, which have powerful abilities to tailor electromagnetic (EM) waves in unusual ways. These special materials have been described by effective media with the continuous medium parameters.1, 2, 3, 4, 5 The effective permittivity and permeability can be tailored to reach the values beyond possible in nature. Hence such metamaterials behave completely different from the conventional materials. In the past decade, metamaterials constructed by artificially resonant particles6 have been presented to manipulate the EM waves,7, 8, 9, 10, 11, 12, 13, 14 resulting in a lot of anomalous physical phenomena such as the negative refraction,15, 16, 17, 18 perfect imaging,19, 20 and invisible cloaking.21, 22, 23, 24, 25, 26, 27, 28

For the conventional digital metamaterials, the digital units usually have the same shape, and different phase responses are achieved by varying their geometry parameters.29, 31, 32, 33, 35 However, the phase sensitivities of the units with similar structures are correlated to the phase responses at the initial frequency, and hence such two values are not chosen freely. To overcome this restriction, we propose the idea to design the frequency coding units by using differently shaped particles. The differently shaped particles with the same phase response at the initial frequency can experience different phase sensitivity over the frequency, which add another degree of freedom to the coding metamaterials. Owing to the different phase sensitivity of the digital units, the phase differences between two or more digital units will change dramatically as the frequency varies.

From the above discussions, frequency coding metamaterials can not only be used at the initial and ending frequencies based on the spatial‐frequency encoded patterns, but also work in the whole operating frequency band with different controls of radiation EM energy. Now we discuss the nonperiodic frequency coding metamaterials. Based on Equation (9), the phase distribution of periodic frequency coding metamaterials is not uniformly distributed in the frequency band except at the initial frequency f0 and ending frequency f1. However, the nonperiodic frequency coding metamaterial has uniformly distributed phase response in the whole frequency band, in which the direction of main energy will gradually change with the frequency according to the generalized Snell’s law.

In summary, we proposed the concept of frequency coding metamaterials, which can explore the frequency‐domain property of metamaterials. The key substance to the frequency coding metamaterial is different phase sensitivities over the frequency domain of the metamaterials. We employed four differently shaped digital units to physically utilize the different sensitivity properties. The proposed method provides another degree of freedom to construct metamaterials, and opens new possibilities to control the electromagnetic waves at different frequencies. By using the 1‐bit digital units “0–0” and “0–1,” and 2‐bit digital units “00–00,” “00–01,” “00–10,” and “00–11” with predesigned coding sequences, we can manipulate electromagnetic waves in the frequency domain, which can achieve different functions over frequency (e.g., frequency sweeping) without redesigning the structure. In this manuscript, the digital units were designed to have same phase responses at the initial frequency, but it is not necessary. The digital units with different initial phase states can be further investigated to achieve more flexible different functions. The proposed concepts and methods can also be extended to the terahertz frequencies and even to the optical region.

To experimentally validate the performance of the frequency coding metamaterials, two samples were fabricated, as shown in Figure7a,b, which correspond to the coding layouts given in Figure 3a,c, respectively. The metamaterials were fabricated by printing planar metallic structures on the top surface of a commercial F4B substrate with dielectric constant 2.65 and loss tangent of 0.003. Both metamaterial samples had an area of 192 × 192 mm2 (5.28 × 5.28λ2 at the central frequency 8.25 GHz) and contained 32 × 32 = 1024 digital units. Each digital unit occupied an area of 6 × 6 mm2 (0.165 × 0.165λ2). The photograph of the experimental setup for the measurement of far‐field energy patterns in the horizontal plane is illustrated in Figure 7c. A wideband horn antenna with the working bandwidth from 6 to 12 GHz was employed as the feeding antenna to generate the quasi‐plane waves for the frequency coding metamaterial. Both the feeding antenna and the sample were coaxially mounted on a supporting board at the distance of 1.8 m, and could be automatically rotated 360° in the horizontal plane with high precision.

The authors declare no conflict of interest.




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